Studies of laser resonators and beam propagation using fast transform methods
Abstract
The quasi-fast Hankel transform (FHT) algorithm is improved and tested for beam propagation calculations in cylindrical coordinates in order to develop an efficient method for the numerical computation of optical diffraction effects. Accuracy criteria are established and relationships between optical Fresnel number and numerical sampling parameters are found. Extensive application of this propagation scheme to resonator eigenmode analysis is carried out. The analytic solutions of the perturbed Quassian modes of an unbalanced antiresonant ring laser cavity are studied by perturbation theory. This resonator has the property of exhibiting transverse mode selection even with infinite diameters for all mirrors and apertures. Second harmonic generation in nonlinear materials with beam diffraction, pump depletion, and arbitrary beam profiles all taken into consideration are investigated. Numerical calculations are done with the use of the FHT in cylindrical coordinates, and fast fourier transforms in rectangular coordinates. Theory is confirmed with an experiment using an unstable resonator Nd: YAG output beam pumping KDP crystal.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1980
- Bibcode:
- 1980PhDT........93S
- Keywords:
-
- Diffraction Propagation;
- Fast Fourier Transformations;
- Hankel Functions;
- Laser Cavities;
- Perturbation Theory;
- Algorithms;
- Resonators;
- Lasers and Masers