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Mie theory is a powerful method to model electromagnetic scattering from a multilayered sphere. Usually, the incident beam is expanded to its vector spherical harmonic representation defined by beam shape coefficients, and the multilayer sphere scattering is obtained by the T-matrix method. However, obtaining the beam shape coefficients for arbitrarily shaped incident beams has limitations on source locations and requires different methods when the incident beam is defined inside or outside the computational domain or at the scatterer surface. We propose a 3D angular spectrum method for defining beam shape coefficients from arbitrary source field distributions. This method enables the placement of the sources freely within the computational domain without singularities, allowing flexibility in beam design. We demonstrate incident field synthesis and spherical scattering by comparing morphology-dependent resonances to known values, achieving excellent matching and high accuracy. The proposed method has significant benefits for optical systems and inverse beam design. It allows for the analysis of electromagnetic forward/backward propagation between optical elements and spherical targets using a single method. It is also valuable for optical force beam design and analysis., Agencia Estatal de Investigación (PID2019-107885GB282 C31/AEI/10.13039, PRE2018-084326); Assessment of the Graft 281 Rejection Using Millimeter Waves; Academy of Finland (327640)., Peer Reviewed, Postprint (published version)

In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1 and y0 y0 are arbitrary nonzero real numbers.

In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1 and y0 y0 are arbitrary nonzero real numbers.

In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn, n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1 and y0 y0 are arbitrary nonzero real numbers.

In this paper, we investigate the form of the solutions of two systems of rational difference equations of second order, where the initial conditions are arbitrary nonzero real numbers.

In this paper, we investigate the form of the solutions of two systems of rational difference equations of second order, where the initial conditions are arbitrary nonzero real numbers.

In this paper, we investigate the form of the solutions of two systems of rational difference equations of second order, where the initial conditions are arbitrary nonzero real numbers.

Improving the longitudinal modes coupling in layered spherical structure contributes significantly to corneal terahertz sensing, which plays a crucial role in the early diagnosis of cornea dystrophies. Using a steel sphere to calibrate reflection from the cornea sample assists in enhancing the resolution of longitudinal modes. The requirement and challenges toward applying the calibration sphere are introduced and addressed. Six corneas with different properties are spotted to study the effect of perturbations in the calibration sphere in a frequency range from 100 GHz to 600 GHz. A particle-swarm optimization algorithm is employed to quantify corneal characteristics considering cases of accurately calibrated and perturbed calibrated scenarios. For the first case, the study is carried out with signal-to-noise values of 40 dB, 50 dB and 60 dB at waveguide bands WR-5.1, WR-3.4, and WR-2.2. As expected, better estimation is achieved in high-SNR cases. Furthermore, the lower waveguide band is revealed as the most proper band for the assessment of corneal features. For perturbed cases, the analysis is continued for the noise level of 60 dB in the three waveguide bands. Consequently, the error in the estimation of corneal properties rises significantly (around 30%)., This research was funded by the Agencia Estatal de Investigación PID2019-107885GB-C31/AEI/10.13039, PRE2018-084326, and Academy of Finland Project number 327640., Peer Reviewed, Postprint (author's final draft)

Coupling to longitudinal modes of thin spherical shells, under Gaussian-beam illumination, was explored with a theoretical method based on Fourier-optics analysis and vector spherical harmonics and was scrutinized with an experimental setup. For the theory part, the illumination frequency band was fixed between 100–600 GHz and the outer spherical shell radius of curvature and thickness are 7.5 mm and 0.5 mm, respectively. The shell material was either the lossless cornea or an aqueous effective media representing the cornea. Six different beam-target strategies were introduced being potential candidates for maximum coupling. Two dispersion-tuned beam ensembles with strongly frequency-dependent phase center location have been created with a fixed incident beam 1/e radius and radius of curvature called forward strategies. These computations of different alignments were continued with four beam ensembles of frequency-invariant phase center, constructed from fits to experimental data, oriented at four different axial locations with respect to the spherical shell center of curvature, they are called reverse strategies. Coupling efficiency for all strategies was calculated for different targets including perfect electrical conductor (PEC) sphere, PEC core covered by a cornea loss-free layer and cornea. All scattering strategies contrasted to scattering from equivalent planar targets as a reference with maximum coupling. The results show that, under an ideal calibration, forward strategies are a closer approximation to the plane-wave condition for the cornea. An experimental setup was assembled to explore the simulation approach in a frequency range between 220 GHz to 330 GHz. Two different quartz samples with permittivity of 4.1 were mounted on a water core, acting for a cornea. The first and second quartz radius and thickness were 7.5 mm and 0.5 mm and 8 mm and 1 mm, respectively. An adequate agreement between theory and experiment was confirmed. A particle optimisation, Funding. Agencia Estatal de Investigación (PID2019-107885GB-C31/AEI/10.13039, PRE2018-084326); Academy of Finland (327640)., Peer Reviewed, Objectius de Desenvolupament Sostenible::3 - Salut i Benestar, Postprint (author's final draft)

Submillimeter-wave and THz sensing of cornea leverage the layered tissue structure for assessments of corneal water content and thickness. The cornea is bounded by air on the anterior and an optically thick body of water on the posterior and thus presents as a lossy thin film lying atop a lossy termination. Resolution of the cornea’s lossy longitudinal modes via frequency domain reflectometry in a band sufficiently low (e.g. 220 GHz – 330 GHz) for significant penetration allows simultaneous estimates of corneal tissue water content (CTWC) and central corneal thickness (CCT). However, since the cornea is spherical, efficient coupling to longitudinal modes requires normal incidence across the interrogated area and thus a converging spherical phase front whose curvature matches the corneal surface curvature [1, 2]., Peer Reviewed, Postprint (published version)

An efficient Fourier optics method for synthesizing a required incident beam to compute the internal and scattered electromagnetic fields from known spherical surface electric field distribution is presented. © 2021 IEEE, Peer Reviewed, Postprint (published version)

Wave scattering from a human cornea illuminated with a submillimeter-wave Gaussian beam is explored with Fourier analysis. This new approach enabled us to investigate the cornea as a coated sphere rather than a homogenized one. The cornea was modeled as an aqueous spherical shell using effective medium theory, with 60 percent water, enclosing a sphere of pure water. The corneal model was illuminated at 220 GHz – 330 GHz. The interaction of the incident and back-reflected beam, back-scattered field, and back-scattering from one usual beam-cornea alignment scheme were evaluated; beam waist collocated with the surface apex. The result indicates the amount of difference between the reflection from planar stratified and back-scattering from the cornea in the case of focusing the beam waist at the corneal apex., Peer Reviewed, Postprint (author's final draft)

This paper is written to provide some solutions to the following systems of difference equations: where the initial data are arbitrary non zero real numbers.

Nanocrystalline spinel copper ferrite CuFe2O4 thin film has been studied and synthesized via the electrodeposition-anodization process. Electrodeposited CuFe2 alloys were obtained from aqueous sulphate bath. The formed alloys were electro oxidized (anodized) in aqueous (1 M KOH) solution, at room temperature, to the corresponding hydroxides. The anodized CuFe2 alloy films were annealed in air at 400 0C for 2 h. The parameters controlling of the electrodeposition of CuFe2 alloys such as the bath temperature, agitation and the current density were studied and optimized. The crystal structure, crystal size and microstructure of the produced ferrites were investigated using X-ray diffraction (XRD) and scanning electron microscopy (SEM). XRD shows that CuFe2O4 had a spinel structure and the crystallite size of CuFe2O4 phase was 2 nm. SEM micrograph of the formed ferrite particles shows agglomeration structure morphology with a narrow distribution of the particles.

Nanocrystalline spinel copper ferrite CuFe2O4 thin film has been studied and synthesized via the electrodeposition-anodization process. Electrodeposited CuFe2 alloys were obtained from aqueous sulphate bath. The formed alloys were electro oxidized (anodized) in aqueous (1 M KOH) solution, at room temperature, to the corresponding hydroxides. The anodized CuFe2 alloy films were annealed in air at 400 0C for 2 h. The parameters controlling of the electrodeposition of CuFe2 alloys such as the bath temperature, agitation and the current density were studied and optimized. The crystal structure, crystal size and microstructure of the produced ferrites were investigated using X-ray diffraction (XRD) and scanning electron microscopy (SEM). XRD shows that CuFe2O4 had a spinel structure and the crystallite size of CuFe2O4 phase was 2 nm. SEM micrograph of the formed ferrite particles shows agglomeration structure morphology with a narrow distribution of the particles.