The scattering of left circularly polarized wave from a perfectly electric conducting (PEC) rough surface in isotropic chiral media is investigated. Since a slightly rough interface is assumed, the solution is obtained using perturbation method. Zeroth-order term corresponds to solution for a flat interface which helps in making a comparison with the results reported in the literature. First-order term gives the contribution from the surface perturbations, and it is used to define incoherent bistatic scattering coefficients for a Gaussian rough surface. Higher order solution is obtained in a recursive manner. Numerical results are reported for different values of chirality, correlation length, and rms height of the surface. Diffraction efficiency is defined for a sinusoidal grating.

Scattering from rough surfaces is an interdisciplinary research field which has many applications in optics, communication, and remote sensing. The simplest possible problem is an impenetrable rough interface, and the solution has widely been investigated [

The regions of validity of PM and KA are also well defined [

Numerical methods such as method of moments (MoM) [

Scattering from a penetrable surface has been discussed in [

A chiral medium has widely been explored, and many applications have been proposed in chemistry, optics, elementary particle physics, and electromagnetics [

In all the above cited work, the interfaces are assumed to be flat. At some frequencies, the interface can behave rough. The roughness affects the wave propagation, radiation, and scattering properties. The applications of rough surface scattering can be found in antenna theory, communication, and remote sensing. In this paper, the problem of reflection from a PEC rough interface placed in chiral medium is presented. Rayleigh hypothesis is utilized to get the scattered field. Zeroth-order solution obtained by PMs is used to make a comparison with that of a PEC flat interface in chiral media. Section

Consider a PEC rough surface placed in a chiral medium as shown in Figure

Scattering from a PEC rough surface in chiral media.

A left circularly polarized (LCP) plane wave is incident on the surface at an angle

The field scattered due to PEC rough surface can be written as

The perturbation series of unknown coefficients in spectral domain is

It is assumed that the following conditions are satisfied:

Using the power series for exponentials, the scattered field can be written as

The boundary condition is given by

Applying the above boundary condition at

The above infinite series is solved for unknown coefficients. The zeroth-order terms of both the above equations are

Taking the Fourier transform of the above equations gives

Solving the above equations, zero-order coefficients are obtained:

Putting in (

It corresponds to solution for a flat interface in chiral media, and the expressions are in agreement with those reported in [

Taking the Fourier transfer of the above equations,

From the above equations, it can be noted that the first-order solution can be written in terms of zeroth-order solution. Solving the above equations, first-order coefficients may be written as

Finally, the solution up to any order can be found via recursive computation.

Numerical implementation of the theoretical formulation is done in this section. A rough surface profile has to be selected, and its Fourier transform is calculated. Two cases have been considered here: one is a sinusoidal surface and the other is a Gaussian rough surface. First, consider a sinusoidal surface defined as

In a similar way, the expressions for RCP scattered field can be written. The

Now, consider a rough surface with Gaussian roughness spectrum. The power spectral density

Since both LCP and RCP waves are scattered for LCP incidence, the LCP and RCP incoherent bistatic scattering coefficients can be expressed as

Figure

LCP and RCP scattering coefficients for different values of chirality, where φ_{i} = 30°, ε_{r} = 4, _{c} = 0.35.

LCP and RCP scattering coefficients for different values of rms height, where φ_{i} = 30°, ε_{r} = 4, _{c} = 0.35.

LCP and RCP scattering coefficients for different values of correlation length, where φ_{i} = 30°, ε_{r} = 4,

Scattered field from a PEC rough surface in chiral media has been studied. PM is applied to obtain scattered field components. In general, the higher order scattered field can be obtained using lower order coefficients by utilizing the recursive nature of the problem. Two cases, sinusoidal and Gaussian rough surfaces, are considered, and the expressions of the LCP and RCP incoherent bistatic scattering coefficients have been reported. Scattering pattern is observed for chirality parameter, height, and correlation length of the Gaussian rough surface. Diffraction efficiency has been defined for a rough surface with sinusoidal profile. This analysis can also be used for a triangular grating.

No potential conflicts of interest are reported by the authors.