Determining the response of optical systems in both time and harmonic domains with the singularity expansion method

Abstract

Physical systems are characterized by their transfer operators in the harmonic domain. These operators are usually locally approximated as rational functions or pole expansions. We generalize this result and introduce the Multiple-Order Singularity Expansion Method (MOSEM) which offers an exact description of linear systems in terms of their singularities and Laurent series coefficients or zeros. The interest of this approach is first illustrated by the simple but fundamental case of a dispersive Fabry-Perot cavity, where it provides an analytical expression of the reflected field in both the time and harmonic domains. In a second step, we show that this method must be applied for defining the complex expression of the dielectric permittivity that describes the physical response of a system (the material) to an excitation field. This rigorous expression of the permittivity is shown to provide highly accurate results for a broad range of materials.