Nonlinear Scattering by Anisotropic Dielectric Periodic Structures

Abstract

The combinatorial frequency generation by the periodic stacks of binary layers of anisotropic nonlinear dielectrics is examined. The products of nonlinear scattering are characterised in terms of the three-wave mixing processes. It is shown that the intensity of the scattered waves of combinatorial frequencies is strongly influenced by the constitutive and geometrical parameters of the anisotropic layers, and the frequency ratio and angles of incidence of pump waves. The enhanced efficiency of the frequency conversion at Wolf-Bragg resonances has been demonstrated for the lossless and lossy-layered structures.

Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers

“…However, the concurrent increase of losses considerably reduces the gain. Alternatively, CFG efficiency proved to be higher not at the band edges but in the transparency bands, especially at Wolf-Bragg resonances of the stacks [40]. Additionally, CFG involving two pump waves of different frequencies ω 1 and ω 2 , incident at dissimilar angles, offers extra degrees of freedom in controlling the frequency mixing process and spectrum.…”

“…To evaluate the field amplitudes F r,t in Equation (A12), it is necessary to relate the fields of the nonlinear products generated inside the stack to the field emitted from the QPS. This is accomplished by enforcing the tangential field continuity at the stack external interfaces and applying the modified TMM [40] …”

Nonreciprocal nonlinear scattering by stacked magnetoactive semiconductor layers

“…three-wave mixing process involves simultaneous solution of Maxwell's equations, the current continuity equations, describing the nonlinear dynamics of charges, and the equation of carrier motion. The solution of this problem is considerably simplified by noting that at the pump wave frequencies, the magnetised semiconductor layers can be described by the equivalent linear permittivity tensors for magnetoactive plasma [7] with the components The modified transfer matrix approach [8] has been applied to obtain closed-form expressions for the nonlinear scattering coefficients F r and F t of the waves emitted at the combinatorial frequency ω 3 in the reverse and forward directions of the z-axis, respectively. The amplitudes of the waves generated inside the stack and radiated into the surrounding linear media have been deduced by enforcing the boundary conditions of field continuity at the layer interfaces and the stack surfaces at z = 0, L. The obtained analytical expressions have enabled insight in the nonreciprocal properties of the nonlinear scattering and frequency mixing by the periodic stacks of magnetically biased semiconductor layers illuminated by a pair of obliquely incident plane TM waves.…”

Resonant Combinatorial Frequency Generation Induced by a <italic>PT</italic>-Symmetric Periodic Layered Stack

“…The interest to this topic is connected with the fact that the mixing process in the nonlinear artificial structures can be controlled not by only tailoring the coherence and localisation of the interacting waves but also by altering independently the intensity and phasing of individual pump waves [9]. In earlier studies, it was demonstrated that CFG by two pump waves of frequencies   and   , incident at dissimilar angles, offers additional degrees of freedom in controlling the frequency mixing process and spectrum [10]- [11].…”

“…The wavenumber 2 , In order to examine the three-wave mixing process in the structures, it is necessary to generalise the transfer matrix method (TMM) based analysis for the case of two obliquely incident pump waves [10]. Enforcing the periodic boundary conditions through the whole periodic structure, the fields at the stack outer interfaces can be presented in the form and E x ( 3 ) continuity at the structure interfaces.…”