Nonparaxial eigenmodes of stable resonators

A method to determine the nonparaxial eigenmodes of stable resonators is presented. The method is based on the perturbation theory of Lax et al. For calculating nonparaxial components of the electric field. A matrix formalism which uses a mode expansion into paraxial Hermite-Gaussian modes is applie...

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Bibliographic Details
Published in:IEEE journal of quantum electronics 1999-02, Vol.35 (2), p.198-207
Main Authors: Laabs, H., Friberg, A.T.
Format: Article
Language:English
Subjects:
Diffraction
Eigenvalues and eigenfunctions
Exact sciences and technology
Formalism
Frequency
Frequency shift
Fundamental areas of phenomenology (including applications)
Hermite-Gaussian modes
Laser beams
Laser modes
Laser optical systems: design and operation
Mathematical analysis
Mathematical models
Matrices
Matrix methods
Mirrors
Optical propagation
Optical resonators
Optics
Partial differential equations
Physics
Resonators
Resonators, cavities, amplifiers, arrays, and rings
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Summary:A method to determine the nonparaxial eigenmodes of stable resonators is presented. The method is based on the perturbation theory of Lax et al. For calculating nonparaxial components of the electric field. A matrix formalism which uses a mode expansion into paraxial Hermite-Gaussian modes is applied to describe the nonparaxial propagation and the phase shift at a parabolic and a spherical mirror. Expressions for these matrices are derived analytically. Multiplying all matrices corresponding to a round trip, a matrix for the resonator is obtained. Eigenmodes of the resonator are numerically found by solving the eigenvalue problem. In the special case of paraxial propagation and parabolic mirror profiles, the standard Hermite-Gaussian modes result analytically. Nonparaxial modes of a given resonator are compared for different mirror profiles. It is found that, in the nonparaxial domain, spherical mirrors do not change the mode profile and the frequencies of the transverse modes, in contrast to parabolic mirrors which aberrate the beam profile and cause frequency shifts.
ISSN:0018-9197
1558-1713
DOI:10.1109/3.740741