Transfer function replacement of phenomenological single-mode equations in semiconductor microcavity modeling

Semiconductor microcavities are frequently studied in the context of semiconductor lasers and in application-oriented fundamental research on topics such as linear and nonlinear polariton systems, polariton lasers, polariton pattern formation, and polaritonic Bose-Einstein condensates. A commonly used approach to describe theoretical properties includes a phenomenological single-mode equation that complements the equation for the nonlinear optical response (interband polarization) of the semiconductor. Here, we show how to replace the single-mode equation by a fully predictive transfer function method that, in contrast to the single-mode equation, accounts for propagation, retardation, and pulse-filtering effects of the incident light field traversing the distributed Bragg reflector (DBR) mirrors, without substantially increasing the numerical complexity of the solution. As examples, we use cavities containing GaAs quantum wells and transition-metal dichalcogenides (TMDs).