Analyzing second harmonic generation from arrays of cylinders using Dirichlet-to-Neumann maps

Lijun Yuan, Ya Yan Lu
2009 Journal of the Optical Society of America. B, Optical physics  
We develop an efficient numerical method for analyzing second harmonic generation (SHG) in two-dimensional photonic crystals composed of nonlinear circular cylinders embedded in a linear background medium. Instead of solving the governing inhomogeneous Helmholtz equation for the second harmonic wave in the entire structure directly, we define and solve a locally generated second harmonic field in each cylinder (independent of all other cylinders), then merge the field together using
more » ... r using Dirichlet-to-Neumann (DtN) maps of the unit cells. For linear waves in a unit cell without sources, the DtN map is an operator that maps the wave field to its normal derivative on the boundary and it can be approximated by a small matrix. A highly accurate pseudo-spectral method is used to solve the locally generated second harmonic wave in the cylinders. The method was applied to analyze enhanced SHG when the linear power reflectivity peaks at both the fundamental and second harmonic frequencies.
doi:10.1364/josab.26.000587 fatcat:txsjd3yh25hyzcfg64mvzzdnhi