Владимир Григорьевич Низьев

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We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamics of mode formation. Simulations of an axially symmetrical empty resonator rely on an analytical description of radiation diffraction from a narrow ring. Reflection of an incident wave with a specified amplitude-phase distribution from the mirror is calculated by the Green function method. The process of mode formation is characterized by relaxation oscillations of various frequencies depending on the resonator parameters. The evolution of the relaxation oscillation amplitude can be aperiodic in nature, or it can occur as beats of a different frequency. It has been shown that there is a consistency between the known conditions of paraxial resonance obtained in the approximation of geometric optics and the aperiodic processes of evolution of relaxation oscillation amplitude in mode forming. An investigation has been performed on the factors affecting the time of mode formation. The possibility has been shown for multipass mode suppression and TEM10 mode generation by the use of an absorber mask on the resonator mirror. We developed an iteration algorithm for open resonator simulation and employed it in studying the dynamicsof mode formation. Simulations of an axially symmetrical empty resonator rely on an analyticaldescription of radiation diffraction from a narrow ring. Reflection of an incident wave with a specifiedamplitude-phase distribution from the mirror is calculated by the Green function method. The process ofmode formation is characterized by relaxation oscillations of various frequencies depending on the resonatorparameters. The evolution of the relaxation oscillation amplitude can be aperiodic in nature, or itcan occur as beats of a different frequency. It has been shown that there is a consistency between theknown conditions of paraxial resonance obtained in the approximation of geometric optics and the aperiodicprocesses of evolution of relaxation oscillation amplitude in mode forming. An investigation hasbeen performed on the factors affecting the time of mode formation. The possibility has been shownfor multipass mode suppression and TEM10 mode generation by the use of an absorber mask on the resonator mirror.

1. Introduction

2. Mathematical Model

3. Calculation Results
A. Oscillation Amplitude and Time of Mode Formation
B. Oscillation Period and the Character of Field Amplitude Evolution
C. Laguerre–Gaussian Nonzero Modes

4. Conclusion

Appendix: Wave Reflection from the Round Mirror ofFinite Dimensions

References