Theory of Optical Bistability in Nonlinear Media for Slowly Varying Incident Intensity
Many treatments of bistability in nonlinear media describe the phenomena in the regime when the incident intensity varies slowly compared with the material response time by writing down the transmission of a Fabry-Perot interferometer, τ, as a function of the in-tracavity phase shift in a roundtrip pass, δ: τ = (1+F sin2 δ/2)−1 where F = 4r/(1-r)2 and r is the reflectivity from the surface of the material1,2,3. When the index of refraction is a function of the intensity inside the cavity (Iin), the phase shift is intensity-dependent, and it appears that one can substitute the expression for the intensity-dependent phase shift into the expression for the transmission thereby obtaining an expression for the transmission as a function of the intensity inside the cavity. When this equation is solved in conjunction with an expression for the transmission as a function of the ratio of Iin to the incident intensity (I0), one obtains an expression for τ(I0) which may be multivalued. The flaw in this argument is that the expression for the transmission as a function of phase shift is derived assuming 1inear wave propagation where the superposition principle applies2. But the propagation equation is nonlinear, and the superposition principle is not valid!
KeywordsCoherence Sine Refraction Mandel
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