Deduction of second order time-varying parameter in dispersive media

To reach the second order time domain parameter of dispersive medium, a new deduction method is presented. The observed medium is the water of Debye type, where a plane wave is incident upon air-water interface that results in reflection and transmission coefficient in frequency domain. The deduction processes are: the frequency domain transcendental equations of above parameters are first set up; then time domain transcendental equations of above parameters are reached by the transform; based on an iterative process the expected time domain parameters are last found out. In paper the method has been validated. The deduction process and technical points are described. The obtained results are discussed that exhibits causality. It is expected that the deduction method has a potential of extension application.