Investigation of optical properties of multilayer dielectric structures using prism-coupling technique

Reconstruction of Dielectric Constants of Core and Cladding of Optical Fibers Using Propagation Constants Measurements

“…We use Tikhonov regularization algorithm (see [20]) which is based on the minimization of the Tikhonov functional. Thus, to find regularized solution ε α of problem (16), we minimize the Tikhonov regularization functional…”

“…We now assume that the operator F (ε) defined in (16) is one-to-one and denote by V r (ε) neighborhood of the radius r of ε such that…”

“…In our computations we used p = 0.05 and thus, the noise level was 5%. In the numerical experiments we accounted this noise in perturbed operator (16) and also in the perturbed initial approximations ε 0 = ( ε 0,i , ε 0,e ) = ( β 2 1 /k 2 1 , β 2 1 /k 2 1 ) that we used in (17) instead of ε 0 . The regularization parameter was α = 0.01.…”

“…In our computations we used p = 0.05 and thus, the noise level was 5%. In the numerical experiments we accounted this noise in perturbed operator (16) and also in the perturbed initial approximations…”

“…Universal numerical methods of reconstruction of refractive index of dielectric objects are designed for coefficient inverse diffraction problems and ignore the waveguide properties of the devices (see, for example, [4]). The methods for the determination of the optical characteristics of dielectric waveguides are proposed for waveguides of some special forms (see, for example, [16,18]). For instance, the waveguide spectroscopy is widely used for planar (one-dimensional) multi-layered waveguides [11].…”