Abstract

The optical properties of semiconductor quantum wells embedded in one-dimensional photonic crystal structures are analyzed by a self-consistent solution of Maxwell’s equations and a microscopic many-body theory of the material excitations. For a field mode spectrally below the photonic band edge it is shown that the optical absorption and gain are enhanced, exceeding by more than 1 order of magnitude the values of a homogeneous medium. For the photonic crystal structure inside a microcavity the gain increases superlinearly with the number of wells and for more than five wells exceeds the gain of a corresponding vertical-cavity surface-emitting laser.

© 2005 Optical Society of America

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2003 (1)

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

2002 (2)

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

2001 (4)

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

2000 (1)

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

1999 (4)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

1998 (1)

1997 (2)

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

1996 (2)

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

1989 (2)

1987 (2)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

1986 (1)

S. Schmitt-Rink, C. Ell, and H. Haug, "Many-body effects in the absorption, gain and luminescence spectra of semiconductor quantum-well structures," Phys. Rev. B 33, 1183-1189 (1986).
[CrossRef]

Abram, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Benisty, H.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Benner, S.

Bertolotti, M.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Bhat, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Blank, R.

Bloemer, M. J.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Boroditsky, M.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Bowden, C. M.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Cassagne, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Centini, M.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Chow, W. W.

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, 1999).
[CrossRef]

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Coccioli, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

D'Aguanno, G.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

De La Rue, R. M.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Dowling, J. P.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Dumeige, Y.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Ell, C.

Erchak, A. A.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Fan, B.

Fan, S.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Genack, A. Z.

Gogna, P.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

Han, I. Y.

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Haug, H.

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef] [PubMed]

C. Ell, R. Blank, S. Benner, and H. Haug, "Simplified calculations of the optical spectra of two-and three-dimensional laser-excited semiconductors," J. Opt. Soc. Am. B 6, 2006-2012 (1989); for the evaluation of the screened Coulomb interaction we use C=4.
[CrossRef]

S. Schmitt-Rink, C. Ell, and H. Haug, "Many-body effects in the absorption, gain and luminescence spectra of semiconductor quantum-well structures," Phys. Rev. B 33, 1183-1189 (1986).
[CrossRef]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
[CrossRef]

Haus, J. W.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

Houdré, R.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Hwang, J. K.

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Imada, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Ippen, E. P.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Jang, D. H.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Joannopoulos, J. D.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Jouanin, C.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Kim, C. K.

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

Kim, G. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Kim, S. B.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

Kim, S. H.

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

Koch, S. W.

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef] [PubMed]

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, 1999).
[CrossRef]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
[CrossRef]

Kolodziejski, L. A.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Kopp, V. I.

Krauss, T. F.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Kwon, S. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

Labilloy, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Lee, Y. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Levenson, A.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Loncar, M.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

Manka, A. S.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Meriadec, C.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Monnier, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Murata, M.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Noda, S.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

O'Brian, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Oesterle, U.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Park, H. G.

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Petrich, G. S.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Qui, Y.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

Rakich, P.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Ripin, D. J.

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Ryu, H. Y.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Sadaki, G.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Sagnes, I.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals, Vol. 80 of Springer Series in Optical Sciences (Springer-Verlag, 2001).
[CrossRef]

Scalora, M.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Schäfer, W.

W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer-Verlag, 2002).
[CrossRef]

Scherer, A.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Schmitt-Rink, S.

S. Schmitt-Rink, C. Ell, and H. Haug, "Many-body effects in the absorption, gain and luminescence spectra of semiconductor quantum-well structures," Phys. Rev. B 33, 1183-1189 (1986).
[CrossRef]

Sibilia, C.

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

Song, D. S.

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Song, H. W.

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

Taflove, A.

A. Taflove, Computational Electrodynamics--The Finite Difference Time-Domain Method (Artech-House, 1995).

Tocci, M. D.

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

Tokuda, T.

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

Vidakovic, P.

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

Viswanathan, R.

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

Vithana, H. K. M.

Vrijen, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Wegener, M.

W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer-Verlag, 2002).
[CrossRef]

Weisbuch, C.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, and C. Jouanin, "Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths," Phys. Rev. Lett. 79, 4147-4150 (1997).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

Yablonovitch, E.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yariv, A.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Yoshie, T.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

Appl. Phys. Lett. (8)

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

A. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, J. D. Joannopoulos, E. P. Ippen, G. S. Petrich, and L. A. Kolodziejski, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

H. Y. Ryu, J. K. Hwang, D. S. Song, I. Y. Han, and Y. H. Lee, "Effect of nonradiative recombination on light emitting properties of two-dimensional photonic crystal slab structures," Appl. Phys. Lett. 78, 1174-1176 (2001).
[CrossRef]

M. Imada, S. Noda, A. Chutinan, T. Tokuda, M. Murata, and G. Sadaki, "Coherent two-dimensional lasing action in surface-emitting laser with triangular-lattice photonic crystal structure," Appl. Phys. Lett. 75, 316-318 (1999).
[CrossRef]

J. K. Hwang, H. Y. Ryu, D. S. Song, I. Y. Han, H. W. Song, H. G. Park, Y. H. Lee, and D. H. Jang, "Room-temperature triangular-lattice two-dimensional photonic band gap lasers operating at 1.54 µm," Appl. Phys. Lett. 76, 2982-2984 (2000).
[CrossRef]

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, "Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 80, 3901-3903 (2001).
[CrossRef]

M. Loncar, T. Yoshie, A. Scherer, P. Gogna, and Y. Qui, "Low-threshold photonic crystal laser," Appl. Phys. Lett. 81, 2680-2682 (2002).
[CrossRef]

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, "Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs," Appl. Phys. Lett. 83, 3870-3872 (2003).
[CrossRef]

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. A (3)

M. D. Tocci, M. Scalora, M. J. Bloemer, J. P. Dowling, and C. M. Bowden, "Measurement of spontaneous-emission enhancement near the one-dimensional photonic band edge of semiconductor heterostructures," Phys. Rev. A 53, 2799-2803 (1996).
[CrossRef] [PubMed]

M. Scalora, M. J. Bloemer, A. S. Manka, J. P. Dowling, 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]

H. Haug and S. W. Koch, "Semiconductor laser theory with many-body effects," Phys. Rev. A 39, 1887-1898 (1989).
[CrossRef] [PubMed]

Phys. Rev. B (1)

S. Schmitt-Rink, C. Ell, and H. Haug, "Many-body effects in the absorption, gain and luminescence spectra of semiconductor quantum-well structures," Phys. Rev. B 33, 1183-1189 (1986).
[CrossRef]

Phys. Rev. E (2)

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: applications to nonlinear quadratic interactions," Phys. Rev. E 60, 4891-4898 (1999).
[CrossRef]

J. M. Bendickson, J. P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53, 4107-4121 (1996).
[CrossRef]

Phys. Rev. Lett. (4)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Y. Dumeige, I. Sagnes, P. Monnier, P. Vidakovic, I. Abram, C. Meriadec, and A. Levenson, "Phase-matched frequency doubling at photonic band edges: efficiency scaling as the fifth power of the length," Phys. Rev. Lett. 89, 043901 (2002).
[CrossRef] [PubMed]

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Science (2)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O'Brian, P. D. Dapkus, and I. Kim, "Two-dimensional photonic band-gap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific, 2004).
[CrossRef]

W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer-Verlag, 1999).
[CrossRef]

W. Schäfer and M. Wegener, Semiconductor Optics and Transport Phenomena (Springer-Verlag, 2002).
[CrossRef]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals, Vol. 80 of Springer Series in Optical Sciences (Springer-Verlag, 2001).
[CrossRef]

C.Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic, 2001).
[CrossRef]

C.M.Bowden and A.M.Zheltikov, eds., feature on nonlinear optics of photonic crystals, J. Opt. Soc. Am. B 19, 2046-2296 (2002).

K.Busch, S.Lölkes, R.B.Wehrspohn, and H.Föll, eds., Photonic Crystals--Advances in Design, Fabrication, and Characterization (Wiley-VCH, 2004).
[CrossRef]

A. Taflove, Computational Electrodynamics--The Finite Difference Time-Domain Method (Artech-House, 1995).

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Figures (14)

Fig. 1
Fig. 1

Schematic view of the 1D photonic Bragg structure with 2 N + 1 layers and one QW in the central unit cell. The photonic crystal consists of Al 0.1 Ga 0.9 As and AlAs, and the QW is made from GaAs or In x Ga 1 x As . All transverse fields are linearly polarized in the y direction, i.e., in the plane of the QW, and propagate as a plane wave in the z direction.

Fig. 2
Fig. 2

Transmission (solid curves) and reflection (dashed curves) normalized on the input field for (a) and (b) 33, (c) 49, and (d) 65 unit cells. The photonic crystals are 1D Bragg structures with the center of the optical gap at E L = 1.5 eV ; see the broad range spectrum in (a). In (b)–(d) the spectra are displayed in the vicinity of the lower edge of the optical gap. The zero of the energy axis corresponds to bandgap E G 0 of GaAs. E B 4.25 meV denotes the binding energy of an exciton in three dimensions. Note that the range of the x axis decreases with increasing numbers of unit cells.

Fig. 3
Fig. 3

Logarithmic plot of the linear absorption spectra at zero density for a detuning of Δ E G = 0.4 E B inside a homogeneous medium (solid curve) and inside a Bragg mirror consisting of 49 layers with E L = 1.54 eV (dashed curve). For comparison the transmission of the Bragg structure without the semiconductor is plotted also (dashed–dotted curve). The semiconductor parameters are d cv = 3.5 e Å and dephasing rate γ = 1 meV , which corresponds to low temperature. The light modes that appear below the optical gap of the Bragg mirror are labeled I, II, and III.

Fig. 4
Fig. 4

Normalized linear absorption as a function of detuning Δ E G . The low-temperature exciton resonance is in the vicinity of the upper transmission peak of the Bragg mirror (I), which consists of 49 layers with E L = 1.52 eV . The semiconductor parameters are d cv = 3.5 e Å and dephasing rate γ = 1 meV .

Fig. 5
Fig. 5

Room-temperature absorption/gain for n = 0.1 × 10 12 cm 2 (dashed–dotted curves), n = 0.8 × 10 12 cm 2 (dashed curves), and n = 1.4 × 10 12 cm 2 (solid curves) normalized on the incoming field: (a) homogeneous system, (b) photonic system with 33 unit cells and a detuning of Δ E G = 4.0 E B , (c) 49 unit cells and Δ E G = 5.0 E B , (d) 65 unit cells and Δ E G = 6.0 E B . In (b)–(d) the center of the stop band is at E L = 1.5 eV . The semiconductor parameters are T = 300 K , d cv = 3.5 e Å , and dephasing rate γ = 5 meV . Note that the ranges of the x and y axes are different in all plots.

Fig. 6
Fig. 6

Gain maxima normalized to the gain of a homogeneous medium as function of the detuning between the exciton resonance and the photonic bandgap for 33 (circles), 49 (squares), and 65 (triangles) unit cells, with E L = 1.5 eV . The semiconductor parameters are n = 1.4 × 10 12 cm 2 , T = 300 K , d cv = 3.5 e Å , and γ = 5 meV . The symbols depict the calculated values and the curves are guides to the eye.

Fig. 7
Fig. 7

Time and space dependence of E y ( z , t ) in the middle unit cell of (a) a homogeneous dielectric system and dielectric structures with (b) 33, (c) 49, and (d) 65 unit cells, with E L = 1.5 eV in (b)–(d). Note that these structures contain no QWs. The incident field is linearly polarized in the y direction and propagates as a plane wave in the z direction. The temporal duration of the incoming field is 0.25 ps (FWHM), and its central frequency is resonant to the upper peak of the transmission spectrum of the photonic crystal (I).

Fig. 8
Fig. 8

Space dependence of time-integrated E y ( z , t ) normalized on the input field. The photonic-crystal structure is a 49 unit cell Bragg mirror with E L = 1.54 eV and contains no QWs. The duration of the incoming field is 0.25 ps (FWHM), and its central frequency is tuned to the first three transmission maxima that appear below the photonic bandgap: (b) I, (c) II, and (d) III. (a) The space-dependent dielectric constant. The center of the structure is indicated by the vertical line.

Fig. 9
Fig. 9

Logarithmic plot of the normalized frequency-dependent squared modulus of the electric field E ( ω ) 2 I 0 . The field has been calculated at the center of a 49 unit cell Bragg mirror with E L = 1.54 eV without a QW (solid curve) and with a QW (dashed curve), for a homogeneous dielectric medium (dotted curve), and at the position of a QW that is surrounded by a homogeneous medium (dashed–dotted curve). The semiconductor parameters are d cv = 3.5 e Å and dephasing rate γ = 1 meV , i.e., the same as in Fig. 3.

Fig. 10
Fig. 10

Schematic view of the 1D photonic VCSEL structures. (a) PBE–VCSEL with an eight-layer Bragg mirror on each side. The photonic crystal between the mirrors consists of 2 N + 1 layers with 2 N 1 QWs in the middle 2 N 1 layers. The positions of the QWs correspond to the maxima of the cavity mode. (b) VCSEL with 2 N 1 QWs inside a 2 N λ 2 AlGaAs layer separated by an AlAs spacer from an eight-layer Bragg mirror on each side. The dielectric structures consist of Al 0.1 Ga 0.9 As and AlAs layers, and the QWs are made from GaAs or In x Ga 1 x As . All transverse fields are linearly polarized in the y direction, i.e., in the plane of the QW, and propagate as a plane wave in the z direction.

Fig. 11
Fig. 11

(a) Transmission of a microcavity for different cavity lengths. The Bragg mirrors consist of eight Al As Al 0.1 Ga 0.9 As layers with the central frequency of the stop band E M = 1.42 eV . (b) Transmission of a PBE structure that consists of 15 Bragg layers that are placed inside microcavities consisting of different numbers of mirror layers. The mirror parameters are the same as in (a), the spacer width is 75 nm , and the central frequency of the PBE is E L = 1.56 eV .

Fig. 12
Fig. 12

(a) FWHM of the laser mode in a 13 (triangles), 9 (squares), and 5 (circles) QW–PBE-VCSEL as a function of E L for a 75 nm AlAs spacer. (b) FWHM of the laser mode in a 13 (triangles), 9 (squares), and 5 (circles) QW PBE–VCSEL for E L = 1.56 eV as a function of the spacer thickness. In both cases the microcavity mirrors consists of eight Al As Al 0.1 Ga 0.9 As layers with E M = 1.42 eV . The FWHMs are normalized on the FWHM of the corresponding common QWVCSEL with λ 2 displacement. The symbols depict the calculated values and the lines are guides to the eye.

Fig. 13
Fig. 13

Space dependence of the time-integrated E y ( z , t ) for (a) a VCSEL structure containing 13 QWs, and for PBE–VCSEL structures containing (b) 13, (c) 9, and (d) 5 QWs. The microcavity mirrors consist of eight Al As Al 0.1 Ga 0.9 As layers with E M = 1.42 eV . The thickness of the AlAs spacer is 75 nm , and the central frequencies of the PBE medium are (b) E L = 1.56 eV , (c) E L = 1.58 eV , and (d) E L = 1.62 eV . The thin horizontal lines depict the strength of the field inside the cavity of the VCSEL structure in (a). The frequency of the incoming field is tuned to the cavity mode of each structure.

Fig. 14
Fig. 14

(a) Transmission for a conventional VCSEL with a 14 λ 2 cavity (dashed curve) and a PBE–VCSEL with 15 Bragg layers inside the cavity (solid curve). The microcavity mirrors consist of eight Al As Al 0.1 Ga 0.9 As layers with E M = 1.42 eV . Transmission of the PBE photonic crystal without the surrounding microcavity (dashed–dotted curve). (b)–(d) Gain spectra for a VCSEL (dashed curves) and a PBE–VCSEL (solid curves) for n = 1.4 × 10 12 cm 2 , T = 300 K , d cv = 3.5 e Å , and γ = 5 meV . (b), (c), (d) Gain spectra for structures containing 13, 9, and 5 QWs, respectively. The AlAs spacer is 75 nm and the central frequencies and detunings are (b) E L = 1.56 eV and Δ E G = 9.58 E B , (c) E L = 1.58 eV and Δ E G = 8.95 E B , and (d) E L = 1.62 eV and Δ E G = 6.16 E B .

Equations (14)

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Δ E ̇ = d 2 σ n S ,
Δ E = d t Δ E ̇ = 0 d ω α ( ω ) I 0 ( ω ) ,
α ( ω ) = 1 I 0 d 2 σ [ E * ( r , ω ) × H ( r , ω ) + c.c. ] n ,
t E ( r , t ) = 1 ϵ ( r ) [ × H ( r , t ) t P ( r , t ) ] ,
t H ( r , t ) = 1 μ × E ( r , t ) .
P ( r , t ) = d cv n , k p n , k ( t ) δ ( z z n ) ,
i t p n , k = ( ω n , k e + ω n , k h ) p n , k + Ω n , k ( f n , k e + f n , k h 1 ) + i p n , k t incoh ,
Ω n , k = d cv E n ( t ) + k 1 V k k 1 S p n , k 1 ,
ω n , k e = ϵ n , k e k 1 V k k 1 S f n , k 1 e + Δ ϵ S 2 ,
ω n , k h = ϵ n , k h k 1 V k k 1 S f n , k 1 h + Δ ϵ S 2
V k S = 2 π e 2 ϵ ( k ) L 2 1 k
α ( ω ) = 1 I 0 ω π d 3 r Im [ E * ( r , ω ) P ( r , ω ) ] .
P ( r , ω ) = n χ ( ω ) E n ( ω ) δ ( r r n ) ,
α ( ω ) = 1 I 0 ω π n Im [ χ ( ω ) ] E n ( ω ) 2 .

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