| Abstract: | Despite being open systems described by a non-hermitian wave equation, lasers have traditionally been treated as closed cavities, with the coupling to the continuum included phenomenologically or perturbatively. This approach is ill suited to treating modern complex micro-lasers, and particularly very low-Q systems, such as random lasers. We have developed a unified approach to laser theory which treats the cavity + gain medium as a scattering system described by a non-unitary S-matrix. In this approach, which we call Steady-state Ab initio Laser Theory (SALT), the openness of the cavity is treated exactly, and the non-linear mode competition above threshold is included to infinite order. The lasing threshold is determined by the condition that a pole of the S-matrix reach the real axis, and the multi-mode steady-state is described by a non-linear S-matrix with multiple lasing poles. Solutions of the SALT equations are in excellent agreement with brute force time integration of the semiclassical Maxwell-Bloch laser equations, but are orders of magnitude faster. Random and chaotic lasers can be studied rigorously in this approach, and a number of new results have been obtained. Using input-output theory the approach can be extended to quantum fluctuations of laser properties, and a more general form of the Schawlow-Townes linewidth formula has been derived, which finds results beyond all previous linewidth theories. Applying the time-reversal operator to the laser equations at threshold uncovers a new effect, coherent perfect absorption, in which a lossy cavity described by the complex conjugate of the laser susceptibility, will absorb the incoming version of the threshold mode of the corresponding laser. This effect, which is a generalization of critical coupling to a cavity, has recently been demonstrated experimentally. |
