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Formation of dynamic cavity in a self-starting high-average-power Nd:YAG laser oscillator
Optics Express, Vol. 5, Issue 12, pp. 286-291 (1999)
http://dx.doi.org/10.1364/OE.5.000286
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– Abstract
1. Introduction
2. Principles of laser cavity formation by self-induced refractive index gratings
3. Experimental results
4. Conclusion
– References and links
– Abstract
1. Introduction
2. Principles of laser cavity formation by self-induced refractive index gratings
3. Experimental results
4. Conclusion
– References and links
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Abstract
Self-organization of the dynamic cavity completed by holographic gratings in the novel laser oscillator was studied experimentally and numerically. A key role of the resonant grating of refractive index induced by generating beams in an Nd:YAG laser crystal was determined. Stabilization of the generated pulses and an increase in output power were achieved by use of a vibrating intracavity mirror.
© Optical Society of America
[Optical Society of America ]
1. Introduction
The cavity of a laser oscillator can be formed by resonant dynamic gratings induced
in an active medium by the interference field of generating waves. The observation
of self-starting generation in laser oscillators of such kind has been reported
previously for solid-state active media [1]. Currently, the self-starting solid-state lasers with the
dynamic cavity are being intensively investigated [2–7]. The main advantages of these laser oscillators are
self-adaptation and self-Q-switching of the dynamic cavity with nonlinear mirrors.
These unique properties of the lasers of a new class provide a good beam quality, a
high pointing stability, and a large coherence length of the generated radiation.
I.M. Bel’dyugin, V.A. Berenberg, and A.E. Vasil’ev, et all, “Solid-state lasers with self-pumped PC mirrors in the active medium,” Sov. J. Quant. Electron. 19, 740–742 (1989). [CrossRef]
M.J. Damzen, R.P.M. Green, and K.S. Syed, “Self-adaptive solid-state oscillator formed by dynamic gain-gratings holograms,” Opt. Lett. 20, 1704–1706 (1995). [CrossRef] [PubMed]
Two types of the self-starting laser-oscillators with dynamic cavity have been
recently demonstrated. The first type, based on Nd:YAG and Ti:S laser crystals
(LaCs), incorporated a nonreciprocal transmission element in the loop section of the
cavity formed by the gain grating (GG) [2,3,6]. Another laser oscillator with reciprocal cavity was
reported to be formed by moving resonant refractive index grating (RIG) accompanied
the population grating (PG) induced in a Nd:YAG crystal by the generating beams [4,5]. The latter type of the laser has demonstrated the
capability for generating beams with high average power (as large as 60W) and
near-diffraction-limited quality [7]. In this article, we present the results of numerical and
experimental investigations of the origin and dynamics of the gratings that complete
the reciprocal cavity of a self-starting high-average-power Nd:YAG laser.
M.J. Damzen, R.P.M. Green, and K.S. Syed, “Self-adaptive solid-state oscillator formed by dynamic gain-gratings holograms,” Opt. Lett. 20, 1704–1706 (1995). [CrossRef] [PubMed]
A. Minassian, G.J. Crofts, and M.J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator”, Opt. Lett. 22, 697–699 (1997). [CrossRef] [PubMed]
P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quant. Electron. 34, 465–472 (1998). [CrossRef]
O.L. Antipov, A.S. Kuzhelev, V.A. Vorob’yov, and A.P. Zinov’ev, “Pulse repetitive Nd:YAG laser with distributed feedback by self-induced population grating,” Opt. Comm. 152, 313–318 (1998). [CrossRef]
2. Principles of laser cavity formation by self-induced refractive index gratings
The general idea of the laser oscillator with a cavity completed by the holographic
RIG induced in a LaC can be described for the simplest example of a laser scheme
consisting of a Nd:YAG amplifier and a loop feedback formed with mirrors
M1-M3 (Fig. 1).
Fig. 1. Schematic of a self-starting generator with a loop cavity. M1 is
the vibrating mirror that gives the frequency shift Ω to
reflected waves; k1,…k4 are the wave
vectors of the interacting optical waves
E1,…E4 in the cavity; the traits indicate
the PGs inside the LaC.
Four optical waves (starting initially from amplified spontaneous emission (ASE))
with complex amplitudes
E1
,…E4
can
interfere with each other. The interference fields will induce the PGs, whose
complex amplitudes nij
can be given by:
where i, j=1, 2…4 (i≠j);
Nη
is the amplitude of the Langevin noise
sources for the PGs;
ηij
,ψij
are random delta-correlated functions normalized to 1; time and wave intensities are
normalized to the longitudinal relaxation time of working transition and its
saturation intensity, respectively; and N0
is the
average-in-space population, which is given by:
where Np
(t) is the pump velocity
determined in experiment.
The gratings of population inversion in the laser crystals are accompanied by both
GGs and RIGs. The latters are caused in the Nd:YAG amplifier by the difference in
polarizability of excited and unexcited Nd3+ ions [8]. The RIGs and, generally, the resonant changes of refractive
index can be taken into consideration by the real part of the nonlinear resonant
susceptibility [7,8]. The interaction of the generating waves in LaC by the
mutuial scattering of the waves both on the RIGs and the GGs is described in the
one-spatio-dimensional approximation by the following set of equations (an analoguos
set of equations was used for the steady state analysis of the conditions for the
self-starting generation [7]):
O.L. Antipov, A.S. Kuzhelev, D.V. Chausov, and A.P. Zinov’ev, “Dynamics of refractive index changes in a Nd:YAG laser crystal under Nd3+-ions excitation,” J. Opt. Soc. Am. B 16, 1072–1079 (1999). [CrossRef]
O.L. Antipov, A.S. Kuzhelev, D.V. Chausov, and A.P. Zinov’ev, “Dynamics of refractive index changes in a Nd:YAG laser crystal under Nd3+-ions excitation,” J. Opt. Soc. Am. B 16, 1072–1079 (1999). [CrossRef]
where
σ=σ0
(1+iβ),
σ0
is the cross-section of the
resonant transition; β is the ratio of the real part of
the Nd:YAG resonant susceptibility to the imaginary part [8];
µ=l/c is the walk-off
time in the rod; F
ε is the amplitude of the
Langevin noise source for the optical field;
εi
(z,t)
and φi
(z,t)
are random delta-correlated functions;
N12
=N34
=n12
+n34
,
N13
=N24
=n13
+n24
,
N14
=n14
,
N23
=n23
,
Nij
=
; ‘+z’ corresponds to the
propagation direction of the waves E1
and
E3
.
O.L. Antipov, A.S. Kuzhelev, D.V. Chausov, and A.P. Zinov’ev, “Dynamics of refractive index changes in a Nd:YAG laser crystal under Nd3+-ions excitation,” J. Opt. Soc. Am. B 16, 1072–1079 (1999). [CrossRef]
The Langevin noise sources in Eqs. (1) and (3) determine the initial levels of the PGs and the optical
waves, providing starting conditions of the laser oscillator. In practice, the
population noise is produced by pump fluctuations and spontaneous resonant
transitions and is induced by the broadband nonresonant ASE; the noise source of the
optical field occurs as a result of spontaneous polarization and thermal optical
field in the cavity [9].
A.N. Oraevsky, “Quantum fluctuations and formation of coherency in laser,” J. Opt. Soc. of Am. 5, 933–945 (1988). [CrossRef]
In order that the system shown in Fig. 1 could operate as a laser, the induced gratings must
provide positive feedback by energy transfer from the strongest wave
E4
to the weakest wave
E1
. Such energy transfer can be realized by the GGs in
the presence of a phase-nonreciprocal element in the loop [2,3,6]. In the case of a reciprocal loop cavity only the moving
RIGs that participate in two-wave and four-wave interactions inside the Nd:YAG
amplifier can provide the energy transfer [4,5,7]. The movement of the grating leads to the compensation of
the π/2-phase shift between the RIG and an additional amplification
coefficient of the weak waves. In our scheme the moving RIGs are induced by the
interference field of the optical waves with frequency detuning, in this case the
phase matching of the waves in the cavity occurs as a result of reflection from the
moving intracavity mirror [5,7].
M.J. Damzen, R.P.M. Green, and K.S. Syed, “Self-adaptive solid-state oscillator formed by dynamic gain-gratings holograms,” Opt. Lett. 20, 1704–1706 (1995). [CrossRef] [PubMed]
A. Minassian, G.J. Crofts, and M.J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator”, Opt. Lett. 22, 697–699 (1997). [CrossRef] [PubMed]
P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quant. Electron. 34, 465–472 (1998). [CrossRef]
O.L. Antipov, A.S. Kuzhelev, V.A. Vorob’yov, and A.P. Zinov’ev, “Pulse repetitive Nd:YAG laser with distributed feedback by self-induced population grating,” Opt. Comm. 152, 313–318 (1998). [CrossRef]
The numerical solution of Eqs. (1)–(3) was made for zero initial condition, mirror boundary
conditions (100% reflection from the mirrors M1-M3), and the
weak diffusive reflection (rdif
) of the wave
E4
at the output boundary of the Nd:YAG rod. It
was calculated that the nonlinear generation occurs in the presence of the PG noise
source (when Nη
≠0), at a very
small value of the noise source for the optical wave that propagates in the
direction of generation
(F
ε≈10-7÷10-8),
and even without any “linear” diffusive reflection on the rod
end rdif
=0 (Fig. 2).
Fig 2. Results of numerical calculations: (a) oscillograms of the output wave
I4
when maximum of the unsaturated
amplification coefficient is α0l=1.5
(red curve), α0l=2.0 (blue curve),
and α0l=4.0 (violet curve); the
frequency detuning is Ω=1.25 (red and blue
curves) and Ω=200 (violet curve); the PG noise
is
Nη
=1.39×10-3;
brown curve is the temporal profile of the Nd:YAG amplification; (b)
oscillograms of the population grating N13
(blue
curve) and the output wave intensity I4
(pink
curve) when α0l=4.0 and
Ω=250; (c) dependencies of the peak-pulse
intensity I4
(solid curves) and the energy W
(dashed curves) of the output wave on the amplitude of the PG noise source
at Ω=1.25 (red curves),
Ω=1.5 (blue curves), and
Ω=1.0 (green curves), when
α0l=2.0,
F
ε=10-8.
The numerical calculations showed that at a fixed level of the noise source
amplitudes the generation had the threshold for the unsaturated amplifier gain
(α0
=σ0
N0
)
that depended on the frequency detuning (Ω) of the optical waves inside
the cavity (Fig. 2a). Below the threshold for the amplifier gain only
noise amplification took place (red curve in Fig. 2a), at the threshold the single-pulse generation was
realised (blue curve), and beyond the threshold the pulse train generated (violet
curve).
The investigation of PG indicated that the generation started when the RIG
diffraction efficiency achieved a threshold level that is determined by the
amplification and losses in the cavity. The self-starting generation was not
observed in the absence of the RIG (β=0). At the
beginning of the first peak of generation (and several subsequent peaks) the PG
amplitude and the optical wave intensity increased self-consistently (Fig. 2b). The PG growth continued till the gain saturation by
the high-intensity optical waves.
At the fixed amplifier gain the generation intensity strongly depended on the
amplitude of the PG noise source Nη
(Fig. 2c). The minimum of generation threshold for
Nη
corresponded to the frequency
detuning Ω=1.25. The generation Ω-band
expanded at the large gain. For example, at
α0l=4 the difference in the generated energy
for Ω=1.25 and 250 was about 10%.
3. Experimental results
The cavity of the laser oscillator we studied experimentally was formed by ordinary
mirrors, a Sagnac interferometer (which provided spatio-temporal mode selection [7]), and holographic gratings induced inside the Nd:YAG
amplifiers (Fig. 3). The laser amplifiers (based on Nd:YAG crystals with
1% concentration of Nd3+ ions) had logarithmic gain up to 4.8
at a flash-lamp-pump pulse duration of 0.3 ms and a pump-pulse energy as large as 80
J per each rod.
Fig. 3. Schematic view of the NDFWM investigation of RIG formation in a laser with a
dynamic loop cavity. Diagram of the wave vectors for NDFWM inside Nd:YAG rod
is presented separately.
The self-starting generation was observed in this scheme when the total amplifier
gain exceeded a threshold level. This generation cannot be explained by any linear
scattering of the output beam because it was directed in a black body with
negligible backscattering.
To study the origin and the dynamics of the holographic gratings completing the
cavity the nondegenerate four-wave mixing (NDFWM) measurements were made using an
additional Nd:phosphate glass laser (Fig. 3). The intersecting generation waves
E2
and E4
(at the
resonant wavelength of 1064 nm) induce the PG in the Nd:YAG amplifier. The
large-scale RIG that accompanies the PG was read by an optical wave of the
Q-switched Nd:phosphate glass laser at a wavelength of 1054 nm with a repetition
rate less than 1 Hz. The propagation direction of the reading beam
(ER
) was chosen as optimal for Bragg diffraction on
the recorded grating and was nearly opposite to the direction of one writing
generation beam so that wave synchronism took place. The energy of the testing
single-transverse-mode beam (20 mJ) was much less than thresholds of self-induced
nonlinear optical effects. The diffracted beam (E
D),
which occurred as a result of reflection of the reading beam from the RIG, was
recorded. This recorded signal was really diffracted on the RIG since it was
observed only in the presence of the writing beams of generation and of the reading
beam, simultaneously. The use of orthogonal polarisations of the reading and
generation beams, as well as the different pulse durations of the beams and the
pump, made negligible the level of the noise caused by the writing beams or
spontaneous emission in the recording channel of the diffracted beam. Therefore, the
NDFWM experiments confirmed the existence of the RIG inside the amplifier.
The pulse of the testing laser beam with a duration of 160 ns was synchronised with
some variable delay at the beginning of the generation pulse. By changing this delay
time, we studied the temporal dynamics of the tested RIG. The measured diffraction
efficiency (DE) of the RIG, defined as the ratio of energies of the diffracted and
reading pulses, depended on the delay of the reading pulse at the beginning of
generation. It was measured that a noise signal was approximately the same in the
nonpumped Nd:YAG and in the pumped LaC before generation. The DE strongly increased
(by more than one order of magnitude) after the beginning of laser generation and
decreased after its end (Fig. 4).
Fig. 4. Dependencies of the diffraction efficiency of the RIG on time for time scales
of 5 µs (a) and 100 µs (b): experimental data for DE
(▪), polynomial fit for DE (red line), typical oscillogram of the
generated pulse (blue line), oscillogram of the single-pass unsaturated
amplification coefficient of one amplifier (violet line), and oscillogram of
the flash-lamp pumping (green line).
Measurements on the fast time scale showed that the DE of the resonant RIG began to
increase several microseconds before the onset of generation (Fig. 4a). Formation of the nonlinear RIG mirror that
completes the cavity preceded the first optical generation spike.
The DE of the RIG at the time of generation onset was approximately
5·10-7. Knowing this value of the nonlinear mirror
“reflectivity”, we can estimate the threshold gain of the
amplifiers in the self-starting generator. For generation to start in the cavity
completed by the RIG, the total amplification should be equal to the total losses,
which are caused mostly by the RIG transmission. Then, the single-pass amplification
(K) of each Nd:YAG amplifier at generation threshold must be
Kth
≈(5·10-7)-0.25=44.7.
This estimation of Kth
is in good accord with
experimental measurements of the gain of the Nd:YAG amplifier at the generation
threshold (Fig. 4b). Therefore it is possible to conclude that the
generation in the studied scheme was indeed caused by the self-consistent processes
of the RIG formation and by the increase in the amplitude of the generated waves
that were reflected from the RIG.
The generation pulses and the DE of the RIG were recorded in the presence of some
frequency shift between waves that write the RIG. This shift was realized by means
of the mirror M1 placed on a piezoelectric vibrator. When an ac voltage
with the piezoelectric-resonant frequency of 80 kHz was applied to the piezoelectric
element, the synchronisation of generated pulses with a definite phase
(φ) of the oscillating mirror and an increase in the
pulse amplitudes were observed (compare Fig. 5a and 5b). This fact can be explained by that this phase of
vibration corresponds to the optimal Doppler frequency shift of the waves reflected
from the moving mirror. The presence of the frequency shift optimal for the laser
generation in this experiment is in good accordance with the numerical calculations
that defined the resonant frequency shift provided by the moving intracavity mirror.
The observed generation in the absence of piezo vibration (Fig. 5a and 5e) can be explained by noise vibrations of all mirrors.
Fig. 5. Oscillograms of the laser radiation (top) and the voltage modulating the
mirror displacement (bottom): piezoelectric vibrator switch off (a, e),
piezoelectric vibrator switch on (b-d), the modulation frequency is
ν=80 kHz. (b); ν=1.5 kHz, the phase φ is
nonoptimal (c); ν=1.5 kHz, the phase j is near-optimal (d). The
flash-lamp pump energy per each amplifier is 32 J for (a, b), and 50 J for
(c)-(e). The vertical scales are the same for all oscillograms.
It was also observed experimentally that the duration of the generation pulses
decreased from 400 ns to 200 ns in the presence of mirror vibrations. Such temporal
behaviour of laser generation seems to be similar to the Q-switching in a laser with
an ordinary mirror. However, in the studied laser with a nonlinear mirror the energy
of the pulse train slightly increased because of the self-Q-switching (Fig. 6a), which is the difference from the ordinary Q-switch.
Another generation dynamics was realised when the period of the piezoelectric mirror
oscillations was much greater than the duration of a generation pulse (Fig. 5c-5e). In contrast to the high-frequency modulation, neither
pulse shortening nor ordering of the repetitive pulses was observed. On the other
hand, the energy of the generation pulses was found to be considerably increased at
the “true” phase of the mirror vibrations (Fig. 5d and 6).
Fig. 6. Dependencies of the energy of the generation pulse W and the DE of the RIG on
(a) flash-lamp-pump energy per each amplifier and (b) phase φ of
the voltage that modulates vibrations of an intracavity mirror. In Fig. 6a the mirror vibration is switched off (black
curve), the mirror vibration is at a frequency of ν=80 kHz (red
curve), and at 1.5 kHz with optimal phase (blue curve). Fig. 6b shows the dependence of the DE (squares and
fitted green curve) and the dependence of the energy of generation pulse
(circles and fitted braun curve); the horizontal lines are the energy (top)
and the DE (bottom) when the modulation was switched off, and the flash-lamp
pump energy is 50 J per each amplifier, ν=1.5 kHz.
These dependencies show that the mirror vibrations at a frequency of 1.5 kHz with an
optimal phase led to a strong growth of the RIG diffraction efficiency, a decrease
in the generation threshold, and to an increase in the peak pulse power and the
pulse train energy. These results can also be explained by the resonance of the
frequency detuning of the generating waves which induce the moving RIGs that
complete the laser cavity.
Therefore, the experimental consequence is that the use of the moving mirror inside
the cavity of the self-starting laser allows us to control the dynamics of the
generated beam and increase the DE of the RIG, which results in an increase in the
generated pulse-train energy. Note that the growth of the RIG by use of the
vibrating mirror improved the spatio-temporal quality of the generated beam (which
was demonstrated in Fig. 5). However, in the presence of strong vibrations of the
scheme components (which appeared, in particular, because of the amplifier pump with
a repetition rate of 10–30 Hz) the influence of the mirror movement on
the generation characteristics decreased.
4. Conclusion
The theoretical and experimental investigations have shown that the reciprocal cavity
of a self-starting Nd:YAG laser oscillator can be completed by resonant RIGs, which
are induced in the inverted laser crystal by generating beams. The self-consistent
increase of the moving RIGs and the optical waves beyond threshold results in the
generation of self-Q-switched pulses. The self-starting Nd:YAG laser with cavity on
the RIG is capable to generate high-average-power beams with good quality.
Stabilization of the generating pulses and an increase in the output power are
achieved by use of a vibrating intracavity mirror. The control of the vibrating
mirror offers the possibility of changing parameters of the generating waves.
5. Acknowledgments
This work was supported in part by the EOARD through grant No SPC99-4028 and by the
INTAS through grant No I 97-2112.
References and Links
I.M. Bel’dyugin, V.A. Berenberg, and A.E. Vasil’ev, et all, “Solid-state lasers with self-pumped PC mirrors in the active medium,” Sov. J. Quant. Electron. 19, 740–742 (1989). [CrossRef] | |
M.J. Damzen, R.P.M. Green, and K.S. Syed, “Self-adaptive solid-state oscillator formed by dynamic gain-gratings holograms,” Opt. Lett. 20, 1704–1706 (1995). [CrossRef] [PubMed] | |
A. Minassian, G.J. Crofts, and M.J. Damzen, “Self-starting Ti:sapphire holographic laser oscillator”, Opt. Lett. 22, 697–699 (1997). [CrossRef] [PubMed] | |
O.L. Antipov, A.S. Kuzhelev, V.A. Vorob’yov, and A.P. Zinov’ev, “Pulse repetitive Nd:YAG laser with distributed feedback by self-induced population grating,” Opt. Comm. 152, 313–318 (1998). [CrossRef] | |
O.L. Antipov, S.I. Belyaev, A.S. Kuzhelev, and A.P. Zinov’ev, “Nd:YAG laser with cavity formed by population inversion gratings,” in Laser resonators I, P. Galarneau and A.V. Kudryashov, eds, Proc. SPIE 3267, 181–190 (1998). | |
P. Sillard, A. Brignon, and J.-P. Huignard, “Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator,” IEEE J. Quant. Electron. 34, 465–472 (1998). [CrossRef] | |
O.L. Antipov, A.S. Kuzhelev, and A.P. Zinov’ev, “High average-power solid-state lasers with cavity formed by self-induced refractive index gratings,” in Laser resonators II , A.V. Kudryashov and P. Galarneau, eds., Proc. SPIE 3611, 147–156 (1999). | |
O.L. Antipov, A.S. Kuzhelev, D.V. Chausov, and A.P. Zinov’ev, “Dynamics of refractive index changes in a Nd:YAG laser crystal under Nd3+-ions excitation,” J. Opt. Soc. Am. B 16, 1072–1079 (1999). [CrossRef] | |
A.N. Oraevsky, “Quantum fluctuations and formation of coherency in laser,” J. Opt. Soc. of Am. 5, 933–945 (1988). [CrossRef] |
OCIS Codes
(140.3410) Lasers and laser optics : Laser resonators
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(140.3530) Lasers and laser optics : Lasers, neodymium
(190.4360) Nonlinear optics : Nonlinear optics, devices
ToC Category:
Research Papers
History
Original Manuscript: October 1, 1999
Published: December 6, 1999
Citation
Oleg Antipov, Alexander Kuzhelev, and Dmitry Chausov, "Formation of dynamic cavity in a self-starting high-average-power Nd:YAG laser oscillator," Opt. Express 5, 286-291 (1999)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-12-286
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References
- I. M. Bel'dyugin, V. A. Berenberg, A. E. Vasil'ev, et all, "Solid-state lasers with self-pumped PC mirrors in the active medium," Sov. J. Quant. Electron. 19, 740-742 (1989). [CrossRef]
- M. J. Damzen, R. P. M. Green, K. S. Syed, "Self-adaptive solid-state oscillator formed by dynamic gain-gratings holograms," Opt. Lett. 20, 1704-1706 (1995). [CrossRef] [PubMed]
- A. Minassian, G. J. Crofts, M. J. Damzen, "Self-starting Ti:sapphire holographic laser oscillator," Opt. Lett. 22, 697-699 (1997). [CrossRef] [PubMed]
- O. L. Antipov, A. S. Kuzhelev, V. A. Vorob'yov, A. P. Zinov'ev, "Pulse repetitive Nd:YAG laser with distributed feedback by self-induced population grating," Opt. Comm. 152, 313-318 (1998). [CrossRef]
- O. L. Antipov, S. I. Belyaev, A. S. Kuzhelev, A. P. Zinov'ev, "Nd:YAG laser with cavity formed by population inversion gratings," in Laser resonators I, P. Galarneau and A.V. Kudryashov, eds, Proc. SPIE 3267, 181-190 (1998).
- P. Sillard, A. Brignon, and J.-P. Huignard, "Gain-grating analysis of a self-starting self-pumped phase-conjugate Nd:YAG loop resonator," IEEE J. Quant. Electron. 34, 465-472 (1998). [CrossRef]
- O. L. Antipov, A. S. Kuzhelev, A. P. Zinov'ev, "High average-power solid-state lasers with cavity formed by self-induced refractive index gratings," in Laser resonators II, A.V. Kudryashov and P. Galarneau, eds., Proc. SPIE 3611, 147-156 (1999).
- O. L. Antipov, A. S. Kuzhelev, D. V. Chausov, and A. P. Zinov'ev, "Dynamics of refractive index changes in a Nd:YAG laser crystal under Nd 3+ -ions excitation," J. Opt. Soc. Am. B 16, 1072-1079 (1999). [CrossRef]
- A. N. Oraevsky, "Quantum fluctuations and formation of coherency in laser," J. Opt. Soc. of Am. 5, 933-945 (1988). [CrossRef]
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