Solving the Inverse Problem of Laser with Complex-Valued Field by Physics-Informed Neural Networks

In the resonator of an actual laser oscillator, the complex-valued laser field is extracted from the gain. The inverse problem of the laser is to construct the gain utilizing the given complex-valued laser field, which is essential for the design purpose. However, it is a challenge for conventional numerical methods because the governing equations cannot be solved inversely. In this paper, a deep learning method based on physics-informed neural networks is introduced to solve the inverse laser problem. 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 comparison between the predictions of PINNs and fast Fourier transform numerical solutions shows the average relative error of gain is 6.78%. This method can be generalized to laser design and optimal problems.