Reconstruction of dielectric permittivity profile of a plate with strong frequency dispersion

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

“…Multiplying Eqs. (15) and (24) by R p (z) and H 1p (z), respectively, and subtracting the second product from the first, we obtain…”

“…Now, let us consider what kind of spectroscopic information can be obtained from the coefficients of transformation of an s polarized fundamental wave into a p polarized wave of the second harmonic. Such a transformation is described by formulas (11), (12), (15), and (17). On the right hand side of (15), we know the function (z) because the profile of the component (z) = σ 1 (z) in the class 3 can be recon structed by the above described procedure (in the other classes considered, (z) ≡ 0).…”

“…On the right hand side of (15), we know the function (z) because the profile of the component (z) = σ 1 (z) in the class 3 can be recon structed by the above described procedure (in the other classes considered, (z) ≡ 0). Let R p (z, k z ) be a continuous solution to the homo geneous equation (15) (24) that satisfies the boundary conditions…”

“…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.…”