Finite difference simulation of thermally tuned hexagonal photoniccrystals

摘要

Thermal tuning of hexagonal photonic crystals by absorption of laser energy is examined through finite difference numerical simulation. The photonic crystals are patterned in the device layer of the silicon on insulator (SOI) platform. The thermal equations, which include contributions from laser absorption gain, conduction loss, and radiation loss are combined to obtain a heat balance equation. This governing equation is modeled using a thermodynamic finite difference computation engine. To ensure the stability of the thermal model within the transient regime the velocity of heat propagation is calculated and included as a courant factor controlling the coarseness of the discretization grid and time step interval. The thermal distribution obtained from the numerical simulation, combined with the thermo-optic effect, can be used to alter the initial dielectric distribution of the device layer. The integration of the change in refractive index into the existing dielectric enables the thermal effects to be included into a standard optical finite difference time domain (FDTD) engine. Through the implementation of the optical and thermal simulation tools, the laser thermal tuning of the band gaps and localized states of hexagonal photonic crystals will be explored. The temperature dependence of the central wavelength of the localized states will be calculated.