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Terahertz spectroscopy is a promising method to diagnose ocular diseases, where the cornea is typically imaged by Gaussian beams. However, the beam’s mismatch with the cornea’s spherical surface produces a 5-10 % error in analysis. We investigate cornea spectroscopy with wavefront-modified vector beams, reducing the original analysis error to less than 0.5 %. Vector beams are synthesized by our developed 3D Angular Spectrum Method expanded to vector spherical harmonic presentation, allowing wavefront modification and scattering analysis from 100-layer cornea models. We show that wavefront-modified spherical vector beams possess increased accuracy and non-sensitive focusing on cornea spectroscopy compared to the Gaussian beams. Additionally, we investigate wavefront-modified cylindrical vector beams, which show frequency-dependent scattering power arising from s- and p-polarizations. As a result, these beams are unsuitable for cornea spectroscopy, although they have potential for optical force applications. Wavefront-modified vector beams can be applied to spherical target spectroscopy and optical force applications, such as medicine, medical imaging, and optical tweezers., Assessment of the Graft 332 Rejection Using Millimeter Waves; Academy of Finland (327640), Peer Reviewed, Postprint (published version)

© 2023 Optica Publishing Group under the terms of the Open Access Publishing Agreement. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for noncommercial purposes and appropriate attribution is maintained. All other rights are reserved., The angular spectrum method is a rigorous method to synthesize near and far-field electromagnetic beams from planar field distributions. However, this limitation of planar surfaces has restricted its applicability to beams with simple focal planes. We propose a curved boundary integral method (CBIM) to synthesize electromagnetic beams from arbitrary surfaces to address this limitation and expand the method’s scope to synthesize beams from and between shaped objects. This study presents a detailed theoretical framework behind the CBIM and validates its effectiveness and accuracy with a comprehensive set of simulations. Additionally, we present mathematical proof to support our proposal. The proposed method satisfies Maxwell’s equations and significantly benefits optical systems and inverse beam design. It allows for analyzing electromagnetic forward/backward propagation between optical elements using a single method. It is also valuable for optical force beam design and analysis., Peer Reviewed, Postprint (published version)

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)

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)

Conventional methods for evaluating electromagnetic beams created from spherical electric surface distribution may include full-wave simulations, geometric optics (GO), or physical optics (PO). These methods are extensively studied and accurate given the model fidelity and a suitable wavelength range. However, they cannot assess the incident and scattered electric field from multi-layered spherical objects without considerable computational effort. Fourier optics is a powerful method to obtain incident electric field, which can be easily expanded to vector spherical harmonics (VSH) presentation to accommodate spherical geometry. The VHS presentation is mapped with the T-matrix method to evaluate the internal and scattered fields from the multi-layered dielectric sphere. The limitation of this method is that it is nominally compatible with planar interfaces. In this study, the Fourier-optics method is expanded to model beam propagation from arbitrary electric field distributions positioned on spherical surfaces. This method can be applied to synthesize beams from any surface shape within reasonable frequency-dependent surface details. The method’s main idea is that Riemann’s surface integral combines differential surface elements, which can be approximated as locally planar elements. The Fourier-optics method is applied to each of these differential elements, and the total electric field is the sum of the fields created from them by the superposition principle. The method is readily applicable to the field of THz sensing of corneal tissue hydration and geometry due to the cornea’s layered spherical shell. First, a literature review of the general theory of Fourier optics, vector spherical harmonics, and the T-matrix method is presented. The new modified Fourier-optics method is derived, and the result is mathematically proved. The simulation algorithm was implemented in the MATLAB programming language. The simulations with the new method are compared with correspondi, Pallomaisen pintavirtajaukauman tuottamaa sähkökenttää voidaan simuloida aaltoyhtälöä approksi- moivilla differenssimenetelmillä (finite-difference time domain, FDTD), integraaliyhtälömenetelmillä (finite-element method, FEM) sekä geometrisen optiikan (GO), että aalto-optiikan menetelmillä (physical optics, PO). Nämä menetelmät ovat laajasti tutkittuja ja tarkkoja, kun sopiva aallon- pituusalue otetaan huomioon. Ne eivät kuitenkaan pysty simuloimaan sisäisiä eivätkä sironneita sähkökenttiä monikerroksisista palloista ilman huomattavaa laskennallista työtä. Fourier-optiikka on tehokas työkalu pinnalle saapuvan sähkökentän simulointiin ja se voidaan helposti laajentaa palloharmoniseen vektoriesitykseen (vector spherical harmonics, VSH ). VSH-esitys voidaan kartoittaa T-matriisimenetelmällä monikerroksisen dielektrisen pallon sisäisiin ja sironneisiin kenttiin. Tämän menetelmän rajoitus on, että se on yleisesti yhteensopiva tasomaisen rajapinnan kanssa. Tässä tutkimuksessa Fourier-optiikka menetelmä laajennetaan mallintamaan säteilyä pallomaisten pintojen sähkökentistä. Tätä menetelmää voidaan myös soveltaa mistä tahansa pintamuodosta tulevan säteilyn syntetisoimiseksi. Menetelmän pääidea on, että Riemannin pintaintegraalissa summataan differentiaalisia pintaelementtejä, joita voidaan paikallisesti approksimoida tasomaisilla elementeillä. Fourier-optiikka menetelmää sovelletaan kuhunkin differentiaalielementtiin, ja kokonaissähkökenttä on niistä kertyvien kenttien summa superpositio-periaatteen mukaisesti. Menetelmää voidaan helposti soveltaa sarveis- kalvon kuvantamiseen terahertsitaajuuksilla (THz) sen monikerroksisen pallomaisen geometrian vuoksi. Ensiksi työssä esitetään kirjallisuuskatsaus Fourier-optiikan, sähkökentän palloharmoniseen vektoriesityksen sekä T-matriisimenetelmän teoriasta. Näiden teorioiden perusteella johdetaan uusi modifioitu Fourier-optiikan menetelmä ja tulos todistetaan matemaattisesti. Simulaatioalgoritmi toteutettiin MATLAB-ohjelmointikielel

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)