Wave scattering from a periodic random surface generated by a stationary binary sequence

Diffraction and scattering of TM plane waves from a binary periodic random surface

“…Here, θ is the angle of incidence, k L is the spatial angular frequency of the period L, and 'Im' denotes the imaginary part. Note that a periodic stationary process U (x, z, ω) is not periodic for one sample point ω, but the ensemble average U (x, z, ω) becomes periodic, and U (x, z, ω) satisfies the shift invariance property [2]:…”

“…Although they are theoretically interesting and practically important, diffraction and scattering from such a binary periodic random surface have not been extensively studied. In previous papers [1,2], however, we have studied the diffraction and scattering from a binary periodic random surface generated by a stationary binary sequence. But our discussions were limited to TE wave cases.…”

“…For analysis, we employ the stochastic functional approach [1][2][3][4], which is made up of several steps. First, since the binary sequence is an independent stationary sequence, the binary periodic random surface becomes a periodic stationary process and has the shift invariance property in the probabilistic sense.…”

“…Then, due to the shift invariance property, the scattered wave has the stochastic Floquet form, which is a product of an exponential phase factor and an unknown periodic stationary process. Then, such an unknown periodic stationary process is expressed by a harmonic series representation [2,3], which is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence [2,5,6] generating the periodic random surface and they are represented by a sum of orthogonal binary functional series with band-limited binary kernels [1].…”

“…Then, such an unknown periodic stationary process is expressed by a harmonic series representation [2,3], which is a 'Fourier series' with 'Fourier coefficients' given by mutually correlated stationary processes. These stationary processes are regarded as stochastic functionals of the binary sequence [2,5,6] generating the periodic random surface and they are represented by a sum of orthogonal binary functional series with band-limited binary kernels [1]. Hierarchical equations to determine such band-limited binary kernels are derived from the Neumann boundary condition without approximation.…”