Quantification and analysis of the nonlinear effects in spectral broadening through solid medium of femtosecond pulses by neural network

Supercontinuum generation has been widely applied in laser spectroscopy and few-cycle pulse generation. It is composed of complex and unmeasurable nonlinear optical effects, which influence the final broadened spectrum markedly. To describe and characterize the two key processes, the Kerr effect and ionization, we employ two nonlinear integrals, including the common B integral for the Kerr effect and a P integral for ionization or plasma effect. With these integrals, the contributions of Kerr and plasma effects in the supercontinuum generation are identified and determined quantitatively. Then we utilize machine learning to construct a multilayer perceptron neural network to obtain the solution of the propagation equation for a femtosecond pulse in a solid medium. We employ supervised and unsupervised training with both experimental and simulation data to train the neural network for a better accuracy of the calculation. The trained network can take the input and broadened spectra of the pulse to compute initial laser parameters and the B and P integrals instantly so that the contributions of Kerr and plasma effects in the supercontinuum generation may be quantified in real time, unveiling the nonlinearities behind the spectral evolution. This method provides a more accurate understanding of the physics of the entangled nonlinear optics effects and a faster and more convenient tool in the investigation of nonlinear optics.