Title
All-optical signal processing based on optical parametric
amplification
Advisor(s)
Yuk, TTI; Wong, KKY
Author(s)
Lai, Ming-fai; 黎明輝
Citation
Issued Date
URL
Rights
Lai, M. [黎明輝]. (2008). All-optical signal processing based on
optical parametric amplification. (Thesis). University of Hong
Kong, Pokfulam, Hong Kong SAR. Retrieved from
http://dx.doi.org/10.5353/th_b4150887.
2008
http://hdl.handle.net/10722/54515
The author retains all proprietary rights, (such as patent rights)
and the right to use in future works.
All-Optical Signal Processing based on Optical Parametric
Amplification
by
Lai Ming Fai
B.Eng. (EComE) H.K.U.
A thesis submitted in partial fulfillment of the requirements for
the Degree of Master of Philosophy
at the University of Hong Kong
August 2008
Abstract of thesis entitled
All-Optical Signal Processing based on Optical Parametric
Amplification.
Submitted by
Lai Ming Fai
for the degree of Master of Philosophy
at The University of Hong Kong
in August 2008
To date, optical signal processing operations are primarily based on opticalelectrical-optical (O-E-O) methods. However, O-E-O methods have a much slower
electrical response time which often limits the bit rate of operation. In addition, they
require a costly implementation of ultrahigh speed photodiodes, electronics and data
modulators. This leads to the search for all-optical signal processing in order to avoid
a traditional O-E-O configuration.
One of the promising candidates of achieving all-optical signal processing is
fiber optical parametric amplifier (OPA) based on third-order nonlinear susceptibility
χ(3) in a nonlinear fiber. A major advantage of using χ(3) nonlinear susceptibility is its
femto-second response time, allowing a rapid operation of signal processing
applications potentially for 80Gb/s and beyond. One important phenomenon of χ(3)
nonlinearity in fibers is four-wave mixing (FWM), which is also the core of fiber
OPA. In essence, when two photons at frequencies ω1 and ω2 co-propagate through a
nonlinear medium, two new photons are generated at ω3 and ω4, satisfying
conservation of energy ω1 + ω2 = ω3 + ω4. The efficiency of this progress can be
dramatically increased with appropriate phase matching condition, which is
dependent on the dispersion of the fiber at these four frequencies.
I
OPA also incorporates two other fiber nonlinearities, namely self-phase
modulation (SPM) and cross-phase modulation (XPM). This requires satisfying the
phase matching conditions between two pumps, signal and idler at different
wavelengths. When this is satisfied, the signal and idler will experience exponential
amplification as they propagate through the nonlinear fiber.
An important aspect of OPA which makes it suitable for signal processing
applications is pump depletion. By conservation of energy, OPA pumps will be
depleted due to power transfer to signal and idler. By suitably selecting the
wavelengths and powers of the pump and signal components, nearly complete OPA
pump depletion can be achieved. Substantial OPA pump depletion allows all-optical
signal processing functions, such as all-optical logic gates and regenerators.
Assuming an on-off keying (OOK) bit stream is to be amplified by a continuouswave (CW) OPA pump tuned to allow nearly complete pump depletion, the resultant
OPA pump at the output will be modulated with an inverted copy of the input bit
stream. This effect serves as a basis for the OPA based all-optical signal processing
techniques discussed in this thesis. In addition, the FWM components generated in
the OPA process can also be utilized for signal processing purposes, and its
application will also be presented.
In this thesis, applications for all-optical signal processing based on fiber OPA
are discussed. All-optical logic gates, half adders, and regenerators have been
successfully demonstrated with error free operation based on pump depletion and
FWM effects. An experimental setup on all-optical XOR, OR, NOT, and AND gates
in return-to-zero on-off keying (RZ-OOK) format with picosecond pulsewidths
reveals a possibility for operation at 80 Gb/s and beyond. To highlight the possibility
for higher speed operation, a numerical simulation shows that the proposed scheme
scales very well at 80 Gb/s. In addition, a setup capable of producing XOR and AND
outputs simultaneously, hence a half-adder, is also presented in the thesis, followed
by an all-optical regenerator based on gain depletion technique in OPA.
II
I. DECLARATION
I declare that this thesis represents my own work, except where due
acknowledgement is made, and that it has not been previously included in a thesis,
dissertation or report submitted to this University or to any other institution for a
degree, diploma or other qualifications.
Signed .........................................................
Lai Ming Fai
iii
II. ACKNOWLEDGMENTS
I would like to express my sincere thanks to the following people who help me
in undertaking of this thesis.
First of all, I would like to thank Dr. Kenneth K. Y. Wong for his tolerance,
patience, careful guidance and unceasing support in the supervision of my research.
He always taught me a lot on experimental skill and I have been trained as an
experienced researcher in the field of fiber optic communications under his
supervision. Secondly, I would like to thank Dr. T. I. Yuk for giving me the
opportunity to work in the project. Moreover, I want to thank the University of Hong
Kong for the award of the postgraduate studentship. It has supported my life and
allowed me to focus on the research.
Moreover, I would like to express my gratitude to my collaborator Mr. C. H.
Kwok for his advices and technical ideas associated with my research. He assisted
me with his technical expertise throughout my degree, especially in areas associated
with pico-second pulses. I would also like to thank my colleagues Mr. Henry K. Y.
Cheung and Miss Rebecca W. L. Fung during my first year of my research. They
gave me considerable insights during their experimental works. I always appreciate
Mr. Bill P. P. Kuo and Mr. Edmund. L. Lin for their collaboration with me during my
latter parts of my research, in both theoretical and experimental areas. Finally, I
would also thank Mr. Jia Li, Mr. Yu Liang, Mr. Mengzhe Shen, and Miss Kim K. Y.
Cheung for their interest in my research work.
I would like to give a very special thanks to my parents and my sister. Their
supports are priceless to me.
iv
Table of Contents
Abstract ……………………………………………………………….i
Declaration …..…………………………………………………...….. iii
Acknowledgements ……………………………………………….…. iv
Table of Contents ………………………………………………....….. v
Lists of Figures and Tables …………………………..…………...... viii
Chapter 1 Introduction …………………………………………….. 1
1.1 Motivation ……………………………………………………… 1
1.2 Outline of Thesis ……….………………………………………. 3
References ………………………………………………………….. 4
Chapter 2 Dispersion and Nonlinearity in Optical Fibers……….. 5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Dispersion ………………………………………………….. 5
Kerr Nonlinearity .………………………………………….. 6
Nonlinear Schrodinger Equation ………………………....... 7
Self Phase Modulation (SPM) ……………………………… 8
Cross Phase Modulation (XPM) …………………………… 9
Four-Wave Mixing (FWM) ……………………………..… 10
Stimulated Raman Scattering (SRS) ………..…....…….….. 11
Stimulated Brillouin Scattering (SBS) …………......….….. 12
Chapter 3 Optical Parametric Amplifiers …………………..….. 13
3.1
OPA Gain ………………………………………………….. 13
3.2.1 One-Pump OPA …………………………………………….14
3.2.2 Two-Pump OPA …………………………………………….16
3.3
OPA pump depletion ………………………………….……17
3.4
Deliberate pump depletion…………………………….….....
18
3.5
A typical configuration for one-pump OPA……….……...... 20
3.6
Summary of chapter 3 …………………….……….…….... 20
Chapter 4 All-Optical Signal Processing…..………………….….. 21
4.1
21
4.2
v
All-optical Logic Gates – an overview ………….……....… 21
4.1.2 Previous Implementations of All-Optical gates..…......
All-optical Logic gates based on OPA….……………….… 23
4.2.1 All-optical AND gate …………………....……..….... 25
4.2.2 All-optical difference operator ………………..…...... 26
4.2.3 All-optical XOR gate ………………..…………....... 26
4.2.4 All-optical OR gate ……………... ………………..... 26
4.2.5 All-optical NOT gate ……………………………....... 27
4.2.6 All-optical NOR gate ……………..…………..…...... 27
4.2.7 All-optical XNOR gate…………….. ……….…….... 27
4.2.8 All-optical XOR gate (another implementation) ...…..27
4.3 Overview of all-optical regeneration ………….……...29
4.3.1 Previous Implementation of Regeneration………....... 29
4.3.2 All-optical regeneration based on OPA pump depletion..
29
Chapter 5 Experimental Results for All-Optical Signal Processing
based on OPA ………………..............................…….... 32
5.1
5.2
5.3
5.4
5.5
All-Optical XNOR Gate ………………………………...… 32
5.1.1 Experimental Setup….…….. …………………...… 32
5.1.2 Results and Discussion…….. …………………...… 34
5.1.3 Conclusion….…….. ………………….................… 35
All-Optical XOR Gate ………………………………......… 35
5.2.1 Experimental Setup….…….. …………………...… 35
5.2.2 Results and Discussion…….. …………………...… 36
All-Optical Half-Adder, Theory and Experiment...……...… 37
5.3.1 Theory……………….…….. …………………....… 37
5.3.2 Experimental Setup….…….. …………………...… 38
5.3.3 Results and Discussion…….. …………………...… 39
5.3.4 Conclusion….…….. ………………….................… 41
All-Optical Picoseconds Logic Gate …………………....… 42
5.4.1 Experimental Setup for each logic gate……….....… 43
5.4.1 Effect of SPM on the input pulses…………….....… 44
5.4.3 Experimental Results for picoseconds logic gate …. 45
5.4.4 Conclusion….…….. ………………….................… 52
All-Optical Regenerator……………………….....……...… 53
5.5.2 Results and discussion …………………….….….. 54
5.5.3 Conclusion….…….. ………………….................… 56
Chapter 6 Conclusion and Future Works……………….....……... 58
6.1
6.2
Summary of Research Contributions.................................… 58
Future Work ………………………. …………………....… 58
6.2.1 Enhancements in XOR Gate……….…………...… 58
6.2.2 > 80Gb/s Logic Gates …….. …………………………....… 60
Appendix A
The Split-Step Fourier Method ……….….…..….. 62
Appendix B
List of my Publications ………………..…….….… 66
vi
Appendix C
Appendix D
vii
Abbreviations………… ……….………………. 67
References………… …………………………… 69
Lists of Figures and Tables
Fig. 2.1: Simulation of spectral broadening of picosecond hyperbolic secant pulses
due to SPM. Fiber length is increased from (a) at 1.175km to (c) at 2.5km.
Fig. 2.2: Rising edge of pulse at wavelength λ2 coincides with pulse at λ1.
Fig. 2.3: Numerical simulation of Raman scattering.
Fig. 3.2.1: Typical gain spectrum of one-pump OPA.
Fig. 3.2.2: Typical gain spectra by a one-pump OPA pump. Vertical axis uses a
logarithmic unit.
Fig. 3.2.3: Amplification of noise by two CW OPA pumps. The dashed lines refer to
the signals and idlers amplified by the two pumps.
Fig. 3.3.1: Effect of pump depletion in the spectral domain (a) input (b) output.
Fig. 3.4.1: (a) Input, and (b) output optical spectrum showing pump depletion
effects between two signal modulated pumps.
Fig. 3.5.1: Experimental setup of one-pump OPA. TLS: Tunable laser source. PC:
Polarization controller. PM: Phase modulator. VOA: Variable optical attenuator.
TBPF: Tunable bandpass filter. OSA: Optical spectrum analyzer.
Fig. 4.1.1: XOR gate based on gain depletion.
Fig. 4.1.2: XNOR gate based on gain depletion.
Fig. 4.1.3: All optical XOR gate using UNI.
Fig. 4.2.1: Truth tables of XOR, XNOR, NOT, NOT, OR, and AND gates.
viii
Fig. 4.2.2: AND gate operation.
Fig. 4.2.3(a-b): Truth tables of difference operation filtering at (a) ω1, (b) ω2.
Fig. 4.2.4: XOR gate operation.
Fig. 4.2.7: NOR gate operation.
Fig. 4.2.8: Operation principle of an all-optical XNOR gate.
Fig. 4.2.9: Operation principle of an all-optical XOR gate.
Fig. 4.3.1: All optical regeneration using SPM in HNLF.
Fig. 4.3.2: All optical 3R regeneration using OPA [23].
Fig 4.3.3: OPA pump at output against input signal power.
Fig. 5.1.1: Experimental Setup for XNOR gate.
Fig. 5.1.2:. Input and output waveforms for XNOR gate. Time base: 100 ps/div.
Fig. 5.1.3: Eye diagram of XNOR gate. Time base: 50 ps/div.
Fig. 5.2.1: Experimental Setup for XOR gate.
Fig. 5.2.2: Left: XOR output waveform. Time base: 100ps/div. Right: Eye diagram.
Time base: 50 ps/div.
Fig. 5.3.1: Experimental Setup for half-adder.
Fig. 5.3.2: Bit patterns and eye diagrams for half-adder. Time base: 100 ps/div for
bit patterns, 50 ps/div for eye diagrams.
ix
Fig. 5.3.3: BER curves for half-adder.
Fig. 5.4.1: Experimental Setup for picoseconds logic gate.
Fig 5.4.2: Transfer function between average input power and output peak
power due to SPM.
Fig. 5.4.3: (a) Bit patterns for the inputs and outputs of AND gate, (b) Bit patterns
for the inputs and outputs of XOR, OR, and NOT gates for picoseconds logic gate
experiment. Time base: 100 ps/div.
Fig. 5.4.4: Eye diagrams of (a) XOR, (b) OR, (c) NOT, (d) AND gate output for
picoseconds logic gate experiment. Time base: 50 ps/div.
Fig. 5.4.5: (a) Comparison between the output spectra of the OR and XOR gates,
(b) NOT gate output spectra, (c). AND gate output spectra for picoseconds logic gate
experiment.
Fig. 5.4.6: Bit-error rate for input and output signals of the (a) XOR, OR, and NOT
gates, (b) AND gate for picoseconds logic gate experiment.
Fig. 5.5.1: Experimental setup of OPA-based all-optical signal regenerator.
Fig. 5.5.2: (a). Measured transfer function of the OPA-based all-optical signal
regenerator (b) Plot of the measured BER for (◊) the degraded and (○) the
regenerated signals. Insets show the measured eye diagrams of the degraded and the
regenerated signals.
Fig. 5.5.3: (a). Noisy input signal. (b) Noisy signal after regeneration of OPA-based
all-optical signal regenerator. Time base: 50 ps/div.
Fig. 6.1: Theory of Operation for single wavelength XOR gate.
x
Fig. 6.2: Simulated 80 Gb/s output for (a) XOR- (b) OR- (c) NOT- and (d)
AND-gate.
Fig. 6.3: Experimental Setup for 80Gb/s picosecond logic gates.
xi
Chapter 1
Introduction
1.1 Motivation
High speed all optical networking has been on rising development because of
the increasing needs in worldwide networking demands. These demands stem from
video streaming, online gaming, video conferencing, and many other interactive
multimedia services, which require a low latency high bandwidth connection
between its users. These lead to researches oriented to all-optical networking to
harness more potential bandwidth from all-optical networks.
Recent developments in wavelength-division multiplexing (WDM) allow
multiple channels of information to be transmitted through the same optical fiber at
different wavelengths. Currently, WDM based all-optical networks reach a record
speed of 25.6Tb/s for a single piece of fiber in 2007 [1].
The advent of dispersion-shifted fibers (DSF) allows the zero-dispersion
wavelength to coincide with the wavelength of least attenuation. It reduces the
number of necessary repeaters, which further reduces implementation costs.
However, dopants used in the DSF give rise to stronger Kerr-based nonlinear effects
[2]. This is detrimental to an all-optical network, due to four-wave mixing (FWM)
effects about the zero-dispersion wavelengths. FWM allows signals to change from
one wavelength to another, leading to WDM crosstalk.
However, the detrimental effects of FWM can be utilized to achieve some
desirable functionality. Hence, efforts have been made to increase the FWM effects
in a DSF, such as reducing the effective core area. This allows strong nonlinear
effects on a relatively short piece of fiber, which provides an important device
known as fiber optical parametric amplifier (OPA). OPA allows an exponential gain
of signal and idler components when the pumps, signal, and idlers satisfy certain
phase-matching conditions [3].
Like other optical amplifiers such as semiconductor optical amplifier (SOA),
1
Raman amplifier, or Erbium-doped fiber amplifier (EDFA), OPA can also be used to
amplify signals in an optical network. A major benefit of OPA is its wideband gain
spectrum, and flat gain in two-pump OPA setups [3]. In addition, demonstrations
showed that it can amplify by up to 70dB. In addition, OPA is pattern in-sensitive,
due to its inherent femto-second response time.
By utilizing the femto-second response time of fiber OPA, it is possible to
produce high speed all-optical signal processing elements. This includes regenerators
and logic gates, which are investigated in this thesis. Fiber OPA has a major
advantage over other devices such as SOAs where electronic response time is always
a limiting factor to the bit-rate they can support. Since the traditional O-E-O method
is very costly to implement at speeds of 80Gb/s, fiber OPA proves to be a very
promising candidate for future all-optical signal processing elements.
2
1.2 Outline of Thesis
The rest of this thesis is organized as follows:
Chapter 2 describes some of the nonlinear phenomena in fiber optics as well as
dispersion. These include the Kerr effect, self-phase modulation (SPM), cross-phase
modulation (XPM), stimulated Raman scattering (SRS), stimulated Brillouin
scattering (SBS), and four-wave mixing (FWM).
Chapter 3 is devoted to optical parametric amplifiers. An analytical solution for
the OPA gain spectrum is given under undepleted pump approximations. Numerical
simulations of OPA gain spectra are applied to an HNLF. In addition, a qualitative
description to OPA pump depletion is given, which is the fundamental mechanism
for most of the methods presented in this thesis. Finally, a typical experimental
configuration for OPA is presented.
Chapter 4 describes the theories of operation of all-optical signal processing
based on FWM and pump-depletion in fiber OPA. All-optical XOR, OR, NOT, AND,
XNOR, and NOR gates are produced using the physical phenomena described in
chapter 3. In addition, all-optical regenerators based on OPA pump depletion are also
presented in this chapter.
Chapter 5 presents the experimental setup and results of the signal processing
applications described in the previous chapter. Eye diagrams and BER plots are
presented in this chapter. Return-to-zero (RZ), Non-return-to-zero (NRZ), and
picosecond pulsewidth pulses were used as inputs to the all-optical logic gates across
different experimental configurations. Finally, an experiment on all-optical
regenerator based on OPA pump depletion is presented.
Chapter 6 summarizes this thesis. Some further investigations for future
research efforts include 80Gb/s optical logic gate with single wavelength output are
also outlined in this chapter.
3
Chapter 2
Dispersion and Nonlinearity in Optical Fibers
As light travels down a nonlinear fiber, the interplay between dispersion and
nonlinearity allows many effects to be formed, such as parametric amplification and
soliton propagation. The effects of dispersion alone lead to pulse broadening or pulse
compression. This chapter summarizes the effects of Kerr nonlinearity and
dispersion.
2.1 Dispersion
The refractive index n(ω ) in an optically transparent medium varies with the
frequency of the light ω , which is dependent on the material properties. The
refractive index can be used to derive the propagation constant β (ω ) , using the
relation β (ω ) = nω / c , where c is the speed of light in vacuum and ω is the angular
frequency. With the propagation constant, it is possible to evaluate the group velocity
of light using the following equation:
vg = d ω / d β
-- (2.1.1)
Generally, the group velocity of light varies with its frequency. This results in groupvelocity dispersion (GVD), which leads to pulse broadening or compression. This
effect can be most easily understood by different spectral components propagate at
different group velocities, hence broadening or compressing the pulse.
To quantify the effects of GVD due to differences in group velocity, the quadratic
term of the Taylor’s expansion of β (ω ) about the carrier frequency of the pulse is
taken. The coefficient of the quadratic term, β 2 determines the amount of GVD of
the pulse.
Dispersion in a piece of nonlinear fiber can be mathematically described by [1]
4
i
U% ( z , ω ) = U% (0, ω ) exp( β 2ω 2 z )
2
-- (2.1.2)
where U% ( z , ω ) is the Fourier transform of normalized amplitude U ( z, T ) , and β 2 is
the group velocity dispersion of the pulse.
2.2 Kerr Nonlinearity
2.2.1 Overview of Nonlinearity
When highly coherent light propagates through a nonlinear medium, the refractive
index of the medium varies with optical power. In a χ(3) nonlinear medium, the
relationship is given by:
n = n% + n2 I
-- (2.2.1)
where n2 is the nonlinearity from the χ(3) nonlinear susceptibility, and I is the
intensity of light. The effects on high power coherent light due to Kerr nonlinearity
will be discussed in subsequent sections.
2.2.2 Origins of χ (3) Nonlinearity
In most optical medium, linear polarization is defined
r
r
PL = ε 0 χ (1) E
-- (2.2.2)
r
where P is a vector displaying induced polarization due to the applied electric field,
r
E is a vector of the applied electric field, ε 0 is the permittivity of free space, and
χ (1) is a 3-by-3 matrix that determines the magnitude and direction of the induced
polarization due to the applied electric field.
Eq. (2.2.2) is based on a linear approximation between induced polarization and
electric field. It also assumes that the medium’s response is local and is instantaneous.
This, however, does not accurately account that the electronic response of the optical
medium is not instantaneous and nonlinear in general. In silica, all even orders of
nonlinearity are non-existent since the material is centro-symmetric [2]. Higher
orders nonlinearity such as 4th order or above are generally too weak to be
considered. Hence, the dominate effect from nonlinearity arises from third-order
nonlinear effects.
5
To approximate the effects from third-order nonlinearity, the polarization arise from
third order nonlinearity is given by:
r
rrr
PNL = ε 0 χ (3) M EEE
-- (2.2.3)
This equation now describes the nonlinear polarization given by the E3 for
nonlinearity effects. Together with Eq. (2.2.2), the total polarization is given by
r r
r
r
rrr
P = PNL + PL = ε 0 ( χ (1) E + χ (3) M EEE )
-- (2.2.4)
which can be directly applied to the Maxwell’s equations to solve the propagation of
light in an optically transparent medium. From Eq. (2.2.3), it can be seen that
nonlinear effects occur only when high intensity electromagnetic waves propagate
rrr
through the nonlinear fiber. This is because χ (3) is very small and EEE requires being
very large to have strong nonlinear polarization.
In a dispersion-shifted fiber (DSF), its smaller effective core area of about 55 μm2
allows stronger nonlinear effects by confining light in a smaller cross-section area,
which increases the intensity of light. Additionally, by doping the silica fiber with
GeO2 and further reduction in effective core area, the nonlinearity of the fiber can be
further increased, such as the highly-nonlinear dispersion-shifted fiber (HNL-DSF).
2.3 Nonlinear Schrodinger Equation
Both Kerr nonlinearity and dispersion act on an optical pulse simultaneously to
produce a wide range of effects. To evaluate the interplay between them, the
following nonlinear Schrodinger equation (NLSE) is formulated, up to third order
dispersion but without the consideration of Raman and Brillouin scattering,
iβ ∂ 2 A β3 ∂ 3 A
∂A α
2
+ A+ 2
−
= iγ A A
2
3
∂z 2
2 ∂T
6 ∂T
-- (2.3.1)
where A is the pulse envelope, α is the attenuation per unit length, β 2 and β3 are
the coefficients of the quadratic and cubic terms of the Taylor’s expansion of the
propagation constant about the carrier frequency respectively, and γ is the
nonlinearity coefficient. This equation forms the basis of analysis in the subsequent
chapters, and it is used in the MATLAB simulation program described in Appendix
A.
6
2.4 Self-Phase Modulation (SPM)
Due to Kerr nonlinearity, an optical pulse will acquire a phase-shift proportional to
its instantaneous power when it propagates alone through a nonlinear fiber. This
effect is known as self phase modulation (SPM).
Mathematically, the effect of SPM (without dispersion and attenuation) can be
written as [1].
U ( L, T ) = U (0, T ) exp[iφNL ( L, T )]
---(2.4.1)
2
where φNL ( L, T ) = U (0, T ) γ P0 L , A( z , T ) = P0 U ( z , T ) and A is the pulse amplitude.
From Eq. (2.4.1), the nonlinear phase shift φNL on the pulse shape can lead to
spectral broadening, which is especially apparent in short pulses with high peak
power. This can be understood from the rising edge of the pulse, leading to an
increasing strength of SPM. The consequence is an increasing phase shift on the
rising edge of the pulse. This increasing phase shift essentially translates to a
frequency red-shift, seeding a new red-shifted frequency component. This effect is
particularly strong in picosecond pulses due to its ultra-fast rise time, translating to a
large frequency shift. The opposite effect occurs on falling edges, which shifts the
falling edge to a lower frequency. Hence, a high peak power pulse with picosecond
pulsewidths launched into a HNLF will result in frequency shifts in both directions.
Such numerical simulations on the effects of spectral broadening are shown in the
Fig. 2.1 below:
7
(a)
(b)
(c)
Fig 2.1: Simulation of spectral broadening of picosecond hyperbolic secant pulses
due to SPM. Fiber length is increased from (a) at 1.175km to (c) at 2.5km.
2.5 Cross-phase modulation (XPM)
Similar to SPM, two optical pulses of different frequencies co-propagating through a
nonlinear fiber will induce phase shifts on each other in addition to the nominal SPM
induced phase shift. This effect is known as cross-phase modulation (XPM). The
amount of phase shift is dependent on the optical power of the neighboring pulses
and the relative polarization between the two pulses. The principal reason behind
8
XPM is both pulses’ instantaneous power will contribute to the change in refractive
index due to Kerr nonlinearity. A common application of XPM is to launch a probe
pulse that co-propagates with the rising edge of another pump pulse, which red-shifts
the probe pulse depending on the rate of change of the pump. A schematic of this
effect is shown in Fig. 2.2.
Power
at λ1
at λ2
t
During rising edge of λ2
Fig 2.2: Rising edge of pulse at wavelength λ2 coincides with pulse at λ1 .
.
2.6 Four-wave mixing (FWM)
A combination of dispersion and Kerr-based nonlinear effects can lead rise to fourwave mixing (FWM). Physically, FWM occurs when two signals of different
frequencies co-propagate through a nonlinear medium to generate two idlers at two
new frequencies. The newly generated light satisfies the conservation of energy,
given by:
ω1 + ω2 = ω3 + ω4
-- (2.6.1)
Typically, by launching two pumps with different frequencies ω1 and ω2 into a
highly nonlinear fiber, idlers will be generated at frequencies ω1 + N (ω1 − ω2 ) . These
higher order idlers are generated by FWM between the generated idlers and/or the
pumps itself.
When two pumps at ω1 and ω2 are propagated through a nonlinear fiber, two idlers
at ω3 and ω4 will be generated from noise. The growth of these two idlers depends
9
on the relative phase between the input pulses, given by Δβ in Eq. (2.6.2)
Δβ = β (ω3 ) + β (ω4 ) − β (ω1 ) − β (ω2 )
-- (2.6.2)
It is known [1] that the growth of the two newly generated idler is the strongest
when Δβ = −2γ P , where P is the combined input optical power from the input
signals. With an undepleted pump approximation, the idlers experience an
exponential gain as it travels down the fiber. This result is known as optical
parametric amplification (OPA), which will be described in details in chapter 3.
2.7 Stimulated Raman Scattering (SRS)
When highly coherent light travels down a silica fiber with substantial Kerr
nonlinearity, part of its power will be given up to molecular vibration due to Raman
scattering. This manifests in the frequency domain as a gain in the red-shifted
component. This is due to the photons transferring part of its power to the vibrational
modes of the molecules, hence leaving the photons to a lower energy. In silica fibers,
a broadband gain spectrum with a peak red-shifted from the pump by 13THz is
observed. This gain is observed in both forward and backward propagation directions
with respect to the pump. The Raman gain is a result of non-instantaneous χ(3)
nonlinearity response, as discussed in [1]. The nonlinear Schrödinger equation that
governs wave propagation in nonlinear fibers, can be modified to account for Raman
scattering by:
∞
iβ ∂ 2 A
i ∂
∂A α
2
+ A+ 2
= iγ (1 +
)( A( z, T ) ∫ R(t ') A( z , T − t ') dt ') --(2.7.1),
2
∂z 2
ω0 ∂T
2 ∂T
−∞
τ 12 + τ 22
−t
t
where R (t ) = 0.82δ (t ) + 0.18
exp( ) sin( ) , τ 1 = 12.2 fs , τ 2 = 32 fs , and ω0
2
τ 1τ 2
τ2
τ1
is the center frequency. The parameters τ 1 = 12.2 fs and τ 2 = 32 fs are chosen such
that the simulated gain spectrum and bandwidth matches with the experiments. A
numerical simulation of Raman scattering is shown in Fig. 2.3. The blue shifted peak
is a result of FWM between the Raman peak and the CW light.
10
Fig. 2.3 Numerical simulation of Raman scattering. A peak is located at 13.5THz
red-shifted from the center.
2.8 Stimulated Brillouin Scattering (SBS)
Stimulated Brillouin Scattering (SBS) in an optical fiber is a result of backscattering due to the formation of an acoustic wave generated from electrostriction
[2]. The electrostriction process is powered by a strong, narrow bandwidth, pump
propagating through the nonlinear fiber, since this result in strong E-fields required
for the electrostriction process. The consequence is a modulation of the refractive
index of the fiber, which essentially leads to the formation of a travelling Bragg
grating at the acoustic velocity of the fiber’s material. The final result is a reflected
pump wave downshifted in frequency due to the Doppler’s effect.
The SBS scattering threshold, defined as the input pump power such that the output
stokes power becomes equal to the output pump power, varies with bandwidth and
polarization of the input pump. A figure commonly used to describe the strength of
SBS in a given setup is the threshold power, defined as the input power of which half
of the light is backscattered. For a CW travelling through the nonlinear fiber, the
threshold power is given by [1] in Eq (2.8.1).
PTH =
11
21Aeff
gB L
-- (2.8.1)
where Aeff is the effective area, and gB is 5x10-11 m/W for typical fibers.
The threshold power is increased by 50% if the polarization is scrambled as the pulse
travels down an optical fiber [1]. It is further increased by deliberately spectrally
broadening the input light.
Since SBS is usually detrimental to system, methods are employed to increase this
threshold power. This is commonly achieved by phases dithering, which dramatically
increase the bandwidth of the pump to reduce the effect of SBS, since the broadened
laser linewidth will result in an increase in SBS threshold.
12
Chapter 3 Optical Parametric Amplifiers
The underlying principle of optical parametric amplifier (OPA) is based on
FWM, SPM, and XPM. FWM can transfer power from strong pump(s) to a signal
and an idler. Due to a combination of SPM, XPM, and FWM, there will be an
exponential parametric gain of power on the signal and idler. This gain is known as
OPA. Two common setups for OPA are used; one pump OPA and two pump OPA,
which defers in the number of pumps used and the wavelength allocation of the setup.
The details of their operation are shown in the sections that follow.
3.1
OPA Gain
The following four equations govern the light propagation through the
nonlinear fiber:
(
)
-- (3.1.1)
(
)
-- (3.1.2)
(
)
-- (3.1.3)
(
)
-- (3.1.4)
dA1
2
2
2
2
= iγ A1 ⎡⎢ A1 + 2 A2 + A3 + A4 ⎤⎥ + 2iγ A2* A3 A4 eiΔβ z
⎣
⎦
dz
dA2
2
2
2
2
= iγ A2 ⎡⎢ A2 + 2 A1 + A3 + A4 ⎤⎥ + 2iγ A1* A3 A4 eiΔβ z
⎣
⎦
dz
dA3
2
2
2
2
= iγ A3 ⎡⎢ A3 + 2 A1 + A2 + A4 ⎤⎥ + 2iγ A1 A2 A4*e− iΔβ z
⎣
⎦
dz
dA4
2
2
2
2
= iγ A4 ⎡⎢ A4 + 2 A1 + A2 + A3 ⎤⎥ + 2iγ A1 A2 A3*e− iΔβ z
⎣
⎦
dz
where A1 A2 A3 and A4 are the envelope of four waves at frequencies ω1 ω2 ω3 and
ω4 respectively. γ is the nonlinearity coefficient, i is
−1 , and
Δβ = β (ω3 ) + β (ω4 ) − β (ω1 ) − β (ω2 ) .
Equations (3.1.1-3.1.4) are accurate with undepleted pump assumption for four
waves travelling through a nonlinear fiber. However, more idlers are generated as the
four waves propagate through the nonlinear fiber, which depletes the OPA pumps.
This makes the analysis of using Equations (3.1.1-3.1.4) accurate only when the new
idlers generated are of negligible power.
The gain spectrum can be evaluated easily without resorting to elliptical functions [1]
13
by assuming that the pumps are undepleted as they propagate through the nonlinear
fiber. In addition, there are no other signals propagating through the fiber.
With the assumptions made previously and by following the evaluation of the OPA
gain spectrum in Ref. [2], the gain spectrum is given by:
⎛
κ2 ⎞
Gs = 1 + ⎜ 1 + 2 ⎟ sinh 2 ( gL )
⎝ 4g ⎠
-- (3.1.5)
Gi = Gs − 1
-- (3.1.6)
2
⎡
2
⎛κ ⎞ ⎤
g = ⎢( γ P0 r ) − ⎜ ⎟ ⎥
⎝ 2 ⎠ ⎦⎥
⎣⎢
-- (3.1.7)
κ = Δβ + γ ( P1 + P2 ) = Δβ + γ P0
-- (3.1.8)
2
where Gi is idler gain, Gs is the signal gain, L is the fiber length, κ is the net phase
mismatch, r = 2
P1 P2
, and P0 = P1+P2 is the initial input pumps’ power.
P0
From Eq. (3.1.5), it can be seen that there will be exponential gain on the signal
when g is real. By inspection, this can be achieved by satisfying the following phase
matching condition:
−4γ P0 < Δβ < 0
-- (3.1.9)
In the degenerate case, let P1 = P2 , and Δβ = β (ω3 ) + β (ω4 ) − 2β (ω1 ) , where the
single OPA pump is regarded as two pumps which are indistinguishable in both
frequency and phase.
3.2.1 One-pump OPA
When a single CW pump propagates through a nonlinear fiber with its frequency
slightly into the anomalous dispersion region, an OPA gain spectrum about the
pump’s frequency will be formed. This is achieved by placing the pump slightly into
the anomalous dispersion region to satisfy −4γ P0 < Δβ < 0 for a range of ω about the
pump frequency. The usual wavelength allocation for a single pump OPA setup is
shown in Fig 3.2.1.
14
Power
Single CW pump
OPA Gain Spectrum
λ0 λpump
λ
Fig 3.2.1 Typical gain spectrum of one pump OPA.
To quantify the findings, the diagrams below show the OPA gain spectrum due to a
single pump for different values of β 2 :
(a)
15
(b)
Fig 3.2.2 Typical gain spectra by a one-pump OPA pump with different β2.
3.2.2 Two-Pump OPA
In a two-pump OPA configuration, two pumps are placed symmetrically about the
zero dispersion frequency for phase matching. A typical wavelength allocation
between the pumps and signals are shown in Fig 3.2.3.
Power
λpump1
λ0
λ
λpump2
Fig 3.2.3 Amplification of noise by a CW OPA pump. The dashed lines refer
to the signals and idlers amplified by the two pumps.
A major advantage of using two-pump OPA is its relatively flat gain spectrum such
as demonstrated in Ref. [3]. Additionally, the phase modulation applied to the pumps
16
in certain configurations for SBS suppression will not be transferred to the idlers.
3.3 OPA pump depletion
In the previous section, OPA allows an exponential growth of idlers under the
approximation that the pumps are undepleted during the amplification. This
approximation is valid for evaluating the OPA gain spectrum experimentally by
amplifying ASE noise. However, the situation is different when the OPA pump is to
amplify some signals of significant power. Fig. 3.3.1 describes this scenario.
Consider a one-pump OPA used to amplify two CW signals both within the OPA
gain spectrum:
Power
Strong CW pump
Signals to be amplified
ω
ωpump
(a)
Power
Vastly Depleted CW pump
Signals amplified, but then
depleted to generate idlers
Generation of a wide
spectrum of idlers.
ω
ωpump
(b)
Fig. 3.3.1 Effect of pump depletion in the frequency domain (a) input (b) output of
the fiber.
Originally, the two signals experience exponential gain as it travels through the
17
nonlinear fiber. However, this gain is reduced as they travel down the fiber, since the
gains made on the signals and their idlers are levied from the OPA pump. Hence,
both signals will experience less gain than if only one of them co-propagates with the
pump. The reduced gain on a signal due to the existence of another signal is known
as cross gain modulation (XGM).
Nearly complete pump depletion is possible if appropriate conditions of phase
matching and power levels are chosen [4]. In a single pump configuration, the signal
can be placed at the midway between the peak gain of the OPA gain spectrum and
the pump. This has been demonstrated both analytically and experimentally [4]. To
further increase the effects of pump depletion, a much stronger OPA pump and/or
signal can be launched into the nonlinear fiber. This mechanism of pump depletion is
mainly based on the depletion from the higher order idlers, especially if they are
within the OPA gain spectrum. However, the inclusion of the generation of higher
order idlers does not yield an analytical solution, and only experimental results will
be given in this thesis.
3.4 Deliberate OPA pump depletion
In this configuration, two OPA pumps are set to be within each other’s OPA gain
spectrum. This strong phase-matching allows a very rapid generation of idlers,
resulting in a very rapid depletion of the two OPA pumps.
Fig 3.4.1 illustrates this principle qualitatively. The spectra of two short pulsewidth
(<5ps) pump pulses co-propagating through a nonlinear fiber are shown in Fig
3.4.1(a), and both pulses are launched into each other’s single pump OPA gain
spectrum. Such wavelength allocation will result in an exponential growth of higherorder idler components, resulting in a spectrum shown in Fig 3.4.1(b) at the output.
The original input pumps are depleted due to the rapid growth of higher-order idler
components. The result is a wide continuum on the frequency domain, due to the
wide bandwidth of both the idlers and signal components.
18
Log(Power)
Inputs
OPA Gain Spectra
λ2
λ1
λ0
λ
(a) input
Log(Power)
Depleted Inputs
Continumn
λ2
FWM Idlers
λ1
λ0
λ
(b) output
Fig 3.4.1 (a) Input, and (b) output optical spectrum showing pump
depletion effects between two signal modulated pumps.
19
3.5 A typical configuration for one-pump OPA
In this section, a one-pump OPA configuration is presented. For simplicity, both the
input and output are CW sources.
10Gb/s PRBS data stream
TLS1
PC1
PM
PC3
TBPF1
500m
HNL-DSF
VOA
TBPF2
TLS2
Figure 3.5.1 Experimental setup of one-pump OPA. TLS: Tunable laser source. PC:
Polarization controller. PM: Phase modulator. VOA: Variable optical attenuator.
TBPF: Tunable bandpass filter. OSA: Optical spectrum analyzer.
Fig 3.5.1 shows a simple with a CW light using a CW OPA pump. The nonlinear
medium used was a spool of highly nonlinear dispersion-shifted fiber (HNL-DSF).
The pump was phase modulated with a pseudo-random binary sequence (PRBS) to
suppress stimulated Brillouin scattering (SBS) [4]. It was then connected to an
erbium doped fiber amplifier (EDFA1). The tunable band pass filter (TBPF1)
significantly suppressed the amplified spontaneous emission (ASE) noise from
EDFA1. After that, the pump was amplified again at EDFA2 before entering the
WDM coupler with the signal. The combined waveform was then injected into the
HNL-DSF. The output of the HNL-DSF was attenuated by a VOA before being
filtered for the signal wavelength at TBPF2. The VOA is used to avoid damage to
the TBPF and the OSA. At the OSA, a gain will be recorded depending on the setup
parameters.
3.6 Summary of chapter 3
In this chapter, the theory of OPA has been presented. It is shown mathematically
that when the pumps, signals, and idlers satisfy the phase-mismatch in Eq. (3.19),
exponential gain will be achieved on the signals and idlers. The spectrum for onepump OPA has also been illustrated. The effects of pump depletion are described
qualitatively in this chapter, including methods of deliberately achieving strong
pump depletion using higher order idlers.
20
Chapter 4
All-optical signal processing
All-optical signal processing is of recent interest due to its advantage over traditional
optical-electrical-optical (O-E-O) methods. In this chapter, attention is given to alloptical logic gates and all-optical 2R regenerators. The all-optical logic gates are
produced using pump depleted OPA and FWM methods, in which XOR, XNOR,
NOR, NOT, AND, and OR gates can be generated using a single stage OPA setup.
All-optical 2R regenerators can also be achieved by pump depletion mechanisms.
4.1 All-optical logic gates – an overview
All-optical logic gates have found a large variety of uses for signal processing
applications. All-optical XOR gate, for example, found great uses in all-optical data
comparison for packet address recognition [1], encryption/decryption, parity
checking [2] and generation of pseudorandom bit patterns [3]. All-optical AND gates
had served as sampling gates in optical sampling oscilloscopes [4] owing to their
ultrafast operation compared to traditional electrical methods. All-optical NOT gates
can be used in rectifying inverted optical signal processing elements. Of the many
different possible all-optical gate implementations, most are based on semiconductor
optical amplifiers (SOA) as the nonlinear medium for nonlinear optical signal
processing. Cross-gain modulation (XGM) and cross-phase modulation (XPM) in
SOA have been widely explored in SOA for logic gate implementations [5-9], using
a single or multiple SOAs. Recent technique of using an SOA together with a
detuned filter can provide picosecond response time despite a much longer,
nanosecond-scale carrier recovery time [10]. This may prove to be very desirable
candidate for logic applications requiring XGM effects [5]. However, this approach
requires a very dedicated setting of SOA conditions and filter offset [11].
4.1.2 Previous implementations of all-optical logic gates
Currently, common methods of achieving all-optical logic are based on SOA. Since
XOR/XNOR presents a major use in all-optical logic, a few well known
implementations for XOR/XNOR gates based on SOA are given in this section.
21
(a) A gain depletion based SOA is shown in the Fig. 4.1.1.
Fig. 4.1.1: XOR gate based on gain depletion [12].
When only one pulse propagates through the SOA, it is greatly amplified at the
output. However, when an additional pulse propagates through the SOA, both pulses
will experience less gain due to cross gain modulation in the SOA. In the method
shown in Fig. 4.1.1, bitstream B is launched into the upper SOA with a much higher
power than bitstream A, so that A does not emerge amplified at the output leading to
the logical output AB . By using a setup of two SOAs shown in Fig. 4.1.1, an XOR
output is resulted.
(b) Other gain depletion techniques for SOA is shown in Fig. 4.1.2
Fig. 4.1.2: XNOR gate based on gain depletion [6]
In this method, two high power OOK signals co-propagate through an SOA with
another weak clock signal. In the SOA, FWM effects leads to the generation of the
AND gate, while XGM leads to the generation of the NOR gate. By combining the
AND and NOR outputs, a XNOR output is generated. In the experiment, the authors
[6] presented a 5 Gb/s setup, but it has described the possibility of a detuned filter
technique used for this setup to increase bit-rates.
However, this setup is limited by the electronic response time of the SOAs, limiting
22
the bit rate to less than 10Gb/s. To further increase the performance of this setup,
setup based on detuned filter technique is used [13], which takes advantage of chirp
induced into the optical pulse during in SOA’s gain recovery.
(c) An implementation based on ultrafast nonlinear interferometer (UNI) is shown in
Fig 4.1.3.
Fig. 4.1.3. All optical XOR gate using UNI [14].
The polarization maintaining (PM) fibers delays the TM and TE components of the
pulse differently as shown in Fig. 4.1.3. In the setup, control A causes the pulse in TE
mode to shift by π due to nonlinear interferometry. In a similar reason, control B
shifts the TM mode of the pulse by π. The polarizer is set to pass light only when the
TE or TM component of the light is shifted by π. But when both the TE and TM
mode of the pulse are shifted by π, the pulse maintains the same polarization as if
none of the phase shifts are applied to them. Hence the polarizer blocks the light
completely. This leads to the output being an XOR operation on the two control
inputs. This setup has been successfully demonstrated with a bit rate of 40 Gb/s in
2005 [14].
4.2 All-optical logic gates based on OPA
There have also been substantial applications demonstrated in fiber based optical
parametric amplifier (OPA) for signal processing functions. Examples include
channel multi-casting [15, 16], parametric wavelength conversion [17], signal
regeneration [18], all-optical logic gates [19], and modulation format conversion [20].
23
The greatest triumph of using fiber based OPA over SOA was its inherent
femtosecond response times, governed by the χ(3) nonlinear susceptibility of an
optical fiber. This allows an application based on fiber OPA to attain picosecond
response time without much laborious effect; even though certain non-idealities from
the dispersion of picosecond pulses and self-phase modulation (SPM) within a
nonlinear fiber may result in pulse broadening and spectral broadening that limit the
minimum pulsewidth can be handled by the OPA process in a fiber [21]. An obvious
remedy to reduce pulse broadening through dispersion was to use a shorter nonlinear
fiber, which will require a higher nonlinear coefficient or higher input power. To
prevent SPM spectral broadening while having ultra short pulses, the pulses’ peak
power cannot be exceedingly large. In this section, a qualitative description of such
effects on short pulses is given, and to cope with these effects; the fiber length and
input powers were chosen such that these effects did not degrade the performance of
our system, yet providing sufficient nonlinear effects to realize the targeted logical
operations.
The figure below shows truth tables of the logic gates described in this thesis.
Input s1
Input s2
XOR
XNOR
NOR
NOT (of s1) OR
AND
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
Fig. 4.2.1 Truth tables of XOR, XNOR, NOT, NOT, OR, and AND gates.
4.2.1 All-optical AND gate
By modulating coherent light of two different wavelengths with OOK data and
launching them into a HNL-DSF, the resultant generated idlers by FWM will act as
an AND gate of the two input signals. The actual logic gate output is acquired by
spectrally filtering out one of the generated idler wavelengths. To strengthen the
generated FWM idler, the light is co-polarized with each other. In the experiment
demonstrated in Chapter 5, the data is in RZ-OOK format, with picosecond full
24
width half maximum (FWHM) pulsewidth. Broad signal spectra of these picosecond
RZ-OOK signals require a low dispersion for phase matching in order to generate an
efficient FWM to complete the all-optical logical operation. Since the duty cycle was
very small, a very modest amount of average power can generate a significant FWM
idler. The operation of a FWM-based AND gate is shown in Fig. 4.2.2.
s1
1 0
0 1
s2
1 0
1
HNL-DSF
FWM
0
1 0 0 0
1 0 0 0
Fig. 4.2.2 AND gate operation.
4.2.2 All-optical difference operator
By launching two synchronized on-off keying (OOK) signals with their wavelengths
set to have the OPA gain spectrum covering each other, the difference operation of
the half-subtractor can be produced by filtering out one of the input signals [21].
This can be observed that by applying a filter at ω1, while both signals from ω1 and
ω2 carry data modulated in OOK format, the following truth table in Fig 4.2.3(a) is
achieved. The “0” state at the output when the inputs s1 and s2 are both “1” is based
on the pump depletion mechanism described in section 3.4. Pump depletion occurs
only when both pulses co-propagate through the HNL-DSF. Similarly, by applying a
filter at ω2, a truth table as in Fig 4.2.3(b) is achieved. Notice that the nonlinear
medium utilizing pump depletion effect will generate both of these outputs
simultaneously. Like the FWM-based AND gate, it only requires a modest average
power to successfully achieve strong pump depletion effects, due to the high peak
power of the input pulses with a small duty cycle pulses.
Input s1
Input s2
Output
Input s1
Input s2
Output
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
(a)
(b)
Fig. 4.2.3(a-b). Truth tables of difference operation filtering at (a) ω1, (b) ω2.
25
Based on this difference operator, XOR, OR, and NOT gate will be demonstrated.
They are generated by varying the strength of pump depletion, the choice of data
stream at the inputs, and the choice of filtering at different frequencies at the output.
Their principles of operation are given in the following subsections.
4.2.3 All-Optical XOR gate
The truth table for an XOR gate is shown in Fig. 4.2.4. By comparing Fig. 4.2.3(a)
and Fig. 4.2.3(b) with Fig. 4.1, combining the outputs of the truth tables from Fig.
4.2.3(a) and Fig. 4.2.3(b) will generate the desired XOR gate. This is possible since
both of the truth tables in Fig. 4.2.3(a-b) are generated simultaneously. The effect of
OPA for complete pump depletion of the input signals was maximized to achieve the
truth tables in Fig. 4.2.3(a-b). This was done by aligning the SOPs of the two inputs
and increasing the input power. The operation is summarized in Fig. 4.2.4.
s1
1 0 0
1
HNL-DSF
XGM s1 0 0 0 1
s2
1 0
0
XGM s2 0 0 1 0
1
0 0 1
1
Fig. 4.2.4. XOR gate operation.
4.2.3 All-optical OR gate
The physical operation of an OR gate is shown in Fig. 4.2.5, which suggests a
similar setup for the XOR gate. The generation of an OR gate will require a much
weaker pump depletion effect. To cater for this, the input power and/or polarization
are altered from the XOR gate setup. Hence, when the two signals co-propagate
through the nonlinear medium, each of the input signals is only partially depleted.
Therefore, by extracting the input frequencies at the output through bandpass
filtering, the two half-depleted input signals will sum up to be of similar power level
as any one of the input frequencies at input. Therefore, the XOR gate truth table in
Fig.4.2.1 will no longer attain a “0” from having both input signals as “1”.
HNL-DSF
0 0 1
s1
1 0
0 1
XGM s1
s2
1 0
1
XGM s2
0
0 1 0
Fig. 4.2.5. OR gate operation.
26
1 0 1
1
4.2.5 All-Optical NOT gate
By comparing the NOT gate’s truth table with that of Fig. 4.2.5, if the input s1 in Fig.
4.2.5 is fixed at ‘1’ while letting input s2 vary, the truth table in Fig. 4.2.5 will
degenerate into a NOT gate’s truth table. Hence, in the experiment, input s1 in Fig.
4.2.5 is set to “clk” to resemble an all “1” RZ-OOK bitstream. Notice that it is not
necessary to consider SPM on the input, since the output does not consist of spectral
components at the input wavelength. Therefore, the input power is chosen such that
it is solely optimum for the pump depleted “clk” bitstream. The operation is
summarized in Fig. 4.2.6 below.
HNL-DSF
s1
1 0
0 1
XGM s1 0 1
1 0
0 1
1 0
clk
Fig. 4.2.6. NOT gate operation.
4.2.6 All-optical NOR gate
In a scheme similar to the NOT gate, two input signals both within the OPA gain
spectrum of the pump are launched into the HNLF. Both signals are tuned such that
any one of the signals can deplete the pump. Hence, the pump can only go through
the fiber when both input signals are off. By extracting the pump component, a NOR
output between s1 and s2 are achieved. The operation is summarized in Fig. 4.2.7
below.
HNL-DSF
clk
s1
1
0
0 1
s2
1
0
1
Pump- 0 1 0 0
depletion
0
1 0
0
0
Fig. 4.2.7. NOR gate operation.
4.2.7 All-optical XNOR gate
The operation principle of producing a XNOR gate using a combination of AND,
NOR, and OR gates is similar to that as shown in Ref. [3] except that it requires an
27
extra probe input, which acted as the output of a NOR gate. In our design, the XGM
output is obtained directly from the OPA pump, since it is possible to achieve strong
pump depletion as demonstrated in Ref. [6]. The OPA pump depletes itself whenever
one or more signals are present, because it transfers a majority of its power to the
signal(s). Hence, if XGM effect is present in the pump, it is equivalent to a NOR
operation on the two input signals. Furthermore, strong FWM effect occurring on the
two signals will produce new FWM peaks, where the peaks closest to the two signals
tend to be the strongest. Since the generation of these new peaks require the presence
of both signals in the nonlinear medium, these peaks are essentially the AND output
of the two signals. By combining the XGM and FWM products, this results in a
XNOR output. Fig. 4.2.8 summarizes the operation principle.
Fig. 4.2.8. Operation principle of an all-optical XNOR gate.
4.2.8All-optical XOR gate (another implementation)
A XNOR gate can be produced using a combination of AND, NOR and OR gates as
shown in Ref. [3]. To achieve a XOR gate, a NOT operation is taken place on the
XNOR output. In this work, the AND operation is achieved using the FWM of two
input signals. The NOR is produced using XGM on the pump via optical parametric
amplification (OPA) on the input signals. The NOR and AND signals are coupled
together using a 50/50 coupler to produce a XNOR output. The XNOR output is then
fed into the nonlinear fiber again in the opposite direction along with a counterpropagating pump. XGM operation on this counter-propagating pump causes it to
serve as the XOR of the two input signals. Fig. 4.2.9 summarizes the operation
principle.
28
Fig. 4.2.9. Operation principle of an all-optical XOR gate.
4.3 Overview of all-optical regeneration
An all-optical approach for signal regeneration is favorable to avoid costly and bitrate dependent signal conversion between optical and electrical domains. Examples
of all-optical signal regeneration include four-wave mixing in fiber [1] and
semiconductor optical amplifier [2], cross absorption modulation in electroabsorption modulator [3], cross-phase modulation in nonlinear optical loop mirror [4]
and optical parametric interaction in an optical parametric amplifier (OPA). In
particular, the use of OPA is a promising approach for signal regeneration owing to
its simple structure, intrinsically fast response, and potential signal gain about the
signal regeneration.
4.3.1 Previous implementations of regeneration
Most optical regenerators are capable of both re-amplifying and re-shaping the
output pulses. This is known as a 2R regenerator. If, in addition, it can re-time the
output pulses, the regenerator is known as a 3R regenerator. In the most obvious
approach, the output pulses are converted to electrical using a photodiode, and then
re-converted to optical by a laser diode. But an O-E-O method is typically a much
costlier implementation due to the requirements of high speed receivers and
transmitters. Hence, there is a continued interest to produce all optical regenerators.
29
(a) An approach for 2R regeneration based on SPM was given by Mamyshev in
1998 [22]
Fig. 4.3.1. All optical regeneration using SPM in HNLF [22].
The output filter is detuned from the center to filter out only the broadened part of
the spectrum due to SPM. At a nominal bit-1, the pulse will be broadened by SPM,
and the detuned filter will extract the broadened part of the spectrum. Since SPM
continues to broaden the spectrum at higher powers, filtering at a fixed detuned
wavelength continues to capture a bit-1. Since much of the power is lost to the rest of
the broadened spectrum, there will not be a substantial increase at the fixed detuned
wavelength. This is seen as a reduction of noise at mark level at the detuned filter
output. Conversely, if the pulse is small, the spectral broadening is weak and thus of
insufficient bandwidth to reach the detuned filter’s passband. This is seen as
removing the zero level noise at the SPM output. The author has also plotted the
transfer function of this regenerator scheme, commented on the effects of dispersion,
and analyzed mathematically the choice of filter bandwidth and detuning wavelength
on this regenerator scheme.
(b) A recent attempt of using a HNLF to achieve regeneration is given by Yu et al in
2006 [23]. The principle of operation is shown in Fig. 4.3.2.
Fig. 4.3.2. All optical 3R regeneration using OPA [23].
30
Fig 4.3.2 shows a 3R regenerator setup demonstrated with a bit rate of 40Gb/s. The
authors modulate the OPA pump with a 20GHz clock and launch the pump and the
degraded signal into the HNLF. This allows OPA to amplify only signals with a copropagating OPA pump pulse. Re-timing and re-amplification are achieved by the
amplification only during the clock pulse. Pulse reshaping is achieved by
amplification only at pulse bit slots, shaping the original degraded signal pulses into
the shapes of the clock signals.
4.3.2 All-optical regenerator based on OPA pump depletion
All-optical signal regeneration is achieved by XGM between the degraded signal and
the OPA pump. In the absence of the input signal, the OPA pump power remains high;
whereas this pump power is depleted considerably when there is an input signal
power to the OPA. By extracting the cross-gain modulated pump at the OPA output,
a logic-inverted regenerated signal can be obtained. This allows a strong depletion of
mark-level noise of the input. The state level noise at the input is reduced since the
pump is undepleted when amplifying a small signal. A typical transfer function
between the pump power and input signal power for this operation is shown in Fig.
4.3.3.
Pump Output
Power
Mark and State Level
Noise removed at output
Signal Input
Power
Mark and State Level
Noise at input
Fig 4.3.3. OPA pump at output against input signal power.
To further improve the performance of the setup, it is possible to cascade two stages
of this setup so that both mark level noise and state level noise can be removed by
pump depletion. Cascading the setup also allows a non-inverted output.
31
Chapter 5
Experimental results for all-optical logic gates
In this chapter, discussions of experimental results of all-optical logic gates based on
OPA are given.
5.1.1 All-optical XNOR logic gate
Fig. 5.1.1 Experimental Setup. ODL: Optical delay line. WDMC: WDM band
coupler. VOA: Variable optical attenuator. MZM: Mach-Zehnder modulator. PC:
Polarization controller. DCA: Digital communications analyzer. All couplers are
50/50 couplers unless otherwise stated.
The experimental setup is shown in Fig. 5.1.1. The nonlinear medium used was a
spool of 1km HNL-DSF with nonlinear coefficient of 14W-1km-1 and zero dispersion
wavelength of 1560nm. The pump wavelength was set at 1561.8nm, which was
phase modulated with a 10Gb/s 223-1 PRBS to suppress SBS. It was then connected
to an erbium doped fiber amplifier (EDFA1) to reach output power of 23dBm. The
tunable band pass filter (TBPF1) significantly suppressed the ASE noise from the
EDFA. After that, the pump was amplified to 27dBm at EDFA2 before entering the
WDM coupler.
32
The two signals’ wavelengths were set at 1566.9nm and 1568.5nm. They were
amplitude modulated with an identical NRZ 10Gb/s bit sequence. The tunable delay
line delayed one of the signals such that they were unsynchronized by one bit. They
were then coupled together using a 50/50 coupler before amplified by EDFA3 to a
total output power of about 15dBm.
The amplified pump and signals were then coupled together using a WDM coupler
with a cutoff wavelength of 1564nm. The combined waveform was then injected into
the HNL-DSF. The output of the HNL-DSF was split by a 50/50 coupler, where one
output branch select the pump wavelength, while the other select an idler produced
by FWM from the two signals. The attenuators at each branch reduced optical power
to prevent damage to the tunable band pass filters (TBPF2 & 3) and ensured the 1’s
from the pump and the FWM peaks are of the same power. The optical delay line
(ODL2) was used to compensate the path difference between the two branches. They
were then recombined using another 50/50 coupler and the output was monitored
from a DCA.
33
5.1.2 Results and discussion
Fig. 5.1.2. Input and output waveforms. Time base: 100 ps/div.
Fig. 5.1.3. Eye diagram of the resultant XNOR signal. Time base: 50 ps/div.
Fig. 5.1.2 illustrates the inputs and outputs of the AND, NOR, and XNOR gates. It
can be seen from the figure that the AND output produces a ‘1’ only when both the
inputs are ‘1’. The NOR output produces a ‘1’ only when both inputs are ‘0’. The
last coupler output acted as an OR gate, where it combines the output of the AND
and NOR gates to generate the XNOR.
34
Figure 5.1.3 shows the eye diagram of the resultant XNOR gate. The extinction
ratios of the XNOR, NOR, and AND outputs are about 11dB, 12dB, and 24dB,
respectively. The extinction ratio of the output (XNOR) is dominated by the NOR
gate because it is generally difficult to deplete the pump by 100% [1], leaving a
small residual power at off-state. This can be improved by optimizing the phasematching condition [1]. Note that as the output signals generally preserve the pulse
shapes of input signals, it could be expected that this XNOR gate can support higher
bit rate operation.
5.1.4 Conclusion
An all optical XNOR gate using a single stage OPA has been successfully
demonstrated. The minimal distortion at the output reveals a possibility for higher bit
rate operation. Since this XNOR gate is generated from NOR and AND gates, this
device is capable of providing AND and NOR outputs simultaneously in addition to
its normal XNOR output, which may be useful in simplifying implementation of
compound logic gates.
5.2.1 All-Optical XOR Logic Gate
A direct extension to the XNOR gate in the previous experiment allows the
construction of a XOR gate. This is achieved by converting the two wavelengths
carrying the XOR output bitstream into a single wavelength using an inverting
wavelength converter. This can be done using the same HNLF with a backward
direction OPA.
The experimental setup is shown in Fig. 5.2.1. The nonlinear medium was 1km of
HNL-DSF with nonlinear coefficient of 14W-1km-1 and zero dispersion wavelength
of 1560nm. The forward pump (TLS1) is at 1560.8nm, and the two signals (TLS3
and TLS4) were 1568.4nm and 1566.2nm. The backward wave (TLS2) is at
1563.7nm. The pump waves were phase modulated by a 10Gb/s 231-1 pseudorandom binary sequence (PRBS) to suppress SBS. The two signals were amplitude
modulated with an identical NRZ 10Gb/s bit sequence. They were detuned from
each other by one bit using a tunable delay line. WDMC1 separates the pumps from
the signals. The ASE noise of each amplified pumps were filtered (through TBPF 1
35
and TBPF2) before reamplified to a much higher power using EDFA2 and EDFA3.
The forward pump then couples with the signals and they were fed into the HNLDSF through a circulator 1. At the output, TBF3 and TBF4 then filter out the FWM
and XGM components, and they were re-amplified and coupled with the backward
pump. These coupled waveforms were fed into the fiber in the opposite direction
through circulator 2. The XOR output was then observed by filtering for the
backward pump wavelength through a port on the CIR1.
TLS3
MZM 1
PC5
PC3
TLS4
NRZ data stream
PC4
> 1565 nm
WDMC 1
PC1
1
2
EDFA 2
MZM 2
10Gb/s
PRBS
CIR 1
WDMC 2
PC6
TLS1
> 1565 nm
EDFA 1
TBPF1
PM
3
VOA3
< 1565 nm
TBPF5
EDFA 3
< 1565 nm
PC2
TBPF2
TLS2
Oscilloscope
PC7
PC8
1
TBPF3
VOA1
3
2
CIR 2
TBPF4
1km
HNL-DSF
VOA2
Fig. 5.2.1. Experimental Setup. ODL: Optical delay line. WDMC: WDM band
coupler. VOA: Variable optical attenuator. MZM: Mach-Zehnder modulator. PC:
Polarization controller. CIR: Circulator. All couplers are 50/50 couplers unless
otherwise stated.
5.2.2 Results and discussion
Fig. 5.2.2. Left: XOR output waveform. Time base: 100 ps/div. Right: Eye diagram.
Time base: 50 ps/div.
36
Fig. 5.2.2 shows the output waveform of the XOR gate. The differences in pulse
shapes are due to different processes used to generate the pulses. Since XGM is used
throughout the system, it is hard to achieve a complete depletion [1]. Optimizing the
phase matching condition is known to improve this [1]. An all optical XOR gate
using a single HNL-DSF was successfully demonstrated. The small distortion on the
output pulses suggests a possibility for a higher speed operation.
5.3.1 All-Optical Half-Adder, Theory and Experiment
To reduce the complexity of the previous XOR setup, the pump depletion scheme
described in section 3.3 is used to produce the XOR gate. In addition, the AND gate
is produced simultaneously, hence a half-adder is resulted.
A half-adder is capable of producing AND and XOR operations of two bit streams
simultaneously. In our design, two signals are launched slightly into the anomalous
dispersion region of the HNL-DSF. This will allow phase matching conditions
required for OPA. Only when both of the input signals are ON, FWM will cause the
two signals to distribute its power to the newly generated idler frequencies. These
idlers can serve as an AND operation on the input signals. However, the two signals
will be depleted when they are both ON, due to cross gain modulation (XGM) from
OPA. Hence, the signals at the output will be OFF only when both of the inputs are
ON, or when both inputs are OFF. When either one of the input signals is ON; it will
emerge at the output without much loss of power. Therefore, by coupling the two
signals at the output, an XOR gate is achieved.
37
5.3.2 Experimental Setup
The experimental setup is shown in Fig. 5.3.1 below.
TLS1
MZM 1
PC1
TLS2
10 GHz
Clock
PC3
27-1 PRBS data stream
1km
HNL-DSF
MZM 3
PC2
MZM 2 ODL
PC4
OSC
TBPF1
VOA1
90
OSC
ODL
TBPF2
VOA2
10
TBPF3
VOA3
Fig. 5.3.1. Experimental Setup. ODL: Optical delay line. VOA: Variable optical
attenuator. MZM: Mach-Zehnder modulator. PC: Polarization controller. OSC:
Oscilloscope. All couplers are 50/50 couplers unless otherwise stated.
The nonlinear element was a spool of 1km HNL-DSF, with a zero dispersion
wavelength at 1559nm and nonlinearity coefficient of 14W-1km-1. The two input
signals were at 1561.4nm and 1565.4nm. They were amplitude modulated with 27-1
PRBS signals using Mach-Zehnder modulators. The choice of this sequence was due
to the manual entry of the output bit stream to the error detector for BER
measurements, since the device modified the data from input to output. The optical
delay line after MZM2 was used to ensure that the two signals were detuned from
each other for an integer number of bits. The input signals were then coupled and fed
into MZM3. MZM3 was driven by a 10GHz clock synchronized with the input bit
streams and it effectively converted the two NRZ signals into RZ signals. The result
was then amplified by an EDFA to a total output power of 21dBm before being input
into the HNL-DSF. At the output of the HNL-DSF, the power was split into two
branches using a 90/10 coupler. At the “90%” branch, a 3dB coupler was used to
38
further split the power into two branches. On these two branches, tunable band pass
filters TBPF1 and TBPF2 filtered out each of the two signal wavelengths. VOA1 and
VOA2 were used to attenuate the two signals to prevent damage to TBPF1 and
TBPF2 respectively. They were also used to allow both signals 1 and 2 to attain the
same amplitude for a ‘1’ bit. The optical delay line after TBPF2 was used to
synchronize the two branches. The two branches were then recombined together
using a 3dB coupler to achieve a XOR output. At the “10%” output of the 90/10
coupler, a FWM component at 1569.5nm was filtered using TBPF3 and VOA3 was
used to prevent damage to TBPF3. This FWM component served as the AND
operator on the two input signals.
5.3.3 Results and Discussion
Figure 5.3.2 showed bit patterns of both the input and output. The bit ‘1’s and bit ‘0’s
had been labeled accordingly. The fluctuations at bit ‘0’s at the XOR output were due
to finite rise and fall times of the inputs, since during the bit transitions, there was
insufficient power to deplete the signals by pump depletion. This was confirmed with
the eye diagram, where the fluctuations were inhibited at the pulse edges. The AND
output had a slightly narrower pulse shape, which was also a consequence of finite
rise and fall times.
Fig. 5.3.2 Bit patterns for the inputs and outputs and eye diagrams for the outputs.
Time base: 100 ps/div for bit patterns, 50ps/div for eye diagrams.
39
To quantify the non-idealities at the output, a bit error rate test was performed on the
half-adder. Figure 5.3.3 showed the bit error rate curve for the XOR, AND, and input
signals. At an error rate of 10-9, the power penalty for the AND output is 0.35dB, but
for the XOR output, the power penalty is 1.92dB. The higher power penalty at the
XOR output was believed to be caused by the residues at the rising and falling edges
of the input signals described earlier. ASE noise from the EDFA had also contributed
to the power penalty. The Q factors of the AND output and XOR output were 9.79
and 10.22 respectively. The lower Q factor at the AND output was primarily
attributed to ASE noise.
It is possible to improve the power penalty of the XOR output by reducing the
magnitude of the ripples at the edges that occurred at bit ‘0’. This can be achieved by
increasing the input power to the HNL-DSF of the two signals. However,
suppression of SBS will be required by using phase dithering or by other means.
Additionally, the OPA gain will increase, leading to stronger FWM effects amongst
the generated idlers, which will deplete or amplify each other. ASE noise power from
the EDFA will increase with increasing EDFA output power, leading to increase in
the noise taken by the AND output. Therefore, the XOR output quality will improve
by increasing the input power to the HNL-DSF, while the AND output quality may
improve or degrade depending on the ASE noise.
40
Fig. 5.3.3. BER curves for XOR, AND, and Back-to-Back.
5.3.4 Conclusion
An all-optical half-adder using a single OPA in a HNL-DSF has been successfully
demonstrated. The power penalty of the XOR gate is less then 2dB, and that of the
AND gate is only 0.35dB. The minimal distortions reveal a possibility for much
higher speed of operation, and this has been predicted by theory.
41
5.4 All-Optical Picoseconds Logic Gates
The previous efforts have demonstrated the feasibility of achieving various logic
gates by OPA. Here, the possibility of producing logic gates using OPA with
picosecond pulse widths will be pursued.
MZM 1
PS-source
PC1
PC2
TDL 1
215-1 PRBS data stream
λConversion
PC3
MZM 2
400m
HNL-DSF
PC4
TBPF1
VOA1
TDL 2 TBPF2
VOA2
DCA
Fig. 5.4.1 Experimental Setup. TDL: Tunable delay line. TBPF: tunable band pass
filter. VOA: Variable optical attenuator. MZM: Mach-Zehnder modulator. PC:
Polarization controller. PS-source: Picosecond pulse source. DCA: Digital
Communications Analyzer. All couplers are 50/50 couplers.
Fig. 5.4.1 shows the experimental setup for all four logic gates. The wavelength
conversion utilized a Kerr-shutter based scheme [2]. Optical data was picosecond
pulsewidth RZ-OOK data craved using MZM. The nonlinear medium used was a
spool of 400m HNL-DSF, with a nonlinear coefficient of 11W-1km-1 and a zerodispersion wavelength of 1554nm. Since the output bitstreams for the XOR, OR, and
AND gates were different from the input, therefore they need to be entered manually
for the bit-error rate tester (BERT), hence 215-1 PRBS was used for the experiment.
The relative power level difference between the two signal inputs prior to the entry
of the HNL-DSF was made such that they share an equal strength in XGM after
propagating through the HNL-DSF. This was made to ensure an optimal extinction
ratio in time domain after XGM for the XOR gates. The results were viewed using a
DCA and BERT. The discussions of each of the logic gates were separated into four
different subsections below.
42
5.4.1 Experimental setup for each picoseconds logic gate
(a) XOR Gate
The output wavelength from the ps-source was at 1563.9nm, while the converted
wavelength was at 1557.2nm. PC2 and PC4 were set such that both the inputs were
parallel polarized to ensure stronger XGM effect. The input power prior entry to the
HNL-DSF was 62mW. At the output, TBPF1 filtered out at 1563.9nm, while TBPF2
filters out at 1557.2nm. The combined spectra of the output filters yielded the final
XOR gate.
(b) OR Gate
Like the XOR gate setup, the output wavelength from the ps-source was at 1563.9nm,
while the converted wavelength was at 1557.2nm. However, the SOPs were
deliberately misaligned in order to reduce the strength of the XGM effect.
An equally effective method was to lower the input power as discussed in the theory
section, but changing the relative polarization was chosen between the two signals
since it allowed easier tuning. The output was also spectrally filtered using TBPF1
and TBPF2 for the 1557.2nm and 1563.9nm components, respectively. The
combined spectra of the output filters yielded the final OR gate
(c) NOT Gate
The NOT gate resembles a simplified XOR gate, as discussed in the theory section
except that one of the inputs is simply a clock signal. Here, the MZM1 was off,
allowing light from the ps-source at 1563.9nm to pass through unmodulated,
yielding a clock signal prior entry to the EDFA. Only the converted wavelength at
1557.2nm was modulated with MZM2. At the output of the HNL-DSF, only the
1563.9nm light was filtered out using TBPF1 for the DCA, by setting VOA2 in
excess of 50dB to block the TBPF2 path.
(d) AND Gate
In order to create a strong FWM component from two wide bandwidth pulses, it was
required to separate the two inputs widely in the frequency domain. This can
43
strongly reduce the spectral overlap between the two inputs. The input frequency
separation in the previous XOR, OR, and NOT gates proved to be inefficient in this
matter. Hence, new frequencies were re-assigned to suit our purpose, which turns out
to be 1558.6nm from the ps-source, and the converted wavelength was 1550.2nm.
The total input power was tuned down to 42mW to reduce the strength of FWM.
This effort was made to reduce the power of higher order FWM idlers and possibly
SPM. Like the NOT gate, only one spectral component contained the AND gate
output. The signal at 1567.0nm was extracted using TBPF1, and VOA2 was set to
attenuate 50dB, effectively blocking the TBPF2 path as in Fig. 5.4.1.
5.4.2 Effect of SPM on the input pulses
The input powers of both input signals in this setup were selected such that they
were sufficient for strong depletion of the original signals, but insufficient for selfphase modulation (SPM) to significantly broaden a pulse propagating through the
fiber alone [2]. This allows a 1nm bandwidth BPF to capture most of the pulse’s
power at the output. To quantify the strength of this effect, a 10Gb/s pulsetrain with
5ps FWHM pulsewidth is launched into a piece of 400m HNLF with nonlinearity
coefficient 11W-1km-1. The output is filtered with a BPF with 1nm bandwidth
centered at the center wavelength of the pulse. The transfer function between the
average input power and peak power of the pulse at the filtered output after the
HNLF is shown in Fig. 5.4.2.
Fig 5.4.2 Transfer function between average input power and output peak
power.
44
5.4.3 Experimental Results for Picoseconds Logic Gate
Fig. 5.4.3(a-b) show the bit patterns at both the input and output, which demonstrate
the operating principle. The bit patterns for the AND gate and the (XOR, OR and
NOT) gates are separated into two different diagrams because they used different
power and different wavelengths as inputs. The bit patterns were captured using a
photodetector with 53GHz electrical bandwidth, which was not fast enough to
capture pulses of picosecond FWHM pulsewidths. Therefore, the pulsewidth shown
here did not correspond to the actual pulsewidth. To remedy the problem, an
autocorrelator was used to measure the pulsewidth of inputs and outputs. The
measured FWHM pulsewidths for XOR, OR, AND, and NOT gates were found to be
5.1ps, 4.9ps, 4.1ps, and 4.8ps, respectively. Since the input pulsewidth was 4.6ps,
this revealed a slight broadening. Broadening of the pulses was primarily attributed
to the dispersion of the fiber. To further reduce the effect of dispersion, shorter fibers
could be used, but at a cost of a proportionally higher input power for the gates to
effect. The decreased pulsewidth in AND gate was due to pulse compression in the
FWM process [3]. The setup was currently limited by the optical band-pass filters
used. Narrower pulse-widths are expected if optical band-pass filters of wider
bandwidths were used throughout the experiment.
Input 1 at
1550.2nm
Input 2 at
1558.6nm
FWM at
1567.0nm
(a)
45
Input 1 at
1563.9nm
Input 2 at
1557.2nm
XOR
OR
NOT Input 1
at 1557.2nm
(b)
Fig. 5.4.3 (a) Bit patterns for the inputs and outputs of AND gate, (b) Bit patterns for
the inputs and outputs of XOR, OR, and NOT gates. Time base: 100 ps/div.
Fig. 5.4.4(a-d) show the eye diagrams of the corresponding outputs. Clear eye
openings were achieved for all four gates. The residue at the XOR and NOT gate’s
output at the OFF state shown in Fig. 5.4.4(a) and Fig. 5.4.4(b) was believed to be
caused by incomplete pump depletion when both signals were ON at the input. The
ON states for the XOR and OR gates are less consistent in both power level and
timing as revealed by their noisier mark level in the eye diagrams as shown in Fig.
5.4.4(a) and Fig. 5.4.4(b). The main reason for this was both XOR and OR gates
were composed of different wavelengths, hence the eye diagrams of two pump
depletion processes overlap with each other to form the final eye diagram. Such an
adding process will inevitably induce an increase in variance of both the timing and
power levels at the ON state. The NOT gate output, consisting only of a single
wavelength, did not suffer from the increased variance of the ON state and timing as
46
in the OR and XOR gates, but it still attained incomplete pump depletion effects at
its OFF state as revealed in Fig. 5.4.4(c).
(a)
(b)
(c)
(d)
Fig. 5.4.4 Eye diagrams of (a) XOR, (b) OR, (c) NOT, (d) AND gate output. Time
base: 50 ps/div.
The AND gate shown in Fig. 5.4.4(d) had a larger variance at its ON state. This was
primarily attributed to the continuum-like spectra generated at the HNL-DSF. Such
continuum will significantly degrade the quality of the AND gate, since the
interactions amongst different frequency components would degrade the major
FWM peak.
47
The output spectra for the OR and XOR gates are shown in Fig. 5.4.5(a). The spike
at the 1557.2nm for the XOR gate’s output spectrum was due to a non-ideal Kerrshutter, leading to a very low power continuous wave (CW) component at the output
in addition to the converted picosecond pulses. When comparing the XOR and OR
gate’s spectra, 1.5dB of power difference for each of the original input wavelengths
at 1557.2nm and 1563.9nm was measured. This was revealed on the mark-ratio
difference between XOR and OR gates outputs. The aligned polarizations in the
XOR gate also gave rise to stronger FWM frequencies, which although could serve
as an AND gate in theory, the quality of it was not suffice to serve as an AND gate,
due to the vast amount of FWM effects contributing to the continuum-like spectrum.
(a)
48
(b)
(c)
Fig. 5.4.5 (a) Comparison between the output spectra of the OR and XOR gates,
(b) NOT gate output spectra, (c). AND gate output spectra.
49
Fig. 5.4.5(b) shows the output spectrum of the HNL-DSF when the setup was set for
NOT gate operation. The NOT gate output was filtered out at 1557.2nm. In order to
strengthen the XGM effect of the NOT gate, in which we only require a high
integrity optical signal at 1557.2nm, the input bitstream at 1563.9nm was
deliberately set to a very high power to further enhance the XGM effect. This had
lead to strong SPM effects on the 1563.9nm pulses, causing a trough in the spectrum
as circled in Fig. 5.4.5(b). However, this effect did not have impact on the
performance of the NOT gate, since the NOT gate’s output was at 1557.2nm, the
pump wavelength. Again, there was also a significant FWM peak observed in the
spectrum located at 1569.5nm. In this case, the FWM peak was only a duplicate of
the original input bit stream.
The output spectrum of AND gate shown in Fig. 5.4.5(c) reveals a FWM peaked at
1567.0nm. A filter centered at 1567.0nm was used to select this component, serving
as the output of the AND gate. There was a noticeable peak at 1550nm which is
caused by the non-ideal wavelength conversion process. It also occurred in the
spectra for the XOR and OR gates. This peak corresponds to a CW wave, but it did
not cause any significant impact to the AND gate’s performance due to its much
lower peak power relative to the picosecond optical pulses. The relatively lower
optical signal-to-noise ratio (OSNR) at the AND gate’s spectra was believed to be
the major contributor to its noisier eye diagram.
50
(a)
(b)
51
Fig. 5.4.6 Bit-error rate for input and output signals of the (a) XOR, OR, and NOT
gates, (b) AND gate.
Bit-error rate plots are shown in Fig. 5.4.6(a) for XOR, OR, and NOT gates, and in
Fig. 5.4.6(b) for AND gate. They are separated into two graphs since the two setups
had different frequencies and power; hence the back-to-back performs differently
between the two setups. Power penalties when BER is at 10-9 for OR, XOR, AND,
and NOT gates were recorded as 2.6dB, 1.6dB, -1.1dB, and 1.2dB, respectively. The
back-to-back lines for both diagrams correspond to the BER performance of the
converted signal. The OR gate’s output, shown in Fig. 5.4.6(a), was performing
weakly relative to the rest of the outputs. This was due to the increased mark ratio of
the output. The NOT gate and XOR gate performed similarly with each other. The
slight difference in slope between these two curves was believed to be caused by a
difference of extinction ratios in the time domain, it was easier to achieve stronger
extinction ratio for the NOT gate compared to the XOR gate, which has been
discussed in previous sections.
The gentle slope of the AND gate output was primarily attributed to ASE noise and
FWM noise, as observed at its output spectrum. Mutual FWM within the continuum
of frequencies in the HNL-DSF induced noise into the AND gate. It is worth noting
that this noise did not give rise to an error floor during the BER measurements.
There was also a receiver sensitivity improvement on the AND gate’s output due to
the reduction of mark-ratio at the output. The BER performance of back-to-back line
at the AND gate setup was poorer relative to the XOR/OR/NOT gates setup. This
was mainly due to the non-ideal Kerr-shutter based wavelength conversion scheme,
which gave rise to a weak CW wave after the wavelength conversion. This was
further complicated with the short duty cycle of the pulse, rendering a 3dB penalty at
10-9 BER.
5.4.4 Conclusion for All-Optical Logic Gates
All optical XOR, OR, NOT, and AND gates were successfully demonstrated. FWMbased AND gate had been demonstrated with low power penalties due to lower
mark-ratio. Pulse compression on the AND gate’s output due to FWM has also been
52
observed, resulting in a reduced pulsewidth relative to the outputs [3]. This was
contrasted with the pulse broadening through dispersion and SPM in the HNL-DSF.
XGM effect had also been shown to be a capable mechanism for generating alloptical logic gates. All-optical XOR gate had been achieved by XGM on two input
bit sequences with 1.6dB power penalty. The success on the XOR gate relied on
optimal XGM amongst each of the input bit sequences, while ensuring that SPM did
not broaden the pulses as it traveled through the HNL-DSF. The NOT gate was
created more easily, by allowing the input signal to have a much higher input power
without considering SPM effects. The power penalty of the NOT gate was 1.2dB.
Finally, the OR gate was generated by having an incomplete XGM by misaligning
polarizations between the input signals; otherwise it was the same as the XOR gate
in other aspects. The power penalty of 2.6dB was mainly attributed to the increased
mark-ratio. It was worth noting that signals with a maximum of 5.1ps were recorded,
and the spectrum at the output of the HNL-DSF was merely 20nm wide. This
suggested a possibility of higher bit rate operation. In addition, by using filters with
wider bandwidth, it was possible to have narrower pulses. This indicated a potential
possibility for data rate up to 80Gb/s or beyond.
5.5.1 All-Optical Regenerator
TLS1
MZM 1
PC1
TLS2
231-1
PC3
TBF2
MZM 2
PRBS data stream
PC2
1km
HNL-DSF
10GHz CLK
PC4
TBF3
DCA
TBF1
Fig. 5.5.1 Experimental setup of the proposed OPA-based all-optical signal
regenerator. TLS: Tunable laser source, MZM: Mach-Zehnder modulator, PC:
Polarization Controller, DCA: Digital Communications Analyzer, TBPF: Tunable
Band Pass Filter.
Fig. 5.5.1 shows the schematic of the proposed signal regenerator based on the XGM
in an OPA. In this proof-of-principle demonstration, the 10-Gb/s RZ-OOK signal,
generated by externally modulating a continuous wave (CW) light with a 231–1
PRBS through MZM1, was intentionally degraded by detuning the bias point of the
modulator. The wavelengths of the degraded signal and the pulsed OPA pump were
53
1563.5 nm and 1560 nm respectively. They were then converted into RZ-OOK
signals using MZM2, which was driven by a 10GHz CLK signal. The signal and the
pump were then amplified together using a low power EDFA, followed by filtering
using TBP1 and TBPF2, which were set to filter out at 1563.5 nm and 1560 nm
respectively to remove the ASE noise from the EDFA. The signals were then
recombined together and before launching to the nonlinear gain medium. The
tunable delay line before TBPF2 was used to ensure that the two branches were of
the same length.
The input pump power was chosen to optimize the regeneration performance and
was 19 dBm in this case. The state of polarization of the pump was controlled by a
polarization controller to maximize the nonlinear XGM effect between the signal and
the pump. This OPA-based all-optical signal regenerator used a 1-km-long HNLDSF as the nonlinear gain medium. The zero-dispersion wavelength of this HNLDSF was 1559 nm. Finally, a 0.8 nm 3-dB bandwidth tunable optical bandpass filter
was used to select the pump wavelength as the logic-inverted regenerated output
signal.
5.5.2 Results and Discussion
All-optical signal regeneration is achieved by XGM between the degraded signal and
the OPA pump. In the absence of the input signal, the OPA pump power remains high;
whereas this pump power is depleted considerably when there is an input signal
power to the OPA. By extracting the cross-gain modulated pump at the OPA output,
a logic-inverted regenerated signal can be obtained. As the phase matching condition
is inherent in this single pump OPA within a certain wavelength detune, the optical
parametric process which provides an optical gain to the input signal and hence an
optical loss to the pump, is bit-rate irrelevant. Hence, a higher bit-rate operation is
expected as long as the signal spectrum falls within the gain spectrum of the OPA
where phase matching condition is satisfied.
54
(a)
Before regeneration
After regeneration
log10(BER)
-4
-5
-6
-7
-8
-9
-10
-14
-13
-12
-11
Received Pow er [dBm]
-10
-9
-8
(b)
Fig. 5.5.2 (a). Measured transfer function of the OPA-based all-optical signal
regenerator. (b) Plot of the measured BER for (◊) the degraded and (○) the
regenerated signals.
Fig. 5.5.2 shows the nonlinear transfer function used in the XGM-based regenerator
55
derived experimentally. From the transfer function, the regenerator can easily
suppress noise from the mark level. The plot corresponds to an input pump power of
15.4 dBm. The performance of the all-optical signal regenerator is further quantified
by measuring the BER of the degraded and the regenerated signal as is shown in Fig.
5.5.2(b). The corresponding measured eye diagrams are shown in Fig. 5.5.3. A
receiver sensitivity improvement of 1.3 dB is observed for the regenerated output
when compared with the degraded input signal at 10–9 BER level indicating that the
use of XGM effect in an OPA can successfully improve the signal performance of a
degraded signal.
(a)
(b)
Fig. 5.5.3 (a). Noisy input signal. (b) Noisy signal after regeneration. Time base: 50
ps/div.
5.5.3 Conclusion
The use of XGM in a fiber-based OPA for all-optical signal regeneration is
successfully demonstrated. The proposed scheme has a simple non-interferometric
structure compared with the previous reported schemes. XGM in a fiber-based OPA
has a nonlinear transfer characteristic which can be utilized for signal regeneration.
The signal quality of a degraded 10-Gb/s RZ signal is successfully restored through
XGM to the pulsed pump in an OPA, and a receiver sensitivity improvement of 1.3
56
dB is achieved in this proof-of-principle demonstration. Given the OPA gain
spectrum is wide enough to enclose the signal spectrum in the regeneration, a higher
bit-rate operation can be supported. The estimated maximum bit-rate based on the
phase matching condition for the proposed all-optical signal generator can support
up to 40-Gb/s under the current settings. The results show that the proposed scheme
is potentially a good choice for all-optical signal regeneration in a transmission
system.
57
Chapter 6 Conclusion and Outlook
6.1 Summary of Research Contributions
Optical Parametric Amplifier (OPA) based on highly nonlinear fibers have been
successfully demonstrated to be a useful tool for all-optical signal processing
applications. All-optical signal processing based on pump depletion and XGM have
been presented in this thesis. This includes all-optical logic gates and all-optical
regenerators with error free operation. All-optical gates XOR, OR, NOT, AND, NOR,
and XNOR gates are produced in this thesis. These all-optical logic gates require
only a single stage OPA setup. By utilizing the femtosecond response time of fiberbased OPA, all-optical gates with picosecond pulse widths are made possible and are
also successfully demonstrated.
All-optical regenerators based on OPA pump depletion have been demonstrated. In
the scheme detailed in the thesis, a single stage regenerator based on pump depletion
results in an inverted signal but with mark level noise removed. It is possible to
cascade two stages of OPA based pump-depletion regenerators to result in a noninverting regenerator with noise removal on both mark and state levels.
To summarize the work, the possibilities of all-optical logic gates and regenerators
using OPA-based pump depletion were investigated. This work can be extended for
higher bit-rate operations.
6.2 Future Work
6.2.1 Enhancements in XOR Gate
A current limitation of using OPA pump-depletion based logic gate is its output data
carried on two frequencies. This can be remedied if the pulse widths are shorter,
which utilize stronger SPM effects. The operation is shown in the diagram below:
58
Input Spectra
dBm
Output Spectra
ω2 ω1 ω0
dBm
ω
ω
ω2 ω1 ω0
ω
ω
Filter Passband
ω2 ω1 ω 0
dBm
Filter Passband
Filter Passband
ω 2 ω1 ω0
dBm
Filter Passband
ω2 ω1 ω0
dBm
dBm
Filter Passband
ω
Filter Passband
ω2 ω1 ω0
ω
Fig 6.1: Theory of Operation for single wavelength XOR gate.
SPM will broaden the spectral width of a single pulse propagating through the fiber.
By putting a filter in between the two optical input frequencies, the broadened
spectrum from either one pulse will be filtered at the output. Hence, the output will
compose of a single frequency. When both pulses co-propagates, usual pump
depletion mechanisms will result in a rapid generation of idlers, of which there will
not be enough power to have enough SPM to filter anything at the output.
59
6.2.2 > 80Gb/s logic gates.
A numerical simulation using Optsim® [1] was applied to the same setup described
in section 5.4, except for increasing the bit rate to 80 Gb/s, and setting the input
pulsewidths to 5 ps. The average input powers were 120 mW for each input signal
for the AND gate, and 500 mW for each input signal of the XOR-, OR-, and NOTgate. Noise was taken as a white Gaussian with noise spectral density of -15dB
(mw/THz). The output eye diagrams for XOR-, OR-, NOT-, and AND-gate were
shown in Fig. 6.2. Pulse broadening was negligible after the logical operation, and
error free results with clear eye openings indicated a possibility of 80 Gb/s operation
using the same setup. The small residue at the state-level corresponds to the depleted
pump powers when both pulses of different wavelengths co-propagate through the
fiber, which is also evident in the 10 Gb/s experiment.
(a) XOR
(b) OR
(c) NOT
(d) AND
Fig. 6.2. Simulated 80 Gb/s output for (a) XOR- (b) OR- (c) NOT- and (d)
AND-gate.
Although a numerical simulation has been successfully demonstrated, an experiment
has yet to be carried out on 80Gb/s operation on the all-optical logic gates.
Picosecond pulsewidths at the logic gates’ output indicate a possibility for 80Gb/s
operation in the previous experiments. A step towards verifying the possibility of
true 80Gb/s operation can be achieved using the setup in Fig. 6.3.:
60
Fiber Laser
Synchronized Clock
MLLD
MZM 1
PC1
PC2
TDL 1
VOA1
215-1 PRBS data stream
PC3
MZM 2
PC4
400m
HNL-DSF
10G->80G
TBPF1
VOA3
DCA
TDL 2 TBPF2 VOA2
Fig. 6.3. Experimental Setup. TDL: Tunable Optical delay line. VOA: Variable
optical attenuator. MZM: Mach-Zehnder modulator. PC: Polarization controller.
DCA: Digital Communications Analyzer. MLLD: Mode-locked laser diode. All
couplers are 50/50 couplers unless otherwise stated.
In the setup, a multiplexer was used to turn one of the 10Gb/s bit streams to a 80Gb/s
bitstream. The success of this setup is a necessary condition for true 80Gb/s
operation. By choosing the appropriate signals/wavelengths at the outputs in the
method similar to section 5.4, it provides an indication of possibility of 80Gb/s logic
gates.
61
Appendix A
The Split-Step Fourier Method
The Split-Step Fourier Method is commonly used to solve the nonlinear
Schrödinger equation (NLSE). It belongs to the class of pseudo-spectral methods,
which generally allows up to an order of magnitude higher computing speed over
traditional finite-difference methods [1]. In this appendix, a brief description of the
method from Ref. [1] is presented, followed by some other details of implementation
such as the effects of Raman scattering and higher order dispersion are included.
The simplest case for the NLSE is given by the following [1]:
iβ2 ∂ 2 A
∂A α
2
+ A+
= iγ A A
2
2 ∂T
∂z 2
-- (A.1)
which is discussed in chapter 2, and is accurate for pulses above 10ps, and β2 is not
close to zero. To evaluate equation (A.1) using SSFM, Eq. (A.1) in the following
way [1]:
∂A
= ( Dˆ + Nˆ ) A
∂z
-- (A.2)
iβ2 ∂ 2 α
2
ˆ
− and N̂ = iγ A .
where D = −
2
2 ∂T
2
As its name implies, D̂ stands for the dispersion, and it is a linear operator, while
N̂ is the nonlinear operator. An approximate solution for this is the following [1]:
A( z + h, T ) ≈ exp(hDˆ ) exp(hNˆ ) A( z , T ) .
-- (A.3)
Notice that the operator exp(hDˆ ) can be achieved by Fourier methods. We have [1]
exp(hDˆ ) A( z , T ) = F −1 F [exp(hDˆ ) A( z, T )]
-- (A.4)
where F standing for Fourier Transform. By taking the fact that any derivative in the
time domain corresponds to iω in the transformed domain, the linear part can be
evaluated. With the advent of the Fast Fourier Transform (FFT), equation [A.4] can
be solved very rapidly.
Equation (A.2) corresponds to an analytical solution given by [1]:
62
A( z + h, T ) = exp(h( Dˆ + Nˆ )) A( z , T )
-- (A.5)
The solution presented in (A.5), however, cannot be solved exactly. By using
equation (A.3) as an approximation, we have to take account of the following, given
by the Baker-Hausdorff formula:
h 2 ˆ ˆ h3 ˆ ˆ ˆ ˆ
ˆ
ˆ
ˆ
ˆ
exp(hD ) exp(hN ) = exp(hD + hN + [ D, N ] + [ D − N ,[ D, N ]] + ...
2
12
-- (A.4)
where up to the third order term is given. The square brackets stand for the
commutator, given by [a,b] = ab-ba. Hence, the accuracy of the SSFM is up to the
second order of h.
To further increase the accuracy of this method, a symmetrized SSFM is applied. We
approximate the solution to (A.5) by the following [1]:
h
h
A( z + h, T ) ≈ exp( Dˆ ) exp(hNˆ ) exp( Dˆ ) A( z , T )
2
2
-- (A.5)
We can evaluate the accuracy of the method in (A.5) using the Baker-Hausdorff
formula shown below:
h
h
exp( Dˆ ) exp(hNˆ ) exp( Dˆ )
2
2
2
h
h
h3
h3
h
= {exp( Dˆ + hNˆ + [ Dˆ , Nˆ ] + [ Dˆ ,[ Dˆ , Nˆ ]] − [ Nˆ ,[ Dˆ , Nˆ ]]}exp( Dˆ )
2
4
48
24
2
2
3
3
h
h
h
h
= exp( Dˆ + hNˆ + [ Dˆ , Nˆ ] + [ Dˆ ,[ Dˆ , Nˆ ]] − [ Nˆ ,[ Dˆ , Nˆ ]] +
2
4
48
24
2
3
h3
h
h ˆ 1 h ˆ
h
h
D + [ D + hNˆ + [ Dˆ , Nˆ ] + [ Dˆ ,[ Dˆ , Nˆ ]] − [ Nˆ ,[ Dˆ , Nˆ ]], Dˆ ])
24
2
2
2 2
4
48
2
3
3
h
h
h
h
= exp( Dˆ + hNˆ + [ Dˆ , Nˆ ] + [ Dˆ ,[ Dˆ , Nˆ ]] − [ Nˆ ,[ Dˆ , Nˆ ]] +
2
4
48
24
2
2
3
h ˆ 1 h ˆ ˆ h ˆ ˆ h
D + [ [ D, D] + [ N , D] + [[ Dˆ , Nˆ ], Dˆ ])
2
2 4
2
8
2
3
h
h
h
h3
h
= exp( Dˆ + hNˆ + [ Dˆ , Nˆ ] + [ Dˆ ,[ Dˆ , Nˆ ]] − [ Nˆ ,[ Dˆ , Nˆ ]] + Dˆ +
2
4
48
24
2
2
3
h ˆ ˆ h
[ N , D] + [[ Dˆ , Nˆ ], Dˆ ])
4
16
h3 ˆ ˆ ˆ
h3 ˆ ˆ ˆ
h3 ˆ ˆ ˆ
ˆ
ˆ
= exp(hD + hN + [ D,[ D, N ]] − [ N ,[ D, N ]] + [[ D, N ], D ])
48
24
16
--(A.6)
where we used the fact that [ Dˆ , Dˆ ] = 0 , and only the third order terms have been
63
shown. Notice that in this method, the double commutator [ Dˆ − Nˆ ,[ Dˆ , Nˆ ]] has
disappeared, and hence this method is accurate up to the third order of h.
The method in (A.5) might seemingly require a double amount of linear operations.
But, careful observation on the actual evaluation of (A.2) shows that the steps are
cascaded together. Hence, for example, to evaluate A(z+2h,T) from A(z,T) using
equation (A.5), the resultant is:
h
h
A( z + 2h, T ) ≈ exp( Dˆ ) exp(hNˆ ) exp( Dˆ ) A( z + h, T )
2
2
h
h
h
h
≈ exp( Dˆ ) exp(hNˆ ) exp( Dˆ ) exp( Dˆ ) exp(hNˆ ) exp( Dˆ ) A( z , T )
2
2
2
2
h
h
= exp( Dˆ ) exp(hNˆ ) exp(hDˆ ) exp(hNˆ ) exp( Dˆ ) A( z , T )
-- (A.7)
2
2
where the two cascaded linear step can be evaluated simultaneously using a single
larger step with no decrease in accuracy.
In texts given by [2] it is noticed that the SSFM accuracy can be improved by using
an integral for the nonlinear operator. The main reason behind this was the
symmetrized SSFM assumes a non-changing nonlinear operator along the step size h.
The evaluation of the integral is based on a trapezoidal method, and this requires
iterative methods to obtain A(z+h,T), leading to new types of numerical error
associated with it. Hence, the symmetrized SSFM with the integral is not used in this
research.
To tackle more problems associated with the NLSE, especially with short pulse
widths and associated with the Raman Scattering, the linear and nonlinear operators
need to be modified in the SSFM. A few modified nonlinear operators were shown in
the following:
For higher accuracy in dispersion mainly for use with pulses close to the zerodispersion frequency, ultra-short pulse and for supercontinuum generation, it is
required to have a more accurate description of the propagation constant β (ω ) . This
64
can be done by a Taylor’s expansion on β (ω ) up to a higher order term. The
expansion of β (ω ) using Taylor’s expansion to the power k results in the following
dispersion operator:
β ∂k
n
Dˆ = ∑ k =2 −i k −1 k
k ! ∂T k
-- (A.8)
where β k is the k-th order expansion of β (ω ) using Taylor’s expansion.
This increase in the degree of Taylor’s expansion allows a more accurate description
7for dispersion at frequencies further away from the centre frequency of the pulse. In
the case of supercontinuum generation, the spectrum spans in excess of 800nm,
hence a higher order Taylor’s expansion of the fiber’s dispersion is necessary to
account for the light very far from the centre frequency of the original pulse. A very
similar argument holds for the case of ultra-short pulses. For pulses with centre
frequency close to the zero dispersion frequency, β 2 becomes very small. Hence,
most of the dispersion will be accounted in the higher order components, which
make the use of terms beyond β 2 very important.
2
Fiber nonlinearity was accounted by using the term iγ A A in the NLSE. This,
however, excludes the effect of Raman Scattering. To include Raman Scattering, we
2
replace iγ A A in Eq. A.1 with:
∞
i ∂
2
iγ (1 +
)( A( z , T ) ∫ R(t ') A( z , T − t ') dt ') , where
ω0 ∂T
−∞
R (t ) = 0.82δ (t ) + 0.18
τ 12 + τ 22
t
−t
exp( ) sin( ) , τ 1 = 12.2 fs , τ 2 = 32 fs , and ω0 is the
2
τ 1τ 2
τ2
τ1
centre frequency. This is a bottleneck in the execution of the code, and hence we do
not use this model when knowledge in Raman Scattering is not required. In the code,
we use Fourier Transform to execute the convolution and the differential operator.
The differential operator works by multiplying the Fourier Transformed expression
with i 2π f , and inverse Fourier Transforming the expression. This is more accurate
than the traditional method, where we take the discrete derivative by
x '[n] = x[n] − x[n − 1] , since we can take the assumption that the spectrum is band
limited.
65
Appendix B
List of my Publications
1.
H. K. Y. Cheung, R. W. L. Fung, D. M. F. Lai, P. C. Chui, and K. K. Y. Wong,
“Optical Pulse Generation Using Two-Stage Compression Based on Optical
Parametric Amplifier,” Conference on Lasers and Electro-Optics (CLEO) 2007,
paper no. CWB6.
2.
D. M. F. Lai, B. P. P. Kuo, and K. K. Y. Wong,, “All-Optical XNOR Gate using
Fiber Optical Parametric Amplifier,” OptoElectronics and Communications
Conference (OECC) 2007, Yokohama, Japan.
3.
D. M. F. Lai, E. N. Lin, and K. K. Y. Wong, “All Optical Half Adder using a
Single Highly Nonlinear Dispersion Shifted Fiber,”, European Conference on
Optical Communication 2006 (ECOC 2007), Berlin, Germany.
4.
D. M. F. Lai, C. H. Kwok, T. I. Yuk, and K. K. Y. Wong, “Picosecond AllOptical Logic Gates (XOR, OR, NOT, and AND) in a Fiber Optical Parametric
Amplifier,” Optical Fiber Communication (OFC) 2008, San Diego, USA.
5.
D. M. F. Lai, C. H. Kwok, and K. K. Y. Wong,, “All-Optical Signal
Regeneration using Optical Parametric Amplifier” Conference on Lasers and
Electro-Optics (CLEO) 2008, San Jose, USA.
6.
D. M. F. Lai, C. H. Kwok, and K. K. Y. Wong,, “All-Optical picoseconds logic
gates based on fiber optical parametric amplifier” Under Review at Optics
Express.
66
Appendix C
Abbreviations
2R
3R
ASE
AM
BER
BERT
BPF
CIR
CW
DCA
DSF
EDFA
ER
FBG
FOM
FSK
FWM
FWHM
GVD
HNL-DSF
HNLF
IM
IMDD
MZ
NF
NLSE
NRZ
O-E-O
OOK
OPA
OSA
OTDM
PC
PD
PM
PPP
67
Retiming and reshaping
Retiming, reshaping and reamplification
Amplified spontaneous emission
Amplitude modulator
Bit error rate
Bit error rate tester
Bandpass filter
Circulator
Continuous-wave
Digital communication analyzer
Dispersion shifted fiber
Erbium-doped fiber amplifier
Extinction ratio
Fiber-Bragg grating
Important figures of merit
Frequency shifted keying
Four-wave mixing
Full width at half maximum
Group velocity dispersion
Highly nonlinear dispersion-shifted fiber
Highly nonlinear fiber
Intensity modulator
intensity-modulation direct-detection
Mach-Zehnder
Noise figure
Nonlinear Schrödinger equation
Nonreturn-to-zero
Optical-electrical-optical
On-Off Keying
Optical parametric amplifier
Optical spectrum analyzer
Optical time-division multiplexing
Polarization controller
Photo detector
Phase modulator
Photonic parametric processor
PRBS
RK
RZ
SBS
SMF
SNR
SOA
SOP
SPM
SRS
SSFM
TBPF
TLS
UNI
VOA
WDM
XGM
XPM
68
Pseudo-random bit sequence
Runge-Kutta
Return-to-zero
Stimulated Brillouin scattering
Single-mode fiber
Signal to noise ratio
Semiconductor optical amplifier
State of polarization
Self-phase modulation
Stimulated Raman scattering
Split step Fourier method
Tunable bandpass filter
Tunable laser source
Ultra fast Nonlinear Interferometer
Variable optical attenuator
Wavelength-division multiplexing
Gross-gain modulation
Cross-phase modulation
Appendix D
References
Chapter 1:
[1] A. H. Gnauck, G. Charlet, P. Tran, P. J. Winzer, C. R. Doerr, J. C. Centanni, E. C.
Burrows, T. Kawanishi, T. Sakamoto, and K. Higuma, “25.6-Tb/s WDM
Transmission of Polarization-Multiplexed RZ-DQPSK Signals,” IEEE J.
Lightwave Technol., 24, 1 (2008)
[2] G. P. Agrawal, “Nonlinear Fiber Optics,” 3rd Edition, Academic Press.
[3] K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization
Independent Two-Pump Fiber Optical Parametric Amplifier”, IEEE PTL, 14, 7
(2002)
Chapter 2:
[1]
G. P. Agrawal, Nonlinear fiber optics, Academic Press, 3rd edition, 2001.
[2]
R. W. Boyd, Nonlinear optics, Academic Press, 2nd edition, 2003.
Chapter 3:
[1]
Y. Chen and A. W. Snyder, Opt. Lett, 14, 87 (1989)
[2]
M. C. Ho, “Fiber Optical Parametric Amplifiers and Their Applications in
Optical Communication Systems,” PhD thesis, Stanford University, Jun. 2001.
[3]
K. K. Y. Wong, M. E. Marhic, K. Uesaka, and L. G. Kazovsky, “Polarization
Independent Two-Pump Fiber Optical Parametric Amplifier”, IEEE PTL, 14, 7
(2002)
[4]
M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G. Kazovsky “92% pump
depletion in a continuous-wave one-pump fiber optical parametric amplifier”,
Optics Letters, 26, 9, pp. 620-622
69
Chapter 4:
[1]
T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F.
Gaborit, F. Poingt, and M.Renaud, “Novel scheme for simple label-swapping
employing XOR logic in an integrated interferometric wavelength converter,”
IEEE Photon. Technol. Lett. 13, 750–752 (2001).
[2]
A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity
checker,” Conference on Optical Fiber Communications (OFC) 1999, pp. 137–
139.
[3]
A. J. Poustie, K. J. Blow, R. J. Manning, and A. E. Kelly, “All-optical
pseudorandom number generator,” Opt. Commun. 159, 208-214 (1999).
[4]
M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, and J. Li, “High
Performance Optical-Fiber-Nonlinearity-Based Optical Waveform
Monitoring,” IEEE J. Lightwave Technol. 23, 2012 – 2022 (2005).
[5]
S. Kumar, A. E. Willner, D. Gurkan, K. R. Parameswaran, and M. M. Fejer,
“All-optical half adder using an SOA and a PPLN waveguide for signal
processing in optical networks,” Opt. Express 14, 10255-10260 (2006)
[6]
S. Kumar and A. E. Willner, “Simultaneous four-wave mixing and cross-gain
modulation for implementing an all-optical XNOR logic gate using a single
SOA,” Opt. Express 14, 5092-5097 (2006).
[7]
R. P. Webb, R. J. Manning, G. D. Maxwell, and A. J. Poustie, “40 Gbit/s alloptical XOR gate based on hybrid-integrated Mach-Zehnder interferometer,”
Electron. Lett. 39, 79-81 (2003).
[8]
G. Theophilopoulos, K. Yiannopoulos, M. Kalyvas, C. Bintjas, G. Kalogerakis,
H. Avramopoulos, L. Occhi, L. Schares, G. Guekos, S. Hansmann, R. Dall’Ara,
“40 GHz all-optical XOR with UNI gate,” Conference on Optical Fiber
Communications (OFC) 2001, pp. MB2-1-MB2-3.
[9]
J. Dong, X. Zhang, Y. Wang, J. Xu, and D. Huang, “40Gb/s configurable
photonic logic gates with XNOR, AND, NOR, OR and NOT functions
employing a single SOA,” ECOC, Berlin (2007) paper 3.4.5.
[10] Y. Liu, E. Tangdiongga, Z. Li, S. Zhang, H. D. Waardt, G. D. Khoe, and H. J.
S. Dorren, “Error-Free All-Optical Wavelength Conversion at 160 Gb/s Using
a Semiconductor Optical Amplifier and an Optical Bandpass Filter,” IEEE J.
Lightwave Technol. 24, 230-236.
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[11] Robin P. Giller, Robert J. Manning and David Cotter, “Recovery dynamics of
the ‘Turbo-Switch’”, Optical Amplifiers and their Applications, (OAA),
Whistler, Canada (2006), paper OTuC2.
[12] J. H. Kim, Y. T. Byun, Y. M. Jhon, S. Lee, D. H. Woo, S. H. Kim, “All-optical
half adder using semiconductor optical amplifier based devices,” Optics
Communications, 218, 345-349 (2003).
[13] Y. Liu, E. Tangdiongga, Z. Li, H. de Waardt, A. M. J. Koonen, G. D. Khoe, H.
J. S. Dorren, X. Shu, and I.Bennion, “Error-free 320 Gb/s SOA-based
Wavelength Conversion using Optical Filtering,” in Conference on Optical
Fiber Communications (OFC) 2006, paper PDP28.
[14] R. P. Webb, X. Yang, R. J. Manning, R. Giller, “All-optical 40Gbit/s XOR
gate with dual ultrafast nonlinear interferometer”, Electronics Letters, 41, 25.
[15] K. K. Y. Wong, G.-W. Lu, K. C. Lau, P. K. A. Wai, and L. K.Chen, “Alloptical wavelength conversion and multicasting by cross-gain modulation in a
single stage fiber Optical Parametric Amplifier,” in Conference on Optical
Fiber Communications (OFC) 2007, paper OTuI4.
[16] K. K. Y. Wong, G.-W. Lu, L. K. Chen, “Simultaneous all-optical inverted and
noninverted wavelength conversion using a single-stage fiber-optical
parametric amplifier,” IEEE Photonic Technol. Lett., vol 18, pp 1442-1444,
2006.
[17] K. K. Y. Wong, K. Shimizu, M. E. Marhic, K. Uesaka, G. Kalogerakis, and L.
G. Kazovsky, “Continuous-wave fiber optical parametric wavelength converter
with +40 -dB conversion efficiency and a 3.8-dB noise figure,” Opt. Lett., vol.
28, pp. 692-694, 2003.
[18] S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy,
“All-Optical Regeneration in One- and Two-Pump Parametric Amplifiers
Using Highly Nonlinear Optical Fiber,” IEEE Photonic Technol. Lett., vol. 15,
pp. 957-959, 2003.
[19] D. M. F. Lai, E. N. Lin, K. K. Y. Wong, “All-Optical Half-Adder by Using a
Single-Stage Optical Parametric Amplifier,” ECOC, Berlin (2007) paper 10.2.4.
[20] H. K. Y. Cheung, R. W. L. Fung, D. M. F. Lai, P. C. Chui, and K. K. Y. Wong,
“Optical Pulse Generation Using Two-Stage Compression based on Optical
Parametric Amplifier,” CLEO, Baltimore (2007) paper CWB06.
71
[21] G. P. Agrawal, “Nonlinear Fiber Optics,” 3rd Edition, Academic Press.
[22] P. V. Mamyshev, “All-optical data regeneration based on self-phase
modulation effect,” ECOC, Madrid (1998).
[23] C. Yu, T. Luo, B. Zhang, Z. Pan, M. Adler, Y. Wang, J. E. McGeehan, and A.
E. Willner, “ Wavelength-shift-free 3R Regenerator for 40-Gb/s RZ System by
Optical Parametric Amplification in Fiber,” IEEE PTL, 18, 24 (2006)
Chapter 5:
[1] M. E. Marhic, K. K. Y. Wong, M. C. Ho, and L. G. Kazovsky “92% pump
depletion in a continuous-wave one-pump fiber optical parametric
amplifier”,Optics Letters, 26, 9, pp. 620-622.
[2] G. P. Agrawal, Nonlinear fiber optics, Academic Press, 3rd edition, 2001.
[3] H. K. Y. Cheung, R. W. L. Fung, D. M. F. Lai, P. C. Chui, and K. K. Y. Wong,
“Optical Pulse Generation Using Two-Stage Compression Based on Optical
Parametric Amplifier,” Conference on Lasers and Electro-Optics (CLEO) 2007,
paper no. CWB6.
Chapter 6:
[1] Rsoft Optisim Version 4.0 (2004)
Appendix A:
[1] G. P. Agrawal, Nonlinear fiber optics, Academic Press, 3rd edition, 2001.
[2] J. A. Fleck, J. R. Morris, and M. D. Feit, J. Appl. Phys, 52, 109 (1981).
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