The Harmonic Oscillator and Quantization of Electromagnetic Fields

Abstract

Maxwell’s equations give a description of electricity and magnetism in terms of the electric and magnetic fields, but say very little about the quanta: electrons and photons, that constitute the fields. This field description treats electric and magnetic phenomena like continuum fluids. By quantization, we can treat electromagnetic phenomena from the perspective of the quanta. This is the basis of quantum photonics. We show that photon behavior can be described mathematically by the formalism of the harmonic oscillator. This important principle enables the description of single photon; that is, quantum photon behavior and the quantization of the electromagnetic field. Creation or annihilation of photons is the way that the electromagnetic field exchanges energy with matter. The creation and annihilation operators can be used to describe the emission and absorption of photons in a direct and transparent way, without having to derive the quantum wavefunction in explicit form. We use these operators to analyze stimulated and spontaneous emission (and absorption) of photons, and thus the performance of Lasers, LEDs and photodiodes.