Laser resonator modeling by field tracing: a flexible approach for fully vectorial transversal eigenmode calculation

Abstract

In this work we generalize the scalar Fox and Li algorithm for the dominant transversal resonator eigenmode calculation to a fully vectorial field tracing concept. Therefore we reformulate Fox and Li's scalar integral equation to a set of coupled operator equations. The introduction of a field tracing round trip operator concept shows that, in principle, any modeling technique which can be formulated to operate for electromagnetic fields can be used to simulate light propagation through the different subdomains of the resonator. This allows a flexible, fast, and accurate simulation of the fully vectorial dominant transversal resonator eigenmode. An example is presented to demonstrate the flexibility and accuracy of the field tracing approach.

Fully vectorial laser resonator modeling of continuous-wave solid-state lasers including rate equations, thermal lensing and stress-induced birefringence

“…In our recent work [27] we have shown that the fundamental mode of any kind of laser resonator can be calculated by the fully-vectorial Fox and Li algorithm. The main idea is that an electric field given at an arbitrary plane inside the resonator must reproduce itself after propagating once through the hole resonator.…”

“…Please note that the remaining electric field component E z and the three magnetic components H x , H y , H z can be calculated from V 1 and V 2 on demand by Maxwell's equations [28]. The propagation of the field through the resonator is described by the resonator round trip operator R. This round trip operator consists of a sequence of approximated or rigorous component operators C m and free space operators P m,m−1 for different subdomains m of the resonator [27]: The transversal resonator mode can be calculated in a arbitrary plane using a sequence of diverse component operators C and free space propagation operators P describing a full resonator round trip. Each operator solves Maxwell's equations in a rigorous or approximated manner for a single subdomain of the resonator.…”

“…vectorial, transversal structure of the resonator mode in a plane can be calculated by a sequence of different approximated or rigorous solutions of Maxwell's equations denoted by the operators C m and P m,m−1 in different subdomains of the resonator. As discussed in [27], the component operator might have a diagonal structure…”

“…dependent on the simulation technique applied to propagate the light through the active or passive intracavity component m. The non-diagonal operator components C m, 21 and C m,12 in Eq. 4describe the polarization cross-talk of the light propagation through the component m. In our recent work [27] we have focused on the general structure of the component and free space operators and the resulting structure of Eq. (1).…”

“…The scalar nature of this method was in the past its main limiting factor. Therefore in a previous publication we have presented a very flexible, fully vectorial generalization of the Fox and Li approach for the calculation of the shape of the dominant laser resonator eigenmode [27]. So far we have shown that, in principle, any resonator setup containing all kinds of passive optical components can be simulated.…”