Resonance scattering of electromagnetic waves by a Kerr nonlinear dielectric layer

Resonance Properties of Scattering and Generation of Waves on Cubically Polarisable Dielectric Layers

“…the components U(nκ; z), n = 1, 2, 3, z ∈ [−2πδ,2πδ] , of the fields scattered and generated in the non-linear layer. Similar to the results of the papers Angermann & Yatsyk (2011), Angermann & Yatsyk (2010), Shestopalov & Yatsyk (2010), Yatsyk (2007), Shestopalov & Yatsyk (2007), Kravchenko & Yatsyk (2007), Shestopalov & Sirenko (1989), we give the derivation of these equations for the case of excitation of the non-linear structure by a plane-wave packet (20). Taking into account the representation (23), the solution of (21), (C1) -(C4) in the whole space Q := {q =(y, z) : |y| < ∞, |z| < ∞} is obtained using the properties of the canonical Green's function of the problem (21), (C1) -(C4) (for the special case ε nκ ≡ 1) which is defined, for …”

“…The system of ordinary differential equations (24) and the boundary conditions (26) form a semi-linear boundary-value problem of Sturm-Liouville type, see also Angermann & Yatsyk (2010); Shestopalov & Yatsyk (2007;Yatsyk (2007).…”

“…E 1 (r,2κ)=0 and E 1 (r,3κ)=0, reduces to find the electric field component E 1 (r, κ) determined by the first equation of the system (16). In this case, a diffraction problem 8 for a plane wave on a non-linear dielectric layer with a Kerr-type non-linearity ε nκ = ε (L) (z)+ α(z)|E 1 (r, κ)| 2 and a vanishing right-hand side is to be solved, see Angermann & Yatsyk (2008); Kravchenko & Yatsyk (2007); Serov et al (2004); Shestopalov & Yatsyk (2007) ;Smirnov et al (2005); Yatsyk (2006;2007). The generation process of a field at the triple frequency 3κ by the non-linear dielectric structure is caused by a strong incident electromagnetic field at the frequency κ and can be described by the first and third equations of the system (16) only.…”

Mathematical Models of Electrodynamical Processes of Wave Scattering and Generation on Cubically Polarisable Layers

“…The scattering, generating, energetic, and dielectric properties of the nonlinear layer are illustrated by surfaces in dependence on the parameters of the particular problem. The bottom chart depicts the surface of the value of the residual W (Error) of the energy balance Equation (see (17)) and its projection onto the top horizontal plane of the figure. In particular, by the help of these graphs it is easy to localise that region of parameters of the problem, where the error of the energy balance does not exceed a given value, that is |W (Error) | < const.…”

Quasi-optical Systems Based on Periodic Structures

“…We assume that the main contribution to the non-linearity is introduced by the term P (NL) (r, sω) (cf. Yatsyk (2007), Shestopalov & Yatsyk (2007), Kravchenko & Yatsyk (2007), Angermann & Yatsyk (2008), Yatsyk (2006), Schürmann et al (2001), Smirnov et al (2005), Serov et al (2004)), and we take only the lowest-order terms in the Taylor series expansion of the non-linear part P (NL) (r, sω) = P (NL) 1 (r, sω), 0, 0 of the polarisation vector in the vicinity of the zero value of the electric field intensity, cf. (3).…”