Bistable reflection at the nonlinear interface with linear magnetic properties

The bistable reflection effects of an incident homogeneous plane wave upon an interface between a linear and nonlinear magnetic media are studied. At a nonlinear interface, a plane wave is incident from a linear medium with permittivity e and magnetic permeability μ upon the boundary of a negatively nonlinear medium whose permittivity e varies nonlinearly with the input field intensity. The magnetic permeability μ of the nonlinear medium is constant. It is shown that as the angle of incidence or the intensity of the incident field is varied, hysteresis jumps of the reflection coefficient can be observed as the interface jumps from the transmission or partial reflection regime to the total internal reflection (TIR) regime, and back. No assumption is made about the smallness of the amount of nonlinearity or the incident angle. The derivations of the nonlinear equations associated with such a nonlinear interface are shown in detail. The effects upon the equations when magnetic permeabilities and large nonlinearities are considered can be seen by comparison with previous works. The reflection characteristics are found to be no longer independent of the input wave polarization.