Beam Modes of Lasers with Misaligned Complex Optical Elements

Abstract

A recurring theme in my research is that mathematical matrix methods may be used in a wide variety of physics and engineering applications. Transfer matrix techniques are conceptually and mathematically simple, and they encourage a systems approach. Once one is familiar with one transfer matrix method, it is straightforward to learn another, even if it is from a completely different branch of science. Thus it is useful to overview these methods, and this has been done here. Of special interest are the applications of these methods to laser optics, and matrix theorems concerning multipass optical systems and periodic optical systems have been generalized here to include, for example, the effect of misalignment on the performance of an optical system. In addition, a transfer matrix technique known as generalized beam method has been derived to treat misalignment effects in complex optical systems. Previous theories used numerical or ad hoc analytical solutions to a complicated diffraction integral. The generalized beam matrix formalism was also extended to higher-order beam modes of lasers and used to study mode discrimination in lasers with misaligned complex optical elements.