Quantum Electromagnetics: A New Look—Part II

Abstract

In this work, quantization of electromagnetic fields in a general anisotropic inhomogeneous media is considered. First, the classical Hamiltonian is derived. Once the Hamiltonian is derived, with it the classical equations of motion follow. Next, the fields are elevated to become quantum operators, for which conjugate pairs are endowed with commutators. Since as previously shown, such commutators induce functional derivatives, the quantum equations of motion can be easily derived. Next, the mode decomposition of the fields is demonstrated. Upon substitution into the classical Hamiltonian, each mode then behaves like a simple harmonic oscillator. These oscillators can then be elevated to become quantum harmonic oscillators. Both the traveling wave modes and the standing wave modes are discussed. Furthermore, the longitudinal modes are described. Finally, the case of impressed sources are considered, with the corresponding Hamiltonian and field quantization. The Green's functions for the linear system are presented. Finally, the quantum Maxwell's equations are derived. A short discussion on field-atom interaction is given.