Electromagnetic field quantization in nonlinear and inhomogeneous dielectrics ∗

The electromagnetic field is quantized in nonlinear media whose dielectric functions and nonlinear susceptibilities may vary with space. Given the dielectric function and nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is determined completely by this quantization method. From Heisenberg equations we prove that Maxwell’s equations are satisfied for the field operators. When the nonlinearity goes to zero, this quantization method returns to the generalized canonical quantization procedure developed in Ref.[1] for linear inhomogeneous media. The general formalism is illustrated by applications to quantization of the second-order and third-order nonlinear quasi-steady-state processes. PACS numbers:42.50.-p, 42.65.-k, 11.10.Lm This project was supported by the National Nature Foundation of China. E-mail:[email protected]