Jones matrix physical parameters for inhomogeneous-field-induced media: optical path integral form

An optical medium whose properties vary under external physical influences is termed an inhomogeneous-field-induced medium (IFIM). Studies on the Jones matrix and its associated physical parameters in IFIMs are crucial for analyzing polarized light transmission. We propose an improved ternary model (ITM) derived from the original ternary model, which provides a rigorous derivation of analytical parameter expressions. Because Jones matrix parameters appear within matrix elements, the derivation is divided into two steps. In step 1, matrix elements are expressed as series sums using cascade modeling; in step 2, Jones matrix parameters are formulated as optical path integrals, supported by proofs and equivalence relations for phase-delay terms. Theoretical analysis demonstrates that the ITM retains unitary matrix properties in homogeneous-field-induced media, confirming its general applicability. Numerical simulations, compared with a distributed parameter model, show that the ITM achieves higher accuracy. Overall, we advance the theoretical understanding of Jones matrix representations in IFIMs and provides a foundation for analyzing optical effects in complex multi-physical environments.