Abstract

Doubly resonant second-harmonic generation (SHG) in a monolithic cavity is theoretically analyzed. The general expressions for the intracavity SHG are given both in transmission and in reflection. An important application concerns the case of a non-phase-matchable nonlinear material, for which a well-designed cavity can lead to cavity phase matching of the nonlinear interaction. Indeed, it is shown that both the double-resonance condition and the phase-matching condition for the two counterpropagating second-harmonic intracavity waves can be satisfied with a cavity length equal to the coherence length of the nonlinear process and with well-designed mirror phases. For that purpose, metallic mirrors are well suited, but multilayer mirrors, which act exactly as metallic mirrors as far as the second-harmonic generation process is concerned, can also be used. An optimization of those pseudometallic multilayer mirrors is performed. The possibility of maintaining the double resonance with only one tuning parameter is also theoretically analyzed. Examples are given in which a SHG cavity enhancement of a few tens of thousands may be achieved in a rather simple experimental setup.

© 1997 Optical Society of America

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1995

1994

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47(5), 25–32 (1994).
[CrossRef]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

1993

1992

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

1991

R. Lodenkamper, M. M. Fejer, and J. S. Harris, “Surface emitting second harmonic generation in vertical resonator,” Electron. Lett. 27, 1882–1884 (1991).
[CrossRef]

R. C. Eckard, 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]

R. Schack, A. Sizmann, and A. Schenzle, “Squeezed light from a laser with an internal chi2 nonlinear element,” Phys. Rev. A 43, 6303–6315 (1991).
[CrossRef] [PubMed]

1990

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26, 1253–1258 (1990).
[CrossRef]

1989

1988

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

1985

1983

1982

J. C. Berquist, H. Hemmati, and W. M. Itano, “High power second harmonic generation of 257 nm radiation in an external ring cavity,” Opt. Commun. 43, 437–442 (1982).
[CrossRef]

1981

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

1977

A. I. Ferguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

1976

D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs “stack of plates” using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976).
[CrossRef]

1973

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

1971

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18, 70–73 (1971).
[CrossRef]

1970

R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6, 215–223 (1970).
[CrossRef]

1969

V. R. Costich, “Coatings for 1, 2, even 3 wavelengths,” Laser Focus 41–45 (1969).

1966

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

1965

R. H. Kingston, and A. L. McWhorter, “Electromagnetic mode mixing in nonlinear media,” Proc. IEEE 53, 4–12 (1965).
[CrossRef]

1962

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Anderson, D. B.

D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs “stack of plates” using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Ashkin, A.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Bachor, H. A.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Berquist, J. C.

J. C. Berquist, H. Hemmati, and W. M. Itano, “High power second harmonic generation of 257 nm radiation in an external ring cavity,” Opt. Commun. 43, 437–442 (1982).
[CrossRef]

Bethune, D. S.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bona, G. L.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Boyd, G. D.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Brieger, M.

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Büsener, H.

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Byer, R.

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

Byer, R. L.

Collett, M.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Costich, V. R.

V. R. Costich, “Coatings for 1, 2, even 3 wavelengths,” Laser Focus 41–45 (1969).

Ding, Y. J.

Dixon, G. J.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Dunn, M. H.

A. I. Ferguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

Eckard, R. C.

Eckardt, R. C.

Falk, J.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18, 70–73 (1971).
[CrossRef]

Fejer, M. M.

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47(5), 25–32 (1994).
[CrossRef]

R. Lodenkamper, M. M. Fejer, and J. S. Harris, “Surface emitting second harmonic generation in vertical resonator,” Electron. Lett. 27, 1882–1884 (1991).
[CrossRef]

Ferguson, A. I.

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26, 1253–1258 (1990).
[CrossRef]

A. I. Ferguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

Fiedler, K.

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

Gailhanou, M.

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

Hall, J. L.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Hänsch, T. W.

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

C. Zimmermann, R. Kallenbach, T. W. Hänsch, and J. Sandberg, “Doubly-resonant second-harmonic generation in β-barium-borate,” Opt. Commun. 71, 229–234 (1989).
[CrossRef]

Harris, J. S.

R. Lodenkamper, M. M. Fejer, and J. S. Harris, “Surface emitting second harmonic generation in vertical resonator,” Electron. Lett. 27, 1882–1884 (1991).
[CrossRef]

Hashizume, N.

Hemmati, H.

J. C. Berquist, H. Hemmati, and W. M. Itano, “High power second harmonic generation of 257 nm radiation in an external ring cavity,” Opt. Commun. 43, 437–442 (1982).
[CrossRef]

Hese, A.

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Hitz, C. B.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18, 70–73 (1971).
[CrossRef]

Horowicz, R. J.

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Houdré, R.

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

Ilegems, M.

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

Itano, W. M.

J. C. Berquist, H. Hemmati, and W. M. Itano, “High power second harmonic generation of 257 nm radiation in an external ring cavity,” Opt. Commun. 43, 437–442 (1982).
[CrossRef]

Ito, R.

Jaeckel, H.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Kallenbach, R.

C. Zimmermann, R. Kallenbach, T. W. Hänsch, and J. Sandberg, “Doubly-resonant second-harmonic generation in β-barium-borate,” Opt. Commun. 71, 229–234 (1989).
[CrossRef]

Khurgin, J. B.

Kim, B. G.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Kimble, H. J.

Kingston, R. H.

R. H. Kingston, and A. L. McWhorter, “Electromagnetic mode mixing in nonlinear media,” Proc. IEEE 53, 4–12 (1965).
[CrossRef]

Kondo, T.

Kozlovsky, W. J.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

R. C. Eckard, 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]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

Kürz, P.

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

Lee, S. J.

Lenth, W.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Leuchs, G.

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Lodenkamper, R.

R. Lodenkamper, M. M. Fejer, and J. S. Harris, “Surface emitting second harmonic generation in vertical resonator,” Electron. Lett. 27, 1882–1884 (1991).
[CrossRef]

Lugiato, L. A.

Martini, F. D.

McMullen, J. D.

D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs “stack of plates” using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976).
[CrossRef]

McWhorter, A. L.

R. H. Kingston, and A. L. McWhorter, “Electromagnetic mode mixing in nonlinear media,” Proc. IEEE 53, 4–12 (1965).
[CrossRef]

Mlynek, J.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

Moers, F. v.

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Nabors, C. D.

R. C. Eckard, 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]

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

O’Brien, S.

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

Oesterle, U.

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

Ohashi, M.

Ou, Z. Y.

Paschotta, R.

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

Pereira, S. F.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Persaud, M. A.

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26, 1253–1258 (1990).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Renn, A.

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

Risk, W. P.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Sandberg, J.

C. Zimmermann, R. Kallenbach, T. W. Hänsch, and J. Sandberg, “Doubly-resonant second-harmonic generation in β-barium-borate,” Opt. Commun. 71, 229–234 (1989).
[CrossRef]

Schack, R.

R. Schack, A. Sizmann, and A. Schenzle, “Squeezed light from a laser with an internal chi2 nonlinear element,” Phys. Rev. A 43, 6303–6315 (1991).
[CrossRef] [PubMed]

Schenzle, A.

R. Schack, A. Sizmann, and A. Schenzle, “Squeezed light from a laser with an internal chi2 nonlinear element,” Phys. Rev. A 43, 6303–6315 (1991).
[CrossRef] [PubMed]

Schiller, S.

Sizmann, A.

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

R. Schack, A. Sizmann, and A. Schenzle, “Squeezed light from a laser with an internal chi2 nonlinear element,” Phys. Rev. A 43, 6303–6315 (1991).
[CrossRef] [PubMed]

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[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. 9, 530–541 (1973).
[CrossRef]

R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6, 215–223 (1970).
[CrossRef]

Stanley, R. P.

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

Strini, G.

Tanner, C. E.

Thomson, D. E.

D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs “stack of plates” using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976).
[CrossRef]

Tolchard, J. M.

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26, 1253–1258 (1990).
[CrossRef]

Wagner, G.

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Webb, D. J.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

Welch, D.

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

Wieman, C. E.

Wu, L. A.

Xiao, M.

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Yang, S. T.

Yarborough, J. M.

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18, 70–73 (1971).
[CrossRef]

Zimmermann, C.

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

C. Zimmermann, R. Kallenbach, T. W. Hänsch, and J. Sandberg, “Doubly-resonant second-harmonic generation in β-barium-borate,” Opt. Commun. 71, 229–234 (1989).
[CrossRef]

Appl. Phys. B

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, G. Leuchs, and J. Mlynek, “Squeezing by second-harmonic generation in a monolithic resonator,” Appl. Phys. B 55, 216–225 (1992).
[CrossRef]

R. Paschotta, K. Fiedler, P. Kürz, and J. Mlynek, “Nonlinear mode coupling in doubly resonant frequency doublers,” Appl. Phys. B 58, 117 (1994).
[CrossRef]

Appl. Phys. Lett.

W. J. Kozlovsky, W. P. Risk, W. Lenth, B. G. Kim, G. L. Bona, H. Jaeckel, and D. J. Webb, “Blue light generation by resonator-enhanced frequency doubling of an extended-cavity diode laser,” Appl. Phys. Lett. 65, 525–527 (1994).
[CrossRef]

C. Zimmermann, T. W. Hänsch, R. Byer, S. O’Brien, and D. Welch, “Second harmonic generation at 972 nm using a distributed Bragg reflection semiconductor laser,” Appl. Phys. Lett. 61, 2741–2743 (1992).
[CrossRef]

J. M. Yarborough, J. Falk, and C. B. Hitz, “Enhancement of optical second harmonic generation by utilizing the dispersion of air,” Appl. Phys. Lett. 18, 70–73 (1971).
[CrossRef]

R. P. Stanley, R. Houdré, U. Oesterle, M. Gailhanou, and M. Ilegems, “Ultrahigh finesse microcavity with distributed Bragg reflectors,” Appl. Phys. Lett. 65, 1883–1885 (1994).
[CrossRef]

D. E. Thomson, J. D. McMullen, and D. B. Anderson, “Second-harmonic generation in GaAs “stack of plates” using high power CO2 laser radiation,” Appl. Phys. Lett. 29, 113–115 (1976).
[CrossRef]

Electron. Lett.

R. Lodenkamper, M. M. Fejer, and J. S. Harris, “Surface emitting second harmonic generation in vertical resonator,” Electron. Lett. 27, 1882–1884 (1991).
[CrossRef]

Europhys. Lett.

P. Kürz, R. Paschotta, K. Fiedler, A. Sizmann, and J. Mlynek, “Bright squeezed light by second-harmonic generation in a monolithic resonator,” Europhys. Lett. 24, 449–454 (1993).
[CrossRef]

IEEE J. Quantum Electron.

W. J. Kozlovsky, C. D. Nabors, and R. L. Byer, “Efficient second harmonic generation of a diode-laser-pumped cw Nd:YAG laser using monolithic MgO:LiNbO3 external resonant cavities,” IEEE J. Quantum Electron. 24, 913–919 (1988).
[CrossRef]

A. Ashkin, G. D. Boyd, and J. M. Dziedzic, “Resonant optical second harmonic generation and mixing,” IEEE J. Quantum Electron. 2, 109–124 (1966).
[CrossRef]

R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. 6, 215–223 (1970).
[CrossRef]

A. I. Ferguson and M. H. Dunn, “Intracavity second harmonic generation in continuous-wave dye lasers,” IEEE J. Quantum Electron. 13, 751–756 (1977).
[CrossRef]

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

M. A. Persaud, J. M. Tolchard, and A. I. Ferguson, “Efficient generation of picosecond pulses at 243 nm,” IEEE J. Quantum Electron. 26, 1253–1258 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Laser Focus

V. R. Costich, “Coatings for 1, 2, even 3 wavelengths,” Laser Focus 41–45 (1969).

Opt. Commun.

C. Zimmermann, R. Kallenbach, T. W. Hänsch, and J. Sandberg, “Doubly-resonant second-harmonic generation in β-barium-borate,” Opt. Commun. 71, 229–234 (1989).
[CrossRef]

J. C. Berquist, H. Hemmati, and W. M. Itano, “High power second harmonic generation of 257 nm radiation in an external ring cavity,” Opt. Commun. 43, 437–442 (1982).
[CrossRef]

M. Brieger, H. Büsener, A. Hese, F. v. Moers, and A. Renn, “Enhancement of single frequency SGH in a passive ring resonator,” Opt. Commun. 38, 423–426 (1981).
[CrossRef]

A. Sizmann, R. J. Horowicz, G. Wagner, and G. Leuchs, “Observation of amplitude squeezing of the up-converted mode in second harmonic generation,” Opt. Commun. 80, 138–142 (1990).
[CrossRef]

Opt. Lett.

Phys. Rev.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Phys. Rev. A

R. Schack, A. Sizmann, and A. Schenzle, “Squeezed light from a laser with an internal chi2 nonlinear element,” Phys. Rev. A 43, 6303–6315 (1991).
[CrossRef] [PubMed]

S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A 38, 4931–4934 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett.

R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. 72, 3807–3810 (1994).
[CrossRef] [PubMed]

Phys. Today

M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today 47(5), 25–32 (1994).
[CrossRef]

Proc. IEEE

R. H. Kingston, and A. L. McWhorter, “Electromagnetic mode mixing in nonlinear media,” Proc. IEEE 53, 4–12 (1965).
[CrossRef]

Other

Feature on optical parametric oscillators, J. Opt. Soc. Am. B 10, 1659–1791 (1993).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

V. Berger, “Second harmonic generation using a non birefringent material in a doubly resonant monolithic cavity,” J. Nonlinear Opt. Mater. (to be published).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 132.

A. Yariv, Quantum Electronics (Wiley, New York, 1989), p. 389.

V. Berger, Second Harmonic Generation in a Metal-Semiconductor-Metal Monolithic Cavity (Plenum, Cargese, France, 1995).

S. Schiller, “Principles and applications of optical monolithic total-internal-reflection resonators,” Ph.D. dissertation (Stanford University, Stanford, Calif. 1993).

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Figures (8)

Fig. 1
Fig. 1

Notation used in the calculations.

Fig. 2
Fig. 2

SHG processes in various configurations. The thick striped arrows represent the nonlinear polarization resulting from the square of the electric field at the fundamental frequency. The small perpendicular dashed triangle arrows at their origins represent the direction of the created harmonic field in phase quadrature with this nonlinear polarization. The thin dashed black arrows represent the second-harmonic field. a, In the phase-matched case the SH field grows linearly, and its phase difference with the nonlinear polarization is constant. b, In the non-phase-matched case, as a consequence of the dispersion of the refractive index, the harmonic field is dephased with respect to the square of the fundamental field. After a one coherence-length trip, the nonlinear polarization source interferes destructively with the harmonic field, and the latter is decreasing to zero. c, In the quasi-phase-matching scheme the sign of the nonlinear coefficient is reversed after one coherence length, so the contribution of the nonlinear polarization in the SH field is still positive. d, In a metallic cavity with a phase-matched material the sign of the harmonic field is changed at the metallic reflection (phase equal to π), whereas the square of the fundamental has not changed. The nonlinear polarization then interferes destructively after the metallic reflection with the reflected harmonic field, and the efficiency of such a cavity vanishes. e, In a metallic cavity with a non-phase-matched material, in which the thickness of the cavity is chosen equal to the coherence length of the nonlinear process, the sign reversal of the harmonic field at the metallic reflection exactly compensates for its dephasing during the intracavity trip. Cavity phase matching occurs and results in high nonlinear efficiency. f, With a phase-matched material, multilayer mirrors can be designed with Δφ=2φω-φ2ω=0. The positive interaction between the harmonic field and the nonlinear polarization is conserved after the reflection.

Fig. 3
Fig. 3

Reflection (amplitude, thick curve; phase, thin curve) of a FASH mirror on a KH2PO4 crystal. The thicknesses of the layers are TiO2, 123.7 nm; SiO2, 235.0 nm; TiO2, 76.5 nm; and five pairs (SiO2, 242.0 nm; TiO2, 76.5 nm). The refractive indices used for the calculations are n(λ)=a+b/λ2+c/λ4, where (a, b, c) are equal to (2.22327, 2562200, 0.53153)×1014 for TiO2 and (1.48, 460000, -0.088)×1013 for SiO2. The FASH mirror here is in the thick configuration. With this structure we obtain Δφ=2φω-φ2ω=0 at the fundamental wavelength, 1.064 µm.

Fig. 4
Fig. 4

Reflection of a FASH mirror on a KH2PO4 crystal with Δφ=π. The thicknesses of the layers are TiO2, 105.0 nm; SiO2, 175.0 nm; TiO2, 158.9 nm; and five pairs (SiO2, 116.5 nm; TiO2, 158.9 nm). The FASH mirror here is in the thin configuration.

Fig. 5
Fig. 5

SHG enhancement as a function of the mirror reflectivity for several second-harmonic detunings (the pump field is resonant). In the case of GaAs at 10.6 µm the detuning is less than 0.75%.

Fig. 6
Fig. 6

Reflected SHG enhancement as a function of the mirror reflectivity for several second-harmonic detunings.

Fig. 7
Fig. 7

Maximum possible second-harmonic mirror reflectivity with the possibility of maintaining double resonance with one tuning parameter only (dashed curve). The corresponding gain in the efficiency of the doubly resonant SHG is calculated with respect to a singly resonant case (solid curve). Various second-harmonic processes have been reported. For low-coherence-length processes (high detunings δ), high doubly resonant enhancements are difficult to obtain with one parameter only. With Rω=0.98, the single-resonance enhancement is equal to ηSingleResonance=2500.

Fig. 8
Fig. 8

Same analysis as for Fig. 7 in the reflection case. The ratio ηr/ηr, SingleResonance does not depend on Rω. With Rω =0.96 the single-resonance enhancement is equal to ηr, SingleResonance=40000.

Equations (36)

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ηSingleResonance=T12(1-R1γRr)4,
Er(ω)(z, t)=1/2{Erω(z)exp[i(ωt-kωz)]+c.c.},
PNL2ω=2d(Eω)2.
Er2ωL2=Er2ω-L2-2iωμ02ω dL(Erω)2 sincΔkL2.
ρrω=rrω exp(-iφrω)
Er2ωL2=(Erω)21+rl2ω(rrω)2 exp[-i(φl2ω+2φrω+k2ωL+2kωL)]1-rl2ωrr2ω exp[-i(φl2ω+φr2ω+2k2ωL)](-2iω)μ0/2ωdL sincΔkL2.
Erω=Eincω tlω1-rlωrrω exp[-i(φlω+φrω+2kωL)],
Pr,out2ω=12ZTr2ωEr2ωL22,
Psinglepass2ω=8Z3n3dLω sincΔkL22(Pincω)2.
η=Tr2ωTlω{1+rl2ω(rrω)2 exp[-i(φl2ω+2φrω+k2ωL+2kωL)]}{1-rlωrrω exp[-i(φlω+φrω+2kωL)]}2{1-rl2ωrr2ω exp[-i(φl2ω+φr2ω+2k2ωL)]}2.
ηr=Tl2ωTlω{(rrω)2 exp[-i(2φrω+2kωL)]+rr2ω exp[-i(φr2ω+k2ωL)]}{1-rlωrrω exp[-i(φlω+φrω+2kωL)]}2{1-rl2ωrr2ω exp[-i(φl2ω+φr2ω+2k2ωL)]}2.
φlω+φrω+2kωL0[2π],
φl2ω+φr2ω+2k2ωL0[2π],
2φrω+φl2ω+2kωL+k2ωL0[2π].
2φrω+2kωL-φr2ω-k2ωL0[2π].
kωL0[π],
k2ωL0[π],
2kωL-k2ωLπ[2π].
2kωL=2pπ,
k2ωL=(2p+1)π.
ΔkL=π,
ηDoubleResonance=Tr2ωTlω[1+rl2ω(rrω)2](1-rlωrrω)2(1-rl2ωrr2ω)2.
ηr, DoubleResonance=Tl2ω2Tlω(1-rlω)2(1-rl2ω)2.
2φω-φ2ωπ[2π].
ζ=4λ20λ/2 n(x)exp-4πixλdx×0λ/2 n(x)exp-8πixλdx,
ζ=(n1-n2)28π2[1-exp(2πiα)][exp(4πiα)-1].
αMax=12πarccos-13=0.304.
rω=1+i2(n12-n22)n12+n22+n1n2+i2(n1-n2)2-3n1n2sinh[(N-1)Өω]sinh(NӨω),
r2ω=(4-2i)(n12-n22)4n12+4n22+n1n2-2i(n1-n2)2-9n1n2sinh[(N-1)Ө2ω]sinh(NӨ2ω),
Өω=arg coshn12+n22+n1n23n1n2,
Ө2ω=arg cosh4n12+4n22+n1n29n1n2,
Lnωωπc=p.
p=NINTnω2(n2ω-nω),
k2ωL=(2p+1+δ)π,
δ=1-2 n2ω-nωnωNINTnω2(n2ω-nω).
|δ|n2ω-nωnω.

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