Determining the dielectric permittivity of a one-dimensionally inhomogeneous plate with a strong frequency dispersion and absorption from the reflection and transmission coefficients of s-polarized waves

Determination of the spatial profiles of all components of the quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

“…(31), we took into account that the component is identically zero in the classes con sidered. At the points z = z 1, 2 , the dimensionless amplitude E 2s (z) satisfies the boundary conditions (32) which are analogous to (16). Here (k z ) and…”

“…(14) and (18) by R s (z) and E 1s (z), respectively, and subtracting the second product from the first, we obtain (19) Integrating equality (19) from z 1 to z 2 and applying the integration by parts to calculate the integral of the right hand side of (19) and the boundary condi tions (16), after slight modifications we arrive at the following Fredholm equation of the first kind for the function (z): (20) with known normalizable kernel .…”

“…On the plane surfaces of the plate, the functions E 1s (z) and H 1p (z) satisfy the boundary condi tions (9) and (10), respectively, which follow immedi ately from Maxwell's boundary conditions. With regard to the notations introduced above, we can rewrite them as (16) …”

“…Equations (28) and (29) allow one to uniquely calculate the function H 2 (z) because the linear dielectric properties of the plate are assumed to be known [15][16][17]. Propagation of a wave with magnetic field strength in the plate gives rise to the nonlinear polarization of the medium:…”

“…The linear permittivity of the plate medium can be assumed to be known because the components of the tensors (z, ω) and (z, 2ω), which have a diagonal form in the classes considered, can be determined by the method proposed in [15][16][17] and experimentally implemented for homogeneous media in [18]. There fore, we assume that the function E 1 (z), which is uniquely defined by (11) and (12), is also known.…”