Astigmatic Resonator Research Articles

Control of transverse mode in a He-Ne laser using an astigmatic resonator.

The realization of output of the controllable transverse mode in a laser resonator has always been the key problem in applications of lasers. At present, the theory of optical resonators for passive resonators is relatively mature, but the non-uniformity of gain media greatly affects the output of the laser transverse mode for astigmatic resonators in operation; especially for gas lasers, controllable high-order modes have not been studied. To realize the theory of an astigmatic passive resonator of a gas laser as a good approximation of an active resonator, this paper develops the theory of selecting the laser eigenmode through an astigmatic resonator, and verifies that the two-dimensional tilt of the cavity mirror can break the axial symmetry. Controllable output of the laser mode is realized in real time and conveniently for the first time, to the best of our knowledge. This scheme is not only common to all kinds of lasers, but also has important research significance for the high-order modes required for real-time and rapid regulation of gas lasers under operating conditions.

Rays and fields in general astigmatic resonators

General astigmatic (GA) resonators are discussed in detail. Eigenrays, eigenmodes and eigenvalues (Gouy-factors) of this resonator are evaluated. A stability diagram for such resonators is introduced, which clearly depicts the stable and unstable regions for rays as well as for fields. Eigenrays and their stability regions are evaluated using the ABCD-law. For the beam propagation Collins' integral and the second moment method are applied. The eigenfunctions for rectangular symmetry are the generalized Hermite polynomials multiplied by the Gaussian exponential factor. It is shown that for general astigmatic resonators these polynomials are the product of normal Hermite polynomials. The generating function of the eigenfunctions depends on the special resonator. It is a useful tool for all calculations and it is determined. Furthermore it is shown that the second moment characterization of the modes is a useful and easy to handle procedure to evaluate beam width, beam divergence, radius of curvature and twist of the generalized Gauss–Hermite functions.

Symmetry of the spatial structure of radiation upon transverse mode locking in an astigmatic resonator laser

The influence of the astigmatic resonator parameters on the symmetry of the spatial structure of the radiation intensity is analysed upon transverse mode locking in a nonuniformly pumped laser. Conditions for the transition from the circular symmetry to its violation are found. At a fixed astigmatism of the resonator, the symmetry is determined, first of all, by the resonator length and losses. The theoretical conclusions are confirmed by the experiments with diode end-pumped Nd:YAG and Nd:YLF lasers.

Creation, doubling and splitting of vortices in intracavity second harmonic generation

We demonstrate generation and frequency doubling of unit charge vortices in a linear astigmatic resonator. Topological instability of the double charge harmonic vortices leads to well separated vortex cores that are shown to rotate, and become anisotropic, as the resonator is tuned across resonance.

Thermally bonded Yb:YAG planar waveguide laser

Laser performance of a diode-bar side-pumped Yb:YAG planar multimode waveguide geometry is reported. The waveguide was fabricated by thermal bonding technique with a 100-μm thick and 3-mm long active layer. This configuration offers an excellent confinement of the pump fields. By using an astigmatic resonator, a large overlap of pump and signal fields combined with a good beam quality have been realized. The M 2 values were found to be 1.5 and 4 in the vertical and horizontal directions, respectively. A maximum CW output power of 1.2 W at 1032 nm has been obtained.

Astigmatism in Gaussian-beam self-focusing and in resonators for Kerr-lens mode locking

An analytical treatment for the propagation of astigmatic Gaussian beams in Kerr media is presented. This method, which is valid to the first order in the beam power, allows us to calculate in closed form the nonlinear variations of the spot size and the radius of curvature. This formalism is applied to the calculation of the self-consistent Gaussian mode of an astigmatic resonator with a Kerr medium, such as those used for Kerr-lens mode-locked lasers. Theoretical predictions are confirmed by the experimental results obtained with a femtosecond Ti:sapphire laser. In particular, the design of an optimized resonator permits self-starting of the mode-locking mechanism.

Matrix representation of three-dimensional astigmatic resonators

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.

Optical resonator with an external source: excitation of the Hermite-Gaussian modes

The amplitudes of excited Hermite-Gaussian modes in an astigmatic resonator due to an injected astigmatic Gaussian mode are calculated. Various types of misadjustment are considered: offset ∊; tilt α; mismatch o. For small misadjustments the amplitudes are fast-converging series in the mismatch parameter o and in the misalignment parameter ξ. For mismatch, only even-indexed Hermite-Gaussians appear. The theory is applied to an experimental result involving a 3.15-m square ring interferometer. Formulas for power matching are derived, and control loops to eliminate all but the Gaussian mode are proposed.

Astigmatic resonator for closed-cavity-mode filling enhancement

Astigmatic resonator concepts have been developed and tested in TRW chemical laser facilities. It was demonstrated that this type of resonator is suitable for closed-cavity multiple-mode operation and has good mode filling capability for a laser with a high aspect ratio rectangular gain medium.

Astigmatic Gaussian beams produced by axially asymmetric laser cavities

Gaussian beams generated within astigmatic resonators are themselves astigmatic, having wavefront curvatures and spot sizes that are different when measured in two orthogonal directions. Expressions are derived for the confocal parameters, spot sizes, waist positions, and stability conditions of beams formed within spherical mirror resonators that contain one or more inclined plates (or Brewster-ended laser rods). An expression is also derived for the resonant frequencies of the TEM mn mode in such a resonator. It is shown that the frequency degeneracy between modes of the same m + n is lifted and the frequency splittings are calculated. The astigmatism produced by prisms used for dispersion is also considered and precautions are described for avoiding serious astigmatism in resonators containing such prisms.