Abstract

In this paper, the authors review some of the recent advances in the theory of photonic crystals, drawing examples from their own work in magnetooptical and dynamic photonic crystals. The combination of theory and simulations shows that these crystal structures exhibit rich optical physics effects and can provide new ways to accomplish sophisticated optical information-processing tasks.

© 2006 IEEE

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Appl. Opt. (1)

Appl. Phys. B, Photophys. Laser Chem. (1)

Z. Wang, S. Fan, "Magneto-optical defects in two-dimensional photonic crystals," Appl. Phys. B, Photophys. Laser Chem. 81, 369-375 (2005).

Appl. Phys. Lett. (3)

R. Li, M. Levy, "Bragg grating magnetic photonic crystal waveguides," Appl. Phys. Lett. 86, 251 102 (2005).

C. Koerdt, G. L. J. A. Rikken, E. P. Petrov, "Faraday effect of photonic crystals," Appl. Phys. Lett. 82, 1538-1540 (2003).

S. Fan, "Sharp asymmetric lineshapes in side-coupled waveguide–cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).

Eur. Phys. J. B (1)

A. K. Zvezdin, V. I. Belotelov, "Magneto-optical properties of two dimensional photonic crystals," Eur. Phys. J. B 37, 479-487 (2004).

IEEE J. Quantum Electron. (2)

G. Lenz, B. J. Eggleton, C. K. Madsen, R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37, 525-532 (2001).

W. Suh, Z. Wang, S. Fan, "Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multi-mode cavities," IEEE J. Quantum Electron. 40, 1511-1518 (2004).

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

M. Levy, "The on-chip integration of magneto-optic waveguide isolators," IEEE J. Sel. Topics Quantum Electron. 8, 1300-1306 (2002).

IEEE Photon. Technol. Lett. (3)

M. J. Steel, M. Levy, R. M. Osgood, "High transmission enhanced Faraday rotation in one-dimensional photonic crystal with defects," IEEE Photon. Technol. Lett. 12, 1171-1173 (2000).

N. Kono, M. Koshiba, "General finite-element modeling of 2-D magneto-photonic crystal waveguides," IEEE Photon. Technol. Lett. 17, 1432-1434 (2005).

S. K. Mondal, B. J. H. Stadler, "Novel designs for integrating YIG/air photonic crystal slab polarizers with waveguide Faraday rotators," IEEE Photon. Technol. Lett. 17, 127-129 (2005).

J. Appl. Phys. (3)

K. Nishimura, A. V. Baryshev, T. Kodama, H. Uchida, M. Inoue, "Synthesis of ferrite on $\hbox{SiO}_{2}$ sphere for three-dimensional magneto-photonic crystals," J. Appl. Phys. 95, 6633-6635 (2004).

M. Inoue, K. Arai, T. Fujii, M. Abe, "One-dimensional magnetophotonic crystals," J. Appl. Phys. 85, 5768-5770 (1999).

E. Takeda, N. Todoroki, Y. Kitamoto, M. Abe, M. Inoue, T. Fujii, K. Arai, "Faraday effect enhancement in co-ferrite layer incorporated into one-dimensional photonic crystal working as a Fabry–Pérot resonator," J. Appl. Phys. 87, 6782-6784 (2000).

J. Lightw. Technol. (1)

N. Kono, Y. Tsuji, "A novel finite-element method for nonreciprocal magneto-photonic crystal waveguides," J. Lightw. Technol. 22, 1741-1747 (2004).

J. Magn. Magn. Mater. (1)

Y. Ikezawa, K. Nishimura, H. Uchida, M. Inoue, "Preparation of two-dimensional magneto-photonic crystals of bismuth substitute yttrium iron garnet materials," J. Magn. Magn. Mater. 272–276, 1690-1691 (May 2004).

J. Opt. Soc. Amer. A, Opt. Image Sci. (1)

S. Fan, W. Suh, J. D. Joannopoulos, "Temporal coupled mode theory for Fano resonances in optical resonators," J. Opt. Soc. Amer. A, Opt. Image Sci. 20, 569-572 (2003).

Nature (3)

Y. A. Vlasov, M. O'Boyle, H. F. Harmann, S. J. McNab, "Active control of slow light on a chip with photonic crystal waveguides," Nature 438, 65-69 (2005).

C. Liu, Z. Dutton, C. H. Behroozi, L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses," Nature 409, 490-493 (2001).

J. D. Joannopoulos, P. R. Villeneuve, S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386, 143-147 (1997).

Opt. Express (2)

Opt. Lett. (6)

Photon. Nanostruct.: Fundam. Appl (1)

Z. Wang, S. Fan, "Add–drop filter in two-dimensional magneto-optical photonic crystals and suppression of disorder effects by time-reversal breaking," Photon. Nanostruct.: Fundam. Appl (in press).

Phys. Rev. (1)

U. Fano, "Effects of configuration interaction on intensities and phase shifts," Phys. Rev. 124, 1866-1878 (1961).

Phys. Rev. A, Gen. Phys. (1)

M. F. Yanik, S. Fan, "Stopping and storing light coherently," Phys. Rev. A, Gen. Phys. 71, 013803 (2005).

Phys. Rev. B, Condens. Matter (3)

A. Figotin, I. Vitebskiy, "Electromagnetic unidirectionality in magnetic photonic crystals," Phys. Rev. B, Condens. Matter 67, 165 210 (2003).

N. Stefanou, A. Modinos, "Impurity bands in photonic insulators," Phys. Rev. B, Condens. Matter 57, 12127-12133 (1998).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, C. Manalatou, M. J. Khan, H. A. Haus, "Theoretical investigation of channel drop tunneling processes," Phys. Rev. B, Condens. Matter 59, 15 882-15 892 (1999).

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. (2)

Z. Wang, S. Fan, "Compact all-pass filters in photonic crystals as the building block for high capacity optical delay lines," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 68, 066616 (2003).

A. Figotin, I. Vitebsky, "Nonreciprocal magnetic photonic crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 63, 066609 (2001).

Phys. Rev. Lett. (12)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, M. D. Lukin, "Storage of light in atomic vapors," Phys. Rev. Lett. 86, 783-786 (2001).

E. J. Reed, M. Soljacic, J. D. Joannopoulos, "Color of shock waves in photonic crystals," Phys. Rev. Lett. 90, 203 904 (2003).

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, I. Yokoyama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253 902 (2001).

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A. Haus, "Channel drop tunneling through localized states," Phys. Rev. Lett. 80, 960-963 (1998).

M. F. Yanik, S. Fan, "Stopping light all-optically," Phys. Rev. Lett. 92, 083901 (2004).

M. F. Yanik, S. Fan, "Time-reversal of light with linear optics and modulators," Phys. Rev. Lett. 93, 173 903 (2004).

M. F. Yanik, W. Suh, Z. Wang, S. Fan, "Stopping light in a waveguide with an all-optical analogue of electromagnetically induced transparency," Phys. Rev. Lett. 93, 233 903 (2004).

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

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

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

M. Bayindir, B. Temelkuran, E. Ozbay, "Tight-binding description of the coupled defect modes in three-dimensional photonic crystals," Phys. Rev. Lett. 84, 2140-2143 (2000).

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, M. Lipson, "Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency," Phys. Rev. Lett. 96, 123 901 (2006).

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).

Science (1)

D. Psaltis, "Coherent optical information systems," Science 298, 1359-1363 (2002).

Stud. Appl. Math. (1)

M. F. Yanik, S. Fan, "Dynamic photonic structures: Stopping, storage, and time-reversal of light," Stud. Appl. Math. 115, 233-254 (2005).

Other (6)

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

Photonic Crystals and Light Localization in the 21st Century (Kluwer, 2001).

S. G. Johnson, J. D. Joannopoulos, Photonic Crystals: The Road From Theory to Practice (Kluwer, 2002).

K. Inoue, K. Ohtaka, Photonic Crystals (Springer-Verlag, 2004).

A. K. Zvezdin, V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Inst. Phys., 1997).

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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