Abstract

A twin-crystal device consisting of a pair of two identically cut KTP crystals of length l = 6 mm mounted with their optical axes symmetrically crossed is used to circumvent conversion-efficiency limitations that are due to the aperture effect in type-II (oeo) critically phase-matched second-harmonic generation (SHG) at λ = 1.3 and λ = 2.532 μm. A single-pass increase of as great as 3.2–3.5 times the conversion efficiency of a single crystal is obtained with this angle-tuned device at these wavelengths. This enhancement results from an increased effective coherence length of the interaction compared with that of a single bulk crystal of length 2l. We show that cavity-enhanced critically phase-matched type-II SHG can be easily performed with the twin device, allowing for walk-off as well as phase compensation for the fundamental-resonating ordinary and extraordinary waves at λ = 1.30 μm. Potential implementations of this device in other single-cavity-enhanced parametric interactions, such as doubly resonant optical parametric oscillation and degenerate sum-or difference-frequency mixing, are discussed.

© 1994 Optical Society of America

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    [CrossRef]
  3. J.-J. Zondy, "Comparative theory of type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991); erratum: exp(-x2) in Eq. (3.1a) of this reference should read as exp(-x2/2).
    [CrossRef]
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  5. G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
    [CrossRef]
  6. S. X. Dou, D. Josse, R. Hierle, and J. Zyss, "Comparison between collinear and noncollinear phase matching for second-harmonic and sum-frequency generation in 3-methyl-4-nitropyridine-l-oxide," J. Opt. Soc. Am. B 9, 687 (1992).
    [CrossRef]
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    [CrossRef]
  8. S. A. Akhmanov, A. J. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, p. 534.
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    [CrossRef] [PubMed]
  10. M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
    [CrossRef]
  11. W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
    [CrossRef]
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    [CrossRef]
  13. L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).
  14. T. Yanagawa and L. K. Samanta, "Increased second harmonic output power using walk-off compensation in birefrin-gent crystals," Phys. Condens. Matter 3, 7421 (1991).
    [CrossRef]
  15. 0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
    [CrossRef]
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    [CrossRef]
  18. J. D. Bierlein and H. Vanherzeele, "Potassium titanyl phosphate: properties and new applications," J. Opt. Soc. Am. B 6, 622 (1989).
    [CrossRef]
  19. J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
    [CrossRef]
  20. Z. Y. Ou, S. F. Pereira, E. S. Polzik, and H. J. Kimble, "85% efficiency for cw frequency doubling from 1.08 to 0.54 µm," Opt. Lett. 17, 640 (1992).
    [CrossRef] [PubMed]
  21. A. Ashkin, G. D. Boyd and J. M. Dziedzic, "Resonant optical second harmonic generation and mixing," IEEE J. Quantum Electron. QE-2, 109 (1966).
    [CrossRef]
  22. R. C. Jones, "New calculus for the treatment of optical system," J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  23. F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
    [CrossRef]
  24. D. Lee and N. C. Wong, "Tunable optical frequency division using a phase-locked optical parametric oscillator," Opt. Lett. 17, 13 (1992).
    [CrossRef] [PubMed]

1994 (2)

J.-J. Zondy, M. Abed, and A. Clairon, "Type-II frequency doubling at λ = 1.3 and λ = 2.53 µm in flux-grown potassium titanyl phosphate," J. Opt. Soc. Am. B 11,2004 (1994).
[CrossRef]

F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
[CrossRef]

1993 (2)

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

1992 (4)

1991 (4)

J.-J. Zondy, "Comparative theory of type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991); erratum: exp(-x2) in Eq. (3.1a) of this reference should read as exp(-x2/2).
[CrossRef]

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
[CrossRef]

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

T. Yanagawa and L. K. Samanta, "Increased second harmonic output power using walk-off compensation in birefrin-gent crystals," Phys. Condens. Matter 3, 7421 (1991).
[CrossRef]

1990 (3)

L. K. Samanta, T. Yanagawa and Y. Yamamoto, "Technique for enhanced second-harmonic output power," Opt. Commun. 76, 250 (1990).
[CrossRef]

B. Ya. Zel'dovich, Yu. E. Kapilskii, and A. N. Chudinov, "Interference between second harmonic generated into different KTP crystals," Sov. J. Quantum Electron. 20, 1120 (1990).
[CrossRef]

J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

1989 (2)

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

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
[CrossRef]

1968 (1)

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3397 (1968).
[CrossRef]

1966 (1)

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

1962 (1)

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

1941 (1)

Abed, M.

J.-J. Zondy, M. Abed, and A. Clairon, "Type-II frequency doubling at λ = 1.3 and λ = 2.53 µm in flux-grown potassium titanyl phosphate," J. Opt. Soc. Am. B 11,2004 (1994).
[CrossRef]

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Acef, 0.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. J. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, p. 534.

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 (1962).
[CrossRef]

Ashkin, A.

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

Bhar, G. C.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
[CrossRef]

Bierlein, J. D.

J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

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

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 (1962).
[CrossRef]

Bosenberg, W. R.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
[CrossRef]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3397 (1968).
[CrossRef]

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

Brown, J. B.

J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

Changde, X.

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Chatterjee, U.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
[CrossRef]

Chudinov, A. N.

B. Ya. Zel'dovich, Yu. E. Kapilskii, and A. N. Chudinov, "Interference between second harmonic generated into different KTP crystals," Sov. J. Quantum Electron. 20, 1120 (1990).
[CrossRef]

Clairon, A.

J.-J. Zondy, M. Abed, and A. Clairon, "Type-II frequency doubling at λ = 1.3 and λ = 2.53 µm in flux-grown potassium titanyl phosphate," J. Opt. Soc. Am. B 11,2004 (1994).
[CrossRef]

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Colville, F. G.

F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
[CrossRef]

Das, S.

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
[CrossRef]

Dou, S. X.

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 (1962).
[CrossRef]

Dunn, M. H.

F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
[CrossRef]

Dziedzic, J. M.

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

Gérard, A. H.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Hayasaka, K.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm in β-BaB2O4 crystals with an enhancement cavity," Opt. Lett. 17, 46 (1992).
[CrossRef] [PubMed]

Hierle, R.

Imajo, H.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm in β-BaB2O4 crystals with an enhancement cavity," Opt. Lett. 17, 46 (1992).
[CrossRef] [PubMed]

Jiangrui, G.

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Jing, L.

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Jones, R. C.

Josse, D.

Juncar, P.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Kapilskii, Yu. E.

B. Ya. Zel'dovich, Yu. E. Kapilskii, and A. N. Chudinov, "Interference between second harmonic generated into different KTP crystals," Sov. J. Quantum Electron. 20, 1120 (1990).
[CrossRef]

Kimble, H. J.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3397 (1968).
[CrossRef]

Kovrygin, A. J.

S. A. Akhmanov, A. J. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, p. 534.

Kunchi, P.

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Kurtz, S. K.

S. K. Kurtz, in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part A, p. 241.

Laubacher, D. B.

J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

Laurent, Ph.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Lee, D.

Millerioux, Y.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Ou, Z. Y.

Padgett, M. J.

F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
[CrossRef]

Pelouch, W. S.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
[CrossRef]

Pereira, S. F.

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 (1962).
[CrossRef]

Polzik, E. S.

Rovera, D. G.

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

Samanta, L. K.

T. Yanagawa and L. K. Samanta, "Increased second harmonic output power using walk-off compensation in birefrin-gent crystals," Phys. Condens. Matter 3, 7421 (1991).
[CrossRef]

L. K. Samanta, T. Yanagawa and Y. Yamamoto, "Technique for enhanced second-harmonic output power," Opt. Commun. 76, 250 (1990).
[CrossRef]

Sukhorukov, A. P.

S. A. Akhmanov, A. J. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, p. 534.

Tang, C. L.

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
[CrossRef]

Urabe, S.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm in β-BaB2O4 crystals with an enhancement cavity," Opt. Lett. 17, 46 (1992).
[CrossRef] [PubMed]

Vanherzeele, H.

Watanabe, M.

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm in β-BaB2O4 crystals with an enhancement cavity," Opt. Lett. 17, 46 (1992).
[CrossRef] [PubMed]

Wong, N. C.

Yamamoto, Y.

L. K. Samanta, T. Yanagawa and Y. Yamamoto, "Technique for enhanced second-harmonic output power," Opt. Commun. 76, 250 (1990).
[CrossRef]

Yanagawa, T.

T. Yanagawa and L. K. Samanta, "Increased second harmonic output power using walk-off compensation in birefrin-gent crystals," Phys. Condens. Matter 3, 7421 (1991).
[CrossRef]

L. K. Samanta, T. Yanagawa and Y. Yamamoto, "Technique for enhanced second-harmonic output power," Opt. Commun. 76, 250 (1990).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, in Optical Waves in Crystals, J. Wiley, ed. (Wiley-Interscience, New York, 1984).

Yeh, P.

A. Yariv and P. Yeh, in Optical Waves in Crystals, J. Wiley, ed. (Wiley-Interscience, New York, 1984).

Yimin, L.

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Zel’dovich, B. Ya.

B. Ya. Zel'dovich, Yu. E. Kapilskii, and A. N. Chudinov, "Interference between second harmonic generated into different KTP crystals," Sov. J. Quantum Electron. 20, 1120 (1990).
[CrossRef]

Zondy, J.-J.

J.-J. Zondy, M. Abed, and A. Clairon, "Type-II frequency doubling at λ = 1.3 and λ = 2.53 µm in flux-grown potassium titanyl phosphate," J. Opt. Soc. Am. B 11,2004 (1994).
[CrossRef]

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

J.-J. Zondy, "Comparative theory of type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991); erratum: exp(-x2) in Eq. (3.1a) of this reference should read as exp(-x2/2).
[CrossRef]

Zyss, J.

Acta Opt. Sin. (1)

L. Jing, X. Changde, L. Yimin, G. Jiangrui, and P. Kunchi, "Experimental investigation of frequency doubling in two KTP crystals," Acta Opt. Sin. 11,409 (1991).

Appl. Phys. Lett. (3)

W. R. Bosenberg, W. S. Pelouch, and C. L. Tang, "High efficiency and narrow linewidth operation of a two-crystal optical parametric oscillator," Appl. Phys. Lett. 55, 1952 (1989).
[CrossRef]

J. D. Bierlein, D. B. Laubacher, and J. B. Brown, "Balanced phase matching in segmented KTiOPO4 waveguides," Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

F. G. Colville, M. J. Padgett, and M. H. Dunn, "Continuous-wave, dual cavity, doubly resonant, optical parametric oscillator," Appl. Phys. Lett. 64, 1490 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, "Parametric interaction of focused light beams," J. Appl. Phys. 39, 3397 (1968).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

Opt. Commun. (5)

0. Acef, J.-J. Zondy, M. Abed, D. G. Rovera, A. H. Gérard, A. Clairon, Ph. Laurent, Y. Millerioux, and P. Juncar, "A CO2 to visible optical frequency synthesis chain: accurate measurement of the 473 THz HeNe/I2 laser," Opt. Commun. 97, 29 (1993).
[CrossRef]

L. K. Samanta, T. Yanagawa and Y. Yamamoto, "Technique for enhanced second-harmonic output power," Opt. Commun. 76, 250 (1990).
[CrossRef]

M. Watanabe, K. Hayasaka, H. Imajo, and S. Urabe, "Continuous-wave sum-frequency generation near 194 nm with a collinear double enhancement cavity," Opt. Commun. 97, 225 (1993).
[CrossRef]

J.-J. Zondy, "Comparative theory of type-II versus type-I second harmonic generation with Gaussian beams," Opt. Commun. 81, 427 (1991); erratum: exp(-x2) in Eq. (3.1a) of this reference should read as exp(-x2/2).
[CrossRef]

G. C. Bhar, U. Chatterjee, and S. Das, "A technique for the calculation of phase-matching angle for type-II noncollinear sum-frequency generation in negative uniaxial crystals," Opt. Commun. 88, 381 (1991).
[CrossRef]

Opt. Lett. (3)

Phys. Condens. Matter (1)

T. Yanagawa and L. K. Samanta, "Increased second harmonic output power using walk-off compensation in birefrin-gent crystals," Phys. Condens. Matter 3, 7421 (1991).
[CrossRef]

Phys. Rev. (1)

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

Sov. J. Quantum Electron. (1)

B. Ya. Zel'dovich, Yu. E. Kapilskii, and A. N. Chudinov, "Interference between second harmonic generated into different KTP crystals," Sov. J. Quantum Electron. 20, 1120 (1990).
[CrossRef]

Other (3)

S. K. Kurtz, in Quantum Electronics: A Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part A, p. 241.

A. Yariv and P. Yeh, in Optical Waves in Crystals, J. Wiley, ed. (Wiley-Interscience, New York, 1984).

S. A. Akhmanov, A. J. Kovrygin, and A. P. Sukhorukov, "Optical harmonic generation and optical frequency multipliers," in Quantum Electronics: Treatise, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Part B, p. 534.

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Figures (8)

Fig. 1
Fig. 1

Twin-crystal walk-off-compensated device for type-II (oeo) SHG in the ac plane of KTP. The projections of the extraordinary index surface in the ac plane show the direction of the Poynting vector of the extraordinary ω wave in each crystal. The incoming pump field E(ω) is 45° polarized with respect to the ac plane, with the b axis being along y. Both crystals are approximately phase matched for SHG. The preservation of the relative phase between the fundamental and the harmonic from KTP1 to KTP2 is controlled by independent tilt δiρ of each crystal around the b axis.

Fig. 2
Fig. 2

Experimental setup for simultaneous SH detection and analysis of the fundamental output polarization. PD1, PD2, InAs–InGaAs (at λ = 2.532 μm), Ge–Si (at λ = 1.3 μm) photodetectors; L, lens; IF, interference filter.

Fig. 3
Fig. 3

Lower curve, angular tuning curve of the twin-crystal device at λ = 1.3 μm; upper curve, analyzer intensity transmission of the output fundamental wave versus the δ2 tilt of KTP2 when KTP1 is set to its optimum orientation for maximum SH output (zR = 28 mm). The filled circles are experimental data linked by a spline interpolation (lower solid curve). The arrows along the analyzer transmission curve refer to the direction of polarization (45° to the left or to the right with respect to the ac plane) of the ω output wave, corresponding to either total extinction or maximum transmission. The input polarization corresponds to an arrow pointing to the right.

Fig. 4
Fig. 4

Comparison between single- and twin-crystal-device SH output at λ = 2.532 μm, for which an enhancement factor of 3.5 has been measured. The crystal length is l = 6 mm; φ = 0° and θcut = 56.60°. The (internal) Rayleigh length of the pump is zR = 42 mm. At this wavelength the output recombined ω wave is linearly polarized with its direction parallel to that of the input wave.

Fig. 5
Fig. 5

Plane-wave twin-crystal-device tuning curve when KTP1 is set to its optimum mismatch parameter, ϕ1 = −3ϕ0/8, and KTP2 is tuned near θPM for some values of the spurious phase shift ϕ0 between the fundamental and the SH at KTP2’s input. The width of the twin-crystal tuning curve is practically the same as the width of a single-crystal one.

Fig. 6
Fig. 6

Schematic setup for cavity-enhanced twin-device operation at λ = 1.3 μm. A.P, anamorphic prism pair; λ/2, half-wave plate; IML, cavity mode-matching lenses; M’s, mirrors; EF; edge filter; WP, wave plate (λ/2 or a pair of λ/4) plates; PD’s, photodiodes; CFP, confocal Fabry–Perot.

Fig. 7
Fig. 7

Ring-cavity transmission fringes of a–c, the fundamental wave and d, the harmonic wave. In a–c the ω fringes have the same relative intensity scale. a, Empty cavity. b, When KTP1 is inserted, only the ordinary ω wave resonates; the extraordinary fringe, weakened by walk-off-induced Fresnel losses, is removed. c, When KTP2 is inserted behind KTP1, the extraordinary-fringe system shows as a result of walk-off compensation. d, SH output from mirror M4 when fundamental phase compensation is performed.

Fig. 8
Fig. 8

Cavity-enhanced available SH power when phase compensation of the ordinary and the extraordinary resonating waves is performed by △, angle tuning of KTP2, □, a half-wave plate (the twin device is used at optimum single-pass conversion efficiency); ○, a pair of λ/4 plates when the state of polarization of the ω wave emerging from the device is elliptical (see text).

Equations (23)

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Δ k = k 3 - k 1 - k 2 = 0
n b ( ω ) + n e ( ω , θ PM ) = 2 n b ( 2 ω ) ,
( d n e d θ ) θ PM = - n e 3 2 ( n c - 2 - n a - 2 ) sin ( 2 θ PM ) .
T ω ( α ) = ( I 0 / 2 ) ( 1 + sin 2 α cos φ o , e ) ,
φ T = φ 1 + φ 2 + 2 π λ ( d n e d θ ) θ PM ( δ 1 l 1 + δ 2 l 2 ) φ 1 + φ 2 + 2 π ( δ 1 + δ 2 ) Δ θ ,
A 3 ( z 1 = l 1 ) = i κ A 1 A 2 l 1 exp ( - i ϕ 1 ) sinc ( ϕ 1 ) ,
A 3 ( z 2 ) = i κ A 1 A 2 l 2 exp ( - i ϕ 2 ) sinc ( ϕ 2 ) × exp { i [ ( k 1 + k 2 ) l 1 + ( β 1 + β 2 ) ] } + exp { i [ k 3 l 1 + β 3 ] } A 3 ( z 1 ) .
A 3 ( z 2 ) = i κ A 1 A 2 exp ( i γ ) { l 2 exp [ - i ( ϕ 2 + ϕ 0 ) ] sinc ( ϕ 2 ) + l 1 exp ( + i ϕ 1 ) sinc ( ϕ 1 ) } ,
Γ PW = P 3 / P 1 P 2 = K ( l / w 0 ) 2 T ( ϕ 0 , ϕ 1 , ϕ 2 ) ,
T sinc 2 ( ϕ 2 ) + sinc 2 ( ϕ 1 ) + 2 sinc ( ϕ 2 ) sinc ( ϕ 2 ) cos ( ϕ 1 + ϕ 2 + ϕ 0 ) ,
Γ N = N 2 sinc 2 [ N ( ϕ 1 + ϕ 2 + ϕ 0 ) ] sinc 2 ( ϕ 1 + ϕ 2 + ϕ 0 ) Γ PW .
cos ( 2 ψ ) = 1 - 1 + x 2 x .
P i ( 2 ω ) = j , k = x , y , z ( l , m , n = a , b , c A l i d l m n A m j A n k ) × E j ( ω ) E k ( ω ) ,
d eff ( 2 ω ) = d 15 A a y ( A a x A c y + A c x A a y ) + d 24 A b y ( A b x A c y + A c x A b y ) + 2 d 31 A c y A a x A a y + 2 d 32 A c y A b x A b y + 2 d 33 A c y A c x A c y .
[ a b c ] = [ cos θ 0 - sin θ 0 1 0 sin θ 0 cos θ ] [ x y z ] ,
[ a b c ] = [ - cos θ 0 sin θ 0 1 0 - sin θ 0 - cos θ ] [ x y z ] ,
J · E = λ ( ϕ 1 , ϕ 2 ) E ,
J = [ J 11 J 12 - J 12 * J 11 * ] ,
J 11 = κ exp ( - i φ T 2 ) [ g 1 g 2 - h 1 h 2 cos ( 2 ϕ 1 - 2 ϕ 2 ) - i ( h 2 g 1 cos 2 ϕ 2 + h 1 g 2 cos 2 ϕ 1 ] ,
J 12 = - i κ exp ( + i φ T 2 ) [ h 1 g 2 sin 2 ϕ 1 + h 2 g 1 sin 2 ϕ 2 - i h 1 h 2 sin ( 2 ϕ 1 + 2 ϕ 2 ) ] ,
J 11 = κ exp ( - i φ T 2 ) ( sin 2 2 Ψ - i cos 2 Ψ ) .
λ 2 - 2 Re J 11 λ + J 11 2 = 0.
cos ( 2 ψ ) = 1 - [ 1 + 4 tan 2 ( φ T / 2 ) ] 1 / 2 2 tan ( φ T / 2 )

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