Abstract

Quadrature-amplitude and phase squeezing are theoretically investigated in a planar waveguide geometry where the use of a linear grating fabricated on top of the waveguide reproduces a photonic bandgap structure. The introduction of a nonlinear grating, obtained with a modulation of the nonlinear susceptibility χ(2), provides an additional degree of freedom that allows, together with the linear grating, tuning of the fundamental field in a selected resonance of the transmission spectrum and, at the same time, control of the phase-matching condition between the fundamental and second-harmonic fields. The results show that quadrature-amplitude squeezing is achieved for the fundamental field, increasing the second-harmonic input intensity. The second-harmonic field is tuned in the passband of the photonic bandgap. The low nonlinear conversion efficiency, given by a suitable selection of the mismatch, gives rise to the possibility of having a fundamental field of quite the same intensity, but less noisy than at the entry.

© 2004 Optical Society of America

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  1. M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
    [CrossRef]
  2. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
    [CrossRef] [PubMed]
  3. M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
    [CrossRef]
  4. D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
    [CrossRef]
  5. Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
    [CrossRef]
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    [CrossRef]
  9. M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  16. J. A. Armstrong, N. Bloembergen, J. Ducing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
    [CrossRef]
  17. G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
    [CrossRef]

2002

2001

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

2000

G. Kanter and P. Kumar, “Enhancement of bright squeezing in the second harmonic generation by internally seeding the χ(2) interaction,” IEEE J. Quantum Electron. 36, 916–922 (2000).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

1999

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

1998

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

1997

D. K. Serkland, P. Kumar, M. A. Arbore, and M. M. Fejer, “Amplitude squeezing by means of quasi-phase-matched second-harmonic generation in a LiNbO3 waveguide,” Opt. Lett. 22, 1497–1499 (1997).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

1995

1994

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

R. D. Li and P. Kumar, “Quantum noise reduction in travelling wave second-harmonic generation,” Phys. Rev. A 49, 2157–2166 (1994).
[CrossRef] [PubMed]

1988

M. A. M. Marte and D. F. Walls, “Quantum theory of a squeezed-pump laser,” Phys. Rev. A 37, 1235–1247 (1988).
[CrossRef] [PubMed]

1962

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

Arbore, M. A.

Armstrong, J. A.

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

Bachor, H. A.

Bertolotti, M.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Bloembergen, N.

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

Bloemer, M. J.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bowden, C. M.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bowen, W.

Bowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Byer, R. L.

Centini, M.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

D’Aguanno, G.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Ducing, J.

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

Dumeige, Y.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Fazio, E.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Fejer, M. M.

Ferrari, E.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Haus, J. W.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Kanter, G.

G. Kanter and P. Kumar, “Enhancement of bright squeezing in the second harmonic generation by internally seeding the χ(2) interaction,” IEEE J. Quantum Electron. 36, 916–922 (2000).
[CrossRef]

Kumar, P.

G. Kanter and P. Kumar, “Enhancement of bright squeezing in the second harmonic generation by internally seeding the χ(2) interaction,” IEEE J. Quantum Electron. 36, 916–922 (2000).
[CrossRef]

D. K. Serkland, P. Kumar, M. A. Arbore, and M. M. Fejer, “Amplitude squeezing by means of quasi-phase-matched second-harmonic generation in a LiNbO3 waveguide,” Opt. Lett. 22, 1497–1499 (1997).
[CrossRef]

R. D. Li and P. Kumar, “Quantum noise reduction in travelling wave second-harmonic generation,” Phys. Rev. A 49, 2157–2166 (1994).
[CrossRef] [PubMed]

Lam, P. K.

Lawrence, M.

Levenson, J. A.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Li, R. D.

R. D. Li and P. Kumar, “Quantum noise reduction in travelling wave second-harmonic generation,” Phys. Rev. A 49, 2157–2166 (1994).
[CrossRef] [PubMed]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Marte, M. A. M.

M. A. M. Marte and D. F. Walls, “Quantum theory of a squeezed-pump laser,” Phys. Rev. A 37, 1235–1247 (1988).
[CrossRef] [PubMed]

Nefedov, I.

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Pershan, P. S.

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

Pezzetta, D.

Sagnes, I.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Sakoda, K.

Sauvage, S.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Scalora, M.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Serkland, D. K.

Sibilia, C.

D. Pezzetta, C. Sibilia, M. Bertolotti, J. W. Haus, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Photonic bandgap structures in planar nonlinear waveguides: application to second-harmonic generation,” J. Opt. Soc. Am. B 18, 1326–1333 (2001).
[CrossRef]

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

Vidakovic, P.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Walls, D. F.

M. A. M. Marte and D. F. Walls, “Quantum theory of a squeezed-pump laser,” Phys. Rev. A 37, 1235–1247 (1988).
[CrossRef] [PubMed]

Yamamoto, Y.

Appl. Phys. Lett.

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D’Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001).
[CrossRef]

IEEE J. Quantum Electron.

G. Kanter and P. Kumar, “Enhancement of bright squeezing in the second harmonic generation by internally seeding the χ(2) interaction,” IEEE J. Quantum Electron. 36, 916–922 (2000).
[CrossRef]

J. Mod. Opt.

G. D’Aguanno, C. Sibilia, E. Fazio, E. Ferrari, and M. Bertolotti, “Field phase modulation and input phase and intensity dependence in a nonlinear second order interaction,” J. Mod. Opt. 45, 1049–1066 (1998).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Centini, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. Scalora, M. J. Bloemer, and C. M. Bowden, “Reflectivity control via second-order interaction process in one dimensional photonic band gap structures,” Opt. Commun. 184, 283–288 (2000).
[CrossRef]

Opt. Lett.

Phys. Rev.

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

Phys. Rev. A

M. A. M. Marte and D. F. Walls, “Quantum theory of a squeezed-pump laser,” Phys. Rev. A 37, 1235–1247 (1988).
[CrossRef] [PubMed]

R. D. Li and P. Kumar, “Quantum noise reduction in travelling wave second-harmonic generation,” Phys. Rev. A 49, 2157–2166 (1994).
[CrossRef] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Bowling, C. M. Bowden, R. Viswanathan, and J. W. Haus, “Pulsed second-harmonic generation in nonlinear one-dimensional, periodic structures,” Phys. Rev. A 56, 3166–3174 (1997).
[CrossRef]

Phys. Rev. E

M. Centini, C. Sibilia, M. Scalora, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, C. M. Bowden, and I. Nefedov, “Dispersive properties of finite, one dimensional, photonic band gap structures: application to nonlinear quadratic interactions,” Phys. Rev. E 60, 4891–4898 (1999).
[CrossRef]

Phys. Rev. Lett.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band-gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Other

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

See, for example, M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, Cambridge, UK, 1997), Chap. 2.

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Figures (7)

Fig. 1
Fig. 1

Geometry of the planar guide with respect to the crystal axes, in the case of a Z-cut LiNbO3 substrate. The only guided modes in the Z-cut substrate are the TM ones. ΛL is the period of the linear grating, obtained by etching part of the film layer to simulate in this way a PBG structure.

Fig. 2
Fig. 2

Linear and nonlinear gratings. The linear grating is obtained by etching part of film layer, simulating in this way a PBG structure. The nonlinear grating is obtained by periodically inverting the orientation of the nonlinear susceptibility tensor: The periodically inverted domain is assumed infinite in the x direction and uniform. Shown also are the incoming and outcoming fields.

Fig. 3
Fig. 3

Transmission spectrum of the proposed planar waveguide. Operating the selection δ1=0.007106 µm-1, we tune the fundamental field at the third resonance of the transmission spectrum on the right side of the bandgap.

Fig. 4
Fig. 4

Plots of amplitude squeezing Sxf1(z) for the fundamental forward field (δ1=0.007106 µm-1) during the propagation inside the nonlinear PBG waveguide for two different input values of the second-harmonic field. We consider an intensity for the second-harmonic forward field of 0.01 GW/m2 (dashed line) and of 400 GW/m2 (solid curve). The dotted line shows the amplitude squeezing level for the coherent state [Sxf1(z)=1]. The forward fundamental-field intensity is always fixed at 1 GW/m2.

Fig. 5
Fig. 5

Plots of phase squeezing Syf1(z) for the fundamental forward field during the propagation inside the nonlinear PBG waveguide for two different input values of the second-harmonic field (δ1=0.007106 µm-1). We consider an intensity for the second-harmonic forward field of 0.01 GW/m2 (dashed line) and of 400 GW/m2 (solid curve). The dotted line shows the phase-squeezing level for the coherent state [Syf1(z)=1]. The forward fundamental-field intensity is always fixed at 1 GW/m2.

Fig. 6
Fig. 6

Plots of the amplitude squeezing Sxf1(z) for the fundamental forward field during the propagation inside the homogeneous nonlinear waveguide (δ2=0.1707 µm-1) for two different input values of the second-harmonic field. We consider an intensity for the second-harmonic forward field of 0.01 GW/m2 (dashed line) and of 400 GW/m2 (solid curve). The amplitude-squeezing level for the coherent state is Sxf1(z)=1. The forward fundamental-field intensity is always fixed at 1 GW/m2.

Fig. 7
Fig. 7

Plots of the phase squeezing Syf1(z) for the fundamental forward field during the propagation inside the homogeneous nonlinear waveguide (δ2=0.1707 µm-1) for two different input values of the second-harmonic field. We consider an intensity for the second-harmonic forward field of 0.01 GW/m2 (dashed line) and of 400 GW/m2 (solid curve). The phase-squeezing level for the coherent state is Syf1(z)=1. The forward fundamental-field intensity is always fixed at 1 GW/m2.

Tables (3)

Tables Icon

Table 1 Amplitude and Phase Squeezing for a PBG Structure with Different Values of the Detuning Parameter δ1 and for Different Input Intensities of the Second-Harmonic Signal

Tables Icon

Table 2 Comparison of Amplitude-Squeezing Performance between Different Devicesa

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Table 3 Comparison of Amplitude Squeezing between the Nonlinear PBG Waveguide and an Homogeneous Nonlinear Waveguide that Converts the Same Amount of Fundamentala

Equations (64)

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Eˆ(x, y, z, t)
=miωm2ε0εrV {Aˆm(z)fm(x, y)exp[i(kzmz-ωmt)]-Aˆm+(z)fm*(x, y)exp[-i(kzmz-ωmt)]}εm,
n2(x, y, z)=r(x, y, z)+Δεr(x, y, z),
Δεr(x, y, z)=(n2-1)fa(z)fortxt+h0forx0orxt+h
fa(z)=12+m=- sin(π/2+mπ)(2m+1)π exp2πi2m+1ΛLz,
2Eˆ(r, t)=με0εr 2Eˆ(r, t)t2+μ 2Pˆ(r, t)t2,
d2dz2Aˆm(z)kmzddzAˆm(z),
d2dz2Aˆm+(z)kmzddzAˆm+(z).
m(-2kmz)ddzAˆm(z)fm(x, y)exp[i(kmzz-ωmt)]+ddzAˆm+(z)fm*(x, y)exp[-i(kmzz-ωmt)]=m[-iωm2με0Δεr(r)]{Aˆm(z)fm(x, y)exp[i(kmzz-ωmt)]-Aˆm+(z)fm(x, y)exp[-i(kmzz-ωmt)]}+mn-μχ(r)ωnε02εrV 2t2{Aˆm(z)Aˆn(z)fm(x, y)fn(x, y)exp[i(kmz+knz)z-i(ωm+ωn)t]-Aˆm(z)Aˆn+(z)fm(x, y)fn*(x, y)exp[i(kmz-knz)z-i(ωm-ωn)t]-Aˆm+(z)Aˆn(z)fm*(x, y)fn(x, y)×exp[-i(kmz-knz)z+i(ωm-ωn)t]+Aˆm+(z)Aˆn+(z)fm*(x, y)fn*(x, y)exp[-i(kmz+knz)z+i(ωm+ωn)t]}.
d(x, z)=qdq(x)expiq 2πΛNLz+dq*(x)exp-iq 2πΛNLz,
ddzAˆf1(z)=iKL1Aˆb1(z)exp(i2δ1z)+KNL1Aˆf2(z)Aˆf1+(z)exp(i2δ2z),
ddzAˆb1(z)=-iKL1Aˆf1(z)exp(-i2δ1z)-KNL1Aˆb2(z)Aˆb1+(z)exp(-i2δ2z),
ddzAˆf2(z)=-KNL12Aˆf12(z)exp(-i2δ2z),
ddzAˆb2(z)=KNL12Aˆb12(z)exp(i2δ2z),
KL1=iω1Δε1(x)ff1(x, y)ff1*(x, y)dxdy4,
KNL1=ω12 ω1ε0εrV d1*(x)ff1(x, y)ff1*(x, y)dxdy,
2k1z-2πΛL=-2δ1,
k2z-2k1z-2πΛNL=2δ2,
Aˆij(z)=|Aˆij(z)|exp[iΦij(z)],
aˆij(z)=Aˆij(z)-Aˆij(z),
ddzAˆf1(z)=iKL1Aˆb1(z)exp(i2δ1z)+KNL1Aˆf2(z)×Aˆf1+(z)exp(i2δ2z),
ddzAˆb1(z)=-iKL1Aˆf1(z)exp(-i2δ1z)-KNL1Aˆb2(z)Aˆb1+(z)exp(-i2δ2z),
ddzAˆf2(z)=-KNL12Aˆf1(z)2 exp(-i2δ2z),
ddzAˆb2(z)=KNL12Aˆb1(z)2 exp(i2δ2z),
ddzaˆf1(z)=iKL1aˆb1(z)exp(i2δ1z)+KNL1[Aˆf2(z)aˆf1+(z)+Aˆf1(z)*aˆf2(z)]exp(i2δ2z),
ddzaˆb1(z)=-iKL1aˆf1(z)exp(-i2δ1z)-KNL1[Aˆb2(z)aˆb1+(z)+Aˆb1(z)*aˆb2(z)]exp(-i2δ2z),
ddzaˆf2(z)=-KNL1Aˆf1(z)aˆf1(z)exp(-i2δ2z),
ddzaˆb2(z)=KNL1Aˆb1(z)aˆb1(z)exp(i2δ2z),
Aˆf1(z)=[C1 cos(Δ1z)+C2 sin(Δ1z)]exp(iδ1z),
Aˆb1(z)=C2 Δ1iKL1+C1 δ1KL1cos(Δ1z)+C2 δ1KL1-C1 Δ1iKL1sin(Δ1z)exp(-iδ1z),
Aˆb1(0)=Aˆb1(L=NΛL)=0C2C1=-i δ1Δ1Δ1NΛL=nπn=±1,±2,
Aˆf1(z)=Acos(Δ1z)-i δ1Δ1 sin(Δ1z)exp(iδ1z),
Aˆb1(z)=-iA KL1Δ1 sin(Δ1z)exp(-iδ1z),
Aˆf2(0)=0,
Aˆb2(L=NΛL)=0.
Aˆf2(z)=iKNL1A2(2δ22-6δ1δ2+5δ12-Δ12)8(δ2-δ1)(δ2-δ1-Δ1)(δ2-δ1+Δ1)-KNL1A2 exp[-i2(δ2-δ1)z]8Δ12(δ2-δ1)(δ2-δ1-Δ1)(δ2-δ1+Δ1)×[Δ1(δ2-δ1)(2δ1δ2-3δ12-Δ12)sin(2Δ1z)-2iδ12(δ2-δ1)2 sin2(Δ1z)+iΔ12(δ22-2δ1δ2-2δ12-Δ12)+iΔ12(δ2-δ1)(δ2-3δ1)cos(2Δ1z)],
Aˆb2(z)=A2KL12KNL1 exp[2i(δ2-δ1)z]8Δ12(δ2-δ1)(δ2-δ1+Δ1)(δ2-δ1-Δ1)[2i(δ2-δ1)2 sin2(Δ1z)-2δ1δ2 sin(Δ1z)cos(Δ1z)+2δ1δ2 sin(2Δ1z)-iΔ12]+iΔ12A2KL12KNL1 exp[2i(δ2-δ1)L]8Δ12(δ2-δ1)(δ2-δ1+Δ1)(δ2-δ1-Δ1).
Aˆf2(z)=Aˆf2(0)+iKNL1A2(2δ22-6δ1δ2+5δ12-Δ12)8(δ2-δ1)(δ2-δ1-Δ1)(δ2-δ1+Δ1)-KNL1A2 exp[-i2(δ2-δ1)z]8Δ12(δ2-δ1)(δ2-δ1-Δ1)(δ2-δ1+Δ1)×[Δ1(δ2-δ1)(2δ1δ2-3δ12-Δ12)sin(2Δ1z)-2iδ12(δ2-δ1)2 sin2(Δ1z)+iΔ12(δ22-2δ1δ2-2δ12-Δ12)+iΔ12(δ2-δ1)(δ2-3δ1)cos(2Δ1z)],
Aˆb2(z)=A2KL12KNL1 exp[2i(δ2-δ1)z]8Δ12(δ2-δ1)(δ2-δ1+Δ1)(δ2-δ1-Δ1)[2i(δ2-δ1)2 sin2(Δ1z)-2δ1δ2 sin(Δ1z)cos(Δ1z)+2δ1δ2 sin(2Δ1z)-iΔ12]+iΔ12A2KL12KNL1 exp[2i(δ2-δ1)L]8Δ12(δ2-δ1)(δ2-δ1+Δ1)(δ2-δ1-Δ1).
xˆij(z)=[aˆij(z)+aˆij+(z)]2,
yˆij(z)=[aˆij(z)-aˆij+(z)]2i,
dXˆ(z)dz=G(z)Xˆ(z),
Xˆ(z)=C(z)Xˆ0,
dC(z)dz=G(z)C(z),
Cij(0)=δijforoddindexi,
Cij(L)=δijforevenindexi.
xˆfi(0)xˆfj(0)=14δij,i, j=1, 2,
yˆfi(0)yˆfj(0)=14δij,i, j=1, 2,
xˆfi(0)yˆfj(0)=yˆfi(0)xˆfj(0)=0,ij,
xˆfi(0)yˆfi(0)+yˆfi(0)xˆfi(0)=0,i=1, 2.
xˆbi(L)xˆbj(L)=14δij,i, j=1, 2,
yˆbi(L)yˆbj(L)=14δij,i, j=1, 2,
xˆbi(L)yˆbj(L)=yˆbi(L)xˆbj(L)=0,ij,
xˆbi(L)yˆbi(L)+yˆbi(L)xˆbi(L)=0,i=1, 2.
Sxf1(z)=xˆf12(z)xˆf12(0),Syf1(z)=yˆf12(z)yˆf12(0),
Sxb1(z)=xˆb12(z)xˆb12(L),Syb1(z)=yˆb12(z)yˆb12(L),
Sxf2(z)=xˆf22(z)xˆf22(0),Syf2(z)=yˆf22(z)yˆf22(0),
Sxb2(z)=xˆb22(z)xˆb22(L),Syb2(z)=yˆb22(z)yˆb22(L),
Sxf1(z)=j=18C1j2(z),Syf1(z)=j=18C3j2(z),
Sxb1(z)=j=18C2j2(z),Syb1(z)=j=18C4j2(z),
Sxf2(z)=j=18C5j2(z),Syf2(z)=j=18C7j2(z),
Sxb2(z)=j=18C6j2(z),Syb2(z)=j=18C8j2(z).
d2dz2Aˆf1(z)=KNL12Aˆf2(z)2-|Aˆf1(z)|22Aˆf1(z),
G=KNL1Aˆf2zcosΦf2+2δ2zKL1sin2δ1zKNL1Aˆf2zsinΦf2+2δ2zKL1cos2δ1zKL1sin2δ1zKNL1Aˆb2zcosΦb2+2δ2zKL1cos2δ1zKNL1Aˆb2zsinΦb2+2δ2zKNL1Aˆf2zsinΦf2+2δ2zKL1cos2δ1zKNL1Aˆf2zcosΦf2+2δ2zKL1sin2δ1zKL1cos2δ1zKNL1Aˆb2zsinΦb2+2δ2zKL1sin2δ1zKNL1Aˆb2zcosΦb2+2δ2zKNL1Aˆf1zcosΦf1+2δ2z0KNL1Aˆf1zsinΦf1+2δ2z00KNL1Aˆb1zcosΦb1+2δ2z0KNL1Aˆb1zsinΦb1+2δ2zKNL1Aˆf1zsinΦf1+2δ2z0KNL1Aˆf1zcosΦf1+2δ2z00KNL1Aˆb1zsinΦb1+2δ2z0KNL1Aˆb1zcosΦb1+2δ2zKNL1Aˆf1zcosΦf1+2δ2z0KNL1Aˆf1zsinΦf1+2δ2z00KNL1Aˆb1zcosΦb1+2δ2z0KNL1Aˆb1zsinΦb1+2δ2zKNL1Aˆf1zsinΦf1+2δ2z0KNL1Aˆf1zcosΦf1+2δ2z00KNL1Aˆb1zsinΦb1+2δ2z0KNL1Aˆb1zcosΦb1+2δ2z0000000000000000.

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