Regenerative Modes in Laser Resonators

We will develop a general theory of laser resonators based on an analysis of optimized regenerative optical amplifiers. In particular, we demonstrate that a description of the circulating field in the regenerative amplifier should not be decoupled from the injected field description. Specifically, we solve the following problem: for a given wavelength and gain setting, is there an injected field that will maximize the regenerative gain of an optical regenerative amplifier? Here, we derive the integral equations that solve this problem. The injected field solutions, as well as the simultaneously derived circulating field solutions, provide a unified basis for analyzing optical resonators. The method accurately predicts circulating and injected mode distributions from below threshold, the regenerative amplifier case, to threshold, the laser oscillator case. If we concentrate on the high-regenerative gain limit, the dominant circulating mode from this approach is well-approximated by the dominant self-replicating Fox-Li mode. However, our new laser resonator analysis based on an optimized regenerative amplifier is unifying; it provides accurate agreement with all near- and far-field observations, while also accurately explaining noise accrual, laser mode formation data, and higher order lateral modes. Furthermore, because the underlying equations are Hermitian, the circulating and injected modes that are predicted with this approach are complete and power orthogonal. This regenerative approach to laser resonator analysis retains the strengths of the standard theory while avoiding its pitfalls.