In this diploma work, two versions of the discrete nonlinear Schrödinger (DNLS) equation are used to model a nonlinear layered photonic crystal system; the cubic DNLS (cDNLS) equation and the saturable DNLS (sDNLS) equation. They both have site-dependent coefficients to break mirror symmetry with respect to propagation direction, as well as to describe the linear and nonlinear properties of the system. Analytical solutions taking on plane wave form are, via the backward transfer map, used to derive a transmission coefficient as well as a rectifying factor to quantify the diode effect. The effect of varying site-dependent coefficients is studied in detail. Numerical simulations of Gaussian wave packets impinging on the system, using open boundary conditions, show the breaking of parity symmetry. Evidence of a change in the wave packet dynamics occurring in the transition between the cubic and the saturable DNLS model is presented. A saturated system prevents the wave packet from getting stuck in the nonlinear lattice layers. The transmission properties were found to be very sensitive to slight changes of the system parameters.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-111236 |
| Date | January 2014 |
| Creators | Johansson, Erik |
| Publisher | Linköpings universitet, Teoretisk Fysik, Linköpings universitet, Tekniska högskolan |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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