Simulating nonlinear optical effects in periodically patterned integrated waveguides

Licentiate thesis, 2024

The nonlinear optical coefficients are very small for most materials. This results in a
need for very long waveguides in integrated optics in order to achieve nonlinear optical
processes such as optical parametric oscillation with appreciable efficiency, meter-long
waveguide structures not being uncommon. This in turn makes simulations of nonlin-
ear integrated optical devices challenging. Translationally invariant waveguides can be
simulated using approximate methods such as the the beam envelope method. How-
ever, for more complicated structures, for instance a periodically patterned waveguide,
these approaches becomes unfeasible. In this thesis, we describe how the nonlinear
wave propagation in periodically patterned waveguides can be simulated using the non-
linear Schrödinger equation, including a computational strategy to calculate the coeffi-
cients of the nonlinear Schrödinger equation describing the linear and nonlinear effects
of the optical materials. In particular, we focus on effective meshing strategies for simu-
lations using the finite-element method and an approach to numerically determine the
higher-order dispersion coefficients needed to solve the nonlinear Schrödinger equa-
tion for long, periodically patterned structures.