Optical Performance of Cr:YSO Q-switched Cr:LiCAF and Cr:LiSAF
Lasers
Chih-Kang Chang, Jih-Yuan Chang, Yen-Kuang Kuo*
Department of Physics, National Changhua University of Education, Changhua 500, Taiwan
ABSTRACT
Both Cr:LiCAF and Cr:LiSAF solid state lasers were developed by Payne et al. As transition-metal vibronic lasers the
Cr:LiCAF and Cr:LiSAF exhibit broad emission spectra, long lifetime of the upper laser levels, low nonlinear refractive
indices, low thermal lensing, and low excited state absorption that make both of them unique sources for tunable or
short pulse lasers. In previous work we had experimentally demonstrated that the Cr:YSO could work as a saturable
absorber Q switch for the Cr:LiCAF laser near 780 nm, i.e., the peak of its tuning range. In this work, we theoretically
investigate the optical performance of the Cr:YSO Q-switched Cr:LiCAF laser system over its entire tuning range by
solving the coupled rate equations. The simulation results indicate that the results obtained numerically are in good
agreement with that obtained experimentally. The theoretical simulation also shows that the Cr:YSO may be used as an
effective saturable absorber Q switch for the tunable Cr:LiCAF laser over a major portion of its entire tuning range from
725 nm to 840 nm. On the other hand, the Cr:YSO had also been experimentally demonstrated to be an effective
saturable absorber Q switch for the tunable Cr:LiSAF laser by Munin et al. The optical performance of the Cr:YSO
Q-switched Cr:LiCAF and Cr:LiSAF lasers is numerically studied in this paper.
Keywords: Cr:LiCAF, Cr:LiSAF, Cr:YSO, tunable laser, Q switch, saturable absorber, numerical simulation
1. INTRODUCTION
The Cr:LiCAF (Cr:LiCaAlF6)1 and Cr:LiSAF (Cr:LiSrAlF6)2 solid state lasers are tunable in a very wide spectral range
and were discovered by Payne et al. The Cr:YSO (Cr:Y2SiO5)3 solid-state crystal, which was originally developed for
laser applications, also possesses a very wide emission spectrum that has a peak emission cross-section near 1250 nm.
In 1993, Munin et al. experimentally demonstrated that, in addition to the laser application, the Cr:YSO crystal could
also be utilized as a saturable absorber Q switch for the tunable Cr:LiSAF laser. 4 Subsequently, in 1994 Kuo (one of the
authors of this paper) et al. showed that the Cr:YSO could be used to passively Q-switch the Cr:LiCAF laser at 780 nm,
i.e., the peak of its laser spectrum.5 Unfortunately, the saturable absorber Q switch was misidentified as Cr 4+:GSGG
(Cr4+:Gd3Sc2Ga3O12) at the time of publication.6 A more detailed analysis on the passive Q-switching performance of
the tunable Cr:YSO Q-switched Cr:LiCAF laser system was reported by Kuo et al. in 1995.7 In this work, passive
Q-switching performance of the Cr:LiCAF and Cr:LiSAF lasers with Cr:YSO saturable absorber are numerically
investigated over the entire tuning range of the two lasers.
In an optical resonator the quality factor Q is defined as the ratio of the energy stored in the laser cavity to the energy
loss per cycle. Therefore, the quality factor of a laser resonator can be altered by varying the cavity loss. In the
technique of Q-switching,8,9 energy is stored in the gain medium through optical pumping while the quality factor is
lowered in a particular way, depending on the method used, to prevent from laser oscillation. After a high population
inversion has been developed, the high cavity Q is then restored, or "switched", such that the stored energy can be
released in very short time. The pulsewidth available in this manner is usually in the order of tens of nanoseconds and
the peak power can be several orders higher than that of the ordinary long laser pulse. Q-switching of the solid-state
lasers is important because it provides short duration optical pulses required for laser ranging, nonlinear studies,
medicine and other important applications. Fast optical shutters can be made by using the electro-optic effect in some
solid-state crystals, which become birefringent under the influence of an externally applied electric field, with
polarizing element inside the laser cavity. The polarizer is not required if the laser radiation is polarized (e.g. ruby).
The low-Q state is achieved by applying a voltage to the Q-switch such that the polarization of a linearly polarized laser
light is rotated by 90º after a round trip inside the laser cavity. The laser is prohibited from oscillation in this state due to
the lack of optical feedback. The high-Q state is achieved by turning off the applied voltage such that a linearly
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polarized laser light can get through the optical elements without loss (or with less loss). The pulsewidth of the
Q-switched laser output is usually between 10 and 25 ns with electro-optic Q-switches.
Electro-optic Q-switching is effective. However, besides the expensive crystal and optical elements this method
requires a very fast rising high-voltage pulse source which adds cost and complexity to the overall Q-switched laser
system. In addition, this approach needs several optical elements inside the cavity that introduce extra losses and may
subject to optical damage. Another approach to active Q-switches is based on the acousto-optic effect. In acousto-optic
Q-switches, an acoustic wave is typically launched into the Q-switch (usually fused silica) by a piezo-electric transducer.
The Q-switch acts like a grating when the acoustic wave is present. When the light beam passes through the Q-switch a
portion of the light is diffracted out of the beam by the grating, which thus results in a higher cavity loss or, equivalently,
a lower quality factor. High cavity Q is achieved by turning off the acoustic wave. Compared with electro-optic
Q-switching, acousto-optic Q-switching has low insertion loss and is convenient to use; however, it has relatively slow
switching time and low hold-off ratio.
The active Q-switches, which employ either electro-optic or acousto-optic effect, have been widely used in many of
the industrial applications because they operate reliably over an extended period of time and can be triggered at any
moment within the pumping cycle. However, the overall laser system is rather complicated. Compared to active
Q-switching, passive Q-switching with saturable absorber is economical and simple because it requires less optical
elements inside the laser cavity and no outside driving circuitry. Passive Q-switching is a better choice for those
applications where compactness of the laser is a prime requirement. Organic dyes have long been used as saturable
absorber Q-switches. Dye Q-switching is realized by placing a dye Q-switch consisting of a transparent cell filled with
dye solution in the laser cavity, usually between the laser rod and the totally reflecting mirror. The dye cell is highly
absorptive at low light intensity and can be bleached when the light becomes intense. Short laser pulses with high peak
power can be obtained with the use of a dye Q-switch. However, dye Q-switches suffer from poor chemical stability and
inadequate thermal properties. To overcome this problem flow system is used at the expense of compactness and
simplicity. Semiconductors used as saturable absorber Q-switches have also been reported. Semiconductors possess
high small-signal absorption coefficients when the incident light has photon energies higher than the bandgap. However,
if the wavelength of the incident light is near the band edge, the absorption of the semiconductor can be saturated at
high light-intensity due to the nonlinear effect caused by band-filling. Semiconductor Q-switches have great flexibility
since the bandgap can be engineered to fit specific laser wavelengths. However, damaging of the semiconductor
saturable absorber can be a problem due to the high intensity in Q-switched operation.
Solid-state saturable absorbers based on color centers were reported by several researchers in past few years.10,11
Unfortunately, these saturable absorbers suffer from fading of the optical centers. Another approach to solid-state
Q-switches is based on Cr4+ doped in various crystalline hosts. In 1991, Andrauskas and Kennedy reported passive
Q-switching of the flashlamp-pumped Nd:Y3Al5O12 (Nd:YAG) and Nd:Glass lasers, as well as a diode-pumped
Nd:YAG laser, with Cr4+:Gd3Sc2Al3O12 (Cr4+:GSAG) and Cr4+:Gd3In2Ga3O12 (Cr4+:GIGG) solid-state saturable
absorbers at room temperature.12 Pulsewidths of the Q-switched laser output ranged from 9 to 50 ns and pulse energy
ranged from 3 to 190 mJ. The promising results of these experiments stimulated the interest in developing Cr 4+ doped
saturable absorber Q-switches. Subsequently, in 1992, Miller et al. used the Cr4+:YAG solid-state saturable absorber to
Q-switch a diode-pumped 2-cm-long Nd(1.3%):YAG laser and obtained Q-switched laser pulses of 70 ns and 1.2 mJ at
30 Hz.13 Subsequently, Kuo and many other scientists engaged in developing various durable solid-state saturable
absorbers to be used as passive Q switches for the solid-state lasers at various emission wavelengths.14-22
2. CHARACTERISTICS OF CR:LICAF, CR:LISAF, AND CR:YSO
Trivalent chromium (Cr3+) has been reported to lase in BeAl2O4, GSGG, GSAG, YSGG, and several other laser materials.
In 1988, Steven A. Payne et al. discovered a new Cr3+ doped solid-state laser crystal: Cr3+:LiCaAlF6 (Cr:LiCAF).1 As a
transition-metal vibronic laser Cr:LiCAF exhibits a broad emission spectrum, long lifetime of the upper laser level, low
nonlinear refractive index, low thermal lensing, and low excited state absorption that make it a unique source for
tunable or short pulse lasers. Some of the important material properties of Cr:LiCAF are listed in Table 1. The fact that
Cr:LiCAF has a relatively low melting temperature of 804 ºC, coupled with the natural abundance of the constituent
elements, creates a good possibility of large-scale, inexpensive growth of laser-quality crystals.
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Table 1. Material properties of Cr:LiCAF
Chemical formula
Cr3+:LiCaAlF6
Color
Green
Crystal system
Rhombohedral, uniaxial
Lattice constant
a = 4.996 Å, c = 9.636 Å
Cr atoms / mole %
~9.5 ×1019 /cm3
Main absorption peaks
425 nm and 625 nm
Emission spectrum
660 nm to 1000 nm (peak at ~ 780 nm)
-20
Peak emission cross-section
~ 1.2 ×
cm2
Fluorescence lifetime at 25 ºC
~ 170 µs
Density
2.99 g/cm3
Refractive index at 780 nm
ne = 1.388, no = 1.390
dn/dT
- 4.6 ×10-6 /ºC (//c), - 4.2 ×10-6 /ºC (c)
Nonlinear refractive index n2
0.43 ×10-13 esu
Melting point
804 ºC
Specific heat
0.18
Thermal conductivity
5.14 W/mºC (//c), 4.58 W/mºC (c)
Thermal diffusivity
1.84 ×10-6 m2/s (//c), 1.64 ×10-6 m2/s (c)
Thermal expansion at 25 ºC
3.6 ×10-6 /ºC (//c), 22 ×10-6 /ºC (c)
In Cr:LiCAF only one possible site for Al3+ which may be substituted by Cr3+. Moreover, the Li+, Ca2+ and Al3+ are
very different from each other in terms of charge and size; therefore, disorder is not a significant problem for this
material. The two broad absorption bands near 425 nm and 625 nm, assigned to the 4A2 4T1a and 4A2 4T2
absorption transitions respectively, permit efficient flashlamp pumping. The fluorescence spectra of the Cr:LiCAF,
peaking at ~ 780 nm, are assigned to the 4T2 4A2 transitions. The fluorescence lifetime of the Cr:LiCAF is about 200
µs at 20 ºK and about 170 µs at room temperature.1 The long metastable lifetime makes both flashlamp pumping and
Q-switched operation of the Cr:LiCAF laser superior to that of the Ti:Al 2O3 laser (fluorescence lifetime is 3.2 µs at 25
ºC). The tuning range of the Cr:LiCAF laser had been shown to be at least from 725 nm to 840 nm with a peak near 780
nm.1 The tunability below 725 nm is limited by the internal absorption due to the 4A2 4T2 transitions. At long
wavelengths the tunability is limited by small stimulated emission cross-sections and excited-state absorption.
The Cr:LiSAF has a tuning range from 780 nm to 920 nm with a peak laser wavelength near 845 nm. 2,9,23 The
fluorescence lifetime of Cr:LiSAF is 67 s, which is a little shorter than that of the Cr:LiCAF. However, when
compared to that of the Ti:Al2O3 laser (fluorescence lifetime is 3.2 µs at 25 ºC) which is tunable over the same spectral
range, the long metastable lifetime makes Cr:LiSAF laser a better laser for both flashlamp pumping and Q-switched
operation. Moreover, the peak emission cross-section of the Cr:LiSAF is about four times larger than that of the
Cr:LiCAF. Hence, it is expected that Cr:LiSAF has a better laser performance than Cr:LiCAF.9 The LiSAF host crystal
is uniaxial and the Cr3+ emission is strongly -polarized (E//c). The peak of the 4T2 4A2 emission spectrum occurs at
830 nm and has a cross-section of 4.810-20 cm2. Owing to the internal absorption caused by 4A2 4T2 transitions, the
laser emission spectrum is red-shifted to be peaked near 845 nm.23 Some of the important material properties of
Cr:LiSAF are listed in Table 2.
Similar to the properties of glass, the LiSAF is a rather soft and mechanically weak crystal that is quite different from
sapphire (Al2O3). On the other hand, unlike Ti:Al2O3, flashlamp pumping of Cr:LiSAF is very straight-forward due to
the relatively long lifetime of the upper state level and the excellent overlap of the absorption bands with the emission
of flashlamps. The Cr:LiSAF laser can also be pumped with AlGaInP laser diodes at 670 nm26 and AlGaAs laser diodes
at 752 nm.27 Hence, a compact Cr:YSO Q-switched Cr:LiSAF laser system is feasible. In fact, Cr:LiSAF has found
applications as a flashlamp or diode-pumped laser source.9 The broad emission spectrum of Cr:LiSAF makes this
crystal attractive for the generation and amplification of femtosecond mode-locked pulses. The prospect of a
diode-pumped all solid-state tunable source for femtosecond pulse generation is of particular interest. A wide range of
laser systems such as the small diode-pumped Cr:LiSAF mode-locked oscillators28 and very large flashlamp-pumped
amplifier stages with rod diameters up to 25 mm29 have been fabricated.
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Table 2. Material properties of Cr:LiSAF (After Ref. 9)
Chemical formula
Cr3+:LiSrAlF6
Color
Green
Crystal system
Rhombohedral, uniaxial
Main absorption peaks
440 nm and 650 nm
Emission spectrum
700 nm to 1100 nm (peak at ~ 830 nm)
Peak laser wavelength
~ 845 nm
-20
Peak emission cross-section
~ 4.8 ×
cm2
Fluorescence lifetime at 25 ºC
~ 67 µs
Refractive index
~ 1.41
Scattering loss
0.002 cm-1
Thermal shock resistance
~ 0.4 W/m1/2
Fracture strength
3.9 kg/mm2
Thermal expansion coefficient
22 ×10-6 /ºC
Young’s modulus
100 Gpa
Microhardness
197 kg/mm2
Fracture toughness
0.4 Mpam1/2
Thermal conductivity
3.09 Wm-1K-1
First spectroscopic studies of the Cr4+:YSO and the observation of laser action from 77 up to 257 ºK were reported by
Deka et al. in 1992.3 Room-temperature laser operation of the Cr4+:YSO was also reported by Kück et al. at the 1993
Optical Society of America Topical Meeting on Advanced Solid State Lasers. Some of the important material
parameters of the Cr4+:YSO are listed in Table 3.
Unlike chromium doped YAG and forsterite, in which Cr3+ ions exist in the octahedral sites, Cr4+:YSO is a pure Cr4+
system. The YSO structure contains two distorted octahedral yttrium sites and one distorted tetrahedral silicon site.
Due to size incompatibility the two yttrium sites are not suitable for a chromium ion substitution. The chromium ions
most likely enter the lattice as Cr4+ and substitute for the tetrahedrally coordinated Si4+ ions.4,24,25 Therefore, Cr4+:YSO
can be regarded as a pure tetravalent chromium system and no charge compensation is required for the substitution of
silicon ion by the chromium ion. Since YSO is a biaxial crystal three principal axes of polarization (n 1,n2,n3) can be
defined. The indicatrix axis n2 is parallel to the <010> direction that is a twofold symmetry axis of the crystal. The
indicatrix axes n1 and n3, which correspond to extinction positions when viewing the crystal along n 2 between crossed
polarizers, are perpendicular to each other and to the n2 direction.24
Table 3. Material properties of Cr:YSO
Chemical formula
Cr4+:Y2SiO5
Color
Blue
Crystal system
Monoclinic, biaxial
Lattice constants
a = 10.41 Å, b = 6.72 Å, c = 12.49 Å,  = 102º39'
Cr atoms / mole %
~ 9.7 ×1019 /cm3
Main absorption peaks
390 nm, 595 nm, 695 nm, and 750 nm
Emission spectrum
1000 nm to 1500 nm (peak at ~ 1250 nm)
Fluorescence lifetime at 25 ºC
~ 0.7 µs
Density
4.6 g/cm3
Refractive index
1.8
Melting point
2070 ºC
3. PASSIVE Q-SWITCHING THEORY
The schematic diagram for a solid-state laser with a saturable absorber Q switch is shown in Fig. 1. The laser resonator
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consists of a high-reflecting mirror, with a reflectivity of about 100%, and an output-coupling mirror. The saturable
absorber Q switch can be placed either between the laser crystal and the high reflector or between the laser crystal and
the output coupler. For the lasers under study, flashlamps are usually utilized as the pumping sources.
In our prior paper7 we have proposed three coupled rate equations which may be used to model a laser passively
Q-switched by a solid-state saturable absorber:
dn
 [ K g N g  K a N a   K a ( N a 0  N a )   c ]n ,
(1)
dt
dN g
(2)
 R p   g N g  K g N g n ,
dt
dN a
  a ( N a0  N a )  K a N a n .
(3)
dt
The factor  equals to one for a four-level laser and two for a three-level laser. Other parameters are defined as
following: n is the photon number in the laser cavity; Ng is the population inversion of the laser; Na is the ground state
population of the saturable absorber; Na0 is the initial value of Na; g is the effective decay rate of the upper laser level;
a is the effective relaxation rate of the saturable absorber; Rp is the pumping rate; c is the cavity decay rate; Kg and Ka
are coupling coefficients; and  is the ratio of the excited state absorption cross-section to the ground state absorption
cross-section of the saturable absorber.
Pumping System
Saturable
Absorber
Laser
Output
Laser Crystal
Mirror
(Total Reflector)
Mirror
(Output Coupler)
Figure 1: Schematic diagram for a solid-state laser with a saturable absorber Q switch.
In order to compare the population inversion of the laser to the loss of the overall laser system when interpreting the
numerical simulation results, it is convenient to define a normalized loss parameter, Loss, from Eq. (1) as
Loss 
K a N a  K a ( N a 0  N a )   c
.
Kg
(4)
Equations (1), (2) and (3) need to be solved numerically to obtain the behavior of a specific Q-switched laser system.
However, important characteristics of a saturable absorber Q-switched laser system can be found from analyzing these
three coupled rate equations. Following the method of Siegman,10 for passive Q-switching with a slow-relaxing
saturable absorber, Eq. (1) becomes
1 dn
n
  g 0  ( K a2 N a 0  K g2 N g 0 )
,
n dt
 g0
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(5)
502
where
 g 0  K g N g 0  Ka Na 0   c ,
(6)
When the photon number is small the photon number growth rate is dominated by the first term in the right hand side
of Eq. (5), i.e. g0. Thus, before the saturable absorber starts to saturate the photon number inside the laser resonator
increases at an initial growth rate g0. When the photon number is large the terms inside the parentheses start to take
control. Therefore, for the passive Q-switching to occur both of these two terms have to be positive. After some
manipulation, these two passive Q-switching criteria become
K g N g 0  Ka Na0   c  0,
(7)
2 a La  a Ag


,
2 g Lg  g Aa
(8)
where a and La are the small signal absorption coefficient and crystal length of the saturable absorber, respectively,
g and Lg are the small signal emission coefficient and crystal length of the laser, respectively.
The physical meaning of Eq. (7) is that the gain medium has to be pumped to a level such that the gain of the laser is
greater than the total loss of the laser cavity. Only under this circumstance can the laser signal be built up from the noise.
Equation (7) can be regarded as the first threshold condition for passive Q-switching with slow-relaxing saturable
absorbers. The physical meaning of Eq. (8) is that the saturable absorber must saturate first so that the net
photon-number growth rate can turn upward which in turn allows the generation of a Q-switched laser pulse. If this
condition is not satisfied, the photon number will start to decrease when the light intensity is high and a Q-switched
laser pulse will never develop. Therefore, this equation can be regarded as the second threshold condition for passive
Q-switching with slow-relaxing saturable absorbers. If the first term in Eq. (8) is close to unity, which is usually the
case, and an internal lens is not used, i.e. AgAa, then the absorption cross-section of the saturable absorber at the laser
wavelength,a, must be greater than the emission cross-section of the laser gain medium, g, in order to effectively
Q-switch the laser.
It can be shown that the laser population inversion required for laser action, Ng0, the threshold population inversion
after the saturation of the Q switch, Nth, and the final population inversion after the release of the giant laser pulse, Nf,
can be approximated by the following equations:
N g0 
N th 
K a N a0   c
,
Kg
K a N a 0   c
Kg
N g 0  N f  N th ln(
(9)
,
N g0
Nf
(10)
)  0.
(11)
It can also be shown that the pulse width, pulse, and the output energy, Eout, of the Q-switched giant laser pulses can
be approximated by the following equations:
N g0  N f
 pulse   c
N g0
E out 
 N g0
 N th  N th ln 
 N th
N g0  N f





,
h  c ,
(12)
(13)
where c is the cavity lifetime, h is the photon energy, and c is the output coupling efficiency. Equations (9) to (13)
may be used to quantitatively evaluate the optical performance of a laser that is passively Q-switched with a
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slow-relaxing saturable absorber without actually executing the numerical simulations.
4. NUMERICAL SIMULATIONS
The absorption cross-section of the Cr:YSO and the emission cross-section of the Cr:LiCAF are shown in Fig. 2. It is
obvious that the absorption cross-section of the Cr:YSO is much greater than the emission cross-section of the
Cr:LiCAF. Hence, according to the passive Q-switching theory discussed in section 3, the Cr:YSO may be used to
Q-switch the Cr:LiCAF laser over a major portion of its entire tuning range. In a previous work 7 we experimentally
demonstrated the passive Q-switching of a Cr:LiCAF laser with a Cr:YSO saturable absorber at five specific
wavelengths near 780 nm, the peak of its lasing spectrum. Figure 3 shows the results of our numerical simulation,
assuming the laser polarization is along the n3 axis of the Cr:YSO. The parameters used in this simulation are:  = 1,
length of laser cavity = 34 cm, reflectivity of output coupler R = 0.92, radius of laser beam = 1 mm, dissipative cavity
loss = 1.34, Kg = 3.5910-10 sec-1, Ka = 1.6010-8 sec-1, g = 5.88103 sec-1, a = 1.43106 sec-1,  =0.33, Rp = 1.51022
sec-1, and Na0 = 9.01015.
Since the Cr:YSO crystal utilized in our experiments was damaged in a previous experiment, in this specific
simulation we adjust the value of the dissipative cavity loss inside the laser system so that the simulation results best fit
the output energy and pulsewidth obtained in experiments. As shown in Fig. 3, the results obtained numerically are in
good agreement with that obtained experimentally. From Fig. 3 we also note that, under this specific circumstance, the
Cr:YSO Q-switched Cr:LiCAF laser is operational only in a spectral range from 740 nm to 810 nm, instead of the
whole Cr:LiCAF laser spectrum (725 nm to 840 nm).
2
1.1
n
1
3
6
0.9
0.8
4
0.7
2
2
cm )
-20
2
1.2
n
8
of Cr:LiCAF (10
1.3
1
Emission Cross-Section
n
cm )
-19
of Cr:YSO (10
Absorption Cross-Section
1.4
10
0.6
720
740
760
780
800
820
840
Wavelength (nm)
Figure 2: Absorption cross-section of Cr:YSO and emission cross-section of Cr:LiCAF.
12
80
8
60
6
40
4
dw (Simulation)
dw (Experiment)
2
Eout (Simulation)
Eout (Experiment)
Pulsewidth (ns)
Output Energy (mJ)
10
20
0
0
740
750
760
770
780
790
800
810
Wavelength (nm)
Figure 3: Results of simulation for passive Q-switching of a Cr:LiCAF laser with a Cr:YSO saturable absorber.
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Figure 4 shows n, Ng, and Loss as a function of time for the situation when the laser wavelength is at 780 nm. A giant
laser pulse is developed at a time of 265.4 s after the pumping starts. A second giant laser pulse of almost identical
amplitude appears at a time of 373.0 s, which is 107.6 s away from the first laser pulse. The temporal separation
between the first and the second lasers is shorter than that required to develop the first laser pulse because the laser
population inversion Ng does not reach zero after the release of the first laser pulse.
For comparison purpose, let’s assume that the laser and saturable absorber are perfect in quality and the dissipative
loss inside the laser cavity is zero. The results of the simulation for this specific situation are shown in Fig. 5. A giant
laser pulse is developed at a time of 39.6 s after the pumping starts. A second giant laser pulse of almost identical
amplitude appears at a time of 74.4 s, which is 34.8 s away from the first laser pulse. Hence, it takes less time to
develop the Q-switched laser pulses when the dissipative loss of the laser system is low, as expected from theory.
16
2.4 10
1.6 10
18
16
Loss
2.5 10
16
2 10
Ng
17
16
1.5 10
8 10
n
Ng and Loss
3 10
18
16
1 10
0
15
5 10
17
-8 10
n
0
18
-1.6 10
15
0
50
100
150
200
250
300
350
-5 10
400
Time (s)
Figure 4: n, Ng, and Loss as a function of time for the situation when there is a large dissipative cavity loss inside the Cr:YSO
Q-switched Cr:LiCAF laser system.
3.5 10
17
17
6 10
17
3 10
Loss
17
2.5 10
17
17
2 10
17
2 10
Ng
1.5 10
0
17
n
Ng and Loss
4 10
17
1 10
17
16
-2 10
5 10
n
0
17
-4 10
0
20
40
60
80
100
120
Time (s)
Figure 5: n, Ng, and Loss as a function of time for the situation when there is no dissipative cavity loss inside the Cr:YSO
Q-switched Cr:LiCAF laser system.
Figure 6 shows the output energy and pulsewidth of the first Q-switched laser pulse as a function of wavelength for
the situation with and without dissipative cavity loss inside the laser resonator. It is found that the Cr:YSO Q-switched
Cr:LiCAF laser is operational for the whole Cr:LiCAF laser spectrum from 725 nm to 840 nm under the situation when
there is no dissipative cavity loss inside the laser resonator. From Fig. 5 we also note that the output energy is higher for
the situation without dissipative cavity loss. On the other hand, the pulsewidth is narrower for the situation without
dissipative cavity loss in the right-hand portion (long wavelength portion) of the laser spectrum. For the short
wavelength portion of the laser spectrum, the pulsewidths for the two different situations are much the same. Thus, we
may conclude that the Cr:YSO Q-switched Cr:LiCAF laser system has a better performance when the dissipative cavity
loss is low since it has a wider operational spectral range, a higher output energy in a giant laser pulse, and usually a
narrower pulsewidth in a giant laser pulse.
High-Power Lasers and Applications, Dianyuan Fan, Keith A. Truesdell, Koji Yasui, Editors
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505
80
Output Energy (mJ)
70
60
50
Without Large
Dissipative Cavity Loss
40
30
With Large
Dissipative Cavity Loss
20
10
0
720
740
760
(a)
780
800
820
840
Wavelength (nm)
100
Pulsewidth (ns)
90
With Large
Dissipative Cavity Loss
80
70
60
50
Without Large
Dissipative Cavity Loss
40
30
720
740
760
(b)
780
800
820
840
Wavelength (nm)
Figure 6: (a) Output energy and (b) pulsewidth of the first Q-switched laser pulse as a function of wavelength for the situation
with and without dissipative cavity loss inside the Cr:YSO Q-switched Cr:LiCAF laser system.
The absorption cross-section of the Cr:YSO and the emission cross-section of the Cr:LiSAF in a spectral range from
720 to 1040 nm are shown in Fig. 7. It is obvious that the absorption cross-section of the Cr:YSO is much greater than
the emission cross-section of the Cr:LiSAF. Hence, according to the passive Q-switching theory discussed in section 3,
the Cr:YSO may be used to Q-switch the Cr:LiSAF laser over a major portion of its entire tuning range.
-18
2
-19
6 10
3
3
-19
2
-19
1
4 10
2 10
0
720
2
4
n
-20
1
2
of Cr:LiSAF (10
n
n
cm )
5
Emission Cross-Section
-19
8 10
of Cr:YSO (cm )
Absorption Cross-Section
1 10
0
760
800
840
880
920
960
1000
1040
Wavelength (nm)
Figure 7: Absorption cross-section of Cr:YSO and emission cross-section of Cr:LiSAF.
Let’s now move to the passive Q-switching of the Cr:LiSAF laser with Cr:YSO saturable absorber. Figure 8 shows n,
Ng, and Loss as a function of time for the situation when the Cr:YSO Q-switched Cr:LiSAF laser system is with and
without a large dissipative cavity loss inside the laser resonator. The laser wavelength for this specific simulation is at
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506
845 nm, the peak of the Cr:LiSAF laser spectrum. The parameters used in this simulation are:  = 1, length of laser
cavity = 34 cm, reflectivity of output coupler R = 0.8, radius of laser beam = 1 mm, dissipative cavity loss = 1.34 (or 0),
Kg = 1.3410-11 sec-1, Ka = 7.0010-11 sec-1, g = 1.49104 sec-1, a = 1.43106 sec-1,  =0.33, Rp = 1.51022 sec-1, and Na0
= 9.01015.
As shown in Fig. 8(a), when there is a large dissipative cavity loss inside the laser resonator, a giant laser pulse is
developed at a time of 45.3 s after the pumping starts. A second giant laser pulse of almost identical amplitude appears
at a time of 53.5 s, which is 8.2 s away from the first laser pulse. The temporal separation between the first and the
second lasers is shorter than that required to develop the first laser pulse because the laser population inversion Ng does
not reach zero after the release of the first laser pulse. On the other hand, as shown in Fig. 8(b), when there is no
dissipative cavity loss inside the laser resonator, a giant laser pulse is developed at a time of 10.6 s after the pumping
starts. A second giant laser pulse of almost identical amplitude appears at a time of 17.9 s, which is 7.3 s away from
the first laser pulse.
17
4.8 10
17
15
3.5 10
15
Loss
3 10
15
17
2.5 10
3.2 10
17
15
2.4 10
17
1.6 10
17
Ng and Loss
4 10
2 10
15
1.5 10
Ng
n
5.6 10
15
1 10
16
14
8 10
5 10
n
0
0
16
-8 10
14
-5 10
0
-5
1 10
2 10
-5
(a)
-5
3 10
-5
4 10
-5
5 10
-5
-5
6 10
7 10
8 10
-5
Time (s)
16
4 10
1.5 10
17
16
16
2 10
n
Ng and Loss
3 10
17
1 10
16
5 10
16
1 10
0
0
16
-5 10
0
(b)
-6
5 10
-5
1 10
1.5 10
-5
-5
2 10
Time (s)
Figure 8: n, Ng, and Loss as a function of time for the situation when (a) there is a large dissipative cavity loss (b) there is no
dissipative cavity loss inside the Cr:YSO Q-switched Cr:LiSAF laser system.
Figure 9 shows the output energy and pulsewidth of the first Q-switched laser pulse as a function of wavelength for
the situation with and without dissipative cavity loss inside the laser resonator. It is found that the Cr:YSO Q-switched
Cr:LiSAF laser is operational at least from 780 nm to 920 nm under the situation when there is no dissipative cavity loss
inside the laser resonator. From Fig. 9 we also note that the output energy is higher and the pulsewidth is narrower for
the situation without dissipative cavity loss. This is a little different from the situation of the Cr:YSO Q-switched
Cr:LiCAF laser system, as discussed in previous section. Therefore, we may conclude from the simulation results that
the Cr:YSO Q-switched Cr:LiSAF laser system has a better performance when the dissipative cavity loss is low since it
has a wider operational spectral range, and a higher output energy and a narrower pulsewidth in a giant laser pulse.
High-Power Lasers and Applications, Dianyuan Fan, Keith A. Truesdell, Koji Yasui, Editors
Proceedings of SPIE Vol. 4914 (2002) © 2002 SPIE·0277-786X/02/$15.00
507
30
Output Energy (mJ)
25
Without Large
Dissipative Cavity Loss
20
15
10
With Large
Dissipative Cavity Loss
5
0
-5
780
800
820
(a)
840
860
880
900
920
Wavelength (nm)
-7
1.6 10
-7
1.4 10
With Large
Dissipative Cavity Loss
Pulsewidth (s)
-7
1.2 10
-7
1 10
-8
8 10
Without Large
Dissipative Cavity Loss
-8
6 10
-8
4 10
-8
2 10
780
(b)
800
820
840
860
880
900
920
Wavelength (nm)
Figure 9: (a) Output energy and (b) pulsewidth of the first Q-switched laser pulse as a function of wavelength for the situation
with and without dissipative cavity loss inside the Cr:YSO Q-switched Cr:LiSAF laser system.
5. CONCLUSION
We have theoretically investigated the optical performance of the Cr:YSO Q-switched Cr:LiCAF and Cr:LiSAF lasers.
These simulation results are useful for those readers who are interested in fabricating and knowing the passive
Q-switching performance of these powerful solid-state lasers.
ACKNOWLEDGMENTS
This work is supported by the National Science Council (NSC) of the Republic of China, Taiwan, under grant
NSC-90-2112-M-018-011.
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* ykuo@cc.ncue.edu.tw; phone 886 4 723-2105 ext. 3341; fax 886 4 721-1153; http://ykuo.ncue.edu.tw; Department of Physics,
National Changhua University of Education, Changhua 500, Taiwan
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