Download Numerical Analysis of Fifth-Harmonic Conversion of Low

Jpn. J. Appl. Phys. Vol. 42 (2003) pp. 4318–4324
Part 1, No. 7A, July 2003
#2003 The Japan Society of Applied Physics
Numerical Analysis of Fifth-Harmonic Conversion of Low-Power Pulsed Nd:YAG Laser
with Resonance of Second Harmonic
Lien-Bee C HANG1 , S. C. W ANG1 and A. H. K UNG1;2
1
2
Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu 30050, Taiwan, ROC
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, 10764, Taiwan, ROC
(Received January 22, 2003; accepted for publication March 13, 2003)
A model for the fifth-harmonic generation of pulsed IR lasers involving an external ring cavity resonating at the second
harmonic has been developed. Numerical analysis is performed to show the relative effects of the pulse delay, input
polarization, and orientation of the nonlinear crystals on the fifth harmonic power. The results are validated by published
experimental results. The model is used to analyze and obtain the optimal combination of nonlinear optical crystals for the
fifth-harmonic generation. Our calculation shows that the combination of LiB3 O5 (LBO), CsLiB6 O10 (CLBO), and CLBO
crystals for the second-harmonic, fourth-harmonic, and fifth-harmonic generation steps respectively gives an approximate
conversion of 30% from the fundamental to the fifth harmonic power, resulting in 2 W at 213 nm for an input of 7 W at
1064 nm. [DOI: 10.1143/JJAP.42.4318]
KEYWORDS: second-harmonic generation (SHG), fourth-harmonic generation, fifth-harmonic generation, sum-frequency
generation, -BaB2 O4 (BBO), CsLiB6 O10 (CLBO), deep ultraviolet, diode-pumped
1.
Introduction
High power all-solid-state ultraviolet (UV) and deepultraviolet lasers have been in demand for various industrial
applications such as fabrication of fiber gratings and
precision material processing, and as a precision microsurgery tool. Such applications in turn demand lasers that are
robust, efficient, and easy to operate. In the last few years,
there are several reports on multi-watt solid-state UV lasers
based on fourth-harmonic generation (4HG) of diodepumped lasers.1,2) In most of these reported work, high
power UV generation requires either a very expensive high
power laser, or focusing a low power laser tightly to reach
sufficient intensity for efficient conversion. However, tight
focusing leads to severe thermal beam distortion and
dephasing. In order to overcome these shortcomings, we
developed an alternative method of producing high power
UV radiation with good beam quality and long operating
lifetime that is suitable for use with commercially-available
mid- to low-power diode-pumped solid-state lasers.
Our approach employs a single external ring cavity for
resonance-enhanced second harmonic generation (SHG).
Resonant-cavity enhancement is a powerful technique and
has long been used for frequency doubling of low-peakpower coherent sources. Efficient SHG based on singlyresonant external cavity at the fundamental has been
successfully demonstrated for continuous wave (CW),3–8)
quasi-CW,9,10) or pulsed11) laser. The approach was extended to 4HG by the use of two resonant cavities in
series12,13) and to sum frequency generation (SFG) by
simultaneously resonating at both the fundamental lasers.14)
In our case we incorporate two SHG stages inside one
cavity. The principal idea is to trap the SHG generated in the
first doubling stage inside the ring cavity. The cavity length
is adjusted to equal to an exact multiple of the trapped
wavelength. This enables constructive interference of the
fundamental and the second-harmonic waves to build up the
intracavity intensity of the SHG. Consequently the conversion to the fourth harmonic in the second doubling stage is
E-mail address: [email protected]
substantially increased. The use of external enhancement
cavity makes it possible to employ a larger beam size than in
the single-pass arrangement for the same conversion
efficiency from the fundamental to the fourth harmonic.
Owing to a larger beam size and a widened pulse width
caused by the resonance condition, the peak power density
as well as the energy density of the UV radiation are lower
than those for the single-pass arrangement. Hence the
external cavity enhancement can reduce the heating of the
crystal that is caused mainly by absorption of the fourth
harmonic.
This technique was successfully demonstrated with both a
single-longitudinal-mode Q-switched lasers15,16) and a
diode-pumped multi-longitudinal-mode Q-switched laser,17)
achieving power conversion efficiency from the fundamental
to the fourth harmonic of 39.5% and 30% respectively. More
recently watt-level fourth-harmonic output was obtained.18)
Production of the fifth harmonic by sum-frequency mixing
of the fourth harmonic with the residual fundamental
radiation can conveniently be done in a ‘‘delta’’ configuration of the ring cavity used in latter work. Results of the
generation of the fifth harmonic using this approach were
reported at the same time.
In order to guide the design of future UV generation
systems, a model was developed using plane-wave approximation and a single-longitudinal-mode pulsed laser to
analyze the generation of fourth-harmonic radiation in a
ring cavity that resonates at the second-harmonic wavelength. The parametric dependence of the conversion
efficiency, including dependence on the input laser power,
roundtrip cavity loss, roundtrip phase shift, and the crystal
nonlinear susceptibility, was obtained.16) Separately and
independently, a detailed analysis for third harmonic generation in a ring cavity was reported by Moore and Koch.19)
In this paper, we report the results of a numerical simulation
for the generation of the fifth harmonic by summing the
fourth-harmonic radiation generated from a ‘‘delta’’ ring
cavity and the residual fundamental radiation. We first
present a model calculation using parameters from published
experimental conditions to show and compare the relative
effects of the pulse delay, input polarization, and orientation
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L.-B. C HANG et al.
of the nonlinear crystals on the output power. Finally, since
-BaB2 O4 (BBO) and CLBO nonlinear optical crystals are
quite readily commercially available nowadays for deep UV
generation,20–23) we present a calculation using our model to
compare the merits of using these two crystals for efficient
fourth and fifth-harmonic generation (5HG) of a Q-switched
diode-pumped Nd:YAG laser.
2.
Theoretical Model
2.1 Basic equations
The analysis of 5HG follows closely the one that was
developed for 4HG described in ref. 16. The model assumes
plane-wave interactions and neglects the effects of distributed absorption loss and beam walk-off in the nonlinear
optical crystals. Wave propagation is assumed in the near
field so that optical diffraction is ignored. The optical
arrangement is shown in Fig. 1, which consists of a ‘‘delta’’
ring cavity configuration for the 4HG, and the summing of
the fourth-harmonic output with the collinear residual
fundamental radiation to obtain the fifth harmonic. In the
treatment, we consider first the case of 4HG in the ring
cavity and then calculate the fifth-harmonic summing
process. In order to facilitate both type I and type II
phase-matching, we treat SHG as a degenerate sumfrequency-mixing process. The coupled amplitude equations
for SFG are described by the following set of equations:24–26)
dE1
d !1
ð1aÞ
¼ j
E3 E2
c
dz
n1
dE2
d !2
ð1bÞ
¼ j
E3 E1
c
dz
n2
dE3
d !3
ð1cÞ
¼ j
E1 E 2
c
dz
n3
where !3 ¼ !1 þ !2 , E1 , E2 , E3 are the electric field
amplitudes corresponding to !1 , !2 and !3 respectively. We
assume the plane wave is traveling in the þz direction with
the form ejð!tkzÞ .27) d is the effective nonlinear coefficient
and ni are the indices p
offfiffiffiffiffiffiffiffiffiffiffiffi
refraction at the three respective
frequencies. Let 2i ¼ "0 =0 ni =2, i ¼ i Ei and z0 ¼ z=l,
where l is the length of the NLO crystal, then equations (1a)
to (1c) can be rewritten as:
M3
loss LB
532 nm
delay
Half-wave plate
1064 nm
loss LA
crystal A
for SHG
M1
crystal B
for 4HG
M2
loss L266
and L1064
1064 nm
266 nm
crystal C
for 5HG
213 nm
Fig. 1. Schematic representation of the model used for the numerical
analysis. M1-M3 mirrors are highly reflective for second-harmonic
radiation and highly transmissive for fundamental and fourth-harmonic
light.
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d1
¼ j1 3 2
ð2aÞ
dz0
d2
¼ j2 3 1
ð2bÞ
dz0
d3
¼ j3 1 2
ð2cÞ
dz0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip
ffiffiffiffiffiffiffiffiffiffiffiffi
where
i ¼ lpffiffiffiffiffiffiffiffiffiffiffiffi
2=n1 n2 n3 4 0 ="0 ðd!i =cÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
l 754=n1 n2 n3 ðd!i =cÞ, ji j2 ¼ "0 =0 ni jEp
=2 is the inteni j ffiffiffiffiffiffiffiffiffiffiffiffi
sity of the ith component, i ¼ 1; 2; 3 and 0 ="0 ¼ 377 .
The length of interaction is normalized from l to unity to
facilitate the numerical calculation, and the unit of i is
m=W 1=2 . The input is a single monochromatic pulse with a
Gaussian temporal and transverse spatial profile given by:
r2
t2
ð3Þ
Ef / exp 2 exp 2 ln 2 2
w0
where Ef is the fundamental radiation field, is the temporal
width at full-width-half-maximum, and w0 is the (1/e2 ) beam
waist.
p For type I phase-matched generation, E1 ¼ E2 ¼
Ef = 2 and for type II interaction,
E1 ¼ Ef cos ð4Þ
E2 ¼ Ef sin ð5Þ
where is the angle between the polarization of Ef and the z
axis of the nonlinear crystal.
2.2 Numerical simulation
With reference to Fig. 1, the fundamental is injected into
crystal A, which generates the second harmonic. The second
harmonic is sent through crystal B where the fourth
harmonic is generated. The remaining second harmonic is
directed back into crystal A after a time delay equal to the
roundtrip time of the ring cavity. The leftover fundamental is
allowed to interact with the generated fourth harmonic to
produce the fifth harmonic outside the ring cavity. Each
generation process is represented by its own set of equation
(2a) to (2c). The harmonic generation processes are
considered to be occurring sequentially in time. Lumped
loss is included in each stage. The equations can then be
solved numerically by segmenting the pulse in time and in
space and iteratively calculating the processes for the
segments in time while including the temporal delay and
for the separate segments in space (see ref. 16). Finally, the
segments are integrated to give the pulse energies of the
fourth harmonic or the fifth harmonic as the final result. We
begin the simulation by focusing on the case of using type II
KTiOPO4 (KTP) as the SHG crystal, followed by a BBO
crystal for the 4HG and another BBO for the SFG. This is
chosen since experimental data have been published and
could be used to validate our simulation.16) The values of the
parameters used for this simulation are listed in Table I, and
the effective nonlinear coefficient deff for KTP is on the basis
of ref. 28 and that for BBO is based on ref. 29. We take the
width of time segment as 0.08 ns. In addition, the circularly
symmetric transverse mode amplitude distribution is divided
into thirty-two annular sections, reaching from r ¼ 0 to
r ¼ 2w0 . The intensity in each section is assumed to be
uniform. We also assume that due to the small diffraction
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Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 7A
L.-B. C HANG et al.
Relative conversion to 4th harmonic
Table I. Parameters used in the simulation in §3.
Parameter
Value
Remark
f
1064 (nm)
5 (kHz)
Wavelength of pump laser
Operation frequency
E
1.4 (mJ)
Energy per pulse
wo
0.44 (mm)
Pump beam radius (1/e2 )
23.3 (ns)
Pulse width for pump laser
lCavity
79.2 (cm)
Effective cavity length
lA
5 (mm)
Length of crystal A (KTP)
lB
7 (mm)
Length of crystal B for SHG (BBO)
lC
LA
7 (mm)
1%
Length of crystal C for SFG (BBO)
Loss of SH leaving crystal A and
LB
8%
Loss of SH leaving B and entering A
L1064
19%
Loss of the residual pump laser leaving
L266
14%
Loss of the 4H leaving B and entering C
t
0.08 (ns)
Width of time segment
dSHG (pm/V)
d4HG (pm/V)
3.3
1.6
For type II KTP as the SHG crystal
For type I BBO as the 4HG crystal
d5HG (pm/V)
1.43
For type I BBO as the 5HG crystal
1.0
(1) --- loss 8%
(2) --- loss 20%
(2)
0.5
(1)
0.0
-0.2
-0.1
0.0
0.1
0.2
Phaseshift per roundtrip (wavelength)
entering B for SHG
Fig. 3. Influence of phase, i.e. cavity-length variation on the conversion to
the fourth harmonic radiation for two different losses.
A and entering C
there is no interaction between the different sections. Hence,
each annular section can be analyzed separately.
3.
Results
The functional behavior of the conversion efficiency of
the fundamental radiation to the fourth harmonic on various
parameters such as the input power, the nonlinear coefficient
of the crystals, the cavity length, roundtrip loss, and the
second-harmonic phase shift have already been calculated
and discussed in detail in our previous report.16) Our
simulation is in substantial agreement with that. For nominal
input of 30–50 kW peak power, the fourth-harmonic conversion reaches to more than 10% readily and is quite
insensitive to most of the crystal and cavity parameters. This
insensitivity is generally carried over to the 5HG case. An
example is shown in Fig. 2 where the power conversion of
the fundamental to the fifth harmonic as a function of the
optical losses at the second-harmonic wavelength is dis-
played for the fundamental polarized at 45 relative to the zaxis of the SHG crystal. The conversion efficiency drops by
only a factor of 1.3 when the overall loss at the second
harmonic due to reflection, scattering, and absorption
increases from zero loss to 15%.
It is a necessary condition for external cavity resonance
enhancement to match the phase of the fundamental light
with that of the second-harmonic light at the entrance face of
the SHG crystal. As shown in Fig. 3, in order to keep the
energy conversion to within 10% of its maximum value, the
cavity length has to be maintained to better than about 1/25
of a wavelength (0:02 mm), which is in good agreement
with the previous result in ref. 30. The results of Fig. 3 also
show that the severity of this condition is unchanged for a
large range of optical losses. Experimentally, this requirement on the cavity length stability can be satisfied with an
electronic feed-forward mechanism.
An interesting phenomenon that is particular to the case of
type II SHG is the dependence of the 4HG output and the
5HG output on the orientation of the fundamental input
polarization. The calculated results are shown in Fig. 4. As
can be seen, 4HG is optimized for an input polarized at 45
relative to the z-axis of the KTP crystal. This of course is
expected since SHG in KTP is a type II phase-matching
process. For 5HG, however, the figure shows that optimized
2.0
0.3
0.3
2
2
1
1
0.1
0.1
0
0
10
20
0
30
Power(W)
0.2
0.2
P266(W)
P213(W)
1.5
P266
1.0
P213
0.5
Loss for cavity roundtrip(%)
0.0
0
10
20
30
0.0
40
Loss for cavity roundtrip (%)
Fig. 2. The fifth harmonic power as a function of the optical losses at the
second-harmonic wavelength. The power of the fundamental to the fourth
harmonic as a function of the optical losses is shown in the inset.
0.0
0
20
40
60
80
φ(deg)
Fig. 4. The dependence of the 4HG and the 5HG output on the orientation
of the fundamental input polarization for type II SHG. Where is the
angle between the polarization of the fundamental and z axis of KTP
crystal.
Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 7A
L.-B. C HANG et al.
0
4
8
12
16
0
4
8
12
16
0.48
P213(W)
fifth-harmonic output is obtained with an input polarized at
33 which is quite different from 45 . The reason for this can
be explained as follows. In the crystal arrangement used in
the generation process, the fourth harmonic generated from
the cavity is horizontally polarized. The fifth harmonic is
generated in a type I phase-matched BBO crystal by
summing the fourth-harmonic radiation with that portion
of the fundamental that is also horizontally polarized. If the
4HG conversion is optimized, the residual portion of the
fundamental suitable for 5HG conversion is substantially
depleted. The fifth-harmonic power is thus limited by what is
available at the fundamental. On the other hand, if we rotate
the orientation of the input polarization away from its
optimal position for 4HG, this results in a lower 4HG power
output. The adjustment however reserves a portion of the
fundamental power, making it available for the 5HG
process. The result is that maximum 5HG output is obtained
with an orientation that differs from the value that is optimal
for 4HG. This result is well corroborated by experiment as
reported in ref. 18. Experimentally, this optimal orientation
can easily be realized by simply rotating a half-wave plate in
front of the resonant cavity until maximum fifth-harmonic
power is obtained.
The amount of temporal overlap and spatial overlap of the
input beams in the 5HG crystal will affect the 5HG
conversion efficiency. In the resonant cavity enhancement
configuration, the pulse duration of the second harmonics
and the pulse duration of the fourth harmonics are increased
as a result of entrapment of the second-harmonic pulse in the
cavity. The pulse width of the residual fundamental radiation
is also widened upon the depletion of the pump power in the
SHG process. Figure 5 shows the temporal profile of the
fundamental and its harmonics when the input polarization is
optimized for 5HG. The peak of the 266 nm pulse trails the
peak of the fundamental pulse by 6 ns. Such a pulse delay
will affect the 5HG conversion efficiency. The temporal
difference between the fundamental pulse and the fourth
harmonic can be corrected by introducing a delay path to the
fundamental beam in the optical arrangement. However, as
shown in Fig. 6, the 6 ns delay that is present in the example
calculation reduces the power of the fifth-harmonic output
0.44
0.40
The external delay of 1064 nm vs. 266 nm (ns)
Fig. 6. Effect of external delay (ns) of 1064 nm vs. 266 nm on 5HG.
by only 11.5%. Hence the increased complexity of introducing a pulse delay is not justified except in the most stringent
case where maximum power is required. Experimentally, a
respectable 25% of the fourth harmonic is converted to the
fifth harmonic even without correcting the temporal difference between the two input pulses to the mixing crystal (see
ref. 18).
Our model calculation has ignored the effect of birefringence walk-off in the nonlinear crystals. However in reality
this walk-off in combination with refractive beam transmission through the cavity output mirror due to an oblique
incidence angle can have a devastating effect. Figure 7
shows two ways of orienting the BBO crystal and the output
coupler. In one case, the contribution to beam separation
from each optic offset each other to give a good spatial
overlap of the beams. In the opposite case, the contributions
add to compound the problem. In a real experiment, such a
problem can cause a factor-of-1.5 difference in the output
power as shown in Fig. 8. Both Fig. 7 and Fig. 8 are
reproduced from ref. 18.
FHG crystal BBO
Relative power (a.u.)
4
532nm
266nm
z
1064nm
3
(a)
Fused
Silica
M2
FHG crystal BBO
2
(2)
532nm
1064nm
1
(3)
0
-40
M2
x
1064nm
(1)
-20
0
20
40
4321
z
1064nm
x
266nm
Fused
Silica
(b)
t(ns)
Fig. 5. The temporal profile of 1064 nm and its harmonics optimized for
5HG. Curve (1) is the fundamental power in front of crystal A, curve (2)
is the fourth harmonic power just leaving crystal B, and (3) is the fifth
harmonic power just leaving crystal C.
Fig. 7. Walk-offs produced by a 6.8-mm birefringent crystal and the
output coupler M2. Both the fundamental light and the fourth harmonic
are horizontally polarized, and the second harmonic is vertically
polarized. (a) crystal oriented to reduce beam separation. (b) crystal
oriented 180 from (a), showing increased separation.
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Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 7A
L.-B. C HANG et al.
600
P213nm(mW)
(1)
400
(2)
200
0
0
200
400
600
t(sec)
Fig. 8. Experimental comparison of output power at 213 nm for two
different orientation of the 4HG BBO. Curve (1) with 4HG BBO oriented
to enhance the fourth-harmonic and the fundamental beam overlap. Curve
(2) with the BBO crystal axis flipped 180 .
4.
Comparison of Nonlinear Crystals for Fifth-Harmonic Generation
In the previous section we have established that the
formulation in §2 is effective in describing the physical
phenomena of the fourth- and fifth-harmonic generation
processes. It can therefore be used to predict the performance of different combination of nonlinear crystals for
generating the fifth harmonic of IR lasers. In this section, we
report on the result of calculations on 5HG using various
commonly used nonlinear crystals. For the SHG step, the
available crystals are hydrothermal KTP and type I noncritically phase-matched LBO. For 4HG and 5HG, the
crystals commercially available are BBO and CLBO. Other
crystals, such as Li2 B4 O7 (LB4),31,32) KB5 O8 4H2 O
(KB5),33) K2 Al2 B2 O7 (KABO or KAB),34–36) KB2 Be2 O3 F2
(KBBF),37,38) and CsB3 O5 (CBO),39,40) either have small
second-order nonlinear coefficients for 4HG and 5HG, or
have not been deemed as suitable for high-average-power
use or have not been commercially available, and thus are
not considered here. The combination of crystals selected for
the calculation is shown in Table II. Table III shows the
parameters used for each crystal. The walk-off and phasematching angles for BBO and CLBO crystals are calculated
according to the Sellmeier’s equations in refs. 41 and 42,
respectively. The effective nonlinear coefficients deff for
KTP are based on ref. 28, for LBO based on refs. 43–45,
BBO based on ref. 29, and CLBO based on ref. 46.
Reference 47 shows that the effect of nonorthogonality of
the extraordinary electric filed with the wave vector in the
birefringence crystals should be included. For negative
uniaxial crystals, this is done by replacing , the phasematching angle, with þ where is the birefringent walkoff angle in calculating the effective nonlinear coefficient
deff . We have included this effect in deff in Table III for BBO
and CLBO crystals.
The length of the crystal is chosen to satisfy either the
walk-off limit48,49) (BBO, CLBO) or what is commercially
viable (LBO, KTP). We fix the input power at 1064 nm to be
the same as that used in §3 which is quite readily available
from a medium power Nd:YAG laser offered by a number of
commercial vendors.
The results are shown in Figs. 9(a) to 9(e), which
correspond to crystal combination (a) to (e) in Table II
respectively. The figures display the generated 266 nm
power and the 213 nm power as a function of the length of
the 4HG crystal. In all cases, the length of the SHG crystal
and the length of the 5HG crystal are fixed, and both the
4HG and the 5HG processes are optimized by adjusting the
orientation of the fundamental input polarization to get
maximum output. From Figs. 9(a) and 9(b) or Figs. 9(c) and
9(d), it can be seen that LBO will perform better than KTP in
the SHG process, providing about 50% higher power at
266 nm with everything else being the same. Comparing Fig.
9(a) with 9(c) or Fig. 9(b) with 9(d), we can see that BBO
and CLBO are about equally effective for the 4HG process,
and CLBO is superior to BBO as the 5HG crystal, a
consequence in particular of a longer crystal length because
of CLBO’s smaller walk-off angle by a factor of 3. With the
best combination (LBO, CLBO, CLBO), the conversion of
the fundamental to the fifth harmonic can reach 30%,
resulting in 2 W at 213 nm for an input of 7 W at 1064 nm.
It is interesting to note that while the 4HG process reaches
the saturation behavior at about one half of the maximum
length used in the calculations, the 213 nm power continues
to rise as the 4HG crystal length increases. This implies that
the fundamental power increases as the crystal length. In
Fig. 9(d), we include for display the residual 1064 nm power
as a function of 4HG crystal length, showing that it indeed
Table II. The different combinations of nonlinear optical crystals used in
the numerical simulation.
Combination of Crystals
SHG
4HG
5HG
(a)
(b)
KTP
LBO
BBO
BBO
BBO
BBO
(c)
KTP
CLBO
CLBO
(d)
LBO
CLBO
CLBO
(e)
LBO
BBO
CLBO
Table III. The following parameters are used in the numerical calculations for SHG, 4HG and 5HG.
Crystal
Length (mm)
Walk-off (degree)
configuration
Phase-matching
deff (pm/V)
angle (degree)
KTP type-II
5
<0:3
¼ 90, ¼ 23:3
3.3
LBO NCPM type-I
20
0
¼ 90, ¼ 0
1.04
BBO type-I for 4HG
BBO type-I for 5HG
8
7
4.88
5.5
¼ 47:6
¼ 51:1
1.6
1.43
CLBO type-I for 4HG
20
1.89
¼ 61:1
0.82
CLBO type-I for 5HG
20
1.73
¼ 67:6
0.86
Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 7A
L.-B. C HANG et al.
2 .0
P 266
(a)
P(W)
1 .5
(KTP, BBO, BBO)
1 .0
P 213
0 .5
0 .0
0
1
2
3
4
5
6
7
8
3
P 266
(b)
P(W)
2
(LBO, BBO, BBO)
1
0
0
1
2
3
4
5
6
7
(c)
P(W)
This research was supported by the National Science
Council of the Republic of China under contract NSC 902215-E-001-002 and by Pursuit of Academic Excellence
Program of the Ministry of Education of the Republic of
China.
1
(KTP, CLBO, CLBO)
0
0
4
4
8
12
16
(d)
P 266
P 213
2
(LBO, CLBO, CLBO)
1
0
20
Residual P1064 leaving the SHG crystal
3
P(W)
8
P 266
P 213
0
5
10
15
20
3
P 266
(e)
P 213
2
P(W)
combination of crystals to use for efficient generation to the
5HG using the resonant cavity approach is a 20 mm long
type I noncritical phase-matching LBO crystal for SHG, a
type I 8 mm long BBO crystal for 4HG, and a 20 mm long
type I CLBO crystal for the 5HG step. Many industrial
applications require a high repetition rate. We performed the
calculation for a 10 kHz rate for the case of the best
combination. The average power of the laser at this rate is
9 W. The resulting average power at 213 nm is 1.8 W, about
10% smaller than that at 5 kHz.
Acknowledgments
P 213
2
4323
1
(LBO, BBO, CLBO)
0
0
1
2
3
4
5
6
7
8
Length (mm) of 4HG crystal
Fig. 9. The generated 266 nm power and the 213 nm power as a function
of the length of the 4HG crystal. Part (d) includes the residual
fundamental power as a function of 4HG crystal length. The crystal
combination (SHG, 4HG, 5HG) for each part is indicated in brackets in
the figure. Note that the maximum length of BBO crystal and that of
CLBO crystal for 4HG are 8 mm and 20 mm respectively.
increases. This can easily be explained: as the 4HG crystal
length increases, the single-pass second-harmonic to fourthharmonic conversion is higher which represents a higher loss
at the second harmonic inside the resonant cavity. Hence this
clamps the growth of the second harmonic in the cavity and
results in a ‘‘lower’’ rate of conversion of the fundamental to
the higher harmonics.
A newly developed process in growing CLBO crystals has
resulted in a lower absorption of UV laser light and thus
reducing thermal dephasing during high-power UV generation.50) Past experience in high-average-power UV generation has shown that this is the most important factor in the
superior performance of this material compared with
BBO.22) But in considering the commercial availability of
the crystals, the ease of use, the cost and other practical
issues, the above calculated results suggest that the optimal
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