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Optical materials with a distribution of loss and gain can be used to manipulate waves in fascinating ways, seemingly impossible with ordinary lossless materials. Some recent results have shown that (for planar media) if the spatial distributions of the real and imaginary parts of the permittivity are related to one another by the Kramers-Kronig relations, then reflection can be eliminated. Moreover, if an additional "cancellation condition" is satisfied, then a material can be made invisible for incidence from one side. Here, we give a simple demonstration of these results that should be accessible to undergraduates. In addition, we show how this simple method can be used to prove results about the reflection from permittivity profiles, without ever requiring an exact solution of the Helmholtz equation. [ABSTRACT FROM AUTHOR]

When a planar dielectric medium has a permittivity profile that is an analytic function in the upper or lower half of the complex position plane x = x′ + ix″ then the real and imaginary parts of its permittivity are related by the spatial Kramers-Kronig relations. We find that such a medium will not reflect radiation incident from one side, whatever the angle of incidence. Using the spatial Kramers-Kronig relations, one can derive a real part of a permittivity profile from some given imaginary part (or vice versa) such that the reflection is guaranteed to be zero. This result is valid for both scalar and vector wave theories and may have relevance for designing materials that efficiently absorb radiation or for the creation of a new type of anti-reflection surface. [ABSTRACT FROM AUTHOR]

The transmission of a wave through a randomly chosen "pile of plates" typically decreases exponentially with the number of plates, a phenomenon closely related to Anderson localization. In apparent contradiction, we construct disordered planar permittivity profiles which are complex valued (i.e., have reactive and dissipative properties) that appear to vary randomly with position, yet are one-way reflectionless for all angles of incidence and exhibit a transmission coefficient of unity. In addition to these complex-valued "random" planar permittivity profiles, we construct a family of real-valued, two-way reflectionless and perfectly transmitting disordered permittivity profiles that function only for a single angle of incidence and a narrow frequency range. [ABSTRACT FROM AUTHOR]

This Letter presents a method for making an uneven surface behave as a flat surface. This allows an object to be concealed (cloaked) under an uneven portion of the surface, without disturbing the wave propagation on the surface. The cloaks proposed in this Letter achieve perfect cloaking that only relies upon isotropic radially dependent refractive index profiles, contrary to those previously published. In addition, these cloaks are very thin, just a fraction of a wavelength in thickness, yet can conceal electrically large objects. While this paper focuses on cloaking electromagnetic surface waves, the theory is also valid for other types of surface waves. The performance of these cloaks is simulated using dielectric filled waveguide geometries, and the curvature of the surface is shown to be rendered invisible, hiding any object positioned underneath. Finally, a transformation of the required dielectric slab permittivity was performed for surface wave propagation, demonstrating the practical applicability of this technique. [ABSTRACT FROM AUTHOR]