Coupled Pendulums: A Classical Depiction of Laser Oscillation, Phase Diffusion and Laser Line-width

Abstract

 In this work we have presented an analogy between the coupled vibrations of two classical oscillators and the oscillations that take place in a laser cavity. Our aim is to understand classically the causes that lead to the phase diffusion in a system of coupled classical oscillators and to explore possibilities of any relationship between phase fluctuation and the frequency difference. The equations of motion for the classical oscillators have been derived and solved, for different values of coupling coefficients, to obtain the expressions for the mode frequencies¹.The solutions, while plotted graphically have led us to the conclusion that in classical oscillators the mode frequencies of the oscillators are far apart if their oscillation is heavily coupling dependent and consequently the phase relationship of the oscillators fluctuate vigorously and frequently, which is the converse of what happens in a laser cavity consisting atomic oscillators.