2012/02/16 by Tomáš Dohnal, Dohnal, Tomas, Willy Doerfler +1
Engineering · Physics and Astronomy · #35C20 #35Q61 #41A60 #78M35 #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Optics (physics.optics) #Pattern Formation and Solitons (nlin.PS) #Photonic Crystals and Applications #Photonic and Optical Devices
paper · pdf · doi:10.48550/arxiv.1202.3583
openalex publication_date 2012/02/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Out-of-plane gap solitons in 2D photonic crystals are optical beams localized\nin the plane of periodicity of the medium and delocalized in the orthogonal\ndirection, in which they propagate with a nonzero velocity. We study such gap\nsolitons as described by the Kerr nonlinear Maxwell system. Using a model of\nthe nonlinear polarization, which does not generate higher harmonics, we obtain\na closed curl-curl problem for the fundamental harmonic of the gap soliton. For\ngap solitons with frequencies inside spectral gaps and in an asymptotic\nvicinity of a gap edge we use a slowly varying envelope approximation based on\nthe linear Bloch waves at the edge and slowly varying envelopes. We carry out a\nsystematic derivation of the coupled mode equations (CMEs) which govern the\nenvelopes. This derivation needs to be carried out in Bloch variables. The CMEs\nare a system of coupled nonlinear stationary Schr "odinger equations with an\nadditional cross derivative term. Examples of gap soliton approximations are\nnumerically computed for a photonic crystal with a hexagonal periodicity cell\nand an annulus material structure in the cell.\n