Abstract

We present a calculation on the squeezing performance of a quadratic nonlinear medium in which the phase-matching condition is achieved artificially by a periodic poling of the nonlinear susceptibility. We treat in particular the Kerr-like effect due to cascading of two second-order nonlinearities. We show that interesting performance can be achieved for highly integrable and nonlinear materials, by use of technologies already developed.

© 1997 Optical Society of America

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References

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  1. See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946841988
  2. Special issue on quantum noise reduction in optical systems, E. Giacobino and C. Fabre, eds., Appl. Phys. B 55(3), (1992).
  3. G. I. Stegeman and A. Miller, in Photonics in Switching: Background and Components, J. E. Midwinter, ed. (Academic, Boston, 1993), Chap. 5, p. 81.
    [CrossRef] [PubMed]
  4. K. Otsuka, “Nonlinear antiresonant ring interferometer,” Opt. Lett. 8, 471 (1983).
    [CrossRef] [PubMed]
  5. R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986); R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
    [CrossRef] [PubMed]
  6. K. Bergman, H. A. Haus, and M. Shirasaki, “Analysis and measurement of GAWBS spectrum in a nonlinear fiber ring,” Appl. Phys. B 55, 242 (1992); “Squeezing in a fiber interferometer with a gigahertz pump,” Opt. Lett. 19, 290 (1994).
    [CrossRef] [PubMed]
  7. G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18, 13 (1993).
    [CrossRef] [PubMed]
  8. R. Schiek, M. L. Sundheimer, D. Y. Kim, Y. Baek, G. I. Stegeman, H. Seibert, and W. Sohler, “Direct measurement of cascaded nonlinearity in lithium niobate channel waveguides,” Opt. Lett. 19, 1949 (1994).
    [CrossRef] [PubMed]
  9. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939 (1985); “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
    [CrossRef] [PubMed]
  10. R. D. Li and P. Kumar, “Squeezing in traveling-wave second-harmonic generation,” Opt. Lett. 18, 1961 (1993); “Quantum-noise reduction in traveling-wave second-harmonic generation,” Phys. Rev. A 49, 2157 (1994); “Evolution of quantum noise in the traveling-wave second-harmonic [χ(2)] nonlinear process,” J. Opt. Soc. Am. B JOBPDE 12, 2310 (1995).
    [CrossRef] [PubMed]
  11. Z. Y. Ou, “Propagation of quantum fluctuations in single-pass second-harmonic generation for arbitrary interaction length,” Phys. Rev. A 49, 2106 (1994).
    [CrossRef]
  12. A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
    [CrossRef] [PubMed]
  13. M. A. M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815 (1995).
    [CrossRef]
  14. 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]
  15. M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
    [CrossRef]
  16. C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
    [CrossRef]
  17. W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
    [CrossRef]
  18. M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
    [CrossRef]
  19. G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
    [CrossRef]
  20. M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
    [CrossRef]
  21. A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
    [CrossRef]
  22. S. Janz, C. Fernando, H. Dai, F. Chatenoud, M. Dion, and R. Normandin, “Quasi-phase-matched second-harmonic generation in reflection from AlxGa1−xAs heterostructures,” Opt. Lett. 18, 589 (1993).
  23. K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
    [CrossRef] [PubMed]
  24. M. E. Anderson, M. Beck, M. G. Raymer, and J. D. Bierlein, “Parametric amplification and squeezing in quasi-phase-matched waveguides,” Opt. Lett. 20, 620 (1995).
    [CrossRef] [PubMed]
  25. D. K. Serkland, M. M. Fejer, R. L. Byer, and Y. Yamamoto, “Squeezing in a quasi-phase-matched LiNbO3 waveguide,” Opt. Lett. 20, 1649 (1995).
    [CrossRef]
  26. See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
    [CrossRef]
  27. S. Helmfrid, and G. Arvidsson “Influence of randomly varying domain lengths and nonuniform effective index on second-harmonic generation in quasi-phase-matching waveguides,” J. Opt. Soc. Am. B 8, 797 (1991).
    [CrossRef]
  28. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
    [CrossRef] [PubMed]
  29. R. A. Myers, N. Mukherjee, and S. R. Brueck, “Large second-order nonlinearity in poled fused silica,” Opt. Lett. 16, 1732 (1991).
    [CrossRef] [PubMed]
  30. P. G. Kazansky, L. Dong, and P. St. J. Russell, “High second-order nonlinearities in poled silica fibers,” Opt. Lett. 19, 701 (1994).

1995 (5)

A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
[CrossRef] [PubMed]

M. A. M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef]

K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
[CrossRef] [PubMed]

M. E. Anderson, M. Beck, M. G. Raymer, and J. D. Bierlein, “Parametric amplification and squeezing in quasi-phase-matched waveguides,” Opt. Lett. 20, 620 (1995).
[CrossRef] [PubMed]

D. K. Serkland, M. M. Fejer, R. L. Byer, and Y. Yamamoto, “Squeezing in a quasi-phase-matched LiNbO3 waveguide,” Opt. Lett. 20, 1649 (1995).
[CrossRef]

1994 (3)

1993 (2)

1992 (3)

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

Special issue on quantum noise reduction in optical systems, E. Giacobino and C. Fabre, eds., Appl. Phys. B 55(3), (1992).

1991 (2)

1990 (2)

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

1988 (1)

See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946841988

1987 (1)

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[CrossRef]

1986 (1)

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

1983 (1)

1976 (3)

M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
[CrossRef]

A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
[CrossRef]

M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
[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]

Anderson, M. E.

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]

Arvidsson, G.

Assanto, G.

Baek, Y.

Beck, M.

Bencheikh, K.

K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
[CrossRef] [PubMed]

Berzanskis, A.

A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
[CrossRef] [PubMed]

Bierlein, J. D.

Bierlien, J. D.

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[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]

Brown, J. B.

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

Brueck, S. R.

Byer, R.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

Byer, R. L.

Cantrell, C. D.

M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
[CrossRef]

Chatenoud, F.

Colak, S.

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

Dai, H.

Dion, M.

Dong, L.

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]

Fabre, C.

Special issue on quantum noise reduction in optical systems, E. Giacobino and C. Fabre, eds., Appl. Phys. B 55(3), (1992).

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

Fejer, M. M.

D. K. Serkland, M. M. Fejer, R. L. Byer, and Y. Yamamoto, “Squeezing in a quasi-phase-matched LiNbO3 waveguide,” Opt. Lett. 20, 1649 (1995).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

Feller, K.-H.

A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
[CrossRef] [PubMed]

Feng, D.

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

Fermann, M. E.

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[CrossRef]

Fernando, C.

Ferries, M. C.

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[CrossRef]

Feuer, B.

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Geng, Z. H.

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

Giacobino, E.

Special issue on quantum noise reduction in optical systems, E. Giacobino and C. Fabre, eds., Appl. Phys. B 55(3), (1992).

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

Haas, D.

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Heidmann, A.

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

Helmfrid, S.

Hordvik, A.

A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
[CrossRef]

Huntziger, E.

K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
[CrossRef] [PubMed]

Ieiri, S.

M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
[CrossRef]

Janz, S.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

Karim, D.

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Kazansky, P. G.

Khanarian, G.

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Kim, D. Y.

Levenson, J. A.

K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
[CrossRef] [PubMed]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

Marte, M. A. M.

M. A. M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef]

Mukherjee, N.

Myers, R. A.

Normandin, R.

Norwood, R. A.

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Osaka, M.

M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
[CrossRef]

Otsuka, K.

Ou, Z. Y.

Z. Y. Ou, “Propagation of quantum fluctuations in single-pass second-harmonic generation for arbitrary interaction length,” Phys. Rev. A 49, 2106 (1994).
[CrossRef]

Payne, D. N.

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[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 (1962).
[CrossRef]

Pitch, M. S.

M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
[CrossRef]

Raymer, M. G.

Reynaud, S.

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

Russell, P. St. J.

P. G. Kazansky, L. Dong, and P. St. J. Russell, “High second-order nonlinearities in poled silica fibers,” Opt. Lett. 19, 701 (1994).

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[CrossRef]

Schiek, R.

Schlossberg, H.

A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
[CrossRef]

See, R. C.

M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
[CrossRef]

Seibert, H.

Serkland, D. K.

Sheik-Bahae, M.

Sohler, W.

Stabinis, A.

A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

Sundheimer, M. L.

Szilagyi, A.

A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
[CrossRef]

Takizawa, K.

M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
[CrossRef]

van der Poel, C. J.

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

Van Stryland, E.

Wang, W. S.

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

Yamamoto, Y.

Zhou, Q.

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

Appl. Phys. B (1)

Special issue on quantum noise reduction in optical systems, E. Giacobino and C. Fabre, eds., Appl. Phys. B 55(3), (1992).

Appl. Phys. Lett. (2)

C. J. van der Poel, J. D. Bierlien, J. B. Brown, and S. Colak, “Efficient type I blue second-harmonic generation in periodically segmented KTiOPO4 waveguides,” Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

G. Khanarian, R. A. Norwood, D. Haas, B. Feuer, and D. Karim, “Phase matched second harmonic generation in a polymer waveguide,” Appl. Phys. Lett. 57, 977 (1990).
[CrossRef]

Electron. Lett. (1)

M. C. Ferries, P. St. J. Russell, M. E. Fermann, and D. N. Payne, “Second harmonic generation in an optical fiber by self-written χ(2),” Electron. Lett. 23, 322 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. Byer, “Quasi-phase matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef] [PubMed]

J. Appl. Phys. (2)

M. S. Pitch, C. D. Cantrell, and R. C. See, “Infrared second harmonic generation in nonbirefringent cadmium telluride,” J. Appl. Phys. 47, 3514 (1976).
[CrossRef]

A. Szilagyi, A. Hordvik, and H. Schlossberg, “A quasi phase matched technique for efficient optical mixing and doubling,” J. Appl. Phys. 47, 2055 (1976).
[CrossRef]

J. Cryst. Growth (1)

W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, “Study of LiTaO3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO3 crystals with periodic laminar ferroelectric domains,” J. Cryst. Growth 79, 706 (1986).
[CrossRef]

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

K. Bencheikh, E. Huntziger, and J. A. Levenson, “Quantum noise reduction in quasi-phase-matched optical parametric amplification,” J. Opt. Soc. Am. A 12, 849 (1995).
[CrossRef] [PubMed]

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

Opt. Commun. (2)

M. Osaka, K. Takizawa, and S. Ieiri, “Second harmonic generation in periodic laminar structure of nonlinear optical crystal,” Opt. Commun. 18, 331 (1976).
[CrossRef]

A. Berzanskis, K.-H. Feller, and A. Stabinis, “Squeezed light generation by means of cascaded second-order nonlinearity,” Opt. Commun. 118, 438 (1995).
[CrossRef] [PubMed]

Opt. Lett. (8)

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]

Phys. Rev. A (1)

Z. Y. Ou, “Propagation of quantum fluctuations in single-pass second-harmonic generation for arbitrary interaction length,” Phys. Rev. A 49, 2106 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

M. A. M. Marte, “Sub-Poissonian twin beams via competing nonlinearities,” Phys. Rev. Lett. 74, 4815 (1995).
[CrossRef]

Proc. SPIE (1)

See, for example, Spectroscopic Characterization Techniques for Semiconductor Technology III, Proc. SPIE 946841988

Prog. Opt. (1)

See, for example, S. Reynaud, A. Heidmann, E. Giacobino, and C. Fabre, “Quantum fluctuations in optical systems,” Prog. Opt. 30, 1–85 (1992).
[CrossRef]

Other (5)

G. I. Stegeman and A. Miller, in Photonics in Switching: Background and Components, J. E. Midwinter, ed. (Academic, Boston, 1993), Chap. 5, p. 81.
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, “Broadband parametric deamplification of quantum noise in an optical fiber,” Phys. Rev. Lett. 57, 691 (1986); R. M. Shelby, M. D. Levenson, D. F. Walls, and A. Aspect, “Generation of squeezed states of light with a fiber-optic ring interferometer,” Phys. Rev. A 33, 4008 (1986).
[CrossRef] [PubMed]

K. Bergman, H. A. Haus, and M. Shirasaki, “Analysis and measurement of GAWBS spectrum in a nonlinear fiber ring,” Appl. Phys. B 55, 242 (1992); “Squeezing in a fiber interferometer with a gigahertz pump,” Opt. Lett. 19, 290 (1994).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Resolved forward Brillouin scattering in optical fibers,” Phys. Rev. Lett. 54, 939 (1985); “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244 (1985).
[CrossRef] [PubMed]

R. D. Li and P. Kumar, “Squeezing in traveling-wave second-harmonic generation,” Opt. Lett. 18, 1961 (1993); “Quantum-noise reduction in traveling-wave second-harmonic generation,” Phys. Rev. A 49, 2157 (1994); “Evolution of quantum noise in the traveling-wave second-harmonic [χ(2)] nonlinear process,” J. Opt. Soc. Am. B JOBPDE 12, 2310 (1995).
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Diagram of a periodically inverted medium. The arrows represent the sign of the second-order nonlinear susceptibility. lc represents the coherence length, and li represents the inversion length.

Fig. 2
Fig. 2

Second-harmonic amplitude for a mismatch ε = 1/9 as a function of the normalized propagation length. The solid curve represents the exact solution for the amplitude calculated from Eqs. (9) and (10) for any point ζ. Also represented are the envelope amplitudes obtained from the solution of Eq. (12) (squares) and the approached solution of Eq. (14a) (dashed curve).

Fig. 3
Fig. 3

Second-harmonic phase corresponding to conditions of Fig. 2. The exact solution from Eqs. (9) and (10) for any point ζ is given by the solid curve, and the approached solution obtained from Eq. (14b) is given by the dashed curve.

Fig. 4
Fig. 4

Fundamental phase corresponding to conditions of Fig. 2. The exact solution obtained from Eq. (16) is given by the solid curve. The solution of Eq. (18a) is given by the squares. Also represented the fundamental phase evolution in the absence of QPM (dashed curve).

Fig. 5
Fig. 5

Representation of the second-harmonic field in the complex plane. The exact solution [Eqs. (9) and (10)] is given by the solid curve. The approximation given by Eq. (12) is represented by the dashed curve, and the approximation given by Eq. (13) is represented by squares. Also represented is the result obtained without QPM (dotted curve).

Fig. 6
Fig. 6

Squeezing of the fundamental as a function of the nonlinear phase shift.

Fig. 7
Fig. 7

Squeezing of the fundamental as a function of propagation distance in a QPM LiNbO3 for different values of ε:ε=0.1 (dashed curve), ε=0.017 (squares), and ε=0.001 (solid curve). The power of the fundamental is 50 MW/cm2.

Fig. 8
Fig. 8

Squeezing of the fundamental as a function of propagation distance in a QPM silica fiber for different values of ε:ε=0.1 (dashed curve), ε=0.017 (squares), ε=0.002 (dotted–dashed curve), and ε=0.0005 (solid curve). The power of the fundamental is 50 MW/cm2.

Fig. 9
Fig. 9

Squeezing of the fundamental as a function of propagation distance in a QPM silica fiber for different values of power of the fundamental: 1 MW/cm2 (dashed curve), 10 MW/cm2 (squares), 100 MW/cm2 (dotted–dashed curve), and 50 MW/cm2 (solid curve), with ε=0.002.

Equations (79)

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li=lc(1+ε),
dZˆ1dz=-εp(z)κZˆ1+Zˆ2 exp(-iΔkz),
dZˆ2dz=εp(z)κZˆ12 exp(iΔkz),
κ=deff2ω12ω2n12n2ε0c2V
Zˆi=Zi+zˆi.
dA1dζ=-εpA1*A2 exp(-iΔsζ),
dA2dζ=εpA12 exp(+iΔsζ),
daˆ1dζ=-εp(Aˆ2aˆ1++2A1*aˆ2)exp(-iΔsζ),
daˆ2dζ=εp2A1*aˆ1 exp(+iΔsζ),
Δs=2Δkκ|Z1(0)|,
ζ=12|Z1(0)|κz,
A1(ζ)=Z1(z)|Z1(0)|,
A2(ζ)=2Z2(z)|Z1(0)|
A1(ζ)=A10=1,
dA2dζ=εp exp(+iΔsζ).
A2(ζ)=A2(n)+(-1)niΔs[exp(+iΔsζ)-exp(+iΔsζn)],
A2(ζ)=1Δs{sin(πη)+i[2n+1-cos(πη)]},
u2(ζ)=1Δs(2n+1)2+1-2(2n+1)cos(πη)ζ2πζ,
Φ2(ζ)=atan2n+1-cos(πη)sin(πη)ζπ2.
A2(ζ)=A2(n)+iΔsexp(+iπεn)[exp(+iπεη)+1].
A2(n)=αΔs[exp(+iπεn)-1],
α=1tan(πε/2).
Lc=πΔs(1+ε)ε=πΔS,
A2(n)=2αΔSexp(+iΔSζn/2+iπ/2)sin(ΔSζn/2).
A2(ζ)4πΔSexp(+iΔSζ/2+iπ/2)sin(ΔSζ/2).
u2(ζ)4πΔSsin(ΔSζ/2),
Φ2(ζ)ΔSζ/2+π/2.
dΦ1(ζ)dζ=-(-1)n2π2ΔSsin(ΔSζ/2)×sin(ΔSζ/2+π/2-Δsζ).
dΦ1(ζ)dζ=2π2ΔSsin(ΔSζ/2)cos(ΔSζ/2-πη).
dΦ1(ζ)dζ=4π22ΔS2sin2(ΔSζ/2),
Φ1(ζ)=4π21ΔS2[ζΔS-sin(ζΔS)]
ζ4π2ζΔS.
Φ1(z)=2πλn2 effIz,n2 eff=4π24πλcε0deff2n2ωnω2ΔK,
daˆ1dζ=-(-1)n2π1ΔS[exp(iΔSζ)-1]aˆ1++2aˆ2×exp(-inπ)exp(-iηπ)×exp(-iΔSζ),
daˆ2dζ=(-1)n2aˆ1 exp(inπ)exp(iηπ)exp(iΔSζ).
daˆ1dζ=2iπ2π1ΔS[exp(iΔSζ)-1]aˆ1++2aˆ2×exp(-iΔSζ),
daˆ2dζ=2iπ2aˆ1 exp(iΔSζ).
dbˆ1dζ=4iπ21ΔSbˆ1+-4iπ21ΔSbˆ1,
dbˆ2dζ=-ibˆΔS2.
bˆ1(ζ)=1-iΔS4ζπ2bˆ1(0)+iΔS4ζπ2bˆ1+(0).
aˆ1(ζ)=μ(ζ)aˆ1(0)+ν(ζ)aˆ1+(0),
S1Φ(ζ)=(|μ|-|ν|)2=[1+Φ12(ζ)-Φ1(ζ)]2.
ζn+1-ζn=δ(1+ε+εn).
A2(n+1)=A2(n)+(-1)niΔs[exp(+iΔsζn+1)-exp(+iΔsζn)].
A2(n+1)=A2(n)-exp(iπnε)iΔs[exp(+iπε)×exp(+iπσn+1)+exp(+iπσn)],
A2(n)=iΔsk=0n-1 exp(+ikπε)[exp(+iπε)×exp(+iπσk+1)+exp(+iπσk)],
EA2(n)=A2(n) exp[-(πσ)2/2]+iΔs{1-exp[-(πσ)2/2]}.
E{A2(n)}A2(n) exp[-(πσ)2/2].
E{Φ1}Φ1 exp[-(πσ)2/2].
dX1dζ=-εp[(X1X2+Y1Y2)cos(Δsζ)+(X1Y2-Y1X2)sin(Δsζ)],
dY1dζ=-εp[(X1Y2-Y1X2)cos(Δsζ)-(X1X2+Y1Y2)sin(Δsζ)],
dX2dζ=εp[(X12-Y12)cos(Δsζ)-2X1Y1 sin(Δsζ)],
dY2dζ=εp[2X1Y1 cos(Δsζ)+(X12-Y12)sin(Δsζ)].
xˆ1=12(aˆ1+aˆ1+),
yˆ1=-i2(aˆ1-aˆ1+),
xˆ2=12(aˆ2+aˆ2+),
yˆ2=-i2(aˆ2-aˆ2+),
ddζxˆ1yˆ1xˆ2yˆ2=M(ζ)xˆ1yˆ1xˆ2yˆ2,
M(ζ)=εp-ss2-dd2-ds1sd1-dd2-ss2-sd1-ds1ds1sd100-sd1ds100,
S1=12[S1x+S1y-(S1x-S1y)2+4S1xy2],
D1=12[S1x+S1y+(S1x-S1y)2+4S1xy2],
QS1/D1=12A tan2S1xyS1y-S1xmodπ2.
qˆ1=12(aˆ1 exp(-iQ)+c.c.).
aˆ1=xˆ1+iyˆ1,
aˆ1+=xˆ1-iyˆ1.
qˆ1=xˆ1 cos Q+yˆ1 sin Q.
Δq12=x12cos2 Q+y12sin2 Q+x1y1+y1x1sin Q cos Q.
dV(ζ)dζ=M(ζ)·V(ζ),
V(ζ)=C(ζ)·V(0),
dC(ζ)dζ=M(ζ)·C(ζ).
x12=iC1iVi(0)2=i C1i24,
y12=iC2jVi(0)2=i C2i24,
x1y1+y1x1=2i C1iC2i4.
Δq2=14(S1x cos2 Q+S1y sin2 Q+S1xy sin 2Q),
S1x=iC1i2,S1y=iC2i2,S1xy=iC1iC2i.
Si(ζ)=Δqi2(ζ)minΔqi2(0),Di(ζ)=Δqj2(ζ)maxΔqi2(0),i=1,2.
Si(ζ)=12[Six+Siy-(Six-Siy)2+4Sixy2],
Di(ζ)=12[Six+Siy+(Six-Siy)2+4Sixy2],
QSi/Di(ζ)=12arctan2SixySiy-Sixmodπ2.

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