A Modified Nonlinear Lorentz Model for Third-Order Optical Nonlinearity

Yao Xia () and Jinjie Liu
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Yao Xia: Division of Physics, Engineering, Mathematics, and Computer Science, Delaware State University, Dover, DE 19901, USA
Jinjie Liu: Division of Physics, Engineering, Mathematics, and Computer Science, Delaware State University, Dover, DE 19901, USA

Mathematics, 2025, vol. 13, issue 8, 1-17

Abstract: In this study, we propose a new nonlinear polarization model that modifies the polarization equation to account for the material’s nonlinear response. Specifically, the nonlinear restoring force in our model is reformulated as an electric field-dependent function, derived from the nonlinear Lorentz model. Additionally, we perform a comparative analysis of the Kerr model, the Duffing model, the nonlinear Lorentz model, and our modified nonlinear Lorentz model (MNL) by solving Maxwell’s equations using the finite-difference time-domain (FDTD) method. This research focuses on the third-order nonlinearity of these models under varying light intensities and different ratios of resonant frequency to carrier frequency. First, in the example we studied, our results show that the MNL model produces results closer to the Kerr model when the light intensity is significantly high. Second, the comparison under different resonant frequencies reveals that all models converge to the Kerr model when the carrier frequency is much lower than the resonant frequency. However, when the carrier frequency significantly exceeds the resonant frequency, the differences between the Kerr model and the other models become more noticeable. The third-order nonlinearity of our MNL model aligns more closely with the Kerr model than the nonlinear Lorentz and Duffing models do when the ratio of resonant frequency to carrier frequency is between 1 and 2.

Keywords: Maxwell’s equations; finite-difference time-domain method (FDTD); Duffing model; Kerr nonlinearity; nonlinear Lorentz model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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