Abstract

We analyze the transmission of planar photonic crystal channel waveguides, each of which consists of three missing rows in a triangular lattice of air holes and modified at both ends by constrictions. The structures are fabricated into a GaAs/AlGaAs heterostructure in which an internal source consisting of three layers of quantum dots is embedded. The constrictions induce peculiar spectral features that are used to improve the sensitivity of transmission measurements to propagation losses. Two effects are pointed out: (i) The constrictions act as mirrors, inducing Fabry–Perot fringes on the transmitted spectra, (ii) and the constrictions also induce a mode-mixing process, mostly between the fundamental and the third transverse modes of the waveguides. Using the visibility of the resultant two-mode fringes observed on the transmitted spectra, we extract a quantitative value for propagation losses at λ=1 µm: α1=25 cm-1 (1 dB/100 µm) for the fundamental mode.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2001

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

P. Lalanne and H. Benisty, “Ultimate limits of two-dimensional photonic crystals etched through waveguides: an electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

E. Chow, S. Y. Lon, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ=1.55 μm wavelengths,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

A. Talneau, L. L. Gouezigou, and N. Bouadma, “Quantitative measurements of low propagation losses at 1.55 μm on planar photonic crystal waveguides,” Opt. Lett. 26, 1259–1261 (2001).
[CrossRef]

2000

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

1999

1998

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

1997

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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

1996

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[CrossRef]

1994

P. R. Villeneuve and M. Piché, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
[CrossRef]

1987

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

1984

R. Regener, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1984).
[CrossRef]

1978

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33, 62–64 (1978).
[CrossRef]

Atkin, D. M.

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Benisty, H.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

P. Lalanne and H. Benisty, “Ultimate limits of two-dimensional photonic crystals etched through waveguides: an electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[CrossRef]

Béraud, A.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

Birks, T. A.

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

Bouadma, N.

Cassagne, D.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Chow, E.

Chutinan, A.

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

De La Rue, R. M.

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

Gouezigou, L. L.

Houdré, R.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

Joannopoulos, J. D.

E. Chow, S. Y. Lon, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ=1.55 μm wavelengths,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

Johnson, S. G.

E. Chow, S. Y. Lon, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, “Quantitative analysis of bending efficiency in photonic crystal waveguide bends at λ=1.55 μm wavelengths,” Opt. Lett. 26, 286–288 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

Jouanin, C.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kaminow, I. P.

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33, 62–64 (1978).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Krauss, T. F.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

Labilloy, D.

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

Lalanne, P.

P. Lalanne and H. Benisty, “Ultimate limits of two-dimensional photonic crystals etched through waveguides: an electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

Lon, S. Y.

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

Oesterle, U.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

Olivier, S.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

Piché, M.

P. R. Villeneuve and M. Piché, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
[CrossRef]

Rattier, M.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

Regener, R.

R. Regener, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1984).
[CrossRef]

Roberts, P. J.

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

Rue, R. M. D. L.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Russell, P. St. J.

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

Smith, C. J. M.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (1999).
[CrossRef]

Stulz, L. W.

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33, 62–64 (1978).
[CrossRef]

Talneau, A.

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

P. R. Villeneuve and M. Piché, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
[CrossRef]

Weisbuch, C.

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C. J. M. Smith, T. F. Krauss, R. M. De La Rue, R. Houdré, U. Oesterle, and D. Cassagne, “Optical and confinement properties of two-dimensional photonic crystals,” J. Lightwave Technol. 17, 2063–2077 (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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

Wendt, J. R.

Yablonovitch, E.

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

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

Appl. Phys. B

R. Regener, “Loss in low-finesse Ti: LiNbO3 optical waveguide resonators,” Appl. Phys. B 36, 143–147 (1984).
[CrossRef]

Appl. Phys. Lett.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. Houdré, and U. Oesterle, “Use of guided spontaneous emission of a semiconductor to probe the optical properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 71, 738–740 (1997).
[CrossRef]

I. P. Kaminow and L. W. Stulz, “Loss in cleaved Ti-diffused LiNbO3 waveguides,” Appl. Phys. Lett. 33, 62–64 (1978).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, A. Béraud, D. Cassagne, and C. Jouanin, “Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate,” Appl. Phys. Lett. 76, 532–534 (2000).
[CrossRef]

C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. De La Rue, R. Houdré, and U. Oesterle, “Low-loss channel waveguides with two-dimensional photonic crystal boundaries,” Appl. Phys. Lett. 77, 2813–2815 (2000).
[CrossRef]

IEE Proc.: Optoelectron.

P. R. Villeneuve, S. Fan, S. G. Johnson, and J. D. Joannopoulos, “Three-dimensional photon confinement in photonic crystal of low-dimensional periodicity,” IEE Proc.: Optoelectron. 145, 384–390 (1998).

IEEE J. Quantum Electron.

M. Rattier, H. Benisty, C. J. M. Smith, A. Béraud, D. Cassagne, T. F. Krauss, and C. Weisbuch, “Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry–Pérot resonators,” IEEE J. Quantum Electron. 37, 237–243 (2001).
[CrossRef]

J. Appl. Phys.

H. Benisty, “Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,” J. Appl. Phys. 79, 7483–7492 (1996).
[CrossRef]

P. Lalanne and H. Benisty, “Ultimate limits of two-dimensional photonic crystals etched through waveguides: an electromagnetic analysis,” J. Appl. Phys. 89, 1512–1514 (2001).
[CrossRef]

J. Lightwave Technol.

J. Mod. Opt.

D. M. Atkin, P. St. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic band structure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1051 (1996).
[CrossRef]

Opt. Lett.

Phys. Rev. B

A. Chutinan and S. Noda, “Waveguides and waveguide bends in two-dimensional photonic crystal slabs,” Phys. Rev. B 62, 4488–4492 (2000).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. Olivier, M. Rattier, H. Benisty, C. J. M. Smith, R. M. D. L. Rue, T. F. Krauss, U. Oesterle, R. Houdré, and C. Weisbuch, “Mini stopbands of a one dimensional system: the channel waveguide in a two-dimensional photonic crystal,” Phys. Rev. B 63, 113311 (2001).
[CrossRef]

Phys. Rev. Lett.

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

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 bandgap structures at nearinfrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Prog. Quantum Electron.

P. R. Villeneuve and M. Piché, “Photonic bandgaps in periodic dielectric structures,” Prog. Quantum Electron. 18, 153–200 (1994).
[CrossRef]

Science

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef] [PubMed]

Other

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

Such round trips continue to occur for light excited in the waveguide.

The variation is due to the consideration of different points along the dispersion branches.

D. Labilloy, “Cristaux photoniques bidimensionnels pour le proche infrarouge: propriétés optiques et confinement,” Ph.D. dissertation (Ecole Polytechnique, Palaiseau, France, 1999).

C. G. P. Herben, X. J. M. Leitens, F. H. Groen, and M. K. Smit, “Low-loss and compact phased array demultiplexer using a double-etch process,” presented at the 9th European Conference on Integrated Optics, Turin, Italy, April 13–16, 1999.

B. E. A. Saleh and M. C. Teich, Fundamental of Photonics (Wiley, New York, 1991).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

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Figures (12)

Fig. 1
Fig. 1

(a) Scanning-electron microscope picture of a waveguide of length Lc=160 rows; period a is 260 nm. Arrows indicate the constrictions at both ends. (b) Constrictions at one end of the waveguide.

Fig. 2
Fig. 2

Schematic representations of (a) a W3 waveguide and (b) the multiwaveguide sample. The lengths of the waveguides, Lc, range from 10 to 640 rows, with a scale factor of 2. Note the constrictions at both ends of each waveguide. The various collection configurations of interest are also sketched.

Fig. 3
Fig. 3

Experimental transmission spectra of five planar PC waveguides with constrictions as a function of normalized frequency u=a/λ for the lengths (a) Lc=452a, (b) Lc=226a, (c) Lc=80a, (d) Lc=56a, and (e) Lc=20a. Solid arrows, expected Fabry–Perot fringes; dashed arrows, two-mode fringes, which are discussed below.

Fig. 4
Fig. 4

Solid curves, plots of theoretical calculations for Fabry–Perot fringe spacing versus length of the waveguide. Error bars, Fabry–Perot (dashed) and two-mode (solid) experimentally measured fringes. Regions both below and above the mini stop-band, regions A and B, respectively, are represented in terms of normalized frequency u.

Fig. 5
Fig. 5

Schematic of the input constrictions of a planar PC waveguide. Schematics of the magnetic-field profiles for the fundamental mode and the third mode are also presented.

Fig. 6
Fig. 6

Band diagram ω=ω(β) of a W3 waveguide of type A and with an air-filling factor of 37%. We also show the width of the PBG of an infinite PC and regions A and B. Note the difference in the slopes of modes 1 and 3, which is responsible for the fringe spacing (here, Δβ decreases with increasing u).

Fig. 7
Fig. 7

Schematic explanation of the mode-mixing process that results from the interaction between the launched mode and the constrictions at both ends of the waveguide.

Fig. 8
Fig. 8

Calculated transmission spectra for waveguide lengths (a) Lc=452a, (b) Lc=320a, (c) Lc=226a, (d) Lc=160a, (e) Lc=113a, and (f) Lc=80a as a function of normalized frequency u=a/λ.

Fig. 9
Fig. 9

Solid curves, calculated beat mode fringe spacing versus length of planar PC waveguides in units of rows, for regions A and B. Experimental fringe spacing is indicated by corresponding error bars. Dashed–dotted curves, fringe spacing deduced from the scalar classic waveguide theory for a slab.

Fig. 10
Fig. 10

Simulation of mode beating between the fundamental mode and the third mode over a distance of 40 rows in a PC planar waveguide for both region A and region B. Distances are given in units of rows.

Fig. 11
Fig. 11

Ln(V) plotted as a function of Lc, where V is the fringe visibility and Lc is the length of the cavity in centimeters. The slope of these curves is the loss difference Δα between the fundamental mode and the third mode.

Fig. 12
Fig. 12

Representation of the square of the amplitude of the dielectric vector in a planar PC waveguide for (a) the fundamental mode and (b) the third mode. The vertical scale is logarithmic.

Equations (9)

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

T(λ)=I2(λ)I1(λ)I1front(λ)I2front(λ).
as=a1t11t11 exp(-α1Lc)exp(iβ1Lc)+a1t13t31 exp(-α3Lc)exp(iβ3Lc).
Is=|A0|2[1+|C|2 exp(-ΔαLc)+2C exp(-ΔαLc)cos(ΔβLc)],
V=2C exp[-(Δα/2)Lc]1+|C|2 exp(-ΔαLc).
ΔαA=235 cm-1±15%,ΔαB=205 cm-1±15%.
Γi=holesDi2dSallspaceDi2dS.
α1=25 cm-1±30%(1 dB/100 µm).
TFP=t1-r2 exp(2iξ)exp[-α(λ)Lc]2,
TFP=|t|21+r4 exp[-2α(λ)Lc]-2r2 exp[-α(λ)Lc]cos(2ξ).

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