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Our purpose here is to create a model which will describe the behavior of a laser as it travels around in a ring cavity. The ring cavity consists of four mirrors, an input, and a slab of saturable Kerr material. Three of the mirrors have a reflectivity of 100 percent, while the fourth is under 100 percent, as shown in Figure 1.

Figure 1:   Ring Cavity Laser

As the laser light makes a trip through the cavity, the presence of the slab of saturable kerr material causes the phase of the complex of envelope of the electric field to get shifted. Knowing the nature of the system, we can create a mapping which will model the behavior of the laser as it makes subsequent trips around the cavity. We will see that the system is very sensitive to initial conditions and hence the behavior of the system turns out to be chaotic.