Split-step fourier methods applied to model nonlinear refractive effects in optically thick media

Using the Complex Jacobi Method to Simulate Kerr Non-linear Photonic Components

“…The basic complex Jacobi method (Hadley 2005) is an iterative method which solves the Helmholtz equation on a mesh. Only the fields at equidistant points are calculated.…”

“…Using exp(−jωt) as convention for the time dependent phase factor of the invariant field amplitudes results in the following optimal constants: α 1 = √ 3 − 1j and α 2 = −α * 1 . Derivation of these optimal values for α 1 and α 2 can be found in the original paper (Hadley 2005).…”

“…In this paper several improvements to the recently introduced complex Jacobi (CJ), (Hadley 2005) technique are discussed. The proposed extensions allow modeling of dielectric structures with the instantaneous nonlinear Kerr effect.…”

“…Finite Difference Time Domain (FDTD), (Taflove 1995), Beam Propagation (BPM), (Burzler et al 1996) and eigenmode expansion (EME), (Maes et al 2005) are able to simulate a wide variety of non-linear dielectric wavelength scale components. FDTD gives insight in the time-evolution of the fields by numerically integrating Maxwell's equations in the time domain.…”

Modeling of Kerr nonlinear photonic components with mode expansion

“…Therefore there is a need for accurate and efficient methods to simulate these structures. Among the available methods to model complex non-linear devices we mention the Finite-Difference Time-Domain method (FDTD) (Taflove, 1998) and the Beam Propagation Method (BPM) (Burzler et al, 1996). Each have their specific characterictics.…”