Quantum theory of electromagnetic field propagation

Jan Peřina

Nobuo Nagai, Hirofumi Sanada, Takashi Yahagi

In the electromagnetic field formed by coaxial cables, electromagnetic waves of different frequencies are shown to propagate at the same speed (the speed of light c). Therefore, the variational method, which is based on the fact that electromagnetic waves of different frequencies have different propagation speeds, cannot be applied. In this session, the characteristics of light propagating through an electromagnetic field of glass, suitable for applying the variational method and for constructing lenses, are determined. Although the electromagnetic field is derived from the properties of dielectrics, it has been demonstrated to be equivalent to a circuit that represents the Schrödinger equation used in quantum mechanics. In other words, it may be possible to apply electromagnetic fields from classical physics (circuit theory) to quantum mechanics. Quaternions and wave functions that are considered to be related to complex functions will be the topic of future studies because the Schrödinger equation is a complex function.

Jan Peřina

J Hamilton

It is shown that a careful examination of the concepts involved in radiation damping theory makes it possible to treat the propagation of energy from one atom to another through the electromagnetic field. An exact and continuous solution of the propagation problem is given.

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

Izo I. Abram, E. Cohen

Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.