Abstract

We present a systematic design procedure of photonic crystal (PhC) superprism structures for on-chip spectroscopic applications. In specific, we propose a new figure of merit, namely the angular-group-dispersion–bandwidth–product (AGDBP) to quantitatively describe the spectroscopic performance of PhC superprism structures, and an optimum PhC structure for spectroscopic applications should have large angular group dispersion over a large bandwidth, i.e., a flat-top dispersion profile. We demonstrate the advantage of such a new design consideration by optimizing the geometry of a two-dimensional parallelogram-lattice PhC superprism structure. The performance of such a superprism spectrometer is further analyzed numerically using finite-difference time-domain simulations, which out-performs current implementations in terms of the number of achievable output spectral channels.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Realization of a flat-band superprism on-chip from parallelogram lattice photonic crystals

Jeremy Upham, Boshen Gao, Liam O’Faolain, Zhimin Shi, Sebastian A. Schulz, and Robert W. Boyd
Opt. Lett. 43(20) 4981-4984 (2018)

Composite superprism photonic crystal demultiplexer: analysis and design

Amin Khorshidahmad and Andrew G. Kirk
Opt. Express 18(19) 20518-20528 (2010)

Compact, low cross-talk CWDM demultiplexer using photonic crystal superprism

Damien Bernier, Xavier Le Roux, Anatole Lupu, Delphine Marris-Morini, Laurent Vivien, and Eric Cassan
Opt. Express 16(22) 17209-17214 (2008)

References

  • View by:
  • |
  • |
  • |

  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. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
    [Crossref]
  4. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  5. J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
    [Crossref]
  6. S.-Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771–1773 (1996).
    [Crossref] [PubMed]
  7. 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 (1998).
    [Crossref]
  8. 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 (1999).
    [Crossref]
  9. T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
    [Crossref]
  10. B. Momeni and A. Adibi, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23, 1355–1364 (2005).
    [Crossref]
  11. B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
    [Crossref] [PubMed]
  12. B. E. Nelson, M. Gerken, D. A. B. Miller, R. Piestun, C.-C. Lin, and J. S. Harris, “Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting,” Opt. Lett. 25, 1502–1504 (2000).
    [Crossref]
  13. D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16, 17209–17214 (2008).
    [Crossref]
  14. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
    [Crossref] [PubMed]
  15. T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
    [Crossref]
  16. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [Crossref]
  17. 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 (2005).
    [Crossref]
  18. J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed crosstalk,” Phys. Rev. E 71, 026604 (2005).
    [Crossref]
  19. 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]
  20. D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
    [Crossref]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

2009 (1)

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

2008 (1)

2006 (1)

2005 (4)

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 (2005).
[Crossref]

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed crosstalk,” Phys. Rev. E 71, 026604 (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]

2002 (3)

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
[Crossref]

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
[Crossref]

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

2001 (2)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

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 (1998).
[Crossref]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

1996 (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, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
[Crossref] [PubMed]

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 (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, “Systematic design of superprism-based photonic crystal demultiplexers,” IEEE J. Sel. Areas Commun. 23, 1355–1364 (2005).
[Crossref]

Askari, M.

Baba, T.

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
[Crossref]

Baehr-Jones, T.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed crosstalk,” Phys. Rev. E 71, 026604 (2005).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bernier, D.

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16, 17209–17214 (2008).
[Crossref]

Cassan, E.

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16, 17209–17214 (2008).
[Crossref]

Fan, S.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Gerken, M.

Harris, J. S.

Hietala, V. M.

Huang, J.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

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.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[Crossref] [PubMed]

Jones, E. D.

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 (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 (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 (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 (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 (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 (1998).
[Crossref]

Le Roux, X.

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

Lin, C.-C.

Lin, S.-Y.

Loncar, M.

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
[Crossref]

Lupu, A.

Marris-Morini, D.

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16, 17209–17214 (2008).
[Crossref]

Matsumoto, T.

T. Baba and T. Matsumoto, “Resolution of photonic crystal superprism,” Appl. Phys. Lett. 81, 2325–2327 (2002).
[Crossref]

Miller, D. A. B.

Mohammadi, S.

Momeni, B.

B. Momeni, J. Huang, M. Soltani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi, “Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms,” Opt. Express 14, 2413–2422 (2006).
[Crossref] [PubMed]

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 (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]

Nakamura, M.

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (2002).
[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 (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 (1998).
[Crossref]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Piestun, R.

Rakhshandehroo, M.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Roux, X. L.

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 (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 (1998).
[Crossref]

Scherer, A.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed crosstalk,” Phys. Rev. E 71, 026604 (2005).
[Crossref]

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Soltani, M.

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 (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 (1998).
[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 (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 (1998).
[Crossref]

Villeneuve, P. R.

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Vivien, L.

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

D. Bernier, X. L. Roux, A. Lupu, D. Marris-Morini, L. Vivien, and E. Cassan, “Compact, low cross-talk cwdm demultiplexer using photonic crystal superprism,” Opt. Express 16, 17209–17214 (2008).
[Crossref]

Wang, L.

Witzens, J.

J. Witzens, T. Baehr-Jones, and A. Scherer, “Hybrid superprism with low insertion losses and suppressed crosstalk,” Phys. Rev. E 71, 026604 (2005).
[Crossref]

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
[Crossref]

Yablonovitch, E.

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

Appl. Phys. Lett. (2)

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]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the superprism effect,” IEEE J. Quantum Electron. 38, 909–914 (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]

J. Lightwave Technol. (2)

Nature (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386, 143–149 (1997).
[Crossref]

Opt. Eng. (1)

D. Bernier, E. Cassan, X. Le Roux, D. Marris-Morini, and L. Vivien, “Efficient band-edge light injection in two-dimensional planar photonic crystals using a gradual interface,” Opt. Eng. 48, 070501 (2009).
[Crossref]

Opt. Express (3)

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 (1998).
[Crossref]

Phys. Rev. E (1)

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

Quantum Electron. (1)

J. Witzens, M. Loncar, and A. Scherer, “Self-collimation in planar photonic crystals,”, Quantum Electron. 8, 1246–1257 (2002).
[Crossref]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1 Equi-frequency contours (EFCs) of a 2-D square lattice PhC in the first Brillouin zone. The light beam enters the PhC region at an incidence angle αinc and the “refraction” angle inside the PhC region is labeled as αpc. Solid arrows are the Bloch k vectors indicating the direction of phase velocities of the beams. Dashed arrows normal to the EFC contour indicates the directions of group velocities. Near the band edge in k-space, a small change in frequency leads to a large directional variation in group velocity. Inset: the PhC structure in real space. a1 and a2 are the two basis vectors. The radius of the air holes is r = 0.3a where a = |a1| is the lattice constant.
Fig. 2
Fig. 2 Geometric analysis of beam propagation in a general 2-D PhC. (a), the PhC structure in coordinate space; θ and d are the two adjustable parameters. (b), corresponding reciprocal lattice; k1 is perpendicular to a1 and k2 to a2. (c), EFC plot of the structure. The kx axis is chosen to be along the k2 direction.
Fig. 3
Fig. 3 Optimization results for obtaining a flat-band PhC superprism. (a), P max as a function of position in the two dimensional parameter space. (b) Superprism factor q as a function of the normalized frequency ω plotted for 3 structures: ① P max = 0.839 rad, d = 0.9a1 = 89°; ② Pmax = 0.802 rad,d = 0.9a1 = 83°; ③ P max = 0.809 rad,d = 1.1a1 = 88°.
Fig. 4
Fig. 4 (a) Schematic diagram of a flat-band superprism spectrometer; (b) Spectral transmission of the 8 channels that are evenly spaced over the working bandwidth.

Equations (7)

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

q ( α inc , ω ) = β g ω | α inc ,
tan β g = ω / k y ω / k x .
q = β g / k | α inc ω / k | α inc .
δ k = δ ω d ω / d k ϕ u ^ ϕ ,
tan ϕ = ( ω | k | sin α phc ω k x ) / ω k y ,
q = ( ω k x 2 ω k x k y 2 ω k x 2 ω k y ) cos ϕ + ( ω k x 2 ω k y 2 2 ω k x k y ω k y ) sin ϕ [ ω k x cos ϕ + ω k y sin ϕ ] [ ( ω k x ) 2 + ( ω k y ) 2 ] .
P ( ω 0 ) = q ( ω 0 ) Δ ω .

Metrics