Quantal phase of extreme nonstatic light waves: Step-phase evolution and its effects

The phases are the main factor that affects the outcome of various optical phenomena, such as quantum superposition, wave interference, and light-matter interaction. As a light wave becomes nonstatic, an additional phase, the so-called geometric phase, takes place in its evolution. Then, due to this phase, the overall phase of the quantum wave function varies in a nonlinear way with time. Interestingly, the phase exhibits a step-like evolution if the measure of nonstaticity is extremely high. Such an abnormal phase variation is analyzed in detail for better understanding of wave nonstaticity in this work. As the wave becomes highly nonstatic, the phase factor of the electromagnetic wave evolves in a rectangular manner. However, the shape of the electromagnetic field is still a sinusoidal form on account of the compensational variation of the wave amplitude. The electromagnetic field in this case very much resembles that of a standing wave. The effects accompanying the step-phase evolution, such as modification of the probability distribution and alteration of the wave-interference profile, are analyzed and their implications are illustrated.