Dynamic Extended Beer–Lambert Law with Photodissociation and Recombination

A dynamic extended Beer–Lambert law with photodissociation and recombination is proposed, which is built to describe the interactions between light and molecular gases. The model comprises two spatiotemporally coupled first-order nonlinear partial differential equations. Numerical solutions of these equations systematically reveal the nonlinear transmission properties and steady-state dissociation behavior of the medium from the weak- to intense-light regime. In the weak-light limit, the model naturally reduces to the classic Beer–Lambert law, with the system reaching a steady state characterized by high molecular density and exponential light attenuation. Conversely, in the intense-light regime, low molecular concentration and pronounced photoinduced transparency occurs, and light attenuates linearly instead of exponentially. A method for measuring the recombination rate constant under steady-state conditions is presented, which imposes significantly lower demands on both the light intensity and the temporal resolution of the measurement equipment compared to conventional approaches.