Finite-element mode-solver for nonlinear periodic optical waveguides and its application to photonic crystal circuits

A finite-element method (FEM) is newly formulated for the modal analysis of nonlinear periodic optical waveguides. In order to treat periodicity in the propagation direction, periodic boundary conditions are imposed on the envelope of electromagnetic fields. The validity of this method is verified by way of numerical examples of a PC waveguide composed of nonlinear dielectric pillars placed on square array in the cladding region. Furthermore, the present method is applied to various nonlinear photonic crystal waveguide structures for exploring appropriate structures to enhance the nonlinearity and their nonlinear modal properties are presented, including coupled-resonator optical waveguides.

[1]  J. S. Aitchison,et al.  Ultrafast all‐optical switching in GaAlAs directional couplers at 1.55 μm without multiphoton absorption , 1993 .

[2]  J. Joannopoulos,et al.  Photonic crystals: putting a new twist on light , 1997, Nature.

[3]  A. Scherer,et al.  Coupled-resonator optical waveguide: a proposal and analysis. , 1999, Optics letters.

[4]  D J Richardson,et al.  Nonlinear propagation effects in an AlGaAs Bragg grating filter. , 1999, Optics letters.

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

[6]  Masanori Koshiba,et al.  Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers , 2001 .

[7]  Yuri S. Kivshar,et al.  Nonlinear transmission and light localization in photonic-crystal waveguides , 2002 .

[8]  Masanori Koshiba,et al.  Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems , 2002 .

[9]  Steven G. Johnson,et al.  Photonic-crystal slow-light enhancement of nonlinear phase sensitivity , 2002 .

[10]  Steven G. Johnson,et al.  Optimal bistable switching in nonlinear photonic crystals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Alejandro Martínez,et al.  Planar photonic crystal structure with inherently single-mode waveguides. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  Masanori Koshiba,et al.  Time-Domain Beam Propagation Method for Nonlinear Optical Propagation Analysis and Its Application to Photonic Crystal Circuits , 2003 .

[13]  Masanori Koshiba,et al.  Finite element characterization of chromatic dispersion in nonlinear holey fibers. , 2003, Optics express.

[14]  Shanhui Fan,et al.  High-contrast all-optical bistable switching in photonic crystal microcavities , 2003 .

[15]  Shanhui Fan,et al.  All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry. , 2003, Optics letters.

[16]  Shanhui Fan,et al.  Nonlinear photonic crystal microdevices for optical integration. , 2003, Optics letters.

[17]  John D. O'Brien,et al.  Optimization of a two-dimensional photonic-crystal waveguide branch by simulated annealing and the finite-element method , 2004 .

[18]  R. Osgood,et al.  All-optical tunability of a nonlinear photonic crystal channel drop filter. , 2004, Optics express.

[19]  F Ramos,et al.  All-optical switching structure based on a photonic crystal directional coupler. , 2004, Optics express.