Explicit Formulas for the Fundamental Mode of a Linear Resonator with Elliptic Mirrors and Construction of Higher Order Modes

摘要

A linear resonator bounded by elliptic (hyperbolic) mirrors with noncoinciding principal curvature directions is considered. Explicit analytic formulas describing the fundamental mode of such resonator are derived in the principal approximation. A procedure of constructing higher order modes is developed. The potentialities of the technique are exemplified by considering a resonator with mirrors whose shapes are close to spheres and a resonator with elliptic mirrors whose shapes are close to each other.