Abstract

We present the analysis and design of a new type of photonic crystal (PC) demultiplexers (i.e., preconditioned demultiplexer), in which the simultaneous existence of the superprism effect and the negative effective index for diffraction results in a compact structure by canceling the second-order spectral phase to avoid beam broadening inside the PC. This approach considerably relaxes the requirements for the large area of the structure and the small divergence of the input beam. As a result, the size of the preconditioned demultiplexers varies as N 2.5 (N being the number of wavelength channels) compared to the N 4 variation in the conventional superprism-based PC demultiplexers. We use a generalized effective index model to analyze, design, and optimize these demultiplexing structures. This approximate model can be used to extract all the basic properties of the PC device simply from the band structure and eliminates the need to go through tedious simulations especially for three-dimensional structures. Our results show that the preconditioned superprism-based PC demultiplexers have 2 orders of magnitude smaller size compared to the conventional ones.

© 2006 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
    [CrossRef]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U., 1995).
  5. S. G. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: Photonic crystals," Acta Mater. 51, 5823-5835 (2003).
    [CrossRef]
  6. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  7. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
    [CrossRef]
  8. K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
    [CrossRef]
  9. B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C. C. Lin, and J. S. Harris, Jr., "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
    [CrossRef]
  10. M. Gerken and D. A. B. Miller, "Multilayer thin-film structures with high spatial dispersion," Appl. Opt. 42, 1330-1345 (2003).
    [CrossRef] [PubMed]
  11. L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
    [CrossRef]
  12. A. Lupu, E. Cassan, S. Laval, L. El Melhaoui, P. Lyan, and J. M. Fedeli, "Experimental evidence for superprism phenomena in SOI photonic crystals," Opt. Express 12, 5690-5696 (2004).
    [CrossRef] [PubMed]
  13. T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
    [CrossRef]
  14. B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
    [CrossRef]
  15. A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
    [CrossRef]
  16. T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
    [CrossRef]
  17. C. Luo, M. Soljacic, and J. D. Joannopoulos, "Superprism effect based on phase velocities," Opt. Lett. 29, 745-747 (2004).
    [CrossRef] [PubMed]
  18. B. Momeni and A. Adibi, "An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals," J. Lightwave Technol. 23, 1522-1532 (2005).
    [CrossRef]
  19. M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
    [CrossRef]
  20. J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
    [CrossRef]
  21. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2000).
  22. B. Momeni and A. Adibi, "Systematic design of superprism-based photonic crystal demultiplexers," IEEE J. Sel. Areas Commun. 23, 1355-1364 (2005).
    [CrossRef]
  23. T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
    [CrossRef]
  24. T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. , Part 1 40, 5920-5924 (2001).
    [CrossRef]
  25. J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
    [CrossRef]
  26. B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals," Appl. Phys. Lett. 87, 171104 (2005).
    [CrossRef]

2005 (4)

J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Systematic design of superprism-based photonic crystal demultiplexers," IEEE J. Sel. Areas Commun. 23, 1355-1364 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

B. Momeni and A. Adibi, "An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals," J. Lightwave Technol. 23, 1522-1532 (2005).
[CrossRef]

2004 (6)

2003 (4)

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: Photonic crystals," Acta Mater. 51, 5823-5835 (2003).
[CrossRef]

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

M. Gerken and D. A. B. Miller, "Multilayer thin-film structures with high spatial dispersion," Appl. Opt. 42, 1330-1345 (2003).
[CrossRef] [PubMed]

2002 (3)

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

2001 (1)

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. , Part 1 40, 5920-5924 (2001).
[CrossRef]

2000 (1)

1999 (1)

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

1993 (1)

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]

Adibi, A.

B. Momeni and A. Adibi, "Systematic design of superprism-based photonic crystal demultiplexers," IEEE J. Sel. Areas Commun. 23, 1355-1364 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

B. Momeni and A. Adibi, "An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals," J. Lightwave Technol. 23, 1522-1532 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Baba, T.

T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
[CrossRef]

T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. , Part 1 40, 5920-5924 (2001).
[CrossRef]

Baehr-Jones, T.

J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
[CrossRef]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Cabuz, A. I.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Cassagne, D.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Cassan, E.

Centeno, E.

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

Chung, K. B.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

El Melhaoui, L.

Fedeli, J. M.

Gerken, M.

Harris, J. S.

Hochberg, M.

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Hong, S. W.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

Jaskorzynska, B.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

Joannopoulos, J. D.

C. Luo, M. Soljacic, and J. D. Joannopoulos, "Superprism effect based on phase velocities," Opt. Lett. 29, 745-747 (2004).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: Photonic crystals," Acta Mater. 51, 5823-5835 (2003).
[CrossRef]

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

John, S.

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

Johnson, S. G.

S. G. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: Photonic crystals," Acta Mater. 51, 5823-5835 (2003).
[CrossRef]

Karle, T.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Krauss, T. F.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Laval, S.

Lin, C. C.

Luo, C.

Lupu, A.

Lyan, P.

Matsumoto, T.

Mazilu, M.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Meade, R. D.

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

Miller, D. A. B.

Momeni, B.

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Systematic design of superprism-based photonic crystal demultiplexers," IEEE J. Sel. Areas Commun. 23, 1355-1364 (2005).
[CrossRef]

B. Momeni and A. Adibi, "An approximate effective index model for efficient analysis and control of beam propagation effects in photonic crystals," J. Lightwave Technol. 23, 1522-1532 (2005).
[CrossRef]

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Nelson, B. E.

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Ohsaki, D.

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. , Part 1 40, 5920-5924 (2001).
[CrossRef]

Piestun, R.

Qiu, M.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Scherer, A.

J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
[CrossRef]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Soljacic, M.

Swillo, M.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Thylén, L.

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Trebino, R.

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2000).

Winn, J. N.

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

Witzens, J.

J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
[CrossRef]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Wu, L.

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Photonic band-gap structures," J. Opt. Soc. Am. B 10, 283-295 (1993).
[CrossRef]

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

Acta Mater. (1)

S. G. Johnson and J. D. Joannopoulos, "Designing synthetic optical media: Photonic crystals," Acta Mater. 51, 5823-5835 (2003).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

B. Momeni and A. Adibi, "Optimization of photonic crystal demultiplexers based on the superprism effect," Appl. Phys. B 77, 555-560 (2003).
[CrossRef]

Appl. Phys. Lett. (4)

A. I. Cabuz, E. Centeno, and D. Cassagne, "Superprism effect in bidimensional rectangular photonic crystals," Appl. Phys. Lett. 84, 2031-2033 (2004).
[CrossRef]

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

B. Momeni and A. Adibi, "Adiabatic matching stage for coupling of light to extended Bloch modes of photonic crystals," Appl. Phys. Lett. 87, 171104 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

B. Momeni and A. Adibi, "Systematic design of superprism-based photonic crystal demultiplexers," IEEE J. Sel. Areas Commun. 23, 1355-1364 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Qiu, L. Thylén, M. Swillo, and B. Jaskorzynska, "Wave propagation through a photonic crystal in a negative phase refractive-index region," IEEE J. Sel. Top. Quantum Electron. 9, 106-110 (2003).
[CrossRef]

J. Lightwave Technol. (4)

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

Jpn. J. Appl. Phys. (1)

T. Baba and D. Ohsaki, "Interfaces of photonic crystals for high efficiency light transmission," Jpn. J. Appl. Phys. , Part 1 40, 5920-5924 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Phys. Rev. E (2)

J. Witzens, T. Baehr-Jones, and A. Scherer, "Hybrid superprism with low insertion losses and suppressed cross-talk," Phys. Rev. E 71, 026604 (2005).
[CrossRef]

J. Witzens, M. Hochberg, T. Baehr-Jones, and A. Scherer, "Mode matching interface for efficient coupling of light into planar photonic crystals," Phys. Rev. E 69, 046609 (2004).
[CrossRef]

Phys. Rev. Lett. (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]

Other (2)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2000).

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

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Figures (7)

Fig. 1
Fig. 1

(Color online) In-plane constant frequency contours of the first band of a rotated square lattice photonic crystal in a planar SOI wafer. Coordinates are rotated 45° with respect to the principal lattice vectors of the PC as shown in the right-side figure. This PC has normalized radius of holes of r / a = 0.30 , and normalized thickness of the silicon layer of h / a = 0.60 (a being the lattice constant).

Fig. 2
Fig. 2

(Color online) Configuration for a PC working in the preconditioned superprism regime.

Fig. 3
Fig. 3

(a) Propagation of an arbitrary beam inside a 2D PC. Coordinates ξ and η represent directions parallel and perpendicular to the direction of propagation of the beam, respectively. (b) Directions of (a) are shown on the band structure of the PC (which is represented in the form of a constant frequency contour in the 2D wave-vector plane).

Fig. 4
Fig. 4

(Color online) For a 45° rotated square lattice PC (air holes in Si, r / a = 0.40 ) the profile of the beam envelope at the output is calculated using the direct mode-matching method (solid curve) and the approximate diffractive index method (diamond). The incident light in this calculation is a preconditioned (i.e., broadened) Gaussian beam at normalized wavelength a / λ = 0.197 that illuminates the structure at an angle of 12° with respect to the normal to the interface. The preconditioning is performed so that the effect of the second-order diffraction term vanishes at the output of the PC structure. Good agreement of the accurate and approximate results is clear.

Fig. 5
Fig. 5

(Color online) (a) Parameters for a preconditioned superprism device are depicted for an incident beam coming at an angle α, and for a single channel inside the PC region. (b) The darker pattern trace shows the evolution of an optical beam at a single wavelength throughout the structure without the effect of the second-order diffraction. In this case, δ 3 is the divergence angle of the beam due to the third-order diffraction effect. The brighter pattern is the actual beam profile inside the structure. By compensating the second-order phase, the beam size at the output is the same as that in the assumed structure with zero second-order phase everywhere.

Fig. 6
Fig. 6

Calculated compactness factor (in log10 scale) for different PC lattices on SOI wafers (h is the thickness of the top Si layer, r is the radius of the holes, and a is the lattice constant) are shown along with constant frequency contours of the corresponding PC band. Each contour in the k x k y plane corresponds to a constant frequency. The value of the normalized frequency ( a / λ ) for each constant frequency curve is marked on the contours. In all these cases, the first band of the PC structure is considered. (a) A square lattice slab-type PC with r / a = 0.30 and h / a = 0.60 , and (b) the same square lattice as in (a) with the interface along a direction angled 45° with respect to the principal lattice directions. (c) A triangular lattice with r / a = 0.30 and h / a = 0.60 with the interface along the ΓM direction, and (d) the same triangular lattice as in (c) with the interface along the ΓK direction.

Fig. 7
Fig. 7

(Color online) (a) Dispersion diagram for guiding in an unpatterned SOI wafer with h = 220   nm is shown. (b) Band structure (dotted curves) of a slab-type PC in a SOI wafer (square lattice, r / a = 0.30 , h / a = 0.62 ) and loci of PC modes (solid curves) excited for the incident wave coming from the unpatterned Si slab at different incident angles (in degrees) are shown.

Tables (3)

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Table 1 Cross-Talk Parameters

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Table 2 Design Parameters for Optimal Demultiplexers in a Square Lattice PC b

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Table 3 Design Parameters for Demultiplexers in a Square Lattice PC a

Equations (41)

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P ^ 2 ( k ξ ) = H ( k ξ ) P ^ 1 ( k ξ ) ,
H ( k ξ ) = exp [ j k η ( k ξ ) η 21 ] = exp { j η 21 [ k η 0 + ( k ξ k ξ 0 ) k η / k ξ + 1 2 ( k ξ k ξ 0 ) 2 2 k η / k ξ 2 + ] } ,
w rms 2 = x x 2 I ( x ) d x x I ( x ) d x .
k ξ A ( k ξ ) 2 d k ξ = 1 ,
w rms 2 = k ξ A ( k ξ ) 2 d k ξ + k ξ A ( k ξ ) 2 Φ ( k ξ ) 2 d k ξ ,
A ( k ξ ) = ( w 0 2 π ) 1 / 2 exp ( 1 4 w 0 2 k ξ 2 ) ,
w rms,2 2 = w 0 2 4 + 4 b 2 2 w 0 2 ,
b 2 = 1 2 d 2 Φ d k ξ 2 = 1 2 d 2 k η d k ξ 2 L = L 2 k 0 n e 2 ,
w rms,2 2 = 1 4 w 0 2 ( 1 + L 2 z 2 2 ) ,
w rms,3 2 = w 0 2 4 + w 0 2 π k ξ exp ( 1 2 w 0 2 k ξ 2 ) ( 9 b 3 2 k ξ 4 ) d k ξ = w 0 2 4 + 27 b 3 2 w 0 4 ,
b 3 = 1 6 d 3 Φ d k ξ 3 = 1 6 d 3 k η d k ξ 3 L .
w rms 2 = w 0 2 4 + 3 L 2 ( d 3 k η / d k ξ 3 ) 2 4 w 0 4 .
z 3 = 1 3 ( d 3 k η / d k ξ 3 ) 1 w 0 3 ,
w rms,3 2 = 1 4 w 0 2 ( 1 + L 2 z 3 2 ) .
z 3 = 1 2 k 0 n e 3 w 0 2 ,
n e 3 = 2 w 0 3 k 0 ( d 3 k η / d k ξ 3 ) 1 ,
w rms,4 2 = 1 4 w 0 2 ( 1 + L 2 z 4 2 ) ,
z 4 = 1 2 k 0 n e 4 w 0 2 ,
n e 4 = 2 3 w 0 2 5 k 0 ( d 4 k y / d k 4 ) 1 .
w rms, v 2 = 1 4 w 0 2 ( 1 + L 2 z v 2 ) ,
z v = 1 2 k 0 n e v w 0 2 ,
n e v = ( v 1 ) ! ( 2 v 3 ) ! ! w 0 v - 2 k 0 ( d v k η / d k ξ v ) 1 ,
L = ζ 3 z 3 ,
ζ 3 = K ( X ) η 3 H ( X ) .
L pre n pre cos 2 α = L n e 2 cos 2 θ g ,
L = ζ 3 z 3 = K π w P C | n e 3 | Δ / 2 λ H ( k 0 w P C 2 n e 3 ) ,
L = 2 K w P C 3 w P C 2 Δ 2 3 H | 3 k η / k ξ 3 | .
A = ( w P C z 2 L ) L = 8 K 2 w P C 5 | 3 k η / k ξ 3 | ( w P C 2 Δ 2 3 H | 3 k η / k ξ 3 | ) 2 .
( w P C ) opt = [ 10 3 H Δ | 3 k η k ξ 3 | ] 1 / 2 ,
L opt = 5 K 2 Δ ( w P C ) opt ,
A opt = 25 K 2 2 k 0 n e 2 Δ 2 ( w P C ) opt .
( 3 k η k ξ 3 ) = k ξ ( 2 k η k ξ 2 ) = k ξ ( 1 k 0 n e 2 ) = cos   θ g k 0 2 n 1 n e 2 2   cos   α
× ( n e 2 α ) ,
( w P C ) opt = 1 k 0 n e 2 [ 10 3 H ( θ g / ω ) cos   θ g n 1   cos   α ( n e 2 α ) ] 1 / 2 ( Δ ω ) - 1 / 2 ,
L opt = 5 K 2 k 0 n e 2 [ 10 3 H   cos   θ g n 1   cos   α ( n e 2 α ) ] 1 / 2 ( θ g ω ) - 3 / 2 × ( Δ ω ) - 3 / 2 ,
A opt λ 2 = 25 10 3 H K 2 8 π 2 [ cos   θ g n 1   cos   α ( n e 2 α ) ] 1 / 2 1 n e 2 2 ( θ g ω ) - 5 / 2 × ( Δ ω ) - 5 / 2 ,
C pre = 8 π 2 n e 2 2 25 10 3 H K 2 [ cos   θ g n 1   cos   α ( n e 2 α ) ] - 1 / 2 ( θ g ω ) 5 / 2 ,
A opt λ 2 = ( Δ ω ) - 5 / 2 C pre .
L j = 2 K w i 3 cos 3 θ g j w i 2 Δ j cos 2 θ g j   cos   α 2 3 H | 3 k η / k ξ 3 | j cos 3 α ,
L = max j { L j ( w i ) } ,
L pre = n pre cos 2 α n e 2 cos 2 θ g L ,

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