Time-Dependent Laser Cavity Perturbation Theory: Exploring Future Nano-Structured Photonic Devices in Semi-Analytic way

We present a theoretical framework, which successfully combines two different fields of photonics: i) the laser rate equations and ii) the cavity perturbation theory, focusing particularly on micro-cavity lasers with optical anisotropies. Our approach is formally analogous to quantum-mechanical time-dependent perturbation theory, in which however the gain medium and permittivity tensor distribution are perturbed instead of the Hamiltonian. Using the general vectorial Maxwell-Bloch equations as a starting point, we derive polarization-resolved coupled-mode equations, in which all relevant geometric and anisotropy-related laser parameters are imprinted in its coefficients. Closed-form coupled-mode equations offer physical insights like rate equations approaches and the precision comparable to brute-force numeric routines, thus being the time-saving alternative to finite-difference time-domain methods. The main advantage is that one calculates numerically the shapes of cold-cavity modes used to derive coupled-mode equations for one set of parameters and the broad landscape of parameters of interest is further studied in a perturbative way. This makes the method particularly interesting for semi-analytic studies of state-of-art devices such as the photonic crystal lasers, the liquid-crystal lasers or specifically spin-lasers, in which the interplay between injected spin and cavity birefrigence creates very promising platform for ultrafast data transfer technologies.