Light Sources – II
The Laser and External
Modulation
EE 8114
-Xavier Fernando
A better light source
LED has:
– Large line width (large material dispersion)
– Large beam width (low coupling to the fiber)
– Low output power
– Spontaneous emission (random polarization,
phase, direction etc.)
A better light source addressing all these issues
were needed.
– The Laser is designed to address all these issues
The LASER
Light Amplification by ‘Stimulated Emission’ and Radiation
• Laser is an optical oscillator. It comprises a
resonant optical amplifier whose output is fed
back into its input with matching phase. Any
oscillator contains:
1- An amplifier (with gain-saturation mechanism)
2- A positive feedback system
3- A frequency selection mechanism
4- An output coupling scheme
Fundamental Lasing Operation
• Absorption: An atom in the ground state might
absorb a photon emitted by another atom, thus
making a transition to an excited state.
• Spontaneous Emission: random emission of a
photon, which enables the atom to relax to the
ground state.
• Stimulated Emission: An atom in an excited state
might be stimulated to emit a photon by another
incident photon.
Spontaneous & Stimulated
Emissions
LASER
• In laser, the light amplifier is the pumped active
medium (biased semiconductor region) where emitted
photons stimulate more photon emission.
• Feedback is obtained by placing some kind of reflector
(mirror/filter) in the optical resonator.
• Frequency selection is achieved by the resonators,
which admits only certain modes.
• Output coupling is accomplished by making one of the
resonator mirrors partially transmitting.
Lasing in a pumped active medium
• In thermal equilibrium the stimulated emission is
essentially negligible, since the density of electrons in the
excited state is very small. This is LED like operation with
mostly spontaneous emission.
• Stimulated emission will exceed absorption only if the
population of the excited states is greater than that of the
ground state. This condition is known as Population
Inversion. Population inversion is achieved by various
pumping techniques.
• In a semiconductor laser, population inversion is
accomplished by injecting electrons into the material to fill
the lower energy states of the conduction band.
How a Laser Works
In Stimulated Emission incident and
stimulated photons will have
Attribute
Result
Identical Energy
Narrow line width
Identical Direction
Narrow beam width
Identical Phase
Temporal Coherence
Identical Polarization
Coherently polarized light
Fabry-Perot Laser (resonator)
cavity
Fabry-Perot Resonator
M1
A
M2
Relative intensity
m= 1
1
f
R ~ 0.8
R ~ 0.4
m= 2
 m
B
L
(a)
m= 8
Resonantmodes: kL  m
m  1,2,3,..
(b)
m - 1
m
m + 1

(c)
Schematic illustration of the Fabry-Perot op tical cavity and its p roperties. (a) Reflected
waves interfere. (b) Only standing EM waves,modes, of certain wavelengths are allowed
in the cavity. (c) Intensity vs. frequency for various modes.R is mirror reflectance and
lower R means higher loss from the cavity.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
R: reflectance of the optical intensity, k: optical wavenumber
[4-18]
Fabry-Perot Lasing Cavity
A Fabry-Perot cavity consists of
two flat, partially reflecting
mirrors that establish a strong
longitudinal optical oscillator
feedback mechanism, thereby
creating a light-emitting function.
The distance between the adjacent peaks
of the resonant wavelengths in a FabryPerot cavity is the modal separation. If L
is the distance between the reflecting
mirrors & the refractive index is n, then at
a peak wavelength λ the MS is given by
ModalSeparation 
2
2nL
Laser Diode Characteristics
•
•
•
•
Nanosecond & even picosecond response time (GHz BW)
Spectral width of the order of nm or less
High output power (tens of mW)
Narrow beam (good coupling to single mode fibers)
• Laser diodes have three distinct radiation modes namely,
longitudinal, lateral and transverse modes.
• In laser diodes, end mirrors provide strong optical feedback in
longitudinal direction, so by roughening the edges and cleaving
the facets, the radiation can be achieved in longitudinal
direction rather than lateral direction.
Laser Operation & Lasing Condition
• To determine the lasing condition and resonant frequencies, we
should focus on the optical wave propagation along the longitudinal
direction, z-axis. The optical field intensity, I, can be written as:
I ( z, t )  I ( z)e j (t z )
• Lasing is the condition at which light amplification becomes possible
by virtue of population inversion. Then, stimulated emission rate into
a given EM mode is proportional to the intensity of the optical
radiation in that mode. In this case, the loss and gain of the optical
field in the optical path determine the lasing condition.
• The radiation intensity of a photon at energy h  varies exponentially
with a distance z amplified by factor g, and attenuated by factor 
according to the following relationship:
I ( z)  I (0) expg (h )   (h )z 
[4-20]
n1
R1
Z=0
R2
n2
Z=L
I (2L)  I (0) R1R2 expg (h )   (h )(2L)
[4-21]
 : Opticalconfinement factor,g : gain coefficient
 n1  n2 

α : effectiveabsorptioncoefficient, R  
 n1  n2 
Lasing Conditions:
I (2 L)  I (0)
exp( j 2 L)  1
2
[4-22]
Threshold gain & current density
1  1 

g th   
ln
2 L  R1 R2 
Laser startsto" lase" iff : g  gth
For laser structure with strong carrier confinement, the threshold current
Density for stimulated emission can be well approximated by:
gth  J th
 : constantdependson specificdeviceconstruction
Laser Resonant Frequencies
• Lasing condition, namely eq. [4-22]:
exp( j 2L)  1 
• Assuming

mc
m 
2 Ln
2n

2L  2m , m  1,2,3,...
the resonant frequency of the mth mode is:
m  1,2,3,...
c
2
   m   m1 
  
2 Ln
2 Ln
Spectrum from a Laser Diode
 (  0 ) 
g ( )  g (0) exp
 : spectralwidth
2

2 

Semiconductor laser rate equations
•
Rate equations relate the optical output power, or # of photons per unit
volume,
, to the diode drive current or # of injected electrons per unit
volume, n. For active (carrier confinement) region of depth d, the rate
equations are:

d

 Cn  Rsp 
dt
 ph
Photon rate stimulatedemission  spontaneous emission  photon loss
dn
J
n


 Cn
dt qd  sp
electronrate  injection  spontaneous recombination  stimulatedemission
C : Coefficient expressing the intensityof the opticalemission & absorption process
Rsp :rate of spontaneous emission into the lasing mode
 ph : photon life time
J :Injectioncurrent density
Threshold current Density & excess electron density
•
At the threshold of lasing:
  0, d / dt  0, Rsp  0
fromeq. [4 - 25] Cn   /  ph  0  n 
•
1
C ph
 nth
The threshold current needed to maintain a steady state threshold
concentration of the excess electron, is found from electron rate equation
under steady state condition dn/dt=0 when the laser is just about to lase:
J th nth
nth
0

 J th  qd
qd  sp
 sp
Laser operation beyond the threshold
J  J th
• The solution of the rate equations [4-25] gives the steady state
photon density, resulting from stimulated emission and spontaneous
emission as follows:
s 
 ph
qd
( J  J th )   ph Rsp
External quantum efficiency
• Number of photons emitted per radiative electron-hole pair
recombination above threshold, gives us the external quantum
efficiency.
ext 
i ( g th   )
g th
q dP
dP(mW)

 0.8065[ m]
Eg dI
dI (mA)
• Note that:
i  60%  70%;
ext  15%  40%
Laser P-I Characteristics (Static)
External Efficiency
Depends on the slope
Threshold Current
Laser Optical Output vs. Drive Current
Slope efficiency = dP/dI
The laser efficiency changes
with temperature:
20° C
Optical output
Relationship between optical output and
laser diode drive current. Below the lasing
threshold the optical output is a
spontaneous LED-type emission.
30° C
40° C
50° C
Efficiency
decreases
25
Modulation of Optical Sources
• Optical sources can be modulated either
directly or externally.
• Direct modulation is done by modulating the
driving current according to the message
signal (digital or analog)
• In external modulation, the laser is emits
continuous wave (CW) light and the
modulation is done in the fiber
Why Modulation
• A communication link is established by transmission
of information reliably
• Optical modulation is embedding the information on
the optical carrier for this purpose
• The information can be digital (1,0) or analog (a
continuous waveform)
• The bit error rate (BER) is the performance measure
in digital systems
• The signal to noise ratio (SNR) is the performance
measure in analog systems
Direct Modulation
• The message signal (ac) is superimposed on the
bias current (dc) which modulates the laser
• Robust and simple, hence widely used
• Issues: laser resonance frequency, chirp, turn on
delay, clipping and laser nonlinearity
Light Source Linearity
In an analog system, a time-varying electric analog signal
modulates an optical source directly about a bias current IB.
•With no signal input, the optical power output is Pt. When an
analog signal s(t) is applied, the time-varying (analog) optical
output is: P(t) = Pt[1 + m s(t)], where m = modulation index
For LEDs IB’ = IB
For laser diodes
IB’ = IB – Ith
LED
Laser
diode
29
Modulation of Laser Diodes
• Internal Modulation: Simple but suffers from non-linear effects.
• Most fundamental limit for the modulation rate is set by the photon
life time in the laser cavity:
1
 ph
c
1
1  c
  g th
   ln
n
2 L R1 R2  n
• Another fundamental limit on modulation frequency is the relaxation
oscillation frequency given by:
1
f 
2
1
 sp ph
 I


 1
 I th

1/ 2
Laser Digital Modulation
Optical
Power
(P)
P(t)
Ith
I1
I2
I(t)
Current (I)
t
 I 2  I1 
td   sp ln 

 I 2  I th 
t
• Input current
I2
– Assume step input
I1
• Electron density
– steadily increases until
threshold value is
reached
• Output optical power
– Starts to increase only
after the electrons reach
the threshold
Turn
on
Delay
(td)
Resonance Freq.
(fr)
Turn on Delay (lasers)
• When the driving current suddenly jumps from
low (I1 < Ith) to high (I2 > Ith) , (step input), there
is a finite time before the laser will turn on
• This delay limits bit rate in digital systems
• Can you think of any solution?
 I 2  I1 
td   sp ln 

 I 2  I th 
Relaxation Oscillation
• For data rates of less than approximately 10 Gb/s (typically 2.5
Gb/s), the process of imposing information on a laser-emitted
light stream can be realized by direct modulation.
• The modulation frequency can be no larger than the
frequency of the relaxation oscillations of the laser field
• The relaxation oscillation occurs at approximately
1
f 
2
1
 sp ph
 I


 1
 I th

1/ 2
34
The Modulated Spectrum
Twice the RF frequency
Two sidebands each separated by modulating frequency
Limitations of Direct Modulation
• Turn on delay and resonance frequency are the two
major factors that limit the speed of digital laser
modulation
• Saturation and clipping introduces nonlinear
distortion with analog modulation (especially in multi
carrier systems)
• Nonlinear distortions introduce higher order inter
modulation distortions (IMD3, IMD5…)
• Chirp: Unwanted laser output wavelength drift with
respect to modulating current that result on
widening of the laser output spectrum.
Laser Noise
• Modal (speckle) Noise: Fluctuations in the
distribution of energy among various modes.
• Mode partition Noise: Intensity fluctuations in
the longitudinal modes of a laser diode, main
source of noise in single mode fiber systems.
• Reflection Noise: Light output gets reflected back
from the fiber joints into the laser, couples with
lasing modes, changing their phase, and generate
noise peaks. Isolators & index matching fluids can
eliminate these reflections.
External Modulation
The optical source injects a
constant-amplitude light signal
into an external modulator.
The electrical driving signal
changes the optical power that
exits the external modulator.
This produces a time-varying
optical signal.
The electro-optical (EO) phase
modulator (also called a MachZhender Modulator or MZM)
typically is made of LiNbO3.
Mach-Zhender Principle
• T otalrelativephase differencebetween the two interfering signals :
P haseshift in theupper arm output is L  m
P haseshift in thelower arm output is  L
If m is even - -  constructive interference (inphase)
If m is odd - -  destructiven interference (oppositephase)
Light intensitymodulationwill result for all other values of m
Traveling Wave Phase Modulator
• Much wideband operation is possible due to
the traveling wave tube arrangement (better
impedance matching)
Electro Absorption Modulator
•
•
•
•
•
An EAM is a semiconductor external modulator based on the Franz–Keldysh
effect, i.e., a change in the absorption spectrum caused by an applied
electric field, which changes the bandgap energy.
Most EAM are made in the form of a waveguide with electrodes for applying
an electric field in a direction perpendicular to the modulated light beam.
EAM can operate with much lower voltages and at very high speed (tens of
GHz)
EAM can be integrated with a DFB laser diode on a single chip to form a data
transmitter in the form of a photonic integrated circuit.
EAM can also be used as Photo Detectors in the reverse mode
Distributed Feedback Laser
(Single Mode Laser)
The optical feedback is provided by fiber Bragg Gratings
 Only one wavelength get positive feedback
Fiber Bragg Grating
This an optical notch band reject filter
DFB Output Spectrum
Laser Nonlinearity
x(t)
Nonlinear function y=f(x)
y(t)
x(t )  A cost
y(t )  A0  A1 cost  A2 cos 2t  ...
Nth order harmonic distortion:
 An 
20 log  
 A1 
Intermodulation Distortion
x(t )  A1 cos1t  A2 cos 2 t 
y(t )   Bmn cos(m1  n 2 )t
m,n  0,1,2,...
m, n
Harmonics:
n1 , m 2
Inter-modulated Terms:
1   2 ,21   2 ,1  2 2 ,...
Transmitter Packages
• There are a variety of transmitter packages for different applications.
• One popular transmitter configuration is the butterfly package.
• This device has an attached fiber fly lead and components such as the
diode laser, a monitoring photodiode, and a thermoelectric cooler.
47
Transmitter Packages
Three standard fiber optic transceiver packages
48