QUANTIZED-FIELDS IN A NONLINEAR DIELECTRIC MEDIUM - A MICROSCOPIC APPROACH

Theories which have been used to describe the quantized electromagneti c held interacting with a nonlinear dielectric medium are either pheno menological or derived by quantizing the macroscopic Maxwell equations . Here we take a different approach and derive a Hamiltonian describin g interacting fields from one which contains both field and matter deg rees of freedom. The medium is modeled as a collection of two-level at oms, and these interact with the electromagnetic field. The atoms are grouped into effective spins and the the Holstein-Primakoff representa tion of the spin operators is used to expand them in inverse powers of the total spin. When the lowest order term of the interaction is comb ined with the free atomic and field Hamiltonians, a Hamiltonian descri bing a theory of noninteracting polaritons results. When higher order terms are expressed in terms of polariton operators standard nonlinear optical interactions emerge. These are then compared to the results o f phenomenological and macroscopic theories. The theory is also used t o derive an effective Hamiltonian describing counterpropagating modes in a nonlinear medium.