Abstract

We analyze the phase-matching conditions for second-harmonic generation (SHG) and optical parametric oscillation (OPO) in birefringent nonlinear semiconductor waveguides and apply these results to the model system of ZnGeP2 on a GaP substrate. The analyses and numerical results show that phase matching can be achieved for OPO and SHG for reasonable guide thicknesses throughout much of the infrared, indicating significant potential applications for nonlinear birefringent waveguides. For the fundamental mode of a relatively thick guide the region of phase matching and the phase-matching angles are similar to those in bulk material. However, the waveguide has the added flexibility that phase-matched coupling can occur between the various modes of the guide. For example, the phase-matching region for SHG can be considerably extended by coupling the pump into the guide in the fundamental, m = 0, mode and phase matching to the m = 2 mode of the second harmonic. Significantly, the results indicate, among other things, that ZnGeP2 waveguides with harmonic output in the m = 2 mode can be used for efficient SHG from input radiation in the 9.6–10.6-µm region where bulk efficiencies in this wavelength range are too small to be useful.

© 2001 Optical Society of America

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  1. S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
    [CrossRef]
  2. F. Petrov, F. Rotermund, F. Noack, P. Schunemann, “Femtosecond parametric generation in ZnGeP2,” Opt. Lett. 24, 414–416 (1999).
    [CrossRef]
  3. M. C. Ohmer, R. Pandey, eds., “Emergence of chalcopyrites as nonlinear optical materials,” Materials Research Bulletin, Special Issue (July1998).
  4. G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
    [CrossRef]
  5. K. Kato, “Second-harmonic and sum-frequency generation in ZnGeP2,” Appl. Opt. 36, 2506–2510 (1997).
    [CrossRef] [PubMed]
  6. D. W. Fischer, M. C. Ohmer, “Temperature dependence of ZnGeP2 birefringence using polarized light interference,” J. Appl. Phys. 81, 425–431 (1997).
    [CrossRef]
  7. G. Ghosh, “Sellmeier coefficients for the birefringence and refractive indices of ZnGeP2 nonlinear crystal at different temperatures,” Appl. Opt. 37, 1205–1212 (1998).
    [CrossRef]
  8. N. P. Barnes, K. E. Murray, M. G. Jani, G. Schunemann, T. M. Pollak, “ZnGeP2 parameter amplifier,” J. Opt. Soc. Am. B 15, 232–238 (1998).
    [CrossRef]
  9. G. C. Xing, K. J. Bachmann, “GaP/ZnGeP2 multiple heterostructure,” J. Cryst. Growth 147, 35–38 (1995) and references therein.
    [CrossRef]
  10. R. G. Huntsperger, Integrated Optics: Theory and Technology, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 2.
  11. F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
    [CrossRef]
  12. G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
    [CrossRef]
  13. A. Borghesi, G. Guizzetti, “Gallium phosphide (GaP),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1985), p. 445.
    [CrossRef]
  14. P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.
  15. Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
    [CrossRef]
  16. K. L. Vodopyanov, “Parametric generation of tunable infrared radiation in ZnGeP2 and GaSe pumped at 3 µm,” J. Opt. Soc. Am. B 10, 1723–1729 (1998).
    [CrossRef]

1999

S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
[CrossRef]

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

F. Petrov, F. Rotermund, F. Noack, P. Schunemann, “Femtosecond parametric generation in ZnGeP2,” Opt. Lett. 24, 414–416 (1999).
[CrossRef]

1998

1997

D. W. Fischer, M. C. Ohmer, “Temperature dependence of ZnGeP2 birefringence using polarized light interference,” J. Appl. Phys. 81, 425–431 (1997).
[CrossRef]

K. Kato, “Second-harmonic and sum-frequency generation in ZnGeP2,” Appl. Opt. 36, 2506–2510 (1997).
[CrossRef] [PubMed]

1995

G. C. Xing, K. J. Bachmann, “GaP/ZnGeP2 multiple heterostructure,” J. Cryst. Growth 147, 35–38 (1995) and references therein.
[CrossRef]

1987

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

1971

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
[CrossRef]

G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
[CrossRef]

Andreev, Y. M.

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

Bachmann, K. J.

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

G. C. Xing, K. J. Bachmann, “GaP/ZnGeP2 multiple heterostructure,” J. Cryst. Growth 147, 35–38 (1995) and references therein.
[CrossRef]

Barnes, N. P.

Borghesi, A.

A. Borghesi, G. Guizzetti, “Gallium phosphide (GaP),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1985), p. 445.
[CrossRef]

Boyd, G. D.

G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
[CrossRef]

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
[CrossRef]

Budni, P. A.

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

Buehler, E.

G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
[CrossRef]

Dietz, N.

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

Dimmock, J. O.

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

Ezzo, K.

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

Fischer, D. W.

D. W. Fischer, M. C. Ohmer, “Temperature dependence of ZnGeP2 birefringence using polarized light interference,” J. Appl. Phys. 81, 425–431 (1997).
[CrossRef]

Ghosh, G.

Gribenyukov, A. I.

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

Guizzetti, G.

A. Borghesi, G. Guizzetti, “Gallium phosphide (GaP),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1985), p. 445.
[CrossRef]

Huntsperger, R. G.

R. G. Huntsperger, Integrated Optics: Theory and Technology, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 2.

Jani, M. G.

Kasper, H.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
[CrossRef]

Kato, K.

Lambrecht, W. R. L.

S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
[CrossRef]

Limpijumnong, S.

S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
[CrossRef]

Madarasz, F. L.

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

McCarthy, J. C.

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

McFee, J. H.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
[CrossRef]

Minnigh, S.

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

Murray, K. E.

Noack, F.

Novikov, V. P.

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

Ohmer, M. C.

D. W. Fischer, M. C. Ohmer, “Temperature dependence of ZnGeP2 birefringence using polarized light interference,” J. Appl. Phys. 81, 425–431 (1997).
[CrossRef]

Petrov, F.

Pollak, T. M.

N. P. Barnes, K. E. Murray, M. G. Jani, G. Schunemann, T. M. Pollak, “ZnGeP2 parameter amplifier,” J. Opt. Soc. Am. B 15, 232–238 (1998).
[CrossRef]

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

Rashkeev, S. N.

S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
[CrossRef]

Rotermund, F.

Schunemann, G.

Schunemann, P.

Schunemann, P. G.

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

Storz, F. G.

G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
[CrossRef]

Vodopyanov, K. L.

Voevodin, V. G.

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

Xing, G. C.

G. C. Xing, K. J. Bachmann, “GaP/ZnGeP2 multiple heterostructure,” J. Cryst. Growth 147, 35–38 (1995) and references therein.
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. D. Boyd, E. Buehler, F. G. Storz, “Linear and nonlinear optical properties of ZnGeP2 and CdSe,” Appl. Phys. Lett. 18, 301–304 (1971).
[CrossRef]

IEEE J. Quantum Electron.

G. D. Boyd, H. Kasper, J. H. McFee, “Linear and nolinear optical properties of AgGaS2, CuGaS2, and CuInS2 and theory of the wedge technique for the measurement of nonlinear coefficients,” IEEE J. Quantum Electron. QE-7, 563–573 (1971).
[CrossRef]

J. Appl. Phys.

F. L. Madarasz, J. O. Dimmock, N. Dietz, K. J. Bachmann, “Sellmeir parameters for ZnGeP2 and GaP,” J. Appl. Phys. 87, 1564–1565 (1999). (Note that the paper title in the journal reads ZnGaP2 but should be ZnGeP2.)
[CrossRef]

D. W. Fischer, M. C. Ohmer, “Temperature dependence of ZnGeP2 birefringence using polarized light interference,” J. Appl. Phys. 81, 425–431 (1997).
[CrossRef]

J. Cryst. Growth

G. C. Xing, K. J. Bachmann, “GaP/ZnGeP2 multiple heterostructure,” J. Cryst. Growth 147, 35–38 (1995) and references therein.
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. B

S. N. Rashkeev, S. Limpijumnong, W. R. L. Lambrecht, “Second-harmonic generation and birefringence of some ternary pnictide semiconductors,” Phys. Rev. B 59, 2737–2748 (1999).
[CrossRef]

Sov. J. Quantum. Electron.

Y. M. Andreev, V. G. Voevodin, A. I. Gribenyukov, V. P. Novikov, “Mixing of frequencies of CO2 and CO lasers in ZnGeP2 crystals,” Sov. J. Quantum. Electron. 17, 748–749 (1987).
[CrossRef]

Other

M. C. Ohmer, R. Pandey, eds., “Emergence of chalcopyrites as nonlinear optical materials,” Materials Research Bulletin, Special Issue (July1998).

R. G. Huntsperger, Integrated Optics: Theory and Technology, 2nd ed. (Springer-Verlag, New York, 1984), Chap. 2.

A. Borghesi, G. Guizzetti, “Gallium phosphide (GaP),” in Handbook of Optical Constants, E. D. Palik, ed. (Academic, New York, 1985), p. 445.
[CrossRef]

P. A. Budni, K. Ezzo, P. G. Schunemann, S. Minnigh, J. C. McCarthy, T. M. Pollak, “2.8-µm pumped optical parametric oscillation in ZnGeP2,” in Advanced Solid-State Lasers, J. Dubé, L. Chase, eds., Vol. 10 of OSA, Proceedings Series, (Optical Society of America, Washington, D.C., 1991), pp. 335–338.

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Figures (2)

Fig. 1
Fig. 1

Calculated phase-matching angles for SHG and OPO in a 16-µm ZnGeP2 waveguide with a GaP substrate and cladding layer compared with similar curves for bulk material.

Fig. 2
Fig. 2

Calculated phase-matching angles for SHG in the 16-µm ZnGeP2 waveguide of Fig. 1 pumped in the m = 0 mode with output in the m = 2 mode compared with the m = 0 to m = 0 coupling of Fig. 1 and that of the bulk material.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ktno2-nTM21/2=m+1π-tan-1ns2no2-nTM21/2no2nTM2-ns21/2-tan-1nc2no2-nTM21/2no2nTM2-nc21/2,
ktn2-nTE21/2=m+1π-tan-1n2-nTE21/2nTE2-ns21/2-tan-1n2-nTE21/2nTE2-nc21/2,
1n2=cos θno2+sin θne2,
nTE2λ=nTMλ.
1λP=1λS+1λI,
nTMλPλP=nTEλsλs +nTEλIλI.

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