An Experimental "Toy" Model of a Randomly Fluctuating "Optical Field"

To gain some insight into the characteristics of fluctuating optical fields, we present here the results of what we hope is an instructive Mathematica experiment.  In essence, we attempt to model the output of an oscillator -- e.g.,a radiating atom --which is interrupted and dephased by a set of random collisions. That output over some short interval of time is depicted below

COLLISION INTERRUPTED OSCILLATOR

The amplitude of the oscillator is assumed to be constant in time, but its phase is randomly interrupted at a set of  collision times which are distributed normally-- i.e. according to a Gaussian probability distribution function. The distribution is characterized by a mean collision time  and a variance of .  A sample of the random phase modulation is shown below:

In the next figure the experimentally observed Fourier spectrum (magnitude) of the collision-broadened (phase modulated) oscillator is compared with a similar experimental observations of the spectrum of a stable oscillator at the same nominal frequency -- in this case 

Looking in a bit more detail, the experimentally observed real and imaginary components of the collision-broadened and stable spectrum is shown in the next figure



In the next set of figures, the experimentally observed power spectrum of the phase modulated signal is compared to that of a stable oscillator at the same nominal frequency.
 




In the next set of figures, the experimentally observed auto correlation of the phase modulated signal is compared to that of a stableoscillator at the same nominal frequency.
 
 

For comparison we look also at the case of 

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This page was prepared and is maintained by R. Victor Jones, jones@deas.harvard.edu
Last updated April 24, 2000