Abstract

We present a comprehensive and systematic investigation of the fundamental physical limitations of Faraday isolation performance at high average powers that are due to thermally induced birefringence. First, the operation of various Faraday isolator designs by use of arbitrary orientation of cubic magneto-optic crystals is studied theoretically. It is shown that, for different Faraday isolator designs, different crystal orientations can optimize the isolation ratio. Second, thermo-optic and photoelastic constants for terbium gallium garnet crystals grown by different manufacturers were measured. Measurements of self-induced depolarization are made for various orientations of crystallographic axes. The measurements are in good agreement with our theoretical predictions. Based on our results, it is possible to select a crystal orientation that optimizes isolation performance at high average powers, resulting in a 5-dB enhancement over nonoptimized orientations.

© 2002 Optical Society of America

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    [CrossRef]
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2000 (4)

E. A. Khazanov, “Characteristic features of the operation of different designs of the Faraday isolator for high average laser-radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 147–151 (2000).
[CrossRef]

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

1999 (3)

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29, 59–64 (1999) [Kvant. Elektron. (Moscow) 26, 59–64, (1999).

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

1997 (2)

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

1992 (2)

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

T. V. Zarubina, G. T. Petrovsky, “Magnetooptical glasses made in Russia,” Opt. Zh. (J. Opt. Technology) 59, 48–52 (1992).

1980 (1)

L. N. Soms, A. A. Tarasov, V. V. Shashkin, “On the problem of depolarization of linearly polarized light by a YAG:Nd3+ laser rod under conditions of thermally induced birefringence,” Sov. J. Quantum Electron. 10, 350–351 (1980) [Kvant. Elektron. (Moscow) 7, 619–621, (1980)].

1979 (1)

L. N. Soms, A. A. Tarasov, “Thermal deformation in color-center laser active elements. 1. Theory,” Sov. J. Quantum Electron. 9, 1506–1508 (1979) [Kvant. Electron. (Moscow) 6, 2546–2551, (1979)].

1978 (1)

V. S. Averbakh, A. A. Betin, V. A. Gaponov, “Effects of stimulated self-action and scattering in gases and their influence on propagation of optical radiation (review),” Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) 21, 1077–1106 (1978).

1971 (1)

1970 (1)

W. Koechner, D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. QE-6, 557–566 (1970).
[CrossRef]

1967 (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” Appl. Phys. 38, 5149–5153 (1967).

1966 (1)

1964 (1)

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Andreev, N.

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, “Measurements of thermooptic characteristics of magnetoactive glasses,” in Conference on Lasers and Electro-Optics (CLEO/US), in OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 499–500.

Andreev, N. F.

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

Averbakh, V. S.

V. S. Averbakh, A. A. Betin, V. A. Gaponov, “Effects of stimulated self-action and scattering in gases and their influence on propagation of optical radiation (review),” Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) 21, 1077–1106 (1978).

Babin, A.

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, “Measurements of thermooptic characteristics of magnetoactive glasses,” in Conference on Lasers and Electro-Optics (CLEO/US), in OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 499–500.

Betin, A. A.

V. S. Averbakh, A. A. Betin, V. A. Gaponov, “Effects of stimulated self-action and scattering in gases and their influence on propagation of optical radiation (review),” Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) 21, 1077–1106 (1978).

Boley, B. A.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Dover, New York, 1960).

Dixon, R. W.

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” Appl. Phys. 38, 5149–5153 (1967).

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Eguchi, T.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Eichler, H. J.

H. J. Eichler, O. Mehl, J. Eichler, “Multi-amplifier arrangements with phase conjugation for power scaling of solid state lasers with high beam quality,” in Solid State Lasers VIII, R. Scheps, ed., Proc. SPIE3613, 166–176 (1999).
[CrossRef]

Eichler, J.

H. J. Eichler, O. Mehl, J. Eichler, “Multi-amplifier arrangements with phase conjugation for power scaling of solid state lasers with high beam quality,” in Solid State Lasers VIII, R. Scheps, ed., Proc. SPIE3613, 166–176 (1999).
[CrossRef]

Gaponov, V. A.

V. S. Averbakh, A. A. Betin, V. A. Gaponov, “Effects of stimulated self-action and scattering in gases and their influence on propagation of optical radiation (review),” Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) 21, 1077–1106 (1978).

Gursel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Hirano, Y.

Y. Hirano, S. Yamamoto, T. Tajime, H. Taniguchi, M. Nakamura, “High average power, room temperature operation of PPMgLN OPO,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), postdeadline papers, pp. 13–14.

Izawa, Y.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kan, H.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kanabe, T.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kandasamy, R.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kanzaki, T.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kato, Y.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kawada, Y.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kawashima, T.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Khazanov, E.

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, “Measurements of thermooptic characteristics of magnetoactive glasses,” in Conference on Lasers and Electro-Optics (CLEO/US), in OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 499–500.

Khazanov, E. A.

E. A. Khazanov, “Characteristic features of the operation of different designs of the Faraday isolator for high average laser-radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 147–151 (2000).
[CrossRef]

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

E. A. Khazanov, “Compensation of thermally induced polarization distortions in Faraday isolators,” Quantum Electron. 29, 59–64 (1999) [Kvant. Elektron. (Moscow) 26, 59–64, (1999).

E. A. Khazanov, “Suppression of self-induced depolarization of laser radiation in Faraday isolators,” in Optical Pulse and Beam Propagation, Y. B. Band, ed., Proc. SPIE3609, 181–192 (1999).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Reitze, “Investigation of self-induced distortions of laser radiation in lithium niobate and terbium gallium garnet,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 250–251.

Kiselev, A.

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, “Measurements of thermooptic characteristics of magnetoactive glasses,” in Conference on Lasers and Electro-Optics (CLEO/US), in OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 499–500.

Koechner, W.

W. Koechner, D. K. Rice, “Birefringence of YAG:Nd laser rods as a function of growth direction,” J. Opt. Soc. Am. 61, 758–766 (1971).
[CrossRef]

W. Koechner, D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. QE-6, 557–566 (1970).
[CrossRef]

Kulagin, O.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

Kulagin, O. V.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Reitze, “Investigation of self-induced distortions of laser radiation in lithium niobate and terbium gallium garnet,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 250–251.

Lai, K. S.

K. S. Lai, R. Wu, P. B. Phua, “Multiwatt KTiOPO4 optical parametric oscillators pumped within randomly and linearly polarized Nd:YAG laser cavities,” in Nonlinear Materials, Devices, and Applications, J. W. Pierce, ed., Proc. SPIE3928, 43–51 (2000).
[CrossRef]

Mal’shakov, A. N.

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

Matsui, H.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Mehl, O.

H. J. Eichler, O. Mehl, J. Eichler, “Multi-amplifier arrangements with phase conjugation for power scaling of solid state lasers with high beam quality,” in Solid State Lasers VIII, R. Scheps, ed., Proc. SPIE3613, 166–176 (1999).
[CrossRef]

Miyajima, H.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Miyamoto, M.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Movshevich, B.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

Nakai, S.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Nakamura, M.

Y. Hirano, S. Yamamoto, T. Tajime, H. Taniguchi, M. Nakamura, “High average power, room temperature operation of PPMgLN OPO,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), postdeadline papers, pp. 13–14.

Nakatsuka, M.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford University, London, 1964).

Okada, Y.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Palashov, O.

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

N. Andreev, A. Babin, A. Kiselev, O. Palashov, E. Khazanov, O. Shaveleov, T. Zarubina, “Thermooptical constant of magneto-active glasses,” J. Opt. Technol. 67, 556–558 (2000).
[CrossRef]

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, “Measurements of thermooptic characteristics of magnetoactive glasses,” in Conference on Lasers and Electro-Optics (CLEO/US), in OSA 1999 Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 499–500.

Palashov, O. V.

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

Pasmanik, G.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

Pasmanik, G. A.

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

Petrovsky, G. T.

T. V. Zarubina, G. T. Petrovsky, “Magnetooptical glasses made in Russia,” Opt. Zh. (J. Opt. Technology) 59, 48–52 (1992).

Phua, P. B.

K. S. Lai, R. Wu, P. B. Phua, “Multiwatt KTiOPO4 optical parametric oscillators pumped within randomly and linearly polarized Nd:YAG laser cavities,” in Nonlinear Materials, Devices, and Applications, J. W. Pierce, ed., Proc. SPIE3928, 43–51 (2000).
[CrossRef]

Poteomkin, A. K.

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

Quelle, F. W.

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Reitze, D.

E. Khazanov, N. Andreev, A. Babin, A. Kiselev, O. Palashov, D. Reitze, “Suppression of self-induced depolarization of high-power laser radiation in glass-based Faraday isolators,” J. Opt. Soc. Am. B 17, 99–102 (2000).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Reitze, “Investigation of self-induced distortions of laser radiation in lithium niobate and terbium gallium garnet,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 250–251.

Reitze, D. H.

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

Rice, D. K.

W. Koechner, D. K. Rice, “Birefringence of YAG:Nd laser rods as a function of growth direction,” J. Opt. Soc. Am. 61, 758–766 (1971).
[CrossRef]

W. Koechner, D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. QE-6, 557–566 (1970).
[CrossRef]

Robinson, C. C.

Rodchenkov, V.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

Scott, A.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

Sergeev, A. M.

N. F. Andreev, O. V. Palashov, A. K. Poteomkin, A. M. Sergeev, E. A. Khazanov, D. H. Reitze, “45dB Faraday isolator for 100W average radiation power,” Quantum Electron. [Kvant. Elektron. (Moscow)] 30, 1107–1108 (2000).
[CrossRef]

Shashkin, V. V.

L. N. Soms, A. A. Tarasov, V. V. Shashkin, “On the problem of depolarization of linearly polarized light by a YAG:Nd3+ laser rod under conditions of thermally induced birefringence,” Sov. J. Quantum Electron. 10, 350–351 (1980) [Kvant. Elektron. (Moscow) 7, 619–621, (1980)].

Shaveleov, O.

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Soan, P.

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

Soms, L. N.

L. N. Soms, A. A. Tarasov, V. V. Shashkin, “On the problem of depolarization of linearly polarized light by a YAG:Nd3+ laser rod under conditions of thermally induced birefringence,” Sov. J. Quantum Electron. 10, 350–351 (1980) [Kvant. Elektron. (Moscow) 7, 619–621, (1980)].

L. N. Soms, A. A. Tarasov, “Thermal deformation in color-center laser active elements. 1. Theory,” Sov. J. Quantum Electron. 9, 1506–1508 (1979) [Kvant. Electron. (Moscow) 6, 2546–2551, (1979)].

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Tajime, T.

Y. Hirano, S. Yamamoto, T. Tajime, H. Taniguchi, M. Nakamura, “High average power, room temperature operation of PPMgLN OPO,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), postdeadline papers, pp. 13–14.

Taniguchi, H.

Y. Hirano, S. Yamamoto, T. Tajime, H. Taniguchi, M. Nakamura, “High average power, room temperature operation of PPMgLN OPO,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), postdeadline papers, pp. 13–14.

Tanner, D.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

Tarasov, A. A.

L. N. Soms, A. A. Tarasov, V. V. Shashkin, “On the problem of depolarization of linearly polarized light by a YAG:Nd3+ laser rod under conditions of thermally induced birefringence,” Sov. J. Quantum Electron. 10, 350–351 (1980) [Kvant. Elektron. (Moscow) 7, 619–621, (1980)].

L. N. Soms, A. A. Tarasov, “Thermal deformation in color-center laser active elements. 1. Theory,” Sov. J. Quantum Electron. 9, 1506–1508 (1979) [Kvant. Electron. (Moscow) 6, 2546–2551, (1979)].

Terada, M.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Weiner, J. H.

B. A. Boley, J. H. Weiner, Theory of Thermal Stresses (Dover, New York, 1960).

Weiss, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Wu, R.

K. S. Lai, R. Wu, P. B. Phua, “Multiwatt KTiOPO4 optical parametric oscillators pumped within randomly and linearly polarized Nd:YAG laser cavities,” in Nonlinear Materials, Devices, and Applications, J. W. Pierce, ed., Proc. SPIE3928, 43–51 (2000).
[CrossRef]

Yamamoto, S.

Y. Hirano, S. Yamamoto, T. Tajime, H. Taniguchi, M. Nakamura, “High average power, room temperature operation of PPMgLN OPO,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 39 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), postdeadline papers, pp. 13–14.

Yamanaka, M.

T. Kanabe, T. Kawashima, H. Matsui, Y. Okada, Y. Kawada, T. Eguchi, R. Kandasamy, Y. Kato, M. Terada, M. Yamanaka, M. Nakatsuka, Y. Izawa, S. Nakai, T. Kanzaki, H. Miyajima, M. Miyamoto, H. Kan, “Laser-diode-pumped 10-J × 10-Hz Nd:glass slab laser system,” in Advanced High-Power Lasers, M. Osinsk, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 190–197 (2000).
[CrossRef]

Yoshida, S.

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Reitze, “Investigation of self-induced distortions of laser radiation in lithium niobate and terbium gallium garnet,” in Conference on Lasers and Electro-Optics (CLEO), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 250–251.

Zarubina, T.

Zarubina, T. V.

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

T. V. Zarubina, G. T. Petrovsky, “Magnetooptical glasses made in Russia,” Opt. Zh. (J. Opt. Technology) 59, 48–52 (1992).

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser-Interferometer-Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. (1)

R. W. Dixon, “Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners,” Appl. Phys. 38, 5149–5153 (1967).

IEEE J. Quantum Electron. (3)

W. Koechner, D. K. Rice, “Effect of birefringence on the performance of linearly polarized YAG:Nd lasers,” IEEE J. Quantum Electron. QE-6, 557–566 (1970).
[CrossRef]

N. Andreev, E. Khazanov, O. Kulagin, B. Movshevich, O. Palashov, G. Pasmanik, V. Rodchenkov, A. Scott, P. Soan, “A two-channel repetitively pulsed Nd:YAG laser operating at 25 Hz with diffraction-limited beam quality,” IEEE J. Quantum Electron. 35, 110–114 (1999).
[CrossRef]

E. A. Khazanov, O. V. Kulagin, S. Yoshida, D. Tanner, D. Reitze, “Investigation of self-induced depolarization of laser radiation in terbium gallium garnet,” IEEE J. Quantum Electron. 35, 1116–1122 (1999).
[CrossRef]

Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) (1)

V. S. Averbakh, A. A. Betin, V. A. Gaponov, “Effects of stimulated self-action and scattering in gases and their influence on propagation of optical radiation (review),” Izv. Vyssh. Ucheben. Zaved. Radiofiz. (Sov. Radiophys.) 21, 1077–1106 (1978).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

J. Opt. Technol. (1)

Opt. Zh. (J. Opt. Technol.) (1)

T. V. Zarubina, A. N. Mal’shakov, G. A. Pasmanik, A. K. Poteomkin, “Comparative characteristics of magnetooptical glasses,” Opt. Zh. (J. Opt. Technol.) 64, 67–71 (1997).

Opt. Zh. (J. Opt. Technology) (1)

T. V. Zarubina, G. T. Petrovsky, “Magnetooptical glasses made in Russia,” Opt. Zh. (J. Opt. Technology) 59, 48–52 (1992).

Quantum Electron. (2)

N. Andreev, O. Palashov, E. Khazanov, G. Pasmanik, “Four-channel pulse-periodic Nd:YAG laser with diffraction-limited output radiation,” Quantum Electron. 27, 565–569 (1997) [Kvant. Elektron. (Moscow) 24, 581–585 (1997)].

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K. S. Lai, R. Wu, P. B. Phua, “Multiwatt KTiOPO4 optical parametric oscillators pumped within randomly and linearly polarized Nd:YAG laser cavities,” in Nonlinear Materials, Devices, and Applications, J. W. Pierce, ed., Proc. SPIE3928, 43–51 (2000).
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Figures (8)

Fig. 1
Fig. 1

Cartesian xyz and cylindrical rφ z coordinates. k and E are the wave vector and the polarization of the electric field of the laser, and e 1 and e 2 are eigenpolarizations at a point (r, φ).

Fig. 2
Fig. 2

Experimental (in a single-pass scheme) and theoretical dependences of depolarization on power for three of the crystals in Table 2: diamonds, sample 1; triangles, sample 2; circles, sample 3.

Fig. 3
Fig. 3

Experimental (in a two-pass scheme) and theoretical dependences of depolarization on power for crystal sample 8, θ = 0°, open squares, thin line; θ = 45°, filled squares, thick line; sample 4 crosses and dotted line.

Fig. 4
Fig. 4

Geometry of the experiment for the measurement of depolarization at an arbitrary orientation.

Fig. 5
Fig. 5

Depolarization in crystal sample 8 versus angle α at θ = 90° and β = 21°.

Fig. 6
Fig. 6

Theoretical (lines) and experimental (points) dependences of depolarization normalized to p 2 in crystal sample 8 versus angle β at α = 0°, and α = 45° (θ = 90° in both cases).

Fig. 7
Fig. 7

Dependence of depolarization at R = 5, ξ = 2.2, p = 1 in the (a) traditional design and (b) the FIQR design at β = 0° (curve 1); β = 22.5° (curve 2); β = 45° (curve 3); β = 54.8° (curve 4); β = 67.5° (curve 5); β = 90° (curve 6). Note that the amplitude variance of the depolarization ratio is quite small in (b).

Fig. 8
Fig. 8

Coordinates xyz rotated relative to the abc crystal pattern.

Tables (2)

Tables Icon

Table 1 Values of the Constants for Flat-Shaped and Gaussian Beams at Different R

Tables Icon

Table 2 Parameters of TGG Crystals and Isolation Ratios Obtained with the Traditional Design (1/γ0min), and the FIQR Design (1/γR) at a Laser Power of 300 W

Equations (24)

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Q=1LdLdTn0341+ν1-νp11-p12.
γ0=2π2P002πdφ 0R0 δl2 sin22Ψ-2θ-π/4Irrdr,γR=π/2-22π4P002πdφ 0R0 δl4Irrdr,Ir=I0fr2r02,P0=2πI00R0 fr2r02rdr=πr02I00R fydy,y=r2r02,  R=R02r02,
δl=kL n032B11-B222+4B1221/2,tan2Ψ=2B12B11-B22.
γ0=p2π2Fd1+Hd2+sin4θFd7+Hd3-cos4θFd8+Hd6,
γR=π/2-22p42π42Nd12+M4d1d2+d42+d52+K2d22+d32+d62,
p=Lλα0Qκ P0,
d1=a12+b121-ξ2,d2=12a22+2a32+b321-ξ2+a2+b31-ξξ+ξ2,d3=12a22-b321-ξ2+a2-b31-ξξ,d4=2a1a2+b1b21-ξ2+2a11-ξξ,d5=2a1a3+b1b31-ξ2+2b11-ξξ,d6=a3a2+b31-ξ2+2a31-ξξ,d7=a12-b121-ξ2, d8=2a1b11-ξ2,
F=0R fg2y, Rdy0R fdy3,H=0R fh2dy0R fdy3,K=0R fh4dy0R fdy5M=0R fh2g2y, Rdy0R fdy5, N=0R fg4y, Rdy0R fdy5.
fy=exp-y,  fy=1 for y<10 for y>1,
tan4θopt=-Fd7+Hd3Fd8+Hd6,
γ0min=γ0θopt=p2π2Fd1+Hd2-Fd7+Hd32+Fd8+Hd621/2.
γ0001=p2π2 Hsin22θ+π4+ξ2 cos22θ+π4,
γR001=3π/2-22p48π4 Kξ4+23 ξ2+1,
γ0111=p29π2 H1+2ξ2,
γR111=π/2-22p481π4 K1+2ξ4.
γH=0θ=π28 γ0θ+π/8.
B11-B22=p11-p12Σa11-ξ+Δ cos2φ×a21-ξ+ξ+Δ sin2φa31-ξ,2B12=p11-p12Σb11-ξ+Δ cos2φb21-ξ+Δ sin2φb31-ξ+ξ,
a1=-sin2 βcos2 β-cos2 α sin2 αcos2 β+1,a2=1-sin2 β cos2 β-cos2 α sin2 αcos2 β+12,a3=-sin 4α cos βcos2 β+14,b1=sin 4α cos β sin2 β4,b2=a3,  b3=sin2 2α cos2 β,
Δ=εrr-εφφ,  Σ=εrr+εφφ-2εzz,
Δ=1+ν1-ν1LdLdT1r20rdTdr r2dr,Σ=1+ν1-ν1LdLdT1R020R0dTdr r2dr-rR0dTdrdr.
dTdr=-α0I0κr022r0r2/r02 fydy.
B11-B22=-Qα0I0πr02πκn03ga11-ξ+h cos2φa21-ξ+ξ+h sin2φa31-ξ,2B12=-Qα0I0πr02πκn03gb11-ξ+h cos2φb2×1-ξ+h sin2φb31-ξ+ξ,
gy, R=1R0Rdz 0z fxdx-yRdzz0z fxdx,hy=1y0ydz 0z fydy.
qR, y=0R1-exp-zR-zRzdz-0y1-exp-zzdz

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