Computing photonic band structures by Dirichlet-to-Neumann maps: The triangular lattice

An efficient semi-analytic method is developed for computing the band structures of two-dimensional photonic crystals which are triangular lattices of circular cylinders. The problem is formulated as an eigenvalue problem for a given frequency using the Dirichlet-to-Neumann (DtN) map of a hexagon unit cell. This is a linear eigenvalue problem even if the material is dispersive, where the eigenvalue depends on the Bloch wave vector. The DtN map is constructed from a cylindrical wave expansion, without using sophisticated lattice sums techniques. The eigenvalue problem can be efficiently solved by standard linear algebra programs, since it involves only matrices of relatively small size.

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

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

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

[4]  Kazuaki Sakoda,et al.  Photonic bands of metallic systems. I. Principle of calculation and accuracy , 2001 .

[5]  Zhang,et al.  Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations. , 1990, Physical review letters.

[6]  P. Kuchment,et al.  An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials , 1999 .

[7]  H. Yang,et al.  Finite difference analysis of 2-D photonic crystals , 1996 .

[8]  K. Sakoda,et al.  Photonic bands of metallic systems. II. Features of surface plasmon polaritons , 2001 .

[9]  R. McPhedran,et al.  Photonic band structure calculations using scattering matrices. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  Nicorovici,et al.  Photonic band gaps for arrays of perfectly conducting cylinders. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Steven G. Johnson,et al.  Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. , 2001, Optics express.

[13]  Tsuyoshi Ueta,et al.  Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods , 1998 .

[14]  Leung,et al.  Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media. , 1990, Physical review letters.

[15]  Chin-Ping Yu,et al.  Applications of the finite difference mode solution method to photonic crystal structures , 2004 .

[16]  H. Hernández-Figueroa,et al.  Novel numerical method for the analysis of 2D photonic crystals: the cell method. , 2002, Optics express.

[17]  A. Maradudin,et al.  Photonic band structure of two-dimensional systems: The triangular lattice. , 1991, Physical review. B, Condensed matter.

[18]  D. Dobson.  An Efficient Method for Band Structure Calculations in 2D Photonic Crystals , 1999 .

[19]  D. Larkman,et al.  Photonic crystals , 1999, International Conference on Transparent Optical Networks (Cat. No. 99EX350).

[20]  Ya Yan Lu,et al.  Photonic bandgap calculations with Dirichlet-to-Neumann maps. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[21]  John B. Pendry,et al.  Calculating photonic band structure , 1996 .

[22]  Maradudin,et al.  Photonic band structures of two-dimensional systems containing metallic components. , 1994, Physical review. B, Condensed matter.

[23]  Jean-Michel Lourtioz,et al.  Wavelet method for computing band diagrams of 2D photonic crystals , 2006 .

[24]  A. Maradudin,et al.  PHOTONIC BAND STRUCTURES OF TWO-DIMENSIONAL SYSTEMS FABRICATED FROM RODS OF A CUBIC POLAR CRYSTAL , 1997 .

[25]  Robert Rogowski,et al.  Photonic band gap analysis using finite-difference frequency-domain method. , 2004, Optics express.

[26]  Sukky Jun,et al.  Moving least-square method for the band-structure calculation of 2D photonic crystals. , 2003, Optics express.

[27]  Chien-Chung Chang,et al.  Two Classes of Photonic Crystals with Simultaneous Band Gaps , 2004 .

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

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