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Logarithm of the absolute value of the PEC boundary condition error: PEC submicron wire, r σ = 0.5λ 0 , Φ = 75 • .
Source publication
An efficient forward scattering model, based on the Method of Auxiliary Sources, is formulated for perfectly electrically conducting (PEC) and penetrable nanowires on dielectric substrates. The accuracy of the model is investigated parametrically, with emphasis on future application in an inverse scattering scheme. The model is tested on families o...
Citations
... In view of existence results such as the theorem of Cauchy-Kovalevsky [5,Theorem 9.4.5] or the propagation of singularities of solutions to the analytic Cauchy problem [24], this question is central in theà priori estimation of the domain of analytic continuability of solutions across the boundary. This, in turn, is applicable, e.g., in the stability and convergence analysis of 'interior source methods', which is, a family of promising numerical methods for direct and inverse elliptic boundary problems [2,3,[8][9][10][11]. ...
We relate the domains of analytic continuation of Dirichlet and Neumann boundary data for Helmholtz problems in two or more independent variables. The domains are related à priori, locally and explicitly in terms of complex polyrectangular neighbourhoods of planar pieces of the boundary. To this end we identify and characterise a special subspace of the standard pseudodifferential operators with real-analytic symbols. The result is applicable in the estimation of the domain of analytic continuation of solutions across planar pieces of the boundary.
... Fast nondestructive characterization of micro-and nanostructures on substrates is key in the design, production, and quality control of modern functional nanomaterials. A number of forward scattering models for particles on substrates were developed [1][2][3][4][5], and various optical characterization techniques were described and validated experimentally [6][7][8][9][10]. In Bidirectional Reflectance Distribution Function (BRDF) measurements, the considered structure is illuminated monochromatically, and its size, shape, or material composition is estimated from the measured angular resolved reflected field intensity. ...
... Therefore, the SW cross-section estimation is here based on a single BRDF measurement over a relatively narrow, 40° aperture. In Karamehmedović et al. [5,11] we described an efficient forward scattering model applicable in the numerical reconstruction of submicron particles on perfectly planar ('smooth') substrates, based on a single measured angular-resolved scattering pattern. In [11] we used this model in conjunction with the decomposition method, described in general in Colton and Kress [12], Section 7.3, to estimate the cross-section radius of perfectly conducting and silver (Ag) submicron wires on smooth Si substrate from simulated scattering data. ...
... In [11] we used this model in conjunction with the decomposition method, described in general in Colton and Kress [12], Section 7.3, to estimate the cross-section radius of perfectly conducting and silver (Ag) submicron wires on smooth Si substrate from simulated scattering data. In this paper, we extend the scattering model of [5,11] to handle particles on rough substrates, and we validate the model against experimental data. The substrate roughness is represented by a heuristic, denoised surface transfer function computed from the measured bare-substrate BRDF. ...
An efficient forward scattering model is constructed for penetrable 2D submicron particles on rough substrates. The scattering and the particle-surface interaction are modeled using discrete sources with complex images. The substrate micro-roughness is described by a heuristic surface transfer function. The forward model is applied in the numerical estimation of the profile of a platinum (Pt) submicron wire on rough silicon (Si) substrate, based on experimental Bidirectional Reflectance Distribution Function (BRDF) data.
... In Karamehmedović et al. [15], we made an extensive numerical study of an efficient MAS-based model for forward scattering by PEC and penetrable submicron wires on substrates (see Eremina et al. [16,17] for a related model for gold and silver spheroidal particles on glass.) Our purpose here is to use the model of [15] to construct an efficient inversion scheme of the Kirsch-Kress type for sizing of such PEC and highly conductive penetrable wires. ...
... In Karamehmedović et al. [15], we made an extensive numerical study of an efficient MAS-based model for forward scattering by PEC and penetrable submicron wires on substrates (see Eremina et al. [16,17] for a related model for gold and silver spheroidal particles on glass.) Our purpose here is to use the model of [15] to construct an efficient inversion scheme of the Kirsch-Kress type for sizing of such PEC and highly conductive penetrable wires. As a test problem, we estimate the cross-section radius of a PEC or silver (Ag) penetrable wire positioned on a semi-infinite silicon (Si) substrate. ...
... To describe how the objective functional f is computed, we need to briefly recapitulate the forward model for PEC particles on substrates examined in Karamehmedović et al. [15]. In Figure 1, the incident field propagates in the negative y direction, and it is given by ...
A numerical method is presented for sizing of highly conductive penetrable and perfectly electrically conducting (PEC) submicron wires on substrates. For efficiency, the Method of Auxiliary Sources is used in the forward model of the inverse Kirsch-Kress Method. The radius of the circular cross section of PEC and silver wires positioned on a semi-infinite silicon substrate is estimated based on numerically simulated scattered far field. The illumination is monochromatic, transverse electric (TE) polarised, and with fixed angle of incidence. Average relative errors smaller than 1% and 5% are achieved for PEC and penetrable wires, respectively, in the dynamic ranges 0.2-1.3 and 0.8-1.3 times the operating free-space wavelength, respectively. In all cases, the inversion time is less than 1 sec.
We use experimental Bidirectional Reflectance Distribution Function data to construct a heuristic surface transfer function for a rough contaminated substrate. The transfer function is then used in conjunction with our already validated, efficient numerical solver for scattering by particles on smooth surfaces to achieve fast and accurate computation for scattering by nano-structures embedded in rough substrates. We show that the order in which the heuristic surface transfer function and the scattering solver are used influences the numerical results.
