Closed-form Maker fringe formulas for poled polymer thin films in multilayer structures

We report new closed-form expressions for Maker fringes of anisotropic and absorbing poled polymer thin films in multilayer structures that include back reflections of both fundamental and second-harmonic waves. The expressions, based on boundary conditions at each interface, can be applied to multilayer structures containing a buffer and a transparent conducting oxide layer, which might enhance multiple reflections of fundamental and second-harmonic waves inside a nonlinear thin film layer. This formulation facilitates Maker fringe analysis for a sample containing additional multilayer structures on either side of a poled polymer thin film. Experimental data and numerical simulations are given to indicate the importance of inclusion of such a reflective layer in analyses for reliable characterization of second-harmonic tensor elements.