Modeling of discontinuities in photonic crystal waveguides with the multiple multipole method.

A method for the simulation of discontinuities in photonic crystal defect waveguides is presented. This frequency domain technique is based on the multiple multipole method. In contrast with other known techniques, spurious reflections (due to the impedance mismatch at the waveguide terminations) are avoided. The absence of spurious reflections allows one to characterize precisely the intrinsic behavior of the sole discontinuity, reducing at the same time the size of the simulation domain. To achieve a perfect impedance matching, the guided modes of infinitely long waveguides corresponding to the input and output channels of the discontinuity are first computed using a supercell approach. Then, the discontinuity is fed with one of the previously computed modes, and the fields transmitted or reflected towards the discontinuity arms are matched to the modal fields corresponding to each output waveguide. This method allows one to compute the intrinsic transmission and reflection coefficients of the discontinuity (i.e., coefficients not altered by additional effects such as finite crystal size, etc.). The procedure is presented in detail using some simple discontinuities as test cases. Then, it is applied to the computation of the coupling from a waveguide to free space and for the analysis of a filtering T junction.

[1]  A Yariv,et al.  Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry. , 2000, Optics letters.

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

[3]  Ch. Hafner.  Multiple multipole (MMP) computations of guided waves and waveguide discontinuities , 1990 .

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

[5]  Christian Hafner,et al.  Post-modern Electromagnetics: Using Intelligent MaXwell Solvers , 1999 .

[6]  Didier Felbacq,et al.  Multiplexing and demultiplexing with photonic crystals , 1999 .

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

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

[9]  Xu,et al.  Scattering-theory analysis of waveguide-resonator coupling , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  M. Koshiba,et al.  Time-domain beam propagation method and its application to photonic crystal circuits , 2000, Journal of Lightwave Technology.

[11]  J. Joannopoulos,et al.  Bound states in photonic crystal waveguides and waveguide bends , 1998 .

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

[13]  D W Prather,et al.  Multichannel wavelength division multiplexing with photonic crystals. , 2001, Applied optics.

[14]  T. Happ,et al.  Photonic crystal tapers for ultracompact mode conversion. , 2001, Optics letters.

[15]  A. Boag,et al.  Narrow-band microcavity waveguides in photonic crystals. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  Christian Hafner,et al.  Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  Steve Haake,et al.  Physics, technology and the Olympics , 2000 .

[18]  Steven G. Johnson,et al.  Waveguide branches in photonic crystals , 2001 .

[19]  D. Felbacq,et al.  Cross waveguides in biperiodic two-dimensional photonic crystals , 2001 .

[20]  Thomas Søndergaard,et al.  Energy flow in photonic crystal waveguides , 2000 .

[21]  Alan B. Tayler,et al.  New methods for solving elliptic equations , 1969 .

[22]  S Fan,et al.  Single-mode waveguide microcavity for fast optical switching. , 1996, Optics letters.

[23]  Toshihiko Baba,et al.  Observation of light propagation in photonic crystal optical waveguides with bends , 1999 .

[24]  Shanhui Fan,et al.  Absorbing boundary conditions for FDTD simulations of photonic crystal waveguides , 1999 .

[25]  M. Koshiba,et al.  High-performance absorbing boundary conditions for photonic crystal waveguide simulations , 2001, IEEE Microwave and Wireless Components Letters.

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

[27]  R. Stoffer,et al.  Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters , 2000 .

[28]  Thomas F. Krauss,et al.  Photonic crystals in the optical regime — past, present and future , 1999 .

[29]  J. Joannopoulos,et al.  Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal , 1998, Science.

[30]  Shanhui Fan,et al.  Coupling of modes analysis of resonant channel add-drop filters , 1999 .

[31]  K. J. Dean,et al.  Waves and Fields in Optoelectronics: Prentice-Hall Series in Solid State Physical Electronics , 1984 .

[32]  Christian Hafner,et al.  Band structure computations of metallic photonic crystals with the multiple multipole method , 2002 .

[33]  Sailing He,et al.  Antennas based on modified metallic photonic bandgap structures consisting of capacitively loaded wires , 2001 .

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

[35]  C. Hafner.  The generalized multipole technique for computational electromagnetics , 1990 .

[36]  Henri Benisty,et al.  Modal analysis of optical guides with two‐dimensional photonic band‐gap boundaries , 1996 .

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

[38]  Gérard Tayeb,et al.  Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities , 1997 .

[39]  Sailing He,et al.  Surface modes in two-dimensional dielectric and metallic photonic band gap structures : a FDTD study , 2001 .

[40]  Hirohito Yamada,et al.  Photonic crystal line defect waveguide directional coupler , 2001 .

[41]  Amnon Yariv,et al.  Propagation and second-harmonic generation of electromagnetic waves in a coupled-resonator optical waveguide , 2000 .

[42]  Near-field optics with photonic crystals , 2000, QELS 2000.

[43]  T. Baba,et al.  Analysis of finite 2D photonic crystals of columns and lightwave devices using the scattering matrix method , 1999 .

[44]  Christian Hafner,et al.  The 3D electrodynamic wave simulator : 3D MMP software and user's guide , 1993 .

[45]  S. Noda,et al.  Waveguides and waveguide bends in two-dimensional photonic crystal slabs , 2000 .