Abstract

We analyze and investigate experimentally the output stability and the frequency tuning characteristics of weakly triply resonant silver gallium sulfide (AgGaS2) optical parametric oscillators. These oscillators are subject to thermally induced bistability and passive self-frequency-locking phenomena. The robust self-frequency-locking on a single-mode pair (thermal lock) originates from the material’s ability to correct external cavity-length perturbations, which would normally cause a mode hop, by increasing or decreasing the optical path length of the cavity through the thermo-optic effect triggered by the intracavity signal–idler power fluctuations. The Fourier frequency bandwidth of this passive servo is limited to ∼1 kHz by the thermal diffusion time constant, which is proportional to the ratio of the specific heat to the thermal conductivity Cp/Kc. A thermal feedback servo gain as high as 180 is obtained, owing to the large thermal figure of merit η=(dn/dT)/Kc of AgGaS2, leading to routine passive mode-hop-free operation for more than 30 min, without the need for an external cavity-length servo. Analysis of the stability range of the thermally loaded standing-wave resonator shows that thermal lensing is less critical for shorter doubly resonant optical parametric oscillator cavities employing shorter-curvature mirrors, in agreement with experimental observations. When a doubly resonant oscillator operates near the boundary of the power stability range a self-pulsing behavior is observed on a number of axial mode pairs. This self-pulsing is found to originate from the destabilization of a self-locked cw state, and the transition from self-pulsing to the stable self-frequency-locked state is found to be controlled by the pump frequency detuning. The passive stability allows the single-parameter frequency tuning to be studied. Under pure thermal lock operation the oscillators show a tendency to resist the pump frequency and temperature tuning processes. When an external cavity-length servo is implemented continuous tuning over 850 MHz, by means of the pump frequency tuning (Δνs/Δνp0.66), and over 100 MHz, by means of the crystal temperature (Δνs/ΔT250 MHz/°C), is obtained. These tuning ranges are in good agreement with calculations based on a cold doubly resonant oscillator.

© 1999 Optical Society of America

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  53. R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
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1999 (1)

1998 (8)

G. M. Gibson, M. H. Dunn, and M. J. Padgett, “Application of a continuously tunable, cw optical parametric oscillator for high-resolution spectroscopy,” Opt. Lett. 23, 40–42 (1998).
[CrossRef]

A. Douillet and J.-J. Zondy, “Low-threshold, self-frequency-stabilized AgGaS2 continuous-wave subharmonic optical parametric oscillator,” Opt. Lett. 23, 1259–1261 (1998).
[CrossRef]

E. J. Mason and N. C. Wong, “Observation of two distinct phase states in a self-phase-locked type II phase-matched optical parametric oscillator,” Opt. Lett. 23, 1733–1735 (1998).
[CrossRef]

J. D. Lindsay, G. A. Turnbull, M. H. Dunn, and M. Ebrahimzadeh, “Doubly resonant continuous-wave optical parametric oscillator pumped by a single-mode diode laser,” Opt. Lett. 23, 1889–1891 (1998).
[CrossRef]

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

Y. C. Chen and W. Z. Lin, “Thick lens model for self-focusing in Kerr medium,” Appl. Phys. Lett. 73, 429–431 (1998).
[CrossRef]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

1997 (9)

A. Sennaroglu, A. Askar, and F. M. Atay, “Quantitative study of laser beam propagation in a thermally loaded absorber,” J. Opt. Soc. Am. B 14, 356–363 (1997).
[CrossRef]

J.-J. Zondy and D. Touahri, “Updated thermo-optic coefficients of AgGaS2 from temperature-tuned noncritical 3ω− ω→2ω infrared parametric amplification,” J. Opt. Soc. Am. B 14, 1331–1338 (1997).
[CrossRef]

G. S. Agarwal and S. D. Gupta, “Model for mode hopping in optical parametric oscillators,” J. Opt. Soc. Am. B 14, 2174–2180 (1997).
[CrossRef]

J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am. B 14, 2481–2497 (1997).
[CrossRef]

P. L. Hansen and P. Buchhave, “Thermal self-frequency locking of a doubly resonant optical parametric oscillator,” Opt. Lett. 22, 1074–1076 (1997).
[CrossRef] [PubMed]

K. Stoll, J.-J. Zondy, and O. Acef, “Fourth-harmonic generation of a continuous-wave CO2 laser by use of an AgGaSe2/ZnGeP2 doubly resonant device,” Opt. Lett. 22, 1302–1304 (1997).
[CrossRef]

K. An, B. A. Sones, C. Fang-Yen, R. R. Dasari, and M. S. Feld, “Optical bistability induced by mirror absorption: measurement of absorption coefficients at the sub-ppm level,” Opt. Lett. 22, 1433–1435 (1997).
[CrossRef]

D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22, 1553–1555 (1997).
[CrossRef]

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

1996 (2)

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Commun. 127, 69–72 (1996).
[CrossRef]

P. Dubé, L.-S. Ma, J. Ye, P. Jungner, and J. L. Hall, “Thermally-induced self-locking of an optical cavity by overtone absorption in acetylene gas,” J. Opt. Soc. Am. B 13, 2041–2054 (1996).
[CrossRef]

1995 (5)

C. Richy, K. I. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, “Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator,” J. Opt. Soc. Am. B 12, 456–461 (1995).
[CrossRef]

Y. Fang, Y. Cui, and M. H. Dunn, “Thermal dependence of the principal refractive indices of lithium triborate,” J. Opt. Soc. Am. B 12, 638–643 (1995).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

1994 (2)

M. J. Padgett, F. G. Colville, and M. H. Dunn, “Mode selection in doubly-resonant optical parametric oscillators,” IEEE J. Quantum Electron. 30, 2979–2985 (1994).
[CrossRef]

J. D. Beasley, “Thermal conductivities of some novel nonlinear optical materials,” Appl. Opt. 33, 1000–1003 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (4)

D. Lee and N. C. Wong, “Tunable optical frequency division using a phase-locked optical parametric oscillator,” Opt. Lett. 17, 13–15 (1992).
[CrossRef] [PubMed]

D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, and J. G. Fujimoto, “Self-focusing-induced saturable loss for laser mode locking,” Opt. Lett. 17, 511–513 (1992).
[CrossRef] [PubMed]

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

1991 (1)

1990 (1)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

1989 (1)

1988 (1)

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

1987 (2)

R. S. Feigelson and R. K. Route, “Recent developments in the growth of chalcopyrite crystals for nonlinear infrared applications,” Opt. Eng. 26, 113–119 (1987).
[CrossRef]

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

1983 (1)

1980 (1)

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transition in sub/second harmonic generation: I. Semiclassical theory,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

1973 (1)

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[CrossRef]

1969 (1)

S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
[CrossRef]

1968 (2)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused laser beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

1966 (1)

A. Yariv, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

1962 (1)

Acef, O.

Acioli, L. H.

Agarwal, G. S.

Al-Tahtamouni, R.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

An, K.

Askar, A.

Atay, F. M.

Beasley, J. D.

Belanger, P. A.

Bencheikh, K.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Benko, Z.

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

Bierlein, J. D.

Biraben, F.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

Bosenberg, W. R.

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused laser beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Buchhave, P.

Byer, R. L.

Canarelli, P.

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

Cerullo, G.

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Chen, Y. C.

Y. C. Chen and W. Z. Lin, “Thick lens model for self-focusing in Kerr medium,” Appl. Phys. Lett. 73, 429–431 (1998).
[CrossRef]

Clairon, A.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

Cohadon, P. F.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

Colville, F. G.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

M. J. Padgett, F. G. Colville, and M. H. Dunn, “Mode selection in doubly-resonant optical parametric oscillators,” IEEE J. Quantum Electron. 30, 2979–2985 (1994).
[CrossRef]

Cui, Y.

Curl, R. F.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

Dasari, R. R.

Davis, L.

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

de Beauvoir, B.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

De Silvestri, S.

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Debuisschert, T.

Dlugokencky, E. J.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

Douillet, A.

Drummond, P. D.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transition in sub/second harmonic generation: I. Semiclassical theory,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

Dubé, P.

Dunn, M. H.

Ebrahimzadeh, M.

Eckardt, R. C.

Eimerl, D.

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Fabre, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

C. Richy, K. I. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, “Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator,” J. Opt. Soc. Am. B 12, 456–461 (1995).
[CrossRef]

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-II continuous-wave optical parametric oscillation and frequency tuning characteristics,” J. Opt. Soc. Am. B 10, 1668–1680 (1993).
[CrossRef]

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

Fang, Y.

Fang-Yen, C.

Feigelson, R. S.

R. S. Feigelson and R. K. Route, “Recent developments in the growth of chalcopyrite crystals for nonlinear infrared applications,” Opt. Eng. 26, 113–119 (1987).
[CrossRef]

Fejer, M. M.

Feld, M. S.

Felder, R.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

Fields, R. A.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Fincher, C. L.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Fujimoto, J. G.

Fukui, T.

Fukuyama, Y.

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

Gatti, A.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

Georgiev, D.

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Geusic, J. E.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Giacobino, E.

Gibson, G. M.

Gordon, E. K.

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Gupta, S. D.

Hall, J. L.

Hansen, P. L.

Harris, S. E.

S. E. Harris, “Tunable optical parametric oscillators,” Proc. IEEE 57, 2096–2113 (1969).
[CrossRef]

Haus, H. A.

Henderson, A. J.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Herrmann, J.

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Hielscher, A. H.

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

Hilico, L.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

Hollberg, L.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

Horowicz, R. J.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

Huang, D.

Ikegami, T.

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Commun. 127, 69–72 (1996).
[CrossRef]

Innocenzi, M. E.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Jundt, D. H.

Jungner, P.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused laser beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

Kozlovsky, W. J.

Kubota, S.

Kurosu, T.

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

Lang, M.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Lee, D.

Levinstein, H. J.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Lin, W. Z.

Y. C. Chen and W. Z. Lin, “Thick lens model for self-focusing in Kerr medium,” Appl. Phys. Lett. 73, 429–431 (1998).
[CrossRef]

Lindsay, J. D.

Lugiato, L.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

C. Richy, K. I. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, “Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator,” J. Opt. Soc. Am. B 12, 456–461 (1995).
[CrossRef]

Lugiato, L. A.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

Ma, L.-S.

Magni, V.

V. Magni, G. Cerullo, and S. De Silvestri, “ABCD matrix analysis of propagation of Gaussian beams through Kerr media,” Opt. Commun. 96, 348–355 (1993).
[CrossRef]

Marte, M. A. M.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

Mason, E. J.

Masuda, H.

McNeil, K. J.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transition in sub/second harmonic generation: I. Semiclassical theory,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

Mlynek, J.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Myers, L. E.

Nabors, C. D.

Nez, F.

D. Touahri, O. Acef, A. Clairon, J.-J. Zondy, R. Felder, L. Hilico, B. de Beauvoir, F. Biraben, and F. Nez, “Frequency measurement of the 5S1/2(F=3)–5D5/2(F=5) two-photon transition in rubidium,” Opt. Commun. 133, 471–478 (1997).
[CrossRef]

Ohshima, S.

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Commun. 127, 69–72 (1996).
[CrossRef]

Oldano, C.

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

Padgett, M.

Padgett, M. J.

G. M. Gibson, M. H. Dunn, and M. J. Padgett, “Application of a continuously tunable, cw optical parametric oscillator for high-resolution spectroscopy,” Opt. Lett. 23, 40–42 (1998).
[CrossRef]

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

M. J. Padgett, F. G. Colville, and M. H. Dunn, “Mode selection in doubly-resonant optical parametric oscillators,” IEEE J. Quantum Electron. 30, 2979–2985 (1994).
[CrossRef]

Pare, C.

Petrov, K. P.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

Petsas, K. I.

Pierce, J. W.

Richy, C.

Ritsch, H.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

Route, R. K.

R. S. Feigelson and R. K. Route, “Recent developments in the growth of chalcopyrite crystals for nonlinear infrared applications,” Opt. Eng. 26, 113–119 (1987).
[CrossRef]

Rubin, J. J.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Sakuma, E.

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Commun. 127, 69–72 (1996).
[CrossRef]

Schiller, S.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Schneider, K.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Schwob, C.

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

Sennaroglu, A.

Siegman, A. E.

Simon, U.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

Singh, S.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Sizmann, A.

Slyusarev, S.

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

T. Ikegami, S. Slyusarev, S. Ohshima, and E. Sakuma, “Accuracy of an optical parametric oscillator as an optical frequency divider,” Opt. Commun. 127, 69–72 (1996).
[CrossRef]

Smith, R. G.

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[CrossRef]

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Sones, B. A.

Stamm, U.

D. Georgiev, J. Herrmann, and U. Stamm, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Stoll, K.

Stortz, R.

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

Tittel, F. K.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

Touahri, D.

Turnbull, G. A.

Ulman, M.

Van Uitert, L. G.

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

Vanherzeele, H.

Velsko, S.

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Walls, D. F.

P. D. Drummond, K. J. McNeil, and D. F. Walls, “Non-equilibrium transition in sub/second harmonic generation: I. Semiclassical theory,” Opt. Acta 27, 321–335 (1980).
[CrossRef]

Waltman, S.

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

Wiechmann, W.

Wong, N. C.

Yariv, A.

A. Yariv, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

Ye, J.

Yura, H. T.

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Zalkin, A.

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

Zhang, J.

A. J. Henderson, M. J. Padgett, F. G. Colville, J. Zhang, and M. H. Dunn, “Doubly-resonant optical parametric oscillators: tuning behaviour and stability requirements,” Opt. Commun. 119, 256–264 (1995).
[CrossRef]

Zondy, J.-J.

Appl. Opt. (3)

Appl. Phys. B (4)

R. Al-Tahtamouni, K. Bencheikh, R. Stortz, K. Schneider, M. Lang, J. Mlynek, and S. Schiller, “Long-term stable operation and absolute frequency stabilization of a doubly resonant parametric oscillator,” Appl. Phys. B 66, 733–739 (1998).
[CrossRef]

C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66, 685–699 (1998).
[CrossRef]

K. P. Petrov, S. Waltman, U. Simon, R. F. Curl, F. K. Tittel, E. J. Dlugokencky, and L. Hollberg, “Detection of methane in air using diode-laser pumped difference-frequency generation near 3.2 μm,” Appl. Phys. B 61, 553–558 (1995).
[CrossRef]

T. Ikegami, S. Slyusarev, T. Kurosu, Y. Fukuyama, and S. Ohshima, “Characteristics of a cw monolithic KTiOPO4 optical parametric oscillator,” Appl. Phys. B 66, 719–725 (1998).
[CrossRef]

Appl. Phys. Lett. (3)

M. E. Innocenzi, H. T. Yura, C. L. Fincher, and R. A. Fields, “Thermal modelling of continuous-wave end-pumped solid-state lasers,” Appl. Phys. Lett. 56, 1831–1833 (1990).
[CrossRef]

Y. C. Chen and W. Z. Lin, “Thick lens model for self-focusing in Kerr medium,” Appl. Phys. Lett. 73, 429–431 (1998).
[CrossRef]

R. G. Smith, J. E. Geusic, H. J. Levinstein, J. J. Rubin, S. Singh, and L. G. Van Uitert, “Continuous optical parametric oscillation in Ba2NaNb3O15,” Appl. Phys. Lett. 12, 308–310 (1968).
[CrossRef]

IEEE J. Quantum Electron. (4)

P. Canarelli, Z. Benko, A. H. Hielscher, R. F. Curl, and F. K. Tittel, “Measurement of nonlinear coefficient and phase matching characteristics of AgGaS2,” IEEE J. Quantum Electron. 28, 52–55 (1992).
[CrossRef]

R. G. Smith, “A study of factors affecting the performance of a continuously pumped doubly resonant optical parametric oscillator,” IEEE J. Quantum Electron. QE-9, 530–541 (1973).
[CrossRef]

A. Yariv, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

M. J. Padgett, F. G. Colville, and M. H. Dunn, “Mode selection in doubly-resonant optical parametric oscillators,” IEEE J. Quantum Electron. 30, 2979–2985 (1994).
[CrossRef]

J. Appl. Phys. (2)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused laser beams,” J. Appl. Phys. 39, 3597–3639 (1968).
[CrossRef]

D. Eimerl, L. Davis, S. Velsko, E. K. Gordon, and A. Zalkin, “Optical, mechanical and thermal properties of barium borate,” J. Appl. Phys. 62, 1968–1983 (1987).
[CrossRef]

J. Opt. Soc. Am. B (11)

C. Richy, K. I. Petsas, E. Giacobino, C. Fabre, and L. Lugiato, “Observation of bistability and delayed bifurcation in a triply resonant optical parametric oscillator,” J. Opt. Soc. Am. B 12, 456–461 (1995).
[CrossRef]

Y. Fang, Y. Cui, and M. H. Dunn, “Thermal dependence of the principal refractive indices of lithium triborate,” J. Opt. Soc. Am. B 12, 638–643 (1995).
[CrossRef]

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995).
[CrossRef]

P. Dubé, L.-S. Ma, J. Ye, P. Jungner, and J. L. Hall, “Thermally-induced self-locking of an optical cavity by overtone absorption in acetylene gas,” J. Opt. Soc. Am. B 13, 2041–2054 (1996).
[CrossRef]

A. Sennaroglu, A. Askar, and F. M. Atay, “Quantitative study of laser beam propagation in a thermally loaded absorber,” J. Opt. Soc. Am. B 14, 356–363 (1997).
[CrossRef]

J.-J. Zondy and D. Touahri, “Updated thermo-optic coefficients of AgGaS2 from temperature-tuned noncritical 3ω− ω→2ω infrared parametric amplification,” J. Opt. Soc. Am. B 14, 1331–1338 (1997).
[CrossRef]

G. S. Agarwal and S. D. Gupta, “Model for mode hopping in optical parametric oscillators,” J. Opt. Soc. Am. B 14, 2174–2180 (1997).
[CrossRef]

J.-J. Zondy, D. Touahri, and O. Acef, “Absolute value of the d36 nonlinear coefficient of AgGaS2: prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider,” J. Opt. Soc. Am. B 14, 2481–2497 (1997).
[CrossRef]

J. D. Bierlein and H. Vanherzeele, “Potassium titanyl phosphate: properties and new applications,” J. Opt. Soc. Am. B 6, 622–633 (1989).
[CrossRef]

R. C. Eckardt, C. D. Nabors, W. J. Kozlovsky, and R. L. Byer, “Optical parametric oscillator frequency tuning and control,” J. Opt. Soc. Am. B 8, 646–667 (1991).
[CrossRef]

T. Debuisschert, A. Sizmann, E. Giacobino, and C. Fabre, “Type-II continuous-wave optical parametric oscillation and frequency tuning characteristics,” J. Opt. Soc. Am. B 10, 1668–1680 (1993).
[CrossRef]

Nuovo Cimento D (1)

L. A. Lugiato, C. Oldano, C. Fabre, E. Giacobino, and R. J. Horowicz, “Bistability, self-pulsing and chaos in optical parametric oscillators,” Nuovo Cimento D 10, 957–977 (1988).
[CrossRef]

Opt. Acta (1)

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Figures (17)

Fig. 1
Fig. 1

Schematic experimental setup: ECDL, extended-cavity diode laser; FI, 40-dB Faraday isolator; PBS, polarizing beam splitter; LWP, long-wave-pass interference filter; CFP-P, pump wave confocal Fabry–Perot analyzer; TEC, thermo-electric cooler; PZT, piezoelectric transducer. The pump beam is polarized in the plane of the figure; the subharmonics are polarized in the vertical plane. The DRO mirrors are mounted on two separate stable but standard commercial mirror mounts. The crystal temperature is stabilized to better than 20 mK by use of a proportional, integral, and differential controller.

Fig. 2
Fig. 2

Normalized intracavity power y=Pc/Pcm versus the cold cavity detuning δ as given by Eq. (7) for a resonator containing a thermal positive Kerr-like medium (Δ=9). For a fixed frequency ν, δ represents the cavity-length change. The parameter values used are related to the pump frequency. A bistable transmission pattern is obtained, depending on whether δ is increasing or decreasing. The Lorentzian curve (thin curve) is the cold resonator fringe (β=0). For increasing δ, the cavity resonance frequency moves in the direction of the scan as the intracavity power grows, which explains the broader feature compared with the cold resonance width. The thermal lock is effective within the Δ range. The inset represents the intra-cavity power Pc bistability curve as a function of the input pump power Pin (proportional to Pcm, e.g., Δ), for a fixed cold detuning δ=3. The bistable feature can be understood with a graphical solution of Eq. (5), rewritten as Pc/Pcm=[1+(δ-βPc/Γ)2]-1 as a function of Pc. 29 The solution(s) is (are) given by the intersection of a straight line of slope 1/Pcm with a Lorentzian function of Pc centered at P0c(δ)=Γδ/β. Depending on the value of δ, as Pcm increases (starting from a small value), the stable solution(s) is (are) either single valued (power limiting or optical transistor case) or double valued (optical switching case, as in the inset).

Fig. 3
Fig. 3

Idler beam radius versus normalized axial position inside the cavity, measured from the input mirror. The crystal length is lc=15 mm, with n0=2.5 and λ=2.5 µm. The dashed curves correspond to a beam radius without a thermal lens (p=0); the solid curves, to a lens power p=50 D. Curves a and a are plotted for R=10 mm, d=8 mm (L=25 mm, e=2 mm); curves b and b, for R=50 mm, d=8 mm (L=25 mm, e=2 mm); curves c and c for R=50 mm, d=10.5 mm (L=30 mm, e=4.5 mm). The relative effect of thermal lensing is stronger for the loose-focus cavity geometries b and c, for which the two foci are located near the crystal ends. The strong-focus cavity geometry with d/R=0.8 is less affected.

Fig. 4
Fig. 4

Idler beam waist w0(p) versus lens power for the three resonator geometries considered in Fig. 3. Curve a is plotted with R=10 mm, d=8 mm; curve b, for R=50 mm, d=8 mm; curve c for R=50 mm, d=10.5 mm. The cold cavity focusing parameters ξ=lc/b are ξ(a)=0.53, ξ(b)=0.16, and ξ(c)=0.14. For the strong-focusing cold resonator geometry, the stability range is wider and the waist variation smoother.

Fig. 5
Fig. 5

Scanning output pump and subharmonic patterns at threshold for DRO-1 (with AGS-1) set to L=33 mm, showing two consecutive typical self-locked pump fringes on the contracting cavity-length part of the triangular PZT voltage modulation. The input pump power is 375 mW. At low pump power (<50 mW), the corresponding fringe pattern is Lorentzian, with a finesse of 6. These sharp resonances broaden for increasing power, leading to a triangular bistable shape similar to the theoretical curve of Fig. 2. On the expanding length ramp of the PZT voltage modulation (not shown here, but in Fig. 9), the pump fringes look like sharp spikes because of the positive feedback effect of the thermal lock. To proceed to the thermal locking on one pump fringe, the voltage modulation is first disabled. The PZT voltage is then manually increased (ΔL>0) quickly, until a sharp pump spike is detected, and is then decreased smoothly. When the cavity length reenters in resonance, the bias voltage is adjusted to the desired (δ0, P0c) operating point. The output power then remains steady because of the negative thermal feedback. This point can be chosen as close to the maximum fringe intensity (turning point of bistability), but the output may then jump to the stable zero-output state if a large-amplitude perturbation occurs. Because at the threshold the stored subharmonic power is low, the burst of mode pairs on the upper curve displays sharp fringes. In this case self-lock operation on a mode pair cannot be achieved.

Fig. 6
Fig. 6

Reflected (R) and transmitted (T) pump power under self-locked cw operation for DRO-1 set to L=33 mm (circles) corresponding to the time trace shown in Fig. 5 and for DRO-2 set to L=25 mm (triangles) corresponding to the time trace shown in Fig. 10. The double-headed arrow shows the range of input power over which DRO-2 oscillation is observed (incident threshold at 260 mW). The reflected (R) curve for DRO-2 (triangles) is quasi-linear with the incident power up to the threshold, denoting a lower pump-induced thermal lensing effect; then it slightly increases because of the thermal lensing induced by the subharmonics.

Fig. 7
Fig. 7

Horizontal sections of the signal wave angular far-field transverse profile of DRO-2 (with L=30 mm), showing the effect of thermal lensing aberration. The profile sections were recorded with a motor-driven scanning mirror that steers the beam onto a 300-µm-diameter InAs detector. The I values give the relative maximum intensity for each section. The dashed curve on the I=1 section is a Gaussian fit.

Fig. 8
Fig. 8

(a) Close-up time trace of a mode-pair-resolved partial cluster of DRO-1 when operating nearby the boundary of stability range (L=31 mm). The FSR values for the signal and the idler are [see Eq. (32)] FSRs=2341 MHz and FSRi=2413 MHz. The cluster pattern depends strongly on slight misalignments of the DRO cavity. The oscillation begins with an initial spiking, before self-locking takes place. This spiking reflects the time lag in the buildup dynamics of the self-locking mechanism. These spikings were not observed with AGS-2 inserted in the same cavity. (b) Interpretation in terms of the overlap of self-locked signal and idler fringe systems, whose frequencies vary in opposite directions. The broadest mode pair, on the right, corresponds to the one with the lowest cavity frequency mismatch between the signal and the idler and displays the widest self-locking range. The subsequent mode pair termination is due to the pump resonance termination. The dispersion-induced signal–idler cavity mode mismatch decreases from the left to the right of the schematic representation.

Fig. 9
Fig. 9

Trace of the pump and subharmonic output patterns of DRO-1 set to L=29 mm (shortest spacing) under cavity-length sweep operation, showing hysteresis on the increasing length scan. Pump input power is 350 mW. The frequency of the PZT triangular ramp is f=5 Hz. For this cavity-length setting, the DRO output pattern is stable from shot to shot. The mode pairs are grouped into three or four distinct packs of adjacent unresolved pairs during the pump resonance. The pump depletion is nearly 50%.

Fig. 10
Fig. 10

Typical trace of the output pattern of DRO-2 (L=23 mm, FSRs=3293 MHz, FSRi=3390 MHz) showing two successive pump resonances. Input pump power is ∼350 mW. The cavity-length excursion (in nanometers) was calibrated from the PZT voltage required for scanning one pump FSR (λp/2) when the pump power was lowered below threshold. Above threshold, owing to the thermal lock effect, the spacing between the adjacent pump resonances corresponds to a mechanical scan smaller than λp/2. The mode pair resonances, such as the one indicated by the two leftward-pointing arrows, are nearly overlapping owing to the stronger thermal lock that is due to larger stored subharmonic power. From the pump zero line, it can be seen that, with the R=10 mm mirrors, we could not achieve a perfect pump cavity mode matching even below threshold (only half the transmitted pump resonates). The change in cavity length corresponding to the duration of resonance on the broadest subharmonic fringes is seen to be ∼12 nm, comparable with the calculated cavity-length change that causes a hop to an adjacent mode pair ΔLhop=(FSRi-FSRs)/(2FSRs,i)12.3 nm. During the second pump resonance, the extent of self-lock range is smaller, owing to the increasing cavity frequency mismatch between consecutive signal and idler pairs.

Fig. 11
Fig. 11

Long-term output intensity of DRO-2 under cw thermal lock and under active lock operation. The drift under thermal lock corresponds to a room-temperature warming-up period after the air conditioning was turned off. Long-term operation under thermal lock may hence result in a small drift of the subharmonic frequencies: The thermal lock is not an absolute frequency lock. A similar situation is encountered for lasers locked to a reference cavity, which is subject to length drift. The self-lock operation in this figure was intentionally interrupted after ∼30 min. The sidelock servo was interrupted intentionally as well. The additional electronic intensity servo cancels the intensity drift by disabling the thermal servo. Inset: CFP-S single-mode signal output spectrum during the entire recording period.

Fig. 12
Fig. 12

Time response of the thermal servo to a small step voltage applied to the cavity length of DRO-2. The mode pair is self-locked near the half-maximum intensity of the model curve shown in Fig. 2. The step corresponds to a length decrease. The fast transients that follow the step are damped after ∼8 ms. A step with ΔL=-0.5 nm yields the same damping time constant. The calculated thermal diffusion time constant τw2Cp/4Kc is 1.14 ms for a 60-µm idler waist.

Fig. 13
Fig. 13

Typical traces of sustained self-pulsing on the output of DRO-2 [with R=50 mm mirrors and L=30 mm (Ref. 16)] that was set successively under thermal lock on two different specific unstable mode pairs (corresponding to two different cavity-length biases). These oscillations appear only for the loose confocal parameter geometries and when the cluster of modes is clearly resolved, as in Fig. 8. (b) and (c) represent the same self-pulsing mode pair for two different input pump levels: (b) 200 mW, (c) 270 mW. The self-pulsing pattern observed with DRO-1 is similar to the pattern shown in (a).

Fig. 14
Fig. 14

Mode-hop-free signal tuning excursions versus manual pump frequency tuning, under pure thermal lock operation of DRO-2. The DRO operates near the 3:2:1 frequency ratios. Each point corresponds to measured (Δνs, Δνp) values until a mode hop is detected. Δνp=0 corresponds to the starting pump frequency; Δνp>0, to an increase in pump frequency; and Δνp<0, to a decrease. A nonsymmetric signal tuning range is noted (for Δνp>0 the signal frequency maximum excursion is limited to 200 MHz, while for Δνp<0 the maximum excursion is -700 MHz). The self-lock regime favors pump tuning in the negative direction, for which the thermal lock gain of the idler increases. The straight line is the best linear fit of the tuning slope (Δνs/Δνp=0.45).

Fig. 15
Fig. 15

Mode-hop-free signal tuning versus pump frequency tuning under sidelock servo operation. The hysteresis noted in Fig. 14 had disappeared, and the tuning slope has increased to Δνs/Δνp=2/3. The additional sidelock servo has restored full tuning capability.

Fig. 16
Fig. 16

Mode-hop-free continuous and electronical tuning of the signal wave, by application of a triangular voltage wave form to the master laser end-grating PZT (f=0.1 Hz). DRO-2’s cavity is sidelock servoed. The top fringe system is the output of CFP-P biased by a fixed voltage. The bottom fringe system is the transmission of biased CFP-S. Repetitive signal tuning over ∼900 MHz (more than two FSRs) is observed with a tuning slope Δνs=0.66Δνp.

Fig. 17
Fig. 17

Mode-hop-free signal tuning versus the crystal temperature, under sidelock servo operation. Only manual temperature tuning can be performed in our setup. Without the sidelock servo, quasi-systematic mode hops occur when one tries to change the temperature.

Tables (2)

Tables Icon

Table 1 Relevant Optical and Thermal Data of AGS at I=19 °C

Tables Icon

Table 2 Characteristics of the Two DRO’s Described in This Experimenta

Equations (38)

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n(T)=n0+(dn/dT)ΔT.
Δνc=νc(T)-ν0=-ν0 lc(dn/dT)ΔTL+lc(n0-1).
ΔT(r)=αPc4πKc[0.57+ln(2r02/w2)]-12αPcπKcw2r2kPc-12kPcr2,
β=k lc(dn/dT)L+lc(n0-1)
Pc=Pcm1+[ν-ν0(1-βPc)]2/Γ2,
Δ=βPcmν0ΓkFlcPcm(dn/dT)λ,
Δ2y3-2Δδy2+(1+δ2)y-1=0.
δ=δ0+δext+δth.
G1=dPcdδ,
G2=dδthdPc=dδthd(δT)d(δT)dPc=-k FlcλdndT,
dPcdδext=G11-G1G2,
dδdδext=11-G1G2.
1q2+ddz1q+2(dn/dT)n0αPc2πKcw2(z)=0.
MT=1lc/2n00110-p11lc/2n001,
p=1fth=α(dn/dT)PcπKc-lc/2lc/2 dzw2(z).
A=(1-pd)2-(2d-pd2)[2(1-pd)/R+p],
B=(2d-pd2)[2(1-pd)-2(2d-pd2)/R],
C=-[2(1-pd)/R+p][2(1-pd)-2(2d-pd2)/R],
D=-(2d-pd2)[2(1-pd)/R+p]+[1-pd-2(2d-pd2)/R]2.
1q1±=D-A2B±1BA+D22-1.
F(p)=d21-dR2(p-p0)2,
p0=d-11-2 dR1-dR-1.
Δp=d-11-dR-1.
B(p)=2d3(1-d/R)(p-p0)(p-p+),
1q1=-1R-i1d-1Rp-p-p+-p=-1R-iG(p).
1q(z)=-1/R+z[1/R2+G2(p)](1-z/R)2+z2G2(p)-i G(p)(1-z/R)2+z2G2(p).
z0=R1+R2G2(p).
p=α(dn/dT)PcπKc2πλarctand-z0z0RG(p)-arctane-z0z0RG(p),
Ppth=exp[(2αp+αs+αi)lc] εsεiKlc(ks-1+ki-1)-1h,
IiIs=Ti(Ts+2μs)Ts(Ti+2μi),
ΔpΔs<-1+1+Δp22γ<0
δνs,i=c2[L-lc(1-ns,i-νs,i(ns,i/νs,i)]=c2D(νs,i),
ΔνCl=δνsδνiδνi-δνs114.438GHz,
δL=λs2δνsΔνClνiνs+δνsδνi-1λp δνs-δνiδνs+δνi=1.4×10-2λp,
ΔνsΔνp=FiδνsFiδνs+Fsδνi,
ΔνsΔT=2lccδνsδνiFiδνs+FsδνiFiνi niT-Fsνs nsT.
(Δνs)lock=D(νs)νs+D(νi)νi-1×D(νi)νiΔνp-lcnsT-niTΔT,
(Δνs)lock=(0.66Hz/Hz)Δνp-(306.6MHz/°C)ΔT.

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