330nm UV Generation from combined cavity’s DVD laser
diode and nonlinear crystal
(複合共振器構成の DVD-LD と非線形光学結晶による 330nm 紫外光発生)
Vesarach Pratkasem
ID.1075066
A dissertation submitted to
The Kochi University of Technology
in partial fulfillment of the requirements for
The master degree of engineering
Supervisor
Associate Professor Koji Nonaka
Course of Electronic and Photonic Engineering System
The Kochi University of Technology
Kochi, Japan
February 2005
Abstract
The commercial coherent UV light sources such as excimer laser and solid-state laser are complex to
fabricate and have large-scale structure; moreover, they require high manufacturing and maintenance
costs. Because of these disadvantages, the alternative coherent UV light sources that can solve these
problems have been desired. In this thesis, the indirect method to generate UV light from laser diode
is used, that is the using of Second-harmonic generation (SHG) process from β-BaB2O4 (BBO)
crystal. The most cost effective compact size coherent light source in the market is the DVD laser
diode so it is used as the fundamental input light source for the SHG system of this thesis. The SHG
process is the technique that can convert the light a one wavelength to the light at another
wavelength. The wavelength of the generated light is half of the input light. Since the wavelength of
the DVD laser diode is around 660 nm, the generated light has the wavelength around 330 nm,
which is in the UV-A region. But the spectral acceptance bandwidth of the BBO crystal is narrow,
and since the spectrum of the normal DVD laser diode is fluctuate and has wide bandwidth, the
generated UV from SHG process has low and fluctuate power. Therefore, the optical feedback from
diffraction grating is used in order to stabilize and narrow the spectrum of the DVD laser diode.
When the diffraction grating is used, the amount of generated UV power of the SHG system become
stable and is increased to 2.4 times compare to the system without the diffraction grating. The
enhancement in the performance of the SHG system is due to the stability of the spectrum of the
DVD laser diode from the using of optical feedback. Another interesting feature of the using of
diffraction grating is that, the tuning of UV wavelength is possible. The tuning ability comes from
the wavelength selective nature of the diffraction grating. The wavelength of the optical feedback
from the grating depends on the angle of the grating’s normal to the laser diode’s beam direction.
Therefore, when the diffraction grating’s angle is tuned, the feedback wavelength is changed. There
are two factors that limited the tuning range of UV wavelength; the deviation of the optical feedback
direction and the shifting in the gain spectrum of DVD laser diode. From the experiment, UV
wavelength tuning from 329.5 nm to 332 nm, which is according to 2.5 nm tuning range is achieved.
i
Acknowledgement
I would like to start this thesis with my deepest gratitude and indebtedness to my advisor Dr.Koji
Nonaka for his advice, suggestion, and enduring patience throughout the course of my study. He
made my life in Japan very comfortable since his kindness not limit only to the area of academic
field, but also the matter of daily life. It has been an honor to me for having a chance to join his
laboratory.
Also, I would like to thanks to my fellow seminar members: Kenji Ohara, Minako Sako, and Hiroaki
Mizuno. For their help and support during the course of the experimental work. The friendship they
gave me made my studying life in Japan enjoyable. Without them, I don’t think that I can achieve
this far. Thanks to you all.
In addition, I would like give my sincere gratitude to the Rohm Co. ltd. for provided me the supply
of their high quality DVD laser diodes. With their high power DVD laser diodes, I can conduct the
research smoothly and achieve good research’s result.
Finally, I would like to express my sincerely thanks and gratitude to the Kochi University of
Technology (KUT) for provide me the scholarship, which made it possible for me to do this
research.
ii
Table of contents
Abstract
i
Acknowledgement
ii
Table of contents
iii
Chapter 1 Introduction
1.1
Background
1
1.2
Scope and aim of this research
3
Chapter 2 Theoretical Background
2.1
Introduction
4
2.2
Nonlinear effect
4
2.2.1 Second Harmonic Generation (SHG)
6
2.2.2 Uniaxial crystal
7
2.2.3 Phase matching in uniaxial crystal
9
2.3
2.4
2.5
2.2.4 Walk off
10
2.2.5 Phase mismatch factors
12
Laser diode (LD)
12
2.3.1 Light generation process
12
2.3.2 Principle of laser
14
2.3.3 Principle of laser diode
15
2.3.4 Basic laser diode characteristics
16
2.3.4.1 Injection current and temperature characteristics
16
2.3.4.2 Beam spatial characteristic
17
2.3.4.3 Wavelength tuning characteristic
17
Spectrum narrowing and controlling technique
18
2.4.1 Extended Cavity
19
2.4.2 Diffraction grating
20
Optical resonator
22
2.5.1 Phase matching condition
23
iii
Chapter 3 Experimental Setups
3.1
Introduction
27
3.2
System 1: Basic Second harmonic generation system
27
3.3
System 2: SHG system with the spectrum enhanced DVD-LD
29
3.4
System 3: SHG system with the spectrum enhanced DVD-LD and optical resonator
30
Chapter 4 Results and discussion
4.1
Basic Second harmonic generation system
32
4.2
SHG system with spectrum enhanced DVD-LD
35
4.3
SHG system with the spectrum enhanced DVD-LD and optical resonator
41
Chapter 5 Conclusion
43
Appendix
46
iv
Chapter 1
Introduction
1.1 BACKGROUND
Ultra Violet light or known as UV is defined as the light that has wavelength less than 400
nanometers. The applications of the UV in the industries are UV curing, sterilization, and
spectroscopy. For the application that requires high accuracy such as spectroscopy, the coherent and
stable wavelength UV light source is needed. For the commercially used coherent UV light sources
such as excimer laser or solid-state laser, even those systems can produce high-power UV light;
however, they are bulky, complex to fabricate, and require high manufacturing and maintenance cost.
So the coherent UV generation systems, that are low price, small size, and easy to manufacture are
preferred.
Up to present, the most cost effective compact size laser light source is the laser diode (LD). The LD
can be mass-produced by the same photolithographic techniques as electronic circuit so the price is
low. The package size of LD is approximately 0.5x0.5x0.3 mm, which is not much larger than the
size of matchstick head. Due to this small size, laser diodes are widely used in the products such as
CD or DVD player. In the past, one of the disadvantages of using LD compares to the normal
solid-state laser is the low optical power. The optical power of the laser diode is in the range of
10-20 mW. However, due to the advance in the semiconductor technology, it is now possible to
acquire the LD that can produce optical power of more than 40 mW, such as the high power DVD
writer’s laser diode [1].
The main problem of using laser diode to generate UV is the difficulties of the fabrication of the
laser diode that can emit light in UV range. Since that condition require a wide band gap
semiconductor material. The shortest UV wavelength laser diode known by author is the Ultra Violet
LD [2] which have center wavelength around 375 nm. So, in order to generate shorter wavelength
UV, the indirect UV generation technique must be used.
Generally, the technique used in solid-state lasers to indirect generate light in UV region is the
frequency conversion process, which can be applied to LD as well. Frequency conversion process is
the technique that converts light at one frequency to another frequency by the nonlinear interaction
1
in nonlinear optical crystal. So, by the frequency conversion process, it is possible to achieve the
new range of light wavelength from existing laser sources. In the frequency conversion process, the
most frequent used technique in UV generation is the Second-harmonic generation (SHG), where the
generated light’s wavelength is half of the fundamental input (see Fig 1.1). The advantage of this
technique compares to another techniques in frequency conversion process is that only one light
source can be used.
Fundamental light, ω
Fundamental light, ω
Generated light, 2ω
Nonlinear Optical Crystal
Fig. 1.1: Second-Harmonic generation (SHG) process.
But to apply SHG process to LD there are some limitation that need to be concern. First, the
spectrum acceptance bandwidth for UV generation of nonlinear optical crystal is narrow, which can
be in the order of less than 0.1 nm. But the spectrum bandwidth of a conventional FP-LD can be
larger than 0.2 nm under normal operation. Second problem concerns the spectrum of LD is that, the
spectrum is normally fluctuate due to operational conditions of LD. These problems will lead to the
low UV generation efficiency. Another problem of using LD is that, the fundamental input power
from LD is low compares to solid-state laser sources; this will lead to very low generated UV power,
which might not be enough for some real applications.
In order to control and narrow LD spectrum, there are many techniques both optical and electrical
[3]. The simplest technique is the using of extended cavity from diffraction grating to provide optical
feedback to LD [4]. The advantage of this technique is the simplicity since it needs only one piece of
diffraction grating to control the spectrum of LD. To increase the amount of generated UV, the
increasing of fundamental optical from LD is required. But LD has a limit in the optical power that it
can generate, so the external optical power amplification technique is required. The general
technique used to increase the fundamental optical power, is the using of optical resonator which can
amplified the optical power up to more than 100 times theoretically.
Both optical resonator technique and bandwidth narrowing technique are normally studied separately
for UV generation system. The ring resonator technique are mostly used in the SHG of solid-state
2
lasers [5], while LD narrowing technique are used to control LD spectrum only [4] but not in the
manner of UV generation. So the result of the combination of these techniques for UV generation
system from LD is studied in this thesis.
1.2 SCOPE AND AIM OF THIS RESEARCH
The main objective of this research is to design the UV generation system using commercially
DVD-LD and nonlinear optical crystal for spectroscopy application. The technique used to generate
UV, the Second-harmonic generation is studied and the amount of UV generated solely from this
technique is determined. Then the enhancement techniques; extended cavity and optical resonator
are applied. The extended cavity technique from diffraction grating is studied, and the effect of the
using of this technique to the amount of generated UV is determined. After the spectrum of the LD is
controlled, the optical resonator technique will be added to the UV generation system, to increase the
optical power of fundamental light, and then its effect to UV generation system is studied.
REFERENCES
[1]
ROHM CO., LTD, “DVD-Record High power red laser diode, RLD65PZB5”.
[2]
NICHIA Corp., “Ultra Violet Laser Diode, NDHU110APAE2”.
[3]
Carl E. W., Leo H., “Using diode lasers for atomic physics”, Rev. Sci. Instrum.,
Vol.62, No.1, pp. 10-13, 1991.
[4]
Mark W. F., Adam M., “Spectral Characteristics of External-Cavity Controlled
Semiconductor Lasers”, IEEE J. Quantum Electron, Vol.QE-17, No. 1, pp. 44-59, 1981.
[5]
Z.Y. Ou, S.F. Pereira, E.S. Polzik, H.J. Kimble, “85% efficiency for cw frequency
doubling from 1.08 to 0.54 µm”, Opt. Lett., Vol. 17, No. 9, 1992.
3
Chapter 2
Theoretical Background
2.1 INTRODUCTION
In this chapter, general theories and reviews of some of the topics, which are related to the scope of
this research, are presented. The main aim of this research is the UV generation from DVD-LD using
Second-Harmonic generation (SHG) in nonlinear optical crystal. Thus, in order to gain the
understanding of the UV generation mechanism, the general theories and information of the
nonlinear optical crystal and the laser diode are explained. In addition, the LD spectrum controlling
techniques are discusses and reviewed, for it will be used to control the spectrum of LD to enhance
the amount of generated UV. Finally, due to the requirement of the increasing of the fundamental
input power from a laser diode, the optical power amplification technique is used. Therefore, the
theories and the related information of the optical resonator are presented.
2.2 NONLINEAR EFFECT
Under normal condition where the applied electric field is weak, the polarization interaction of a
dielectric material is assumed to be in linear manner.
P = κ 0E
(2.1)
Where, P is the vector of dielectric polarization, E is the electric field, and κ0 is the linear dielectric
susceptibility.
When the applied electric field is intense, the electrons of a dielectric material will no longer
oscillate linearly with the applied electric field, and nonlinear terms will appear in the induced
polarization of the material. So the polarization in the material can be expressed as a power series of
applied electric field E as followed [1]
P = κ0E + χ (2) EE + χ (3) EEE + ...
(2.2)
Where χ(2), χ(3), and so on are the nonlinear dielectric susceptibility coefficients (square, cubic, and
4
so on, respectively). Note that, for weakly nonlinear condition as in the case of eq. 2.1, the linear
term dominates all the nonlinear term, κ0E >> χ(2)E2 >>χ(3)E3.
Consider the two traveling waves E1 and E2 travel in the dielectric material. They can be written as a
superposition as
E (t ) = E1eiω1t + E2 eiω2t + cc.
(2.3)
Substitute eq. 2.3 into the square nonlinearity term of eq. 2.2, the interaction will generate the
following terms [2].
The second harmonic of the wave at frequency ω1:
P2 ω1 = χ (2) ( E12 ei 2 ω1t + c.c.)
(2.4)
The second harmonic of the wave at frequency ω2:
P2 ω2 = χ (2) ( E22 ei 2 ω2t + c.c.)
(2.5)
Generation of the sum frequency ω1+ω2:
Pω1 +ω2 = 2χ (2) ( E1 E2 ei ( ω1 +ω2 ) + c.c.)
(2.6)
Generation of the difference frequency ω1-ω2:
Pω1 −ω2 = 2χ (2) ( E1 E2 ei ( ω1 −ω2 ) + c.c.)
(2.7)
The time independent (dc) component
PDC = 2 | χ(2) | (| E12 | + | E22 |)
(2.8)
Equation 2.4 and 2.5, show the second harmonic of both traveling waves, while eq. 2.6 and 2.7 give
the sum and difference frequency generation respectively. Equation 2.8 shows the dc components of
the interaction. Above equations show that the propagation of electromagnetic waves through
nonlinear optical crystals can generate the vibrations at second harmonic, the sum and difference,
and the dc components of the fundamental frequencies.
5
2.2.1 SECOND HARMONIC GENERATION (SHG)
For the crystal that have a symmetry center, the square dielectric nonlinear susceptibility χ(2) is zero,
so these crystals can not produce the first nonlinear generation process as explained in eq.2.4-2.8.
But in the case of crystal without a symmetry centre, χ(2) is not equal to zero, so the first nonlinear
process is possible, these crystals are called anisotropic crystals. The nonlinear optical crystals are a
class of anisotropic materials that include all material that crystallize in the tetragonal and hexagonal
system. The nonlinear optical crystal used in this research is one type of anisotropic crystals called
uniaxial crystal. It is called uniaxial because it has a single optic-axis. For the frequency conversion
process used in this thesis, it is the special case of sum-frequency conversion (SFG) of the uniaxial
crystal, called second-harmonic generation (SHG).
In order to produce noticeable sum-frequency conversion process in the uniaxial crystals, the
phase-matching condition of three interaction waves must be fulfilled.
k 3 = k 2 + k1
(2.9)
The ki is the wave-vector corresponding to the frequencies ωi
ki =
ωi n(ωi )
ωi
2πni
=
=
= 2πni ν i
c
υ(ωi )
λi
(2.10)
Where υ(ωi) is the phase velocity, n(ωi) the refractive index, λi the wavelength, and νi is the wave
number. Equation 2.9 means that the interaction of wave vectors, k1 and k2, and the generated
wave k3, must be in phase over the interaction region. The interaction of this manner is called
sum-frequency conversion (SFG) which can be either collinear or non-collinear (see Fig. 2.1) [1].
k1
k1
k2
k3
k2
k3
(a)
(b)
Fig. 2.1: (a) Collinear or scalar phase matching, (b) Non-collinear or vector phase matching of
three waves mixing [1].
6
As state before, the frequency conversion process used in this research is called second-harmonic
generation (SHG). It is a special case of SFG where, ω1=ω2; ω3=2ω1. Consider scalar
phase-matching condition, for SHG condition, eq.2.9 can be written as;
k3 = 2k1
(2.11)
n3 = n1
(2.12)
Since ω3 = 2ω1, eq. 2.11 implies that
For the interaction of three waves in isotropic crystal, eq. 2.12 is never fulfilled because of normal
dispersion (n1<n3). But in the case of uniaxial crystals that have different indices of refraction
along the different crystal axes, this condition is possible under interaction of differently polarized
waves.
2.2.2 UNIAXIAL CRYSTAL
In uniaxial crystals, there exists a special axis called optical axis (Z-axis). The plane contains
optical-axis and the wave vector k of the light wave is called principle plane. The light wave that
polarizes normal to the principle plane is called ordinary beam or o-beam, while the wave that
polarizes parallel to principle plane is called extraordinary beam or e-beam. The refractive index
of o-beam does not depend on the propagation direction, while the e-beam does (see Fig. 2.3). So,
in uniaxial crystal, the refractive index depends on both direction of propagation and polarization
direction.
The refractive indices of the o-beam and e-beam in the plane normal to the optical-axis are
denoted by no and ne respectively. There are two types of uniaxial crystals, in the case of no>ne,
the crystal is negative. If no<ne, crystal is called positive. As state before that the refractive indices
of e-beam is depend on the direction of propagation, it can be approximately determined by
following equation [1]
n e (θ) = no
1 + tan 2 θ
1 + (no / ne ) 2 tan 2 θ
Where, polar angle θ is the angle between the Z-axis and the wave vector k.
7
(2.13)
Optical axis
Wave-vector k
θ
Principle plane
Ordinary polarization
Extraordinary polarization
Fig. 2.2: Polarization direction of the wave vector and the principle plane of the uniaxial crystal.
no
Optical-axis
no
k
Optical-axis
k
θ
θ
ne
no
no ne
ne(θ)
ne(θ)
(b)
(a)
Fig. 2.3: Dependence of refractive index on light propagation direction and polarization, negative
(a) and positive (b), uniaxial crystals.
The commonly used uniaxial crystals for frequency conversion process are β-barium borate
(β-BaB2O4, BBO), lithium triborate (LiB3O5), potassium titanyl phosphate (KTiOPO4, KTP), and
lithium niobate (LiNbO3). This research use BBO crystal for SHG process due to its high conversion
efficiency.
8
2.2.3 PHASE MATCHING IN UNIAXIAL CRYSTAL
There are 2 types of phase-matching in uniaxial crystals
1.) Type I phase-matching; where the mixing waves have the same polarization direction
ko1 + ko 2 = k3e
(2.14)
k1e (θ) + k2e (θ) = ko 3
(2.15)
2.) Type II phase-matching; where the mixing waves have orthogonal polarization direction.
ko1 + k2e (θ) = k3e (θ)
(2.16)
k1e (θ) + ko 2 = k3e (θ)
(2.17)
ko1 + k2e (θ) = ko3
(2.18)
k1e (θ) + ko 2 = ko 3
(2.19)
This thesis uses SHG of eq. 2.14 in BBO, where the fundamental input waves are in ordinary
polarization, while the generated wave is in extraordinary polarization. The interaction of the
waves of this condition is shown in Fig. 2.4
From Fig. 2.4, it can be seen that the condition of eq. 2.11 and 2.12 are fulfilled. Equation 2.11 is
fulfilled at the point where the circle of ordinary refractive index at frequencies ω1 crosses the
ellipse of the extraordinary refractive index at frequencies ω3, as shown in fig. 2.4(a). Or for eq.
2.12 as in Fig. 1.5(b), where the circle of ordinary wave 2ko1 crosses the ellipse of extraordinary
ke3(θ). The angle that fulfills these conditions is called phase-matching angle (θ). To generated
high Second-harmonic generation efficiency, the direction between optical axis and propagating
vector must be equaled to this phase-matching angle.
9
Optical-axis
Optical-axis
k
k
ke3(θ) = 2ko1
ne3(θ) = no1
ne1(θ)
θ
θ
ne1
ke1
ko1
ne3
ke3
no1
2ko1
no3
ko3
(a)
(b)
Fig. 2.4: SHG phase matching in negative crystal, in refractive indices coordinate (a) and wave
vectors coordinate (b).
2.2.4 WALK OFF
When using phase-matching of different polarization waves, the interaction direction between
waves will physically separate from each other as they propagate through the nonlinear optical
crystal. This phenomenon is called “walk-off”. This is due to that the direction of propagation of
the wave phase (wave vector k) is not coincides with the direction of the wave energy, Poynting
vector (s). The direction of the Poynting vector is defined as the normal to the tangent of the wave
vector k to the curve of refractive index (see Fig. 2.5).
For the case of o-beam, the curve of the index of refraction is circle so the direction of the
Poynting vector (s) is coincided with the wave vector (k). But for e-beam, the curve of index of
refraction is elliptical that the wave vector and the Poynting vector are not overlapped. So the
propagation between o-beam and e-beam is not overlap as propagate along the crystal (see Fig.
2.6).
10
Optical axis
Optical axis
k
o
s
θ
k,s
n
θ
ρ
ne
(a)
(b)
Fig. 2.5: Direction of wave vector k, and Poynting vector s in negative uniaxial crystal for
extraordinary wave (a), and ordinary wave (b).
The walk-off angle (ρ) is defined as the angle between the wave vector of the generated wave and
its Poynting vector. The “walk-off” affects the frequency conversion length of uniaxial crystal.
Because when walk-off is too large, the interacting waves (k1 and k3) will not overlap spatially in
the entire crystal and eventually the conversion process is terminated.
Optical axis
o-beam
k1
k1
ρ
s1
θ
k3
s3
e-beam
k1
k3
Fig. 2.6: Propagation of fundamental wave k1 and generated wave k3 in uniaxial crystal. The
walk-off angle ρ is the angle between the wave vector k3 and Poynting vector s3.
11
2.2.5 PHASE MISMATCH FACTORS
In actual nonlinear conversion, the situation is slightly different from ideal. In practice, the
conversion efficiency is governed by the phase-mismatch factor (△k). Phase-mismatch factor is a
function of crystal temperature (T), frequencies of the interaction waves (ν), and deviation from
phase matching angle (θ).
∆k (T , δθ, ν) ∂ (∆k )
∂ (∆k )
∂ (∆k )
∆T +
∆θ +
∆ν
∂T
∂ (δθ)
∂ (ν )
(2.20)
Where, ∆k is the total wave mismatch, ∆T is the temperature mismatch from phase-matching
angle’s temperature of the crystal, ∆θ is the deviation from phase-matching angle, and ∆ν is the
mismatch from phase-matching frequencies. To achieve high conversion efficiency, these
mismatch need to be controlled to be as small as possible. The temperature mismatch can be
controlled by the temperature controller applied to the crystal. Angular mismatch can be
controlled by tuning the angle of the crystal, and the using of appropriate focus lengths when the
focused beam is used. While the frequency mismatch can be controlled by narrowing and
stabilizing the spectrum of input light sources.
2.3 LASER DIODE (LD)
In this section, the general information of the fundamental input light source of this research, the
laser diode (LD), is explained. Begin with the mechanism of light generation process in
semiconductor materials to gain the understanding of the relationship between the emitted
wavelength and the energy band gap of the material. Next, the principle of laser light sources is
described to explain the origin of coherent light generation mechanism in laser sources. Then, the
basic structure and characteristics of LD are shown.
2.3.1 LIGHT GENERATION PROCESS
In
semiconductor material, there are 2 relevant energy states that form the bands of energy levels
of atom;
Valence band: Ground-state energy level, this is the lower energy band and is nearly full in
equilibrium in the normal condition. The electron of the atoms in this state can be excited to the
higher energy level by the insertion of external energy such as; heat, light, or electricity.
12
Conduction band: Excited energy level, the higher energy band and is nearly empty in the normal
condition. The electrons in this band have higher energy level than the electrons in valence band.
Electrons in conduction band can make a transition to the valence band by release the energy.
The transition process is shown in figure 2.7, the electrons from conduction band move to the
valance band to recombine with the holes (vacant of electron); the result of this recombination is the
emission of photon, which is a particle of light. The energy of the emitted photon is corresponds to
the difference in energy level between Conduction band and Valance band.
Electron
- - - - - - - - -
Conduction
Band
Photon (Light wave)
Band gap
Hole
+ + + + + + + + +
Valence
Band
Fig. 2.7: Energy band of semiconductor material.
The wavelength of the emitted light can be approximately determined by the band gap energy, Eg
[eV], of the semiconductor material, as followed
λg = hc / Eg
(2.21)
Where λg is the wavelength of the emitted light, h is the Plank’s constant, and c is the light constant.
As can be seen from eq. 2.21, the choice of the emitted wavelength depends on the type of the
compound semiconductor materials with the different band gap. Since there are many semiconductor
materials available with different band gap energy, the choice of wavelength can be widely selected
from visible to far infrared region. But as the emitted wavelength degrease, the band gap increase;
this mean that in order to generate shorter wavelength, higher energy is needed to excited electron to
conduction band.
13
2.3.2 PRINCIPLE OF LASER
Laser or so called (Light Amplification by Stimulated Emission of Radiation) is the light sources that
can produce high coherent light output. Laser diode is one type of these lasers. In order for a laser to
produce coherent light, there are 3 basic steps together.
Population inversion: This is the first process of the lasing mechanism. Population inversion is the
number of electrons in excited state versus the electrons in ground state. The population inversion of
the semiconductor material can be increased by applying the energy (in the case of laser diode,
injection current), so the electrons in the ground state are excited to the excited state.
Spontaneous emission: In this process photons are produced by the recombination of electrons and
holes as explained in previous section.
Stimulated emission: In this process, when photon hits the electron that is already in the excited state,
that electron will absorb photon energy and jump to the higher energy level, then releases the
received energy, then emits another photon that have the same phase and energy as the input photon.
So, there will be 2 same identical photons output, generally speaking, have same wavelength.
To generate the coherent light, the oscillation part is needed. The oscillation principle of the laser is
as same as the oscillation of the electronic devices, it needs the feedback part. To make a feedback,
the two opposing parallel cleaved facets of semiconductor provide reflective optical feedback, hence
forming as Fabry-Perot resonator as shown in Fig. 2.8. The light which propagates towards the
mirror is amplified by the stimulated emission and reflect back and forth between the mirrors, until
the standing wave is formed and this standing wave have constant phase parallel to the reflecting
mirrors. Once the power inside cavity is high enough it will be coupled out of the cavity through one
of the mirror that have few percents of transmission.
The basic equation of the standing wave inside the cavity is as followed
L=
Where
m.λ
2nref
(2.22)
L is the cavity length, λ is the wavelength of light in the active layer, nref is the refractive
index of the material, and m is the integer.
14
R
R
Refractive index n
1
2
m
Mirror
Mirror
Standing wave
L
Fig. 2.8: Standing wave of longitudinal mode in Fabry-Perot resonator [4].
2.3.3 PRINCIPLE OF LASER DIODE
In semiconductor material the charge carrier are electrons and holes. The semiconductor materials
can be doped with the impurity to improve the density of the charge carrier. The semiconductor is
doped with electron as majority carrier is called n-type material, while the semiconductor that is
doped with holes as majority carrier is called p-type material.
Basically, Laser diode (LD) is the p-n junction semiconductor that converts the electrical energy to
the optical energy. In the laser diode, the light emitted part called the active layer is made from
p-type semiconductor, and the corresponding output wavelength is depending on energy gap of this
layer. Generally, the material of the active layer is made from compound material such as gallium
arsenide (GaAs), and combination of another material.
V
Electron
Mirror
(Partial transmitted)
n-layer
p-layer
p-layer
Transmitted
Light
Hole
Electrode
Fig. 2.9: Basic structure of p-n laser diode [4].
15
In order to generate light, the active layer is inserted between the p-n junctions as shown in Fig. 2.9.
The electrons from n-type region and holes from p-type region are injected to the active layer by the
forward bias current from the 2 electrodes, and make a lasing process as explained in the section
2.3.2. Since the p-type cladding layer have larger energy gap than the active layer, the electrons from
n-type cladding layer can not pass through due to the energy barrier, so they are confined within the
active layer. And if the n-type layer has wider energy band gap than the active layer, it will have
smaller refractive index than the active layer, and act as a light confinement. So this type of structure
of p-n layers, will not only act as carrier confinement but also light confinement.
2.3.4 BASIC LASER DIODE CHARACTERISTICS
2.3.4.1 INJECTION CURRENT AND TEMPERATURE CHARACTERISTICS
The output power of a typical semiconductor diode laser as a function of injection current (I-L
characteristic) and temperature is shown in the fig. 2.10 [6]. The sudden change in the slope of each
curve is the onset of a laser action, the electric current at this point is called threshold current of the
laser diode. It can be seen that the different in the temperature affect the threshold current of the laser
diode. As the temperature increase, the threshold current increase, and the slope of the I-L line
decrease as the efficiency decrease.
Fig. 2.10: Example of output power vs. injection current for a typical laser diode [6].
16
2.3.4.2 BEAM SPATIAL CHARACTERISTIC
Because the light is emitted from a small rectangular region, the output of a diode laser has a large
divergence. There are two types of radiation angle of laser diode beam, perpendicular and parallel to
the p-n junction plane of laser diode. The perpendicular direction have larger spreading angle than
the parallel one since the refractive index different along the lateral is larger than that along the
transverse direction. Normally, this spreading beam can be collimated by using lens with a small f
number such as aspheric lens. Since the laser diode is operate in the single transverse mode, thus
collimated beam will be elliptical in shape. But this elliptical laser diode beam can be transformed
into nearly circular beam by the using of Anamorphic prism pair, if such circular shape is required.
Active layer
θ// (Parallel deviation angle)
θ┴
(Perpendicular deviation angle)
Fig. 2.11: The rectangular shape of the gain region leads to the elliptical radiation beam.
2.3.4.3 WAVELENGTH TUNING CHARACTERISTIC
For some applications that the specific wavelength is not available from the commercial laser diode,
the user has to tune the center wavelength of the laser diode to the required value. A diode laser’s
wavelength is determined primarily by the band gap of the semiconductor material and then by the
junction’s temperature and current density [5]. But the band gap is not under the control of the user,
so the tuning must be done in temperature and current density.
Temperature tuning: this can be used to tune the wavelength of the laser diode because the optical
path length of the cavity and the dependence of the gain curve depend on the temperature. The
temperature tuning followed the stair-case characteristic from mode jumping due to the different in
value of the optical length change and the gain curve change.
17
Injection current: Change in the injection current affects both the diode temperature and change the
carrier density which also changes the index of refraction, and these in turn, change the wavelength.
2.4 SPECTRUM NARROWING AND CONTROLLING TECHNIQUE
To achieve high efficiency second-harmonic generation (SHG), the spectrum of the fundamental
input light sources need to less or at least equal to the spectrum-acceptance bandwidth (the mismatch
from phase-matching frequency ∆ν) of the nonlinear optical crystal at the specific phase-matching
angle (section 2.3.5). For example; the spectrum-acceptance bandwidth of the nonlinear optical
crystal used in this research at the fundamental input at 660 nm is approximately 0.114 nm. Whereas
from observation, the spectrum bandwidth of the DVD laser diode is sometimes larger than 0.2 nm
(See Fig. 2.12). Another problem is that, even the DVD laser diode is said to be operated in single
mode, it will often not run in a single mode for all injection current. The lasers will always be
multimode for very low injection currents, but even at much higher currents there are often range of
current and temperature where the laser will continue to operate in several modes, with mode
competition and hopping [7]. These problems will lead to the low SHG conversion efficiency, and
Intensity
the fluctuation of the power of the generated UV.
△λ=0.285 nm
Wavelength
Fig. 2.12: Spectrum of DVD-LD without the extended cavity, it can be seen that the emitted
spectrum bandwidth is not narrow. (Operate at 135 mA injection current).
There are many factors that contribute to the linewidth of the laser diode, but the most fundamental
is that the laser cavity is so short so that the Schawlow-Townes linewidth is significant [5]. But for
the commercial laser diodes such as DVD writer’s laser diodes, the linewidth is larger than
Schawlow-Townes value due to the fluctuation in the carriers, the temperature, and the complex
susceptibility of the laser. Still, the using of Schawlow-Townes formula can be apply to narrow the
linewidth of the DVD laser diodes, that the increasing of the quality factor (Q) of the laser’s
18
resonator will reduce the linewidth of the laser diode.
2.4.1 EXTENDED CAVITY
There are many techniques both optically and electronically to narrow and control the center
wavelength of a diode laser. This research uses the optically one due to the simplicity.
The unique characteristic of the laser diodes compare to another type of laser light sources is that;
the laser diode is extremely sensitive to the optical feedback. The sensitivity of the laser diode to the
optical feedback arises from a combination of factors [5]; the gain curve is very flat as a function of
wavelength, the cavity finesses is low, and the cavity of laser diode is very short. As a result of these
factors, the overall gain of the laser diode has an extremely dependence on wavelength, and there are
few photon in the cavity so the lasing frequency is easily perturbed. So the using of selective optical
feedback can be used to control the emission wavelength of laser diodes. And since laser diodes have
broad gain spectrum, it is possible to amplify light over a wide range of wavelength, this will lead to
tuning of the oscillation wavelength.
The basic configuration of the optical feedback technique is to reflect small portion of output of laser
diode to the laser diode output facet (See Fig. 2.13). Various laboratories [5] have shown that if only
one of the facets of a laser diode is AR coated, the laser’s linewidth can be narrowed and its
oscillation frequency can be controlled by providing external frequency selective optical feedback.
Fortunately, many high power commercial lasers such as DVD laser diode are already have reduced
reflectance coating on the output facet and have high reflector on the back facet, so no further
enhancement on laser diode’s structure is needed.
HR
AR
Optical feedback
（Frequency Selected)
Transmitted Light
Frequency Selective
Component
(Small Reflectance)
Laser Diode’s
Active region
Fig. 2.13: Basic optical feedback configuration.
The optical elements used for this purpose are such as simple mirrors, etalons, fiber cavities, or
grating. This research uses the grating because it is most common and least expensive to purchase,
19
while provides the ability of wavelength tuning. The pioneer research of the using of grating to
control laser diode spectrum was done by Flemming and Mooridan [7] as they can make the single
mode operation from multimode laser diode. The laser configuration that use grating as a feedback is
called extended cavity diode lasers (ECDL) [7,8,9,10,12], the result of these researches show the
stable, tunable, and single-frequency operation of the laser diode. This grating configuration is called
extended cavity not external cavity since the cavity of the laser diode is typically extended by a
grating, which use the optical feedback to dominate the feedback from laser diode output facet [11].
However, the external cavity is the system that employs optical feedback from separate cavity to
reduce the linewidth. More over, the extended cavity are much easier to use and more reliable than
the external cavity, For example, extended cavity diode laser using grating shows much better
frequency stabilization than external cavity since external cavity usually require four independent
actuators to set the wavelength; the current, the etalon, the length of feedback cavity, and the
position of a mirror used to adjust the path length to the external cavity. For the extended cavity
there are only 2 actuators; current and grating [11].
2.4.2 DIFFRACTION GRATING
To provide the wavelength selected optical feedback, the diffraction grating is used. Diffraction
grating is the collection of reflecting elements that are separated by the distance in the order of light
wavelength. There are two types of grating; transmission and reflection. There are many researches
that use transmission diffraction grating for ECDL system [9]. Even those transmission grating have
an advantage of constant beam direction over reflection grating, the transmission grating have higher
price, and more difficult to obtain than its counterpart. From author knowledge, the transmission
diffraction gratings used for ECDL have to be manufactured by order [9]. While, reflection
diffraction gratings are already in the market with the wide range of quality and price. So this
research uses reflection diffraction grating.
Reflection grating consists of grating imposed on the reflection surface, such that when the
monochromatic light imposed on grating surface, the light will diffracted into discrete direction as
shown
20
Incident light
Grating normal
Reflected light
Diffracted light
α
β0
Diffracted light
β+1
β-1
d
Fig. 2.14: Reflection diffraction grating
The relationships between each parameter are explained by the grating equation.
mλ = d (sin α + sin β)
(2.23)
Where, m is the order of refraction, d is the spacing between grove, α is the incident angle, and β is
the diffraction angle.
From equation 2.23, at the 0th order reflection, grating will act as normal mirror. But for +1st order
diffraction beam, if α = β+1, light will reflect back collinear with the incident beam. The setup of the
grating respect to the incident beam at this angle condition is called Littrow configuration.
Incident
beam
1st order diffraction
beam
Reflected diffraction
grating
α=β+1
β0
0th order reflection
beam
Fig. 2.15: Littrow configuration.
21
Using Littrow configuration, eq. 2.23 change to
mλ = 2d sin α
(2.24)
From equation 2.24, it can be seen that the choice of first order diffraction wavelength is depend on
the incident angle of the incident beam. This characteristic can be used to tune the reflected
wavelength which will lead to the tuning of the oscillation wavelength of the laser diodes.
2.5 OPTICAL RESONATOR
To order to increase the amount of generated UV, the fundamental input optical power has to be
increased. But the amount of optical power that laser diode can generate has a limitation, due to the
effect of gain saturation, so another method other than the increasing of the laser diode injection
current is required.
The common technique used to increase the amount of optical power is the using of optical
resonator. There are many researches use optical resonator to enhance the efficiency of frequency
conversion process of solid-sate laser [14-20]. The pioneer paper that uses optical resonator to
enhance the frequency conversion efficiency is conducted by A.Ashkin, G.D. Boyd, and J.M.
Dziedzic [14]. In their report, they proposed that the using of optical resonator can result in the
increasing of generated optical power up to 500 times. Another research done by group of Z.Y. Ou,
S.F. Pereira, E.S. Polzik, and H.J. Kimble, shows the conversion efficiency of second harmonic
generation up to 85% [16]. So, the using of optical resonator is one of the required techniques in
frequency conversion system. The resonator can be used to enhance the fundamental wave,
generated wave, or both. This research uses optical resonator to enhance the amount of fundamental
power. This is simply means of storing of fundamental energy in the high-Q cavity to increase the
flux of fundamental power passing through the nonlinear optical crystal, thereby increase the
generation of second harmonic power.
22
2.5.1 PHASE MATCHING CONDITION
Consider the basic optical resonator as shown in figure below.
r 1,t
EIn
r 2,t
1
2
EC
ERe
M2(Movable)
M1
Fig. 2.16: Fundamental resonator with mirrors M1 and M2 [14].
Assume that M1 and M2 are lossless mirrors, where M2 is made movable to adjust the length of the
resonator. Define r1 and r2 as the reflection coefficient, and t1 and t2 as the transmission coefficient.
By definition of lossless mirrors
r1 + t1 = 1 = r2 + t2
(2.25)
Define rReso as a resonator reflectance parameter originates from the optical components inside
resonator such as; mirror M2, and nonlinear optical crystal, or other components. It is the reflection
ratio seen by the propagating wave as it propagate through resonator, reflected at M2, and propagate
back to mirror M1.
Use the self-consistency equations of Febry-Perot Interferometer.
EC = t1 EIn + r1rReso EC e − iϕ
(2.26)
ERe = r1 EIn + t1rReso EC e −iϕ
(2.27)
*
Solving the above equations and using the relationship, P = E·E , leads to the following
23
equations
PC
T1
=
PIn (1 − R R ) 2 + 4 R R sin 2 ϕ
1 Reso
1 Reso
2
2
2 ϕ
PRe ( R1 − RReso ) + 4 R1 RReso sin 2
=
ϕ
PIn
(1 − R1 RReso ) 2 + 4 R1 RReso sin 2
2
(2.28)
(2.29)
Where, PIn, PRe, and PC, respectively, are the incident power, reflect power, and the power inside the
mirror M1 of the resonator. And φ is the round-trip phase shift within the resonator.
At resonance, term sin2φ/2 = 0, so eq. 2.28 and eq.2.29 change to
PC
T1
=
PIn (1 − R1 RReso ) 2
(2.30)
2
PRe ( R1 − RReso )
=
PIn
(1 − R1 RReso ) 2
(2.31)
If R1 = RReso, equation 2.31 implies that there will be no reflection, PRe = 0. This condition is called
Impedance-matching condition. Consider the ideal case where mirrors are lossless, T=1-R, eq. 2.30
can be written as
PC
1
=
PIn 1 − RReso
(2.32)
It can be seen that the enhancement of the optical power is solely depends on resonator reflectance
parameter. If resonator have low loss, the amount of power circulate inside resonator will be large.
For example; if RReso = 0.99, the enhancement of input power is 100 times. Since the amount of
generated power for frequency conversion process is described by the square of fundamental power,
the enhancement of SHG will be 10,000. But it should be noted that this value is only occur in theory,
in reality there are many factors that limit the enhancement; such as non ideal mirrors, mismatch
24
from phase-matching condition, and other factors that contribute to loss.
REFERENCES
[1]
V.G. Dimitriev, G.G. Gurzadyan, D.N. Nikogosyan, “Handbook of Nonlinear Optical
Crystals”, Vol. 64 2nd rev. edition A.E. Siegman, ed. (Springer, New York, 1997).
[2]
D.L. Mills, “Nonlinear Optics: Basic Concepts”, 2nd edition, ed. (Springer, New York,
1998).
[3]
A. Yariv, “Quantum Electrons”, 3rd edition, ed. (John Wiley and Sons, New York, 1988).
[4]
Y. Suematsu, A.R. Adams, “Handbook of Semiconductor Lasers and Photonic Integrated
Circuits”, ed. (Chapman & Hall, London, 1994).
[5]
Carl E. W., Leo H., “Using diode lasers for atomic physics”, Rev. Sci. Instrum.,
Vol.62, No.1, pp. 10-13, 1991.
[6]
“Laser Diode User’s Manual”, Sharp Corporation, pp.17, (1998)
[7]
M. W. Flemming, A. Mooridian, “Spectral Characteristics of External-Cavity Controlled
Semiconductor Lasers”, IEEE J. Quantum Electron, Vol.QE-17, No. 1, pp. 44-59, 1981.
[8]
K. Hayasaka, “Frequency stabilization of an extended-cavity violet diode laser by resonant
optical feedback”, Optics Comm. 206, pp.401-409, 2002.
[9]
T. Laurila, T. Joutsenoja, R. Hernberg, M. Kuittinen, “Tunable external-cavity diode laser
at 650 nm based on a transmission diffraction grating”, Applied Op., Vol.41, No.27,
pp.5632-5637, 2002.
[10]
H. Patrick, C.E. Wieman, “Frequency stabilization of a diode laser using simultaneous
optical feedback from a diffraction grating and narrowband Fabry-Perot cavity”, Rev. Sci.
Instrum., Vol.62, No.11, pp. 2593-2595, 1991.
[11]
A. Wicht, M. Rudolf, P. Huke, R. Rinjkeff, K. Danzmann, “Grating enhanced external
cavity diode laser”, Appl. Phys. B, 2003.
[12]
R.S. Conroy, A. Carleton, A. Carruthers, B.D. Sinclair, C.F. Rae, K. Dholakia, “A visible
extended cavity diode laser for the undergraduate laboratory”, Am. J. Phys., Vol.68(10),
pp.925-931, 2000.
[13]
H. Kogelnik, T. Li, “Laser Beams and Resonators”, Appl. Op., Vol.5(10), pp. 1550-1567,
1966.
[14]
A. Ashkin, G.D. Boyd, J.M. Dziedzic, “Resonant Optical Second Harmonic Generation
and Mixing”, IEEE J. Quantum Electron, Vol.QE-2, No.6, pp.109-124, 1966.
[15]
E.S. Polzik, H.J. Kimble, “Frequency doubling with KNbO4 in an external cavity”, Opt.
Lett., Vol. 16, No. 18, pp.1400-1402, 1991.
[16]
Z.Y. Ou, S.F. Pereira, E.S. Polzik, H.J. Kimble, “85% efficiency for cw frequency doubling
25
from 1.08 to 0.54 μm”, Opt. Lett., Vol. 17, No.9, pp. 640-642, 1992.
[17]
B. Couillaud, L.A. Bloomfield, T.W. Hansch, “Generation of continuous-wave radiation
near 243 nm by sum-frequency mixing in an external ring cavity”, Opt. Lett., Vol.8, No.5,
pp. 259-261, 1983.
[18]
B. Couillaud, T.W. Hansch, S.G. Maclean, “High power CW sum-frequency generation
near 243 nm using two intersecting enhancement cavities”, Opt. Comm., Vol.50, No.2,
pp.127-129, 1984.
[19]
J. Mes, E.J. van Dujin, R. Zinkstok, S. Witte, W. Hogervorst, “Third-harmonic generation
of a continuous-wave Ti: Sapphire laser in external resonant cavities”, Appl. Phy. Lett.,
Vol.82, No.25, pp.4423-4425, 2003.
[20]
W.J. Kozlovsky, C.D. Nabors, R.L. Byer, “Second-harmonic generation of a
continuous-wave diode-pumped Nd:YAG laser using an externally resonant cavity”, Opt.
Lett., Vol.12, No.12, pp.1014-1016, 1987.
26
Chapter 3
Experimental Setups
3.1 INTRODUCTION
This chapter describes the experimental systems of this research using the knowledge from Chapter
2. The research systems are divided into three main parts; the fundamental Second-harmonic
generation system, The SHG system with the using of extended cavity to control laser diode
spectrum, and the SHG system using extended cavity and optical resonator. The first system is the
fundamental SHG system that uses only 660 nm DVD-LD and BBO crystal to generate UV light.
Next system is the SHG system that the spectrum of the DVD-LD is enhanced by the using of
extended cavity from diffraction grating. The enhancement in the amount of generated UV power is
measured and compare with the first system. The last system is the enhancement of the second
system with the addition of optical resonator to increase the fundamental power in order to increase
the efficiency of SHG.
3.2 SYSTEM 1: BASIC SECOND HARMONIC GENERATION SYSTEM
The basic configuration of the SHG system is mainly consists of the fundamental light source and
the nonlinear optical crystal. The main reason that this thesis use Second-harmonic generation
process instead of another type of sum-frequency conversion process is that, the using of single input
source is possible in this scheme. The fundamental input light of the UV generation system is the
continuous wave (CW) from high power DVD writer’s laser diode that has center wavelength
around 660nm [1]. The laser was operated at constant temperature at 25ºC by temperature controller.
The polarization direction of the fundamental light is set to s-polarization, and this polarization
direction will be used again in system 2 and 3. The reason will be explained in the next section. Note
that, all the experiments in this thesis are based on the fundamental light in s-polarization direction.
To set the polarization direction, the polarization filter and the optical power meter are used to
determine the polarization direction, by measure the amount of light pass through the filter at the
specific angle of the laser diode rotation. The polarization direction of the DVD-LD is then adjusted
according to the optimum value of optical power by adjusting of the goniometer that is attached to
the laser diode’s mount. To collimate the spreading beam of the laser diode, the small focused length
(f = 4.6 mm) aspheric lens is put in front of DVD-LD to make the collimate beam.
27
To monitor the spectrum of the fundamental light, the 8/92 (Reflection 8%, and transmission 92%)
beam-splitter is inserted after aspheric lens. The 8% sampled light from beam splitter is coupled into
Optical Spectrum Analyzer (OSA) via fiber optic cable to observe the spectrum of the system.
UV measurement
Photomultiplier
330 nm
OSA
Beam
dump
660 nm
Prism
330 nm
+
660nm
(Stray light)
SHG
R=8%
660 nm
BBO
DVD-LD
660 nm
T=92%
AL
BS
Beam
dump
HEHS
L2
L1
330 nm
+
660nm
Fig. 3.1: Experimental setup 1. AL: f4.6 mm Aspheric lens, BS: 8/92 Beam-splitter, OSA: Optical
Spectrum Analyzer, L1 and L2: f100 mm Plano-Convex lens, HEHS: High Energy Harmonic
Separator, high reflectance at 330nm but transmits 660 nm light.
The collimated beam of fundamental light (660nm) is focused by lens, L1, which has focus length at
100mm. The using of focus beam is required since the amount of generated UV power is inverse
proportional to the beam area. This focused beam is pumped through the nonlinear optical crystal to
generate UV. The nonlinear optical crystal used in this research is the BBO (β-BaB2O4) crystal. This
BBO crystal is the 36.7° type-I BBO crystal that has the dimension a*b*c = 10mm x 5mm x 5mm, a
is the length along the direction of light propagation. The BBO has AR coating at 650nm and 325nm
to decrease optical loss at the fundamental and UV wavelength. From calculation, the
phase-matching angle of this BBO crystal at 660 nm is around 36° so the pumping light direction is
not exactly normal to crystal surface as in the case of designed 650 nm light. The good point of this
is that, the light that is reflected from crystal surface will not go directly back to laser diode facet,
such that it will disturb the operation of the laser diode. From calculation, the walk-off angle is 4.45°.
After the fundamental light is pumped through the BBO, the SHG process occurs. At the output side
of BBO, 660 nm fundamental light together with the generated UV at 330nm are emitted. The UV
28
light and fundamental light are collimated by another lens, L2, that have focus length at 100 mm.
To separate UV light from fundamental light, the 45° high energy harmonic separator is used. This
high energy harmonic separator is specially coated, so that it has high transparency at 660 nm
fundamental wavelength (reflection is less than 0.1%), but has high reflectance at 330 nm UV
wavelength (approximately 99.9%).
Since the amount of generated UV is not large enough to be accurately measured by commercial UV
photodetector, the photomultiplier is used. But photomultiplier is very sensitive to the stray light, and
since high energy harmonic separator will reflect some amount of fundamental light, so the direct
position of photomultiplier in front of high energy harmonic separator night damage the
photomultiplier due to high power stray light. This problem is solved by insert a prism to further
separate UV and fundamental light direction. Then the photomultiplier is put to measure the amount
of generated UV power from SHG, while the fundamental light is discarded at beam dump (Small
paper box).
3.3 SYSTEM 2: SHG SYSTEM WITH SPECTRUM ENHANCED DVD-LD
The schematic of this experiment setup is shown in Fig. 3.2. For this system, the spectrum
controlling and narrowing technique, the extended cavity is added.
The extended cavity is constructed by insert the diffraction grating between the 8/92 beam-splitter
and lens L1. The grating is chosen such that only a first order refraction of fundamental light can
occur. The diffraction grating used in this research is the 12.7 x12.7 mm, 2400 lines/mm VIS grating
from Edmund optic. For the fundamental light at 660 nm, the angle between the normal of grating
surface and fundamental light direction is calculated to be around 52° for Littrow configuration. The
first order refraction light is reflected back into the laser diode cavity by tuning the grating angle.
The horizontal angle of the grating is tuned by the rotator, while the vertical angle is tuned by
goniometer. The zero-order reflection of the diffraction grating provides the input light to the SHG
part (See Fig. 3.2). Note that, for the s-polarization, it is observed that the first-order diffraction
reflect approximately 10% of the fundamental input power, while the zero-order reflection reflect
approximately 85% of fundamental input power. This ratio is good for making the optical feedback,
while still be able to transmit large portion of fundamental light. For the case of p-polarization, the
reflection is around 80% while the transmission is around 3%. Since the reflection is too high, the
p-polarization direction is not used in this research.
29
Extended Cavity
Diffraction
Grating
SHG
HEHS
T~80%
660 nm
R~10%
BBO
L1
L2
330 nm
+
660nm
Beam
dump
330 nm
+
660nm
(Stray light)
OSA
BS
Prism
330 nm
AL
Photomultiplier
DVD-LD
660 nm
Beam
dump
UV measurement
660 nm
Fig. 3.2: Experimental setup 2. Diffraction grating: 2400 lines/mm VIS diffraction grating, AL: f4.6
mm Aspheric lens, BS: 8/92 Beam-splitter, L1 and L2: f100 mm Plano-Convex lens, HEHS: High
Energy Harmonic Separator, high reflectance at 330nm but transmits 660 nm light.
For another part of the system other than the extended cavity such as SHG and UV measurement
part, the descriptions are as same as the basic SHG system in the previous section.
3.4 SYSTEM 3: SHG SYSTEM WITH SPECTRUM ENHANCED DVD-LD AND
OPTICAL RESONATOR
For this system, the SHG part is inserted inside the optical resonator to enhance the fundamental
wavelength power, thus increase the amount of UV. The optical resonator used in this experiment is
the bowtie-shape cavity (See Fig. 3.3) which is one type of the optical resonator. There and several
advantages of this type of configuration over the Fabry-perot configuration. In a Febry-perot
configuration the light rejected by the input coupling mirror can reflects back into the laser diode,
which may disturb the operation of the laser. For the bowtie configuration, the input coupling mirror
is tilted with respect to the incoming fundamental beam, so this problem does not occur. Also, in a
Fabry-perot configuration, the generated second harmonic light propagates both in forward and
backward directions and it is difficult to combine these beams. In a bowtie configuration, the second
harmonic is generated in the forward direction only.
For this system, the laser beam that is already enhanced by extended cavity is coupled into the
30
bowtie cavity via the input coupling mirror. The input coupling mirror of the resonator is the 45°
s-polarization, 60/40 high energy beam splitter (60% reflection, and 40% transmission) coated at 670
nm. The 60/40 ratio from calculation is use to compensate the loss inside the resonator. Mirror M1,
M2, and M3 are the broadband mirrors that have a high transmission for visible wavelength. For
these mirrors, the reflection at 660 nm is approximately 91% by measurement. In order to adjust the
cavity length for phase-matching condition, mirror M1 is attached to the PZT, which is controlled by
DC voltage source. The generated UV is extracted from the resonator by high energy harmonic
separator, then measure by the same technique as explained in system 1.
Extended Cavity
Diffraction
Grating
T~80%
Ring resonator
Input Coupling
Mirror
PZT
M1
R~10%
SHG
OSA
BS
M3
M2
L1
BBO
L2
HEHS
DVD-LD
AL
Prism
330 nm
660 nm
Photomultiplier
660 nm
Beam
dump
UV measurement
Fig. 3.3: Experimental setup 3. Diffraction grating: 2400 lines/mm VIS diffraction grating, AL: f4.6
mm Aspheric lens, BS: 8/92 Beam-splitter, OSA: Optical Spectrum Analyzer, L1 and L2: f100 mm
Plano-Convex lens, M1, M2, and M3: Broadband mirror for visible wavelength.
31
Chapter 4
Results and Discussion
4.1 BASIC SECOND HARMONIC GENERATION SYSTEM
The experiment is performed by the continuous wave fundamental input from DVD laser diode. The
polarization direction is set to s-polarization. The maximum injection current used in this experiment
is 135 mA. The spreading beam of the DVD-LD is collimated by the aspheric lens. The collimated
beam has an elliptical shape of approximately 6mm x 3mm in diameter. The spectrum of the
DVD-LD is monitored by optical spectrum analyzer (See Fig. 4.1 and 4.2).
(a)
660.11 nm
100 mA
660.74 nm
(b)
659.69 nm
135 mA
80 mA
Fig. 4.1: (a) The spectrum of the DVD-LD at 100 mA injection current, (b) The spectrums of the
DVD-LD at low injection current (80 mA), and high injection current (135 mA).
At low injection current, the spectrum is operate in single mode operation, while at high injection
32
current, the spectrum bandwidth is widen and operate in multimode. Also, it can be seen that when
the injection current is increased, the center wavelength of the DVD-LD is shifted to higher value.
From figure 4.1; at 80 mA injection current, the center wavelength of the laser diode is at 659.69 nm.
While at 135 mA injection current, the center wavelength is shifted to 660.74 nm. From author’s
experience, the amount of shifted in center wavelength is not the same for all laser diodes of the
same model. For example, for the previous DVD-LD that author used; at 135 mA, the center
wavelength is shifted to around 662 nm. At the fix injection current, the spectrum of the DVD-LD
shows the sign of unstable operation. (See Fig. 4.2). At t1 and t3, the spectrum of the DVD-LD is
operate in multimode operation, and has wide spectrum bandwidth. While at t2, the DVD-LD is
operate in single mode operation. This fluctuated spectrum is also occurs even with the using of
temperature controller. From, observation, it is quite impossible to stabilize the spectrum of the
DVD-LD by using the temperature controller or current controller alone.
t3
t2
t1
Fig. 4.2: Spectrum of DVD-LD at 100 mA injection current. The measurement is plot 3 times. The
spectrum is not stable.
When lens L1 is inserted into the system to focus the fundamental beam, due to a small reflection at
the surface of the lens, the angle of the lens have to be tilted a little to avoid the direct optical
feedback to the laser diode. This is to prevent the disturbance from unwanted reflected light. Then
lens L2 is added to re-collimate the beam. When the BBO is first inserted at the focus point of L1,
the surface plane of the BBO is roughly set to be normal to fundamental beam direction since it is
still impossible to accurately set the phase-matching angle yet. After the insertion of high energy
harmonic separator (HEHS), since HEHS is quite thick (0.635 cm), there will be 2 reflection of the
fundamental light that are parallel to each other (See Fig 4.3). At surface 1, the UV along with the
33
small amount of fundamental light are reflected. For surface 2, small amount of fundamental light is
reflected. Since the reflection at surface 2 contain only fundamental light, it is blocked by a sheet of
paper to prevent it from interfering with the UV measurement.
Collimated beam from L2
(Fundamental + UV)
S1
UV+ Small amount of fundamental light
S2
HEHS
Fundamental light
Fundamental light
Fig. 4.3: Two reflections at the HEHS. At surface 1, the UV and small amount of fundamental light
is reflected. While at surface 2, small reflection of fundamental light is occurs.
When prism is inserted, the UV and the fundamental light are separated from each other by some
angle. But the exact location of UV is still unknown, since the light at wavelength of 330 nm is
unable to be detected by bare eyes. And the randomly varying of the position of photomultiplier to
find the location of UV takes a lot of time and inaccurate. Therefore, the exact location of UV is
detected by a UV detection card, which will illuminate at the present of UV light. So, by putting the
UV detection card at the approximate location of UV and vary the angle of BBO, the location of UV
can be found. Then, the photomultiplier is put at that location to measure the amount of UV.
The relationship between the generated UV and the optical power of fundamental input light is
plotted in Fig. 4.4. The result shows the non-uniform line, this is occurring as expect due to the
instability of the fundamental input spectrum. When observing the amount of generated UV from
photomultiplier, the value is not stable; there is the sign of slightly increasing and decreasing in UV
power. From the graph, at the high injection current, the amount of generated UV is saturated, due to
many factors; the saturation of I-L curve of the laser diode, wide spectrum bandwidth, and the
shifted in the center wavelength of DVD-LD. The maximum generated UV at 135 mA injection
current (Fundamental optical power pumped into BBO is 44.79 mW) is 1,236 nW. This is equal to
2.76*10-３% conversion efficiency.
34
From above results, it can be concluded that, the simple UV generation system contains only BBO
and DVD-LD, is possible but it is not good enough for the application that require stable power UV
light source. This is due to the fluctuation of the DVD-LD spectrum that leads to the fluctuation in
UV power. Therefore, the stable spectrum fundamental input is required for SHG system.
Generated UV VS Fundamental light
1400
Generated UV power (nW)
1200
1000
800
600
400
200
0
0
5
10
15
20
25
30
35
Fundamental optical power (mW)
40
45
50
Fig 4.4: Generated UV optical power VS Fundamental optical power.
4.2 SHG SYSTEM WITH SPECTRUM ENHANCED DVD-LD
In this system, the reflection diffraction grating is used to create the extended cavity to stabilize the
fundamental input spectrum from DVD-LD. The VIS 2,400 lines/mm diffraction grating is inserted
between the beam-splitter and Lens L1. The first-order reflection of the grating is used as the optical
feedback to the DVD-LD. Once the first-order reflection is accurately sent back to the laser diode
cavity, the stable operation of the DVD-LD’s spectrum is observed (See Fig. 4.5 and Fig. 4.6). Also,
by tuning the angle of the grating by a rotator, the tuning of the DVD-LD center wavelength is
possible. From observation, the tuning range of the DVD-LD center wavelength is 6 nm for the
injection current of 100 mA (See Fig.4.7). For the tuning range larger than this value, it is seem that
the direction of the first-order reflection light is out of the surface of the laser diode chip. Therefore,
the original emission wavelength of the DVD-LD is back. It should be noting that, even the
35
removing of the temperature controller; this wavelength stability operation does not change.
(a)
660.007 nm
100 mA
(b)
660.019 nm
(135 mA)
660.019 nm
(80 mA)
Fig. 4.5: (a) The spectrum of the DVD-LD at 100 mA, (b) The spectrums of the DVD-LD at low
injection current (80 mA) and high injection current (135 mA).
t1
t2
t3
Fig. 4.6: The stable spectrum of DVD-LD at 100 mA injection current.
36
t4
From figure 4.6, it can be seen that the spectrum of the DVD-LD is operate in single mode operation
with narrower bandwidth compare to the system without grating as in figure 4.1. Also, there is no
difference between center wavelength of DVD-LD at low and high injection current.
666.02 nm
659.45 nm
Fig. 4.7: The 6 nm tuning range of the laser diode’s center wavelength when the grating is used. The
small spectrum at the center of the figure is the original emitted wavelength of the laser diode
without grating.
The center wavelength of the DVD-LD in this experiment is first set to around 660 nm to make it
according to the theoretically value of the DVD-LD. The relationship between the generated UV and
the optical power of fundamental input light of this system at 660nm fundamental wavelength is
plotted in figure 4.8. At injection current of 135 mA, the maximum generated UV is 1,690 nW
(Fundamental optical power is 40.01 mW), the conversion efficiency is 4.22*10-3 %. The
relationship between generated UV and the fundamental input wavelength shows the smooth
curvature relationship. This is due to the stability of the fundamental input wavelength. Also, there is
no sign of saturation in the generated UV power as occur in the previous system. So it might be able
to conclude that, the effect of saturation of the generated UV of system 1 is the result of the spectrum
fluctuation and the shifted in center wavelength of the DVD-LD. But it should be note that, at 135
mA, the maximum fundamental input power for the system with grating is around 40 mW while the
previous system without grating is 45 mW. This 11% reduction in fundamental optical power is due
to the reflection and absorption at the diffraction grating. However, the system with the diffraction
grating still has higher UV generation efficiency than the system without one.
37
Generated UV VS Fundamental light
1800
Generated UV power (nW)
1600
1400
1200
1000
800
600
400
200
0
0
5
10
15
20
25
30
Fundamental Optical power (mW)
35
40
45
Fig. 4.8: Generated UV optical power VS Fundamental optical power.
Generated UV VS Fundamental light
3500
G enerated UV power (nW
3000
2500
System with grating
2000
1500
1000
500
System without grating
0
0
10
20
30
Fundamental Optical power (mW)
Fig. 4.9: Comparison between system 1 and system 2.
38
40
50
I-L Characteristic
50
Optical power (mW)
45
40
With grating
Without grating
35
30
25
20
15
10
5
0
0
20
40
60
80
100
120
140
160
Injection current (mA)
Fig. 4.10: I-L characteristic comparison between system with grating and system without grating
In order to compare the UV generation efficiency between 2 systems, the injection current of the
experiment is set to higher value in order to achieve the approximately same value of fundamental
optical power as the system 1 (See Fig. 4.9). At the fundamental optical power of 44.45 mW, the
generated UV power of system 2 is 2,976 nW. This shows that the efficiency of UV generation of the
system with grating is approximately 2.4 times larger than the system without grating. And since, the
amount of generate UV of system 1 shows the sign of saturation at 135 mA, so it might be able to
assume that, as the injection current of DVD-LD increase, efficiency of UV generation of system 2
compare to system 1 will keep increasing.
Next, the wavelength tuning ability of the DVD-LD is tested. The center wavelength of the
DVD-LD is tuned from 659 nm to 664 nm, which is according to the tuning of 5 nm (2.5 nm UV
tuning range), by tuning the angle of diffraction grating. From figure 4.7, it shows that the center
wavelength of the DVD-LD can be tuned from 659-666 nm, but this tuning range is for the fix
injection current of 100 mA. As the injection current increase, the effect of the wavelength shifting
as showed in figure 4.1 start to compete with the effect of optical feedback. For the wavelength less
than 659 nm, this effect causes the emerging of the original center wavelength of the DVD-LD.
Another limitation of the tuning is due to the optical feedback’s direction misalignment. When the
angle of the grating is tuned, the reflected angle is change, when this angle misalignment is large
enough; the original center wavelength of the DVD-LD is emerging, since the optical feedback is not
directed to the laser diode facet. So, the experiment is conducted at the tuning range of the DVD-LD
that can cover the wide range of injection current, which is 659-664 nm (UV range from 329.5 nm to
39
332 nm). The result of the experiment is shown in figure 4.11. From the graph, it can be seen that the
results show the same trend of stable and smooth relationship. And the amounts of the generated UV
from each center wavelength are close to each other. So it can be concluded that the tuning of UV
wavelength is possible.
Generated UV vs Fundamental for various fundamental wavelength
3500
Generated UV power(nW)
3000
2500
659nm
660nm
661nm
662nm
663nm
664nm
2000
1500
1000
500
0
0
5
10
15
20
25
30
35
40
45
50
Fundamental Optical power(mW)
Fig. 4.11: The amount of generated UV, the center wavelength of the DVD-LD is tuned from
659-664 nm.
I-L Characteristic
50
45
659
660
661
662
663
664
Optical power (mW)
40
35
30
25
nm
nm
nm
nm
nm
nm
20
15
10
5
0
0
20
40
60
80
100
120
140
160
Injection current (mA)
Fig. 4.12: I-L characteristic comparison between tuning wavelength of DVD-LD
40
180
It can be concluded from these results that, the using of extended cavity created by diffraction
grating can enhance the SHG generation, for both wavelength stability and the UV optical power
(2.4 times increase). These enhancements are possible due to the stability and the single mode
operation of the spectrum of the fundamental input light. Also, the using of diffraction grating adds
the UV’s wavelength tuning capability to the SHG system.
4.3 SHG SYSTEM WITH SPECTRUM ENHANCED DVD-LD AND OPTICAL
RESONATOR
The purpose of the experiment in this section is to determine the efficiency of the SHG system when
the resonator is used. Actually, the system in this section is the addition of the previous system. The
center wavelength of the DVD-LD is first tuned to 660 nm by the tuning of grating. Then, the stable
wavelength fundamental light from grating is pumped into the resonator through input coupling
mirror (60/40 Beam splitter). From measurement, the optical power loss inside the resonator is
approximately 40% due to the absorption from mirrors, lens, and BBO crystal. So, to achieve the
impedance matching condition, the 40% transmission beam-splitter is used. The amount of generated
UV power in this experiment is shown in figure 4.13. The graph is plotted between the amount of
generated UV power and the injection current of the DVD laser diode. The plotting of the injection
current is used instead the fundamental optical power is because the exact fundamental optical power
inside the resonator is difficult to measure. Since the insertion of the optical power meter inside the
resonator will interrupt the circling fundamental wave. And to measure the amount of fundamental
power from stray light from the HEHS is not accurate due to low optical power (<1% of total
fundamental power).
From the result, it seems that the resonator created in this experiment is not successful since the
amount of generated is low compare to the system without resonator (System 1 and system 2). The
amount of generated UV power from the system without circling fundamental wave is 246 nW
(Mirror M3 is blocked by a sheet of paper to interrupt the circling light), while the system with
circling wave (The paper is removed) is 369 nW. From theory, the amount of generated UV should
be much more than this value. It is expected to be in the order of sub mW, due to the abrupt
increasing of the fundamental optical power at the resonance condition.
The decreasing in UV power in this system is due to the decreasing of the fundamental input power
from beam-splitter and flat mirrors. Theoretically, at the resonance condition, there will be no
reflection at the beam-splitter. But from the experiment, this condition can not be achieved, so
approximately 60% of the injection fundamental optical power is reflected at the beam-splitter. But
41
none the less, when consider only the amount of generated UV power, specific for this experimental
setup. The using of circling fundamental wave can slightly increase the amount of generated UV.
The 50% increasing of the generated UV power is observed as shown in Fig. 4.13. This increasing in
the generated UV power is due to the circling fundamental power in the system.
Injection current vs Generated UV
Generated UV power (nW)
400
350
300
250
Without resonator
With resonator
200
150
100
50
0
0
50
100
Injection Current (mA)
150
200
Fig. 4.13: The amount of generated UV power of the SHG system using optical resonator.
In conclusion, at present time, the resonator can not be perfectly created. The abrupt increasing in the
amount of fundamental power is not happened as expected. The reason of this failure is possibly
from the inaccuracy of the optical beam alignment in the system. From the observation, as the beam
progress in the resonator, the beam shape is begun to distort and lose its sharpness. This might lead
to the not collimate condition. Another reason is possibly from the high loss in the system. In normal
system of optical resonator, the loss inside the resonator is less than 5%, but the optical loss of the
experimental system in this research is around 40%. Combine all of this reasons, the theoretical
resonator can not be created in this research.
42
Chapter 5
Conclusion
In this thesis, the coherent UV light source from the DVD laser diode and nonlinear optical crystal is
investigated, and the technique to stabilize the laser diode’s spectrum to enhance the efficiency of
SHG process is successfully used.
At the present time, the coherent UV light sources such as excimer laser and solid-state laser are
expensive, bulky, and difficult to fabricate, so the new system of UV generation that can solve these
problems is needed. The best candidate for coherent light source for these problems is the laser diode.
The reasons that laser diode is interested is because it can solve the problem of size and price. But
since the laser diode that can generate the light at UV wavelength is difficult to fabricate due to the
requirement of high energy band-gap semiconductor material, another method to generate UV rather
than the direct emission of photon from semiconductor material must be used. The solution to the
problem is the using of Second-harmonic generation (SHG) process, which is the technique that can
converts the light at one frequency to another frequency, by the using of nonlinear optical crystal.
Normally, laser diode can generated the optical power around 10-20 mW, but due to the high
improvement in the semiconductor technology and the demand of the consumer’s market, the low
price and high power DVD’s laser diodes that can generate optical power greater than 40 mW are
available. However, the problem of the using of DVD laser diode in SHG process is that, the DVD
laser diodes have fluctuate output spectrum. This fluctuation in the spectrum leads to the fluctuation
in the amount of generated UV power. This is because the spectral acceptance bandwidth of the
nonlinear crystal is narrow. This fluctuation in UV power is not good for the application that requires
wavelength and power stability such as spectroscopy. So, the stabilization of the spectrum of DVD
laser diode is needed. The solution to this problem is the using of optical feedback, which the small
amount of the output light from the laser diode is fed back to the laser diode’s facet. Even there are
many techniques that can provide the optical feedback to the laser diode, as the objective of this
research is to create the low cost and easy to fabricate UV light source, the diffraction grating is used
as the optical feedback component. The advantage of the using of diffraction grating over other
techniques is that, only one more component is added to the system. The grating used in this
research is the holographic grating which can be manufacture in mass amount and this mean the
price is low. From the experimental result, it shows that the using of grating can stabilize the
spectrum of the DVD laser diode, and suppress the spectrum bandwidth. Another advantage of the
43
using of diffraction grating is that, the tuning of the center wavelength of the DVD laser diode is
possible since diffraction grating is the wavelength selective optical component. The tuning can be
done by tuning the angle of the diffraction grating such that the wavelength of the feedback is
slightly changed according to the angle. From observation, the DVD laser diode wavelength tuning
range of 6 nm is possible when the injection current is around 100 mA. The problem of the using of
diffraction grating is that it takes some times to set up the direct optical feedback to the laser diode
facet. But this problem can be solved by the good mechanical design. Another minor problem from
the using of diffraction grating is that, the direction of the fundamental optical beam from the laser
diodes is not the same as the original direction of the beam from laser diode. But again this problem
can be solved by the good mechanical design or the using of transmission grating. None the less, the
using of diffraction grating enhances the spectrum condition of the DVD laser diode. This leads to
the enhancement of the SHG process efficiency. The experiment result of the SHG system with the
diffraction grating shows that 2.4 times increasing in the generated UV power is achieved, with the
addition of stable power operation. From the observation it is believed that the amount of
improvement can be greater as the fundamental power of the DVD laser diode is increased, since the
amount of generated UV from the system without grating is saturated at high optical power, while
for the system with grating this saturation is not happened. The tuning ability of the center
wavelength of the DVD laser diode is also another interesting feature of the using of diffraction
grating in SHG process. From the experimental result, the tuning range of the DVD laser diode that
can generate stable UV power is 5 nm (2.5 nm UV wavelength tuning). This decreasing in the tuning
range is the result from the wavelength shifting nature of the laser diodes, as the injection current
increase. The result shows that the amounts of the generated UV power between these wavelengths
are close to each other, so it can be said that the tuning of UV wavelength is possible. Next, the
optical resonator is used in the system. This requirement of optical resonator for the SHS system is
because, even the using of diffraction grating can enhance and stabilize UV power, the amount of
generated UV is still too low to be used in the real application that require the UV power in the order
of several mW. The maximum generated UV for the diffraction grating in this thesis is
approximately 3 μW. So, the technique to increase the amount of fundamental power of SHG
system is needed. But it seems that the optical resonator used in this research is not perfect so the
abrupt increasing of fundamental power as in the theory is not happen. The amount of generated UV
power is less than the system without resonator. But none the less, when compare only to the system
using resonator, when the circling fundamental power is used, the amount of generated UV power is
increase 50%. Still, this system needs to be improved in order to be used in real applications.
For the future of the system in this thesis, the wavelength tuning ability of the system need to be
further investigated. At the present time, even the wavelength tuning is possible, the 2.5 nm UV
44
wavelength tuning range of the system is still not enough to be called tunable UV generation system.
One of the solutions to might be the using of transmission grating. The reason that the experiment
using transmission grating is not conducted in this research is that, the price of this type of grating is
quite high, and the ability of the enhancement from grating for SHG system is unknown at the time
of system design. Another important point that needed to be done is the technique that can increase
the amount of fundamental power for the SHG system. This is actually the most important matter,
since despite the good spectrum condition or the tunable feature; this system will not be much of the
practical used if the amount of UV power is not enough for the real applications. Once this problem
of the increasing of the fundamental power is solved, it is believed that, the system of this thesis will
have a bright future for many applications that require low cost, small size, and simple to fabricate
coherent UV light source.
45
APPENDIX
RAY TRANSFER MATRIX
A propagate light in a given cross section of an optical system is characterized by its distance x from
the optic (z) axis and by the angle or slope x’ with respect to that axis. The ray path passing through
a given structure depends on the optical properties of the structure and on the input condition (x1 and
x1`). The light output quantities x2 and x2` are linearly dependent on the input. This relationship can
be written as
x2
A B x1
=
x2′ C D x1′
(A.1-1)
The ABCD matrix is called the ray transfer matrix. The list of transfer matrix for elementary optical
structures can be found in textbook of A.Yariv “Quantum Electronics” third edition. The propagation
of the light beam through the complete optical resonator system (A sequence of optical components,
nonlinear optical crystal, and propagation distance through air) can be described by the product of
the series of ABCD matrices (From each component).
Light rays that propagate within the resonator system can be described by an n-periodic sequence of
ray transfer matrix as shown in figure A.1.
A B
C D
x0
x0 `
A B
C D
A B
C D
A B
C D
x1
x1 `
A B
C D
xn
xn `
Fig.A.1: Periodic sequence of identical system, each characterized by its ray transfer matrix.
This periodic sequence can be described as either stable or unstable. Sequences are stable when the
trace (A+D) obey the inequality
46
1
−1 < ( A + D ) < 1
2
(A.1-2)
The rays passing through a stable system are periodically reshaped. While the unstable system,
propagation ray will become more and more dispersed as they propagate through the resonator.
47
BASIC PROPERTIES OF BBO (β-BaB2O3)
A.2-1. Structural and Physical Properties
Crystal Structure
Trigonal, space group R3c
Cell Parameters
a = b = 12.532Å, c = 12.717Å, Z = 6
Melting Point
1095±5oC
Transition Temperature
925± 5oC
Optical Homogeneity
△n ≈10-6/cm
Mohs Hardness
4.5
Density
3.85 g/cm3
α < 0.001 cm-1 ( λ = 1064 nm )
α < 0.01 cm-1 ( λ = 532nm )
Linear Absorption Coefficients
α < 0.5 cm-1 ( λ = 2550nm )
Hygroscopic Susceptibility
Low
Resistivity
> 1011 ohm-cm
εT11/εo: 6.7, εT33/εo: 8.1
Relative Dielectric Constant
Tan δ, < 0.001
Thermal Expansion Coefficients
a, 4 x 10-6/K
(in the range of 25oC - 900oC)
c, 36 x 10-6/K
Thermal Conductivity
┴c, 1.2 W/m/K ; ║c, 1.6 W/m/K
A.2-2. Linear Optical properties
Transparency Range
189 - 3500 nm
Refractive Indices
at 1.0642 µm ne = 1.5425, no = 1.6551
at 0.5321 µm ne = 1.5555, no = 1.6749
at 0.2660 µm ne = 1.6146, no = 1.7571
Thermal-Optic Coefficients
dno/dT = - 9.3 x 10-6/oC
dne/dT = -16.6 x 10-6/oC
Sellmeier Equations
N2o(λ) = 2.7359+0.01878/(λ2-0.01822)-0.01354 x λ2 (λ in µm,
T=20oC)
N2e(λ) = 2.3753+0.01224/ (λ2-0.01667)-0.01516 x λ2 ( λ in µm,
48
T=20oC)
A.2-3. Nonlinear Optical properties
Phase-Matching Output Range
189 - 1750 nm
NLO Coefficients
d11 = 5.8 x d36(KDP)
d31 = 0.05 x d11, d22 < 0.05 x d11
Electro-Optic Coefficients
γ11 = 2.7 pm/V, γ22, γ31 < 0.1γ11
Half-Wave Voltage
48 KV (at 1064 nm)
Damage Threshold
at 1.064 µm
5 GW/cm2 (10 ns); 10 GW/cm2 (1.3 ns);
at 0.532 µm
1 GW/cm2 (10 ns); 7 GW/cm2 (250 ps);
at 0.266 µm
120 MW/cm2 (8ns).
49