Photonic band structure theory: assessment and perspectives

Abstract An attempt is made to provide an assessment on the current state of photonic bandstructure theory, a field of research which is at the heart of rapid progress in photonic crystal research. First, different approaches to calculating photonic bandstructures as well as the optical properties of defect structures in photonic crystals are reviewed. Several highlights and applications of photonic bandstructure theory are presented that help to illustrate the tremendous progress the field has seen. Finally, perspectives of photonic bandstructure theory are briefly discussed and an attempt is made to identify possible future developments. To cite this article: K. Busch, C. R. Physique 3 (2002) 53–66

[1]  Chan,et al.  Order-N spectral method for electromagnetic waves. , 1995, Physical review. B, Condensed matter.

[2]  John,et al.  Nonlinear optical solitary waves in a photonic band gap. , 1993, Physical review letters.

[3]  E. Yablonovitch,et al.  Inhibited spontaneous emission in solid-state physics and electronics. , 1987, Physical review letters.

[4]  E. N. Economou,et al.  Tight-Binding Parametrization for Photonic Band Gap Materials , 1998 .

[5]  Michel Piché,et al.  Photonic bandgaps in periodic dielectric structures , 1993 .

[6]  John,et al.  Strong localization of photons in certain disordered dielectric superlattices. , 1987, Physical review letters.

[7]  N. Nicorovici,et al.  Two-dimensional Green's function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[9]  Timothy A. Birks,et al.  Localized function method for modeling defect modes in 2-D photonic crystals , 1999 .

[10]  Nicorovici,et al.  Photonic Band Gaps: Noncommuting Limits and the "Acoustic Band" , 1995, Physical review letters.

[11]  Masaya Notomi,et al.  Superprism phenomena in photonic crystals: toward microscale lightwave circuits , 1999 .

[12]  G. Tayeb,et al.  Numerical evidence of ultrarefractive optics in photonic crystals , 1999 .

[13]  A. Modinos,et al.  Scattering of electromagnetic waves by a disordered two-dimensional array of spheres , 1993 .

[14]  S Fan,et al.  Elimination of cross talk in waveguide intersections. , 1998, Optics letters.

[15]  Leung,et al.  Multiple-scattering calculation of the two-dimensional photonic band structure. , 1993, Physical review. B, Condensed matter.

[16]  Girard,et al.  Generalized Field Propagator for Electromagnetic Scattering and Light Confinement. , 1995, Physical review letters.

[17]  K. Sakoda,et al.  Novel approach to photonic bands with frequency-dependent dielectric constants. , 1998, Optics express.

[18]  H A Haus,et al.  Photonic bands: Convergence problems with the plane-wave method. , 1992, Physical review. B, Condensed matter.

[19]  Andrew G. Glen,et al.  APPL , 2001 .

[20]  K. Busch,et al.  Photonic band structure computations. , 2001, Optics express.

[21]  Chan,et al.  Existence of a photonic gap in periodic dielectric structures. , 1990, Physical review letters.

[22]  Datta,et al.  A7 structure: A family of photonic crystals. , 1994, Physical review. B, Condensed matter.

[23]  G. Tayeb,et al.  Anomalous refractive properties of photonic crystals , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[24]  C. Soukoulis,et al.  Impurity modes in a two-dimensional photonic crystal: coupling efficiency and Q factor , 2000 .

[25]  J. Joannopoulos,et al.  High Transmission through Sharp Bends in Photonic Crystal Waveguides. , 1996, Physical review letters.

[26]  Quang,et al.  Resonant nonlinear dielectric response in a photonic band gap material. , 1996, Physical review letters.

[27]  K. Sakoda,et al.  Numerical method for localized defect modes in photonic lattices , 1997 .

[28]  Nicorovici,et al.  Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[29]  John B. Pendry,et al.  Photonic Band Structures , 1994 .

[30]  Steven G. Johnson,et al.  Linear waveguides in photonic-crystal slabs , 2000 .

[31]  Ekmel Ozbay,et al.  Optimized dipole antennas on photonic band gap crystals , 1995 .

[32]  Ovidiu Toader,et al.  Proposed Square Spiral Microfabrication Architecture for Large Three-Dimensional Photonic Band Gap Crystals , 2001, Science.

[33]  S. John,et al.  COLLECTIVE SWITCHING AND INVERSION WITHOUT FLUCTUATION OF TWO-LEVEL ATOMS IN CONFINED PHOTONIC SYSTEMS , 1997 .

[34]  J. Joannopoulos,et al.  Photonic bound states in periodic dielectric materials. , 1991, Physical review. B, Condensed matter.

[35]  Che Ting Chan,et al.  Photonic band gaps in three dimensions: New layer-by-layer periodic structures , 1994 .

[36]  S. John,et al.  Quantum electrodynamics near a photonic band gap: Photon bound states and dressed atoms. , 1990, Physical review letters.

[37]  Masaya Notomi,et al.  Photonic crystals for micro lightwave circuits using wavelength-dependent angular beam steering , 1999 .

[38]  Susumu Noda,et al.  SPIRAL THREE-DIMENSIONAL PHOTONIC-BAND-GAP STRUCTURE , 1998 .

[39]  A. Modinos,et al.  Effect of stacking faults on the optical properties of inverted opals. , 2001, Physical review letters.

[40]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[41]  P. Robinson,et al.  Effects of disorder on wave propagation in two-dimensional photonic crystals. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  Shanhui Fan,et al.  Design of three-dimensional photonic crystals at submicron lengthscales , 1994 .

[43]  Steven G. Johnson,et al.  Guided modes in photonic crystal slabs , 1999 .

[44]  M. Okano,et al.  Alignment and stacking of semiconductor photonic bandgaps by wafer-fusion , 1999 .

[45]  Leung,et al.  Photonic band structure: The face-centered-cubic case employing nonspherical atoms. , 1991, Physical review letters.

[46]  Shanhui Fan,et al.  Channel Drop Tunneling through Localized States , 1998 .

[47]  Susumu Noda,et al.  Trapping and emission of photons by a single defect in a photonic bandgap structure , 2000, Nature.

[48]  Steven G. Johnson,et al.  Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap , 2000 .

[49]  O. B. McMahon,et al.  Effect of surface composition on the radiation pattern from a photonic‐crystal planar‐dipole antenna , 1994 .

[50]  Ekmel Ozbay,et al.  Propagation of photons by hopping: A waveguiding mechanism through localized coupled cavities in three-dimensional photonic crystals , 2000 .

[51]  I. H. Öğüş,et al.  NATO ASI Series , 1997 .

[52]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[53]  Kurt Busch,et al.  PHOTONIC BAND GAP FORMATION IN CERTAIN SELF-ORGANIZING SYSTEMS , 1998 .

[54]  C. Chan,et al.  Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals , 2001 .

[55]  Kok-Ming Leung,et al.  Diamondlike photonic band-gap crystal with a sizable band gap , 1997 .

[56]  Che Ting Chan,et al.  Photonic Band Gaps in Two Dimensional Photonic Quasicrystals , 1998 .

[57]  David Cassagne,et al.  Generalized Wannier function method for photonic crystals , 2000 .

[58]  Kurt Busch,et al.  Photonic bandgap formation and tunability in certain self-organizing systems , 1999 .

[59]  Albert Birner,et al.  Large birefringence in two-dimensional silicon photonic crystals , 2001 .

[60]  Kurt Busch,et al.  Liquid-Crystal Photonic-Band-Gap Materials: The Tunable Electromagnetic Vacuum , 1999 .

[61]  P. Lalanne,et al.  Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion , 2001 .

[62]  Pochi Yeh,et al.  Electromagnetic propagation in birefringent layered media , 1979 .

[63]  John D. Joannopoulos,et al.  Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides , 2001 .

[64]  Inward and outward integral equations and the KKR method for photons , 1993, cond-mat/9310040.

[65]  E. N. Economou,et al.  Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials , 2000 .

[66]  J. Joannopoulos,et al.  Accurate theoretical analysis of photonic band-gap materials. , 1993, Physical review. B, Condensed matter.

[67]  G. Ozin,et al.  Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres , 2000, Nature.

[68]  Vos,et al.  Preparation of photonic crystals made of air spheres in titania , 1998, Science.

[69]  M. Sigalas,et al.  Effect of disorder on photonic band gaps , 1999 .

[70]  J. Pendry,et al.  Calculation of photon dispersion relations. , 1992, Physical review letters.

[71]  Wang,et al.  Multiple-scattering theory for electromagnetic waves. , 1993, Physical review. B, Condensed matter.

[72]  Zheng,et al.  Robust photonic band gap from tunable scatterers , 2000, Physical review letters.

[73]  J. G. Fleming,et al.  A three-dimensional optical photonic crystal , 1998 .

[74]  Masaya Notomi,et al.  Self-collimating phenomena in photonic crystals , 1999 .

[75]  Zhao-Qing Zhang,et al.  Multiple-scattering approach to finite-sized photonic band-gap materials , 1998 .

[76]  Masaya Notomi,et al.  Superprism Phenomena in Photonic Crystals , 1998 .