Abstract

Propagation of optical beams through a photonic crystal (PC) is analyzed and modeled. It is shown that the propagation effects for beams with slow spatial variations can be effectively modeled by diffraction behavior obtained directly from band structure. In particular, we present here an approximate model based on defining an effective index for the PC that can be used to analyze the propagation of optical beams inside the PC using the well-known analytic formulas for wave propagation in bulk media. The model presented here allows for considerable reduction in computation time and complexity. It also allows us to obtain more intuitive and design-oriented information about beam propagation effects inside PCs. We apply this model to several practical cases and show that its results agree very well with direct (time-consuming) numerical simulations.

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  13. 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. Lightw. Technol., vol. 17, no. 11, pp. 2032-2038, Nov. 1999.
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  19. H. Kosaka, T. Kawashima, A. Tomita, T. Sato and S. Tawakami, "Photonic-crystal spot-size converter", Appl. Phys. Lett., vol. 76, pp. 268-270, Jan. 2000.
  20. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimation phenomena in photonic crystals", Appl. Phys. Lett., vol. 74, pp. 1212-1214, Mar. 1999.
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  24. J. Witzens and A. Scherer, "Efficient excitation of self-collimated beams and single Bloch modes in planar photonic crystals", J. Opt. Soc. Amer. A, vol. 20, pp. 935-940, May 2003.
  25. M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon and E. H. Sargent, "Photonic crystal heterostructures: Waveguiding phenomena and methods of solution in an envelope function approximation", Phys. Rev. B, vol. 65, p. 125 318, Mar. 2002.
  26. A. Taflove, Computational Electrodynamics. The Finite Difference Time-Domain Method, Norwood, MA: Artech House, 1995.
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  28. G. Tayeb and D. Maystre, "Rigorous theoretical study of finite-size two dimensional photonic crystals doped by microcavities", J. Opt. Soc. Amer. A, vol. 14, pp. 3323-3332, Dec. 1997.
  29. S. Boscolo and M. Midrio, "A fast algorithm for the simulation of propagation in large-area 2-D photonic crystal devices", J. Lightw. Technol., vol. 20, no. 10, pp. 1869-1875, Oct. 2002.
  30. M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap", Phys. Rev. B, vol. 62, pp. 10 696-10705, Oct. 2000.
  31. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses , Norwell, MA: Kluwer Academic, 2000, ch. 2.
  32. N. W. Ashcroft and D. Mermin, Solid State Physics,: International Thomson, 1976.
  33. J. T. Veredeyen, Laser Electronics, Englewood Cliffs, NJ: Prentice-Hall, 1995, ch. 3.
  34. 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. Topics Quantum Electron., vol. 9, no. 1, pp. 106-110, Jan. 2003.

Opt. Express (1)

Other (33)

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics", Phys. Rev. Lett., vol. 58, no. 20, pp. 2059-2062, May 1987.

S. John, "Strong localization of photons in certain disordered dielectric superlattices", Phys. Rev. Lett., vol. 58, no. 23, pp. 2486-2489, Jun. 1987.

J. Joannopoulos, R. Meade and J. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, NJ: Princeton Univ. Press, 1995.

S. Fan, A. Mekis, S. G. Johnson and J. D. Joannopoulos, "Manipulating light with photonic crystals", in AIP Conf. Proc., vol. 560, 2001, pp. 57- 76.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer and T. P. Pearsall, "Waveguiding in planar photonic crystals", Appl. Phys. Lett., vol. 77, pp. 1937-1939, Sep. 2000.

O. Painter, J. Vuckovic and A. Scherer, "Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab", J. Opt. Soc. Amer. B, vol. 16, pp. 275-285, Feb. 1999.

A. V. Andreev, A. V. Balakin, I. A. Ozheredov, A. P. Shkurinov, P. Masselin, G. Mouret and D. Boucher, "Compression of femtosecond laser pulses in thin one-dimensional photonic crystals", Phys. Rev. E, vol. 63, p. 016 602, Dec. 2000.

N. I. Koroteev, S. A. Magnitskii, A. V. Tarasishin and A. M. Zheltikov, "Compression of ultrashort light pulses in photonic crystals: When envelopes cease to be slow", Optics Commun. , vol. 159, pp. 191-202, Jan. 1999.

I. V. Shadirvov, A. A. Sukhorukov and Y. S. Kivshar, "Beam shaping by a periodic structure with negative refraction", Appl. Phys. Lett., vol. 82, pp. 3820-3822, Jun. 2003.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays", Phys. Rev. Lett., vol. 86, pp. 3296-3299, Apr. 2001.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer and F. Lederer, "Beam steering in waveguide arrays", Appl. Phys. Lett., vol. 80, pp. 3247-3249, May 2002.

X. Yu and S. Fan, "Bends and splitters for self-collimated beams in photonic crystals", App. Phys. Lett., vol. 83, pp. 3251-3253, Oct. 2003.

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. Lightw. Technol., vol. 17, no. 11, pp. 2032-2038, Nov. 1999.

L. Wu, M. Mazilu, T. Karle and T. F. Krauss, "Superprism phenomena in planar photonic crystals", IEEE J. Quantum Electron., vol. 38, no. 7, pp. 915-918, Jul. 2002.

L. Wu, M. Mazilu and T. F. Krauss, "Beam steering in planar-photonic crystals: From superprism to supercollimator", J. Lightw. Technol., vol. 21, no. 2, pp. 561-566, Feb. 2003.

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism", Appl. Phys. Lett., vol. 81, pp. 2325-2327, Sep. 2002.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals", Appl. Phys. Lett., vol. 81, pp. 1549-1551, Aug. 2002.

B. Momeni and A. Adibi, "Optimization of superprism-based photonic crystal demultiplexers", Appl. Phys. B, vol. 6-7, pp. 555 -560, Nov. 2003.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato and S. Tawakami, "Photonic-crystal spot-size converter", Appl. Phys. Lett., vol. 76, pp. 268-270, Jan. 2000.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Self-collimation phenomena in photonic crystals", Appl. Phys. Lett., vol. 74, pp. 1212-1214, Mar. 1999.

D. N. Chigrin, S. Enoch, C. M. S. Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals", in Proc. SPIE, vol. 4655, Apr. 2002, pp. 63- 72.

J. Witzens, M. Loncar and A. Scherer, "Self-collimation in planar photonic crystals", IEEE J. Sel. Topics Quantum Electron., vol. 8, no. 6, pp. 1246-1257, Nov./Dec. 2002.

J. Witzens and A. Scherer, "Efficient excitation of self-collimated beams and single Bloch modes in planar photonic crystals", J. Opt. Soc. Amer. A, vol. 20, pp. 935-940, May 2003.

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon and E. H. Sargent, "Photonic crystal heterostructures: Waveguiding phenomena and methods of solution in an envelope function approximation", Phys. Rev. B, vol. 65, p. 125 318, Mar. 2002.

A. Taflove, Computational Electrodynamics. The Finite Difference Time-Domain Method, Norwood, MA: Artech House, 1995.

M. Koshiba, Y. Tsuji and M. Hikari, "Time-domain beam propagation method and its application to photonic crystal circuits", J. Lightw. Technol., vol. 18, no. 1, pp. 102-110, Jan. 2000.

G. Tayeb and D. Maystre, "Rigorous theoretical study of finite-size two dimensional photonic crystals doped by microcavities", J. Opt. Soc. Amer. A, vol. 14, pp. 3323-3332, Dec. 1997.

S. Boscolo and M. Midrio, "A fast algorithm for the simulation of propagation in large-area 2-D photonic crystal devices", J. Lightw. Technol., vol. 20, no. 10, pp. 1869-1875, Oct. 2002.

M. Notomi, "Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap", Phys. Rev. B, vol. 62, pp. 10 696-10705, Oct. 2000.

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses , Norwell, MA: Kluwer Academic, 2000, ch. 2.

N. W. Ashcroft and D. Mermin, Solid State Physics,: International Thomson, 1976.

J. T. Veredeyen, Laser Electronics, Englewood Cliffs, NJ: Prentice-Hall, 1995, ch. 3.

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. Topics Quantum Electron., vol. 9, no. 1, pp. 106-110, Jan. 2003.

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