Cavities: Photon Lifetime

The photon lifetime is a time constant
that describes the decay (or the growth) of energy in a cavity. We can
calculate the photon lifetime by considering the rate equation (a differential
equation with time as the independent variable) for the decay of an
initial bunch of photons, *Np*, in the cavity. The applet below
shows a simple two mirror cavity with a "pulse" of photons bouncing back
and forth.

Notice that the number of photons decays after each
reflection from a mirror. The reflection of mirrors 1 and 2 in the picture
are denoted as *R1* and *R2*, respectively. The value of *R*
will be from 1 to 0 (i.e., completely reflecting *R* = 1, and completely
transmitting *R* = 0). The number of photons that left the cavity after one round
trip is [1-*S*]*Np*, where *S* is called the survival factor
and is *R1*R2* for this two mirror cavity.

The photon lifetime for a cavity with refractive index n, and cavity length of l, is defined as:

Comments
to *anc@buffalo.edu*
or *vpc3@eng.buffalo.edu*

Copyright (c) Prof. Alexander Cartwright and Vamsy Chodavarapu

* Department of Electrical Engineering*

*University at Buffalo*, 1999-2001