This paper reports that in the quantization of electromagnetic field in the dielectrics, the wave equation with regard to the Green function is analytically solved by a direct integral method for a quadratic continuous nonlinear absorptive dielectric medium. The quantization of the electromagnetic field in such a nonlinear absorptive dielectric is carried out for which the material dielectric function is assumed as a separable variable about the frequency and the space coordinate. The vacuum field fluctuations for different spatial continuous variations of dielectric function are numerically calculated, which shows that the present result is self-consistent.
A new approach is developed to solve the Green's function that satisfies the Hehmholtz equation with complex refractive index.Especially,the Green's function for the Helmholtz equation can be expressed in terms of a onedimensional integral,which can convert a Helmholtz equation into a Schrdinger equation with complex potential.And the Schrdinger equation can be solved by Feynman path integral.The result is in excellent agreement with the previous work.
