Rapid implementation of the intracavity propagation of complex-valued lasers using physics-informed neural networks

In the resonator of an actual laser oscillator, the complex-valued laser field is extracted from the gain. The propagation of light in a cavity is usually described using the Fast Fourier Transform (FFT). In this paper, a deep learning method based on physics-informed neural networks (PINNs) is introduced to implement the intracavity propagation of complex-valued lasers. The complex-valued laser field and partial differential equation are divided into real and imaginary parts because the optimizer of neural networks cannot deal with the derivation of complex values. A given paraxial wave equation is used as an example to validate the performance of the method. The results of the propagation of complex-valued laser from one interface to another within a cavity containing gain media are presented. The comparative analysis between the predictions yielded by PINNs and numerical solutions via FFT demonstrates remarkable accuracy, with L1 relative errors observed in the real and imaginary components of the laser field at 2.817% and 6.762%, respectively. Notably, the computational efficiency of the trained PINNs is pronounced, requiring a mere 0.43 seconds to reason the complex laser field at any given plane, in contrast to that of up to 17.6 seconds necessitated by FFT computations.