Self-trapping and stable localized modes in nonlinear photonic crystals.

Analytical Investigation of TM Surface Waves in 1D Photonic Crystals Capped by a Self-Focusing Left-Handed Slab

In this paper, the localized TM surface waves of a nonlinear self-focusingleft-handed slab sandwiched between a uniform medium and a one-dimensionalphotonic crystal (1D PC) is analytically investigated. Our method is based on the firstintegral of the nonlinear Maxwell's equations. For the TM surface waves, the presenceof two electric field components makes the analysis difficult. Therefore, we ...

Self-Trapping of Light and Nonlinear Localized Modes in 2D Photonic Crystals and Waveguides

Bloch modes and self-localized waveguides in nonlinear photonic crystals

We present a modeling technique that uses eigenmode expansion to simulate infinite periodic structures with Kerr nonlinearity. Using a unit cell with Bloch boundary conditions, our iterative algorithm efficiently calculates self-consistent two-dimensional Bloch modes. We show how it can be used to study the band structure of nonlinear photonic crystals and to gain rapid insight in the operation...

Resolvent method for computations of localized defect modes of H-polarization in two-dimensional photonic crystals.

We have developed and tested a version of the resolvent (or Green's function) method, based on the shift-inverse of the Maxwellian operator, that ensures stable convergence of iterative computations of localized defect modes of H-polarization in two-dimensional (2D) photonic crystals. The defect states are obtained by solving the eigenvalue problem for an associated compact operator with the ex...

Nonlinear surface modes and Tamm states in periodic photonic structures

We study the formation of nonlinear localized modes and discrete surface solitons near the edges or interfaces of weakly coupled nonlinear optical waveguides, one-dimensional photonic crystals. We draw an analogy between the staggered nonlinear surface optical modes and the surface Tamm states known in the electronic theory. We discuss the crossover between discrete solitons inside the array an...