Phase jumps of π in a laser with a periodically modulated injected signal

Abstract

The dynamics of the phase variable in a laser with injected signal are analyzed as the injected amplitude is modulated by a small periodic term. This term induces quasiperiodic oscillations in the real and imaginary parts of the field variable which make the phase dynamics much more complex than the constant injected signal case in which the real and imaginary parts of the field are periodic. Two-timing analysis, in which the frequency of the periodic component of the injected signal is represented as a small deviation from the fast-time frequency, yields slow-time evolution equations of a periodically forced Toda oscillator. The dynamics near resonance are discussed. A map determining whether the phase jumps up or down by π units is developed based on the slow-time evolution equations.