Figure 7: Unidirectional reflectionlessness of a planar inhomogeneous dielectric structure in which the spatial distributions of the real and imaginary parts of the dielectric permittivity are related by Kramers-Kronig relations.

(A) A wave propagating in the *x*–*y* plane in an inhomogeneous medium with permittivity *ε*(x) (indicated by blue shading). The TE polarization has an electric field pointing only along *z* and the TM polarization has a magnetic field pointing only along *z*. When the real (blue) and imaginary (red) parts of the permittivity are related to one another by the Kramers-Kronig relations (as in B), then the reflection vanishes for all angles of incidence. (B) Permittivity profile *ε*(*x*) given by Equation (7) for parameters *A*=2 and *ξ*=0.1*λ* with *λ*=2π/*k*_{0}. (C and D) Absolute values of the electric field of a line source placed at positions *x*=−5*λ* (C) and *x*=+5λ (D) in the permittivity profile. The region between the vertical dashed lines in (C) indicates the region plotted in (B). (E and F) As in (C and D), with identical parameters, but taking only the real (E) and imaginary (F) parts of the permittivity. The absence of any oscillations in (C) shows that the reflection is completely suppressed for incidence from the left for all incident angles [100].