Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part III: piecewise-homogeneous grading.

In Parts I [Appl. Opt.58, 6067 (2019)APOPAI0003-693510.1364/AO.58.006067] and II [Appl. Opt.61, 10049 (2022)APOPAI0003-693510.1364/AO.474920], we used a coupled optoelectronic model to optimize a thin-film CIGS solar cell with a graded-bandgap photon-absorbing layer, periodically corrugated backreflector, and multilayered antireflection coatings. Bandgap grading of the CIGS photon-absorbing layer was continuous and either linear or nonlinear, in the thickness direction. Periodic corrugation and multilayered antireflection coatings were found to engender slight improvements in the efficiency. In contrast, bandgap grading of the CIGS photon-absorbing layer leads to significant enhancement of efficiency, especially when the grading is continuous and nonlinear. However, practical implementation of continuous nonlinear grading is challenging compared to piecewise-homogeneous grading. Hence, for this study, we investigated piecewise-homogeneous approximations of the optimal linear and nonlinear grading profiles, and found that an equivalent efficiency is achieved using piecewise-homogeneous grading. An efficiency of 30.15% is predicted with a three-layered piecewise-homogeneous CIGS photon-absorbing layer. The results will help experimentalists to implement optimal designs for highly efficient CIGS thin-film solar cells.

Transport of intensity and phase: applications to digital holography [Invited].

We first review transport of intensity and phase and show their use as a convenient tool to directly determine the unwrapped phase of an imaged object, either through conventional imaging or using digital holography. For both cases, either the traditional transport of intensity and phase, or with a modification, viz., electrically controllable transport of intensity and phase, can be used. The use of digital holography with transport of intensity for 3D topographic mapping of fingermarks coated with columnar thin films is shown as an illustrative application of this versatile technique.

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells. Part II: optimal antireflection front-surface texturing.

In Part I [Appl. Opt.59, 1018 (2020)APOPAI0003-693510.1364/AO.381246], we used a coupled optoelectronic model to optimize a thin-film AlGaAs solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated Ag backreflector combined with localized ohmic Pd-Ge-Au backcontacts, because both strategies help to improve the performance of AlGaAs solar cells. However, the results in Part I were affected by a normalization error, which came to light when we replaced the hybridizable discontinuous Galerkin scheme for electrical computation by the faster finite-difference scheme. Therefore, we re-optimized the solar cells containing an n-AlGaAs photon-absorbing layer with either a (i) homogeneous, (ii) linearly graded, or (iii) nonlinearly graded bandgap. Another way to improve the power conversion efficiency is by using a surface antireflection texturing on the wavelength scale, so we also optimized four different types of 1D periodic surface texturing: (i) rectangular, (ii) convex hemi-elliptical, (iii) triangular, and (iv) concave hemi-elliptical. Our new results show that the optimal nonlinear bandgap grading enhances the efficiency by as much as 3.31% when the n-AlGaAs layer is 400 nm thick and 1.14% when that layer is 2000 nm thick. A hundredfold concentration of sunlight can enhance the efficiency by a factor of 11.6%. Periodic texturing of the front surface on the scale of 0.5-2 free-space wavelengths provides a small relative enhancement in efficiency over the AlGaAs solar cells with a planar front surface; however, the enhancement is lower when the n-AlGaAs layer is thicker.

Thermal hysteresis in scattering by VO2 spheres.

Vanadium dioxide (VO2) transforms from purely monoclinic to purely tetragonal when heated from 58°C to 72°C, and the transformation is reversible but hysteretic. Electromagnetically, VO2 transforms from a dissipative dielectric to another dissipative dielectric if the free-space wavelength is λ0<1100nm; it transforms from a dissipative dielectric to a plasmonic metal (or vice versa) if λ0>1100nm. Calculating the extinction, total scattering, absorption, radiation pressure, backscattering and forward-scattering efficiencies of a VO2 sphere, we found clear signatures of thermal hysteresis in (i) the forward-scattering, backscattering, and absorption efficiencies for λ0<1100nm, and (ii) the forward-scattering, backscattering, total scattering, and absorption efficiencies for λ0>1100nm. Vacuum and null-permittivity quasistates occur between 58°C and 72°C, when tetragonal VO2 is a plasmonic metal, once each on the heating branch and once each on the cooling branch of thermal hysteresis. But none of the six efficiencies show significant differences between the two quasistates.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part II: finite-difference algorithm and double-layer antireflection coatings.

In Part I [Appl. Opt.58, 6067 (2019)APOPAI003-693510.1364/AO.58.006067], we used a coupled optoelectronic model to optimize a thin-film C u I n 1-ξ G a ξ S e 2 (CIGS) solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated backreflector. The increase in efficiency due to the periodic corrugation was found to be tiny and that, too, only for very thin CIGS layers. Also, it was predicted that linear bandgap-grading enhances the efficiency of the CIGS solar cells. However, a significant improvement in solar cell efficiency was found using a nonlinearly (sinusoidally) graded-bandgap CIGS photon-absorbing layer. The optoelectronic model comprised two submodels: optical and electrical. The electrical submodel applied the hybridizable discontinuous Galerkin (HDG) scheme directly to equations for the drift and diffusion of charge carriers. As our HDG scheme sometimes fails due to negative carrier densities arising during the solution process, we devised a new, to the best of our knowledge, computational scheme using the finite-difference method, which also reduces the overall computational cost of optimization. An unfortunate normalization error in the electrical submodel in Part I came to light. This normalization error did not change the overall conclusions reported in Part I; however, some specifics did change. The new algorithm for the electrical submodel is reported here along with updated numerical results. We re-optimized the solar cells containing a CIGS photon-absorbing layer with either (i) a homogeneous bandgap, (ii) a linearly graded bandgap, or (iii) a nonlinearly graded bandgap. Considering the meager increase in efficiency with the periodic corrugation and additional complexity in the fabrication process, we opted for a flat backreflector. The new algorithm is significantly faster than the previous algorithm. Our new results confirm efficiency enhancement of 84% (resp. 63%) when the thickness of the CIGS layer is 600 nm (resp. 2200 nm), similarly to Part I. A hundredfold concentration of sunlight can increase the efficiency by an additional 27%. Finally, the currently used 110-nm-thick layer of M g F 2 performs almost as well as optimal single- and double-layer antireflection coatings.

Enhanced efficiency of graded-bandgap thin-film solar cells due to concentrated sunlight.

A systematic study was performed with a coupled optoelectronic model to examine the effect of the concentration of sunlight on the efficiencies of CIGS, CZTSSe and AlGaAs thin-film solar cells with a graded-bandgap absorber layer. Efficiencies of 34.6% for CIGS thin-film solar cells and 29.9% for CZTSSe thin-film solar cells are predicted with a concentration of 100 suns, the respective one-sun efficiencies being 27.7% and 21.7%. An efficiency of 36.7% is predicted for AlGaAs thin-film solar cells with a concentration of 60 suns, in comparison to 34.5% one-sun efficiency. Sunlight concentration does not affect the per-sun electron-hole-pair (EHP) generation rate but reduces the per-sun EHP recombination rate either near the front and back faces or in the graded-bandgap regions of the absorber layer, depending upon the semiconductor used for that layer, and this is the primary reason for the improvement in efficiency. Other effects include the enhancement of open-circuit voltage, which can be positively correlated to the higher short-circuit current density. Sunlight concentration can therefore play a significant role in enhancing the efficiency of thin-film solar cells.

Left/right asymmetry of the dipole field due to reflection from a periodic multilayer of a topological insulator and a columnar thin film.

The problem of a vertical electric dipole radiating above a periodic multilayer whose unit cell comprises a layer of a topological insulator (TI) and a columnar thin film (CTF) was solved in order to investigate the left/right asymmetry of the total electric field in the far zone in the half-space containing the dipole. Occurring in a wide range of the polar observation angle, the left/right asymmetry of Eϕ is due to both the CTFs and the TI layers. Occurring in a narrow range of the polar observation angle, the left/right asymmetry of Eθ is entirely due to the TI layers. For presently available values of the magnitude of the surface admittance γTI of TIs, significant left/right asymmetry occurs if the number of unit cells in the periodic TI/CTF multilayer is high enough.

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells.

An optoelectronic optimization was carried out for an $ {{\rm Al}_\xi }{{\rm Ga}_{1 - \xi }}{\rm As} $AlξGa1-ξAs (AlGaAs) solar cell containing (i) an $ n $n-AlGaAs absorber layer with a graded bandgap and (ii) a periodically corrugated Ag backreflector combined with localized ohmic Pd-Ge-Au backcontacts. The bandgap of the absorber layer was varied either sinusoidally or linearly. An efficiency of 33.1% with the 2000-nm-thick $ n $n-AlGaAs absorber layer is predicted with linearly graded bandgap along with silver backreflector and localized ohmic backcontacts, in comparison to 27.4% efficiency obtained with homogeneous bandgap and a continuous ohmic backcontact. Sinusoidal grading of the bandgap is predicted to enhance the maximum efficiency to 34.5%. Thus, grading the bandgap of the absorber layer, along with a periodically corrugated Ag backreflector and localized ohmic Pd-Ge-Au backcontacts, can help realize ultrathin and high-efficient AlGaAs solar cells for terrestrial applications.

Magnetically tunable metasurface comprising InAs and InSb pixels for absorbing terahertz radiation.

A magnetically tunable metasurface comprising meta-atoms with InSb-patched, InAs-patched, and unpatched pixels was simulated using commercial software to maximize the absorption of normally incident radiation in the terahertz spectral regime, with the patches decorating the illuminated face of a gold-backed polyimide substrate. Maximum absorptance of 0.99 and minimum absorptance of 0.95 can be obtained in 0.14-0.23-THz-wide bands in the 2-4-THz spectral regime, with an average tuning rate of 0.3THzT-1 and 0.24-THz dynamic range when the controlling magnetostatic field is aligned parallel to the incident electric field. The use of both InSb and InAs patches is much superior to the use of patches of only one of those materials. The design can be adapted for neighboring spectral regimes by exploiting the scale invariance of the Maxwell equations.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading: erratum.

Typographical errors in a few equations in [Appl. Opt.58, 6067 (2019)APOPAI0003-693510.1364/AO.58.006067] are corrected.

Tricontrollable pixelated metasurface for absorbing terahertz radiation.

The incorporation of materials with controllable electromagnetic constitutive parameters allows the conceptualization and realization of controllable metasurfaces. With the aim of formulating and investigating a tricontrollable metasurface for efficiently absorbing terahertz radiation, we adopted a pixel-based approach in which the meta-atoms are biperiodic assemblies of discrete pixels. We patched some pixels with indium antimonide (InSb) and some with graphene, leaving the others unpatched. The bottom of each meta-atom was taken to comprise a metal-backed substrate of silicon nitride. The InSb-patched pixels facilitate the thermal and magnetic control modalities, whereas the graphene-patched pixels facilitate the electrical control modality. With proper configuration of patched and unpatched pixels, and with proper selection of the patching material for each patched pixel, the absorptance spectra of the pixelated metasurface were found to contain peak-shaped features with maximum absorptance exceeding 0.95, full-width-at-half-maximum bandwidth of less than 0.7 THz, and maximum-absorptance frequency lying between 2 THz and 4 THz. The location of the maximum-absorptance frequency can be thermally, magnetically, and electrically controllable. The lack of rotational invariance of the optimal meta-atom adds mechanical rotation as the fourth control modality.

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading.

The power conversion efficiency of an ultrathin CuIn1-ξGaξSe2 (CIGS) solar cell was maximized using a coupled optoelectronic model to determine the optimal bandgap grading of the nonhomogeneous CIGS layer in the thickness direction. The bandgap of the CIGS layer was either sinusoidally or linearly graded, and the solar cell was modeled to have a metallic backreflector corrugated periodically along a fixed direction in the plane. The model predicts that specially tailored bandgap grading can significantly improve the efficiency, with much smaller improvements due to the periodic corrugations. An efficiency of 27.7% with the conventional 2200-nm-thick CIGS layer is predicted with sinusoidal bandgap grading, in comparison to 22% efficiency obtained experimentally with homogeneous bandgap. Furthermore, the inclusion of sinusoidal grading increases the predicted efficiency to 22.89% with just a 600-nm-thick CIGS layer. These high efficiencies arise due to a large electron-hole pair generation rate in the narrow-bandgap regions and the elevation of the open-circuit voltage due to a wider bandgap in the region toward the front surface of the CIGS layer. Thus, bandgap nonhomogeneity, in conjunction with periodic corrugation of the backreflector, can be effective in realizing ultrathin CIGS solar cells that can help overcome the scarcity of indium.

Enhanced left/right asymmetry in reflection and transmission due to a periodic multilayer of a topological insulator and an anisotropic dielectric material.

Very weak left/right asymmetry in reflection and transmission is offered by a layer of a topological insulator on top of a layer of an anisotropic dielectric material, but it can be enhanced very significantly by using a periodic multilayer of both types of materials. This is an attractive prospect for realizing one-way terahertz devices, because both types of materials can be grown using standard physical-vapor-deposition techniques.

Thermally sensitive scattering of terahertz waves by coated cylinders for tunable invisibility and masking.

Temperature-sensitive scattering of terahertz (THz) waves by infinitely long, cylindrical core-shell structures was theoretically studied. Each structure is a dielectric cylinder coated with an InSb shell illuminated by either a transverse-electric (TE) or a transverse-magnetic (TM) plane wave. InSb is a thermally tunable semiconductor showing a transition from dielectric to plasmonic state at THz frequencies. Accordingly, the total scattering efficiency (TSE) can be thermally tuned for both polarization states of the incident plane wave. The spectral locations of the maxima and minima of the TSE of an InSb-coated cylinder can be exploited for cloaking the core. At least three scenarios lead to the strong suppression of scattering by a single core-shell structure in different spectral regimes when the temperature is fixed. The excitation of localized surface-plasmon resonances is the feature being common for two of them, while the effect of volumetric resonance dominates in the third scenario. Regimes that are either highly or weakly sensitive to the core material were identified. Weak sensitivity enables masking, i.e., the core material cannot be identified by a far-zone observer. The TSE minima are usually significantly sensitive to the polarization state, but ones with weak sensitivity to the polarization state also exist.

Experimental and theoretical investigation of the co-occurrence of linear and circular dichroisms for oblique incidence of light on chiral sculptured thin films.

Theory shows that a slab of a dielectric structurally chiral material (DSCM) exhibits both linear and circular dichroisms because of its anisotropy and structural chirality, for normal as well as oblique incidence. This conclusion was confirmed by fabricating a chiral sculptured thin film and measuring the spectra of its reflectances and transmittances, both linear and circular. Signatures of the circular Bragg phenomenon are evident in the spectra of all reflectances, transmittances, absorptances, and dichroisms. Reversal of the structural handedness of a DSCM and rotation of the projection of the direction of propagation of the incident light clockwise instead of counterclockwise about the axis of helicoidal nonhomogeneity simultaneously changes the sign of circular dichroism but has no effect on linear dichroism.

Plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material.

The extended boundary condition method can be used to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative permeability dyadic. The scattered and internal field phasors can be expanded in terms of appropriate vector spherical wavefunctions with unknown expansion coefficients, whereas the incident-field phasors can be similarly expanded but with known expansion coefficients. The scattered-field coefficients are related to the incident-field coefficients through a matrix. The scattering, absorption, and extinction efficiencies were calculated thereby in relation to the propagation direction and the polarization state of the incident plane wave, the constitutive-anisotropy parameters, and the nonsphericity parameters of the ellipsoid, when the eigenvectors of the real permittivity dyadic are aligned along the three semi-axes of the ellipsoid. As the electrical size of the ellipsoid increases, multiple lobes appear in the scattering pattern. The total scattering efficiency can be smaller than the absorption efficiency for some configurations of the incident plane wave but not necessarily for others. The nonsphericity of the object has a stronger influence on the total scattering efficiency than on the absorption efficiency. The forward-scattering efficiency increases monotonically with the electrical size for all configurations of the incident plane wave, and so does the backscattering efficiency for some configurations. For other configurations, the backscattering efficiency has an undulating behavior with increase in electrical size and is highly affected by the shape and the constitutive anisotropy of the ellipsoid. Even though the ellipsoid is not necessarily a body of revolution, it is anisotropic, and it is not impedance matched to free space, the backscattering efficiency can be minuscule but the forward-scattering efficiency is not. This feature can be useful for harvesting electromagnetic energy.

Scattering by a three-dimensional object composed of the simplest Lorentz-nonreciprocal medium.

The simplest Lorentz-nonreciprocal medium has the constitutive relations (D=ϵ0E-Γ×H and B=µ0H+Γ×E). Scattering by a three-dimensional object composed of this medium was investigated using the extended boundary condition method. Scattering by this object in free space must be attributed to nonzero Γ=|Γ|. The differential scattering efficiency is immune to the transformation of the incident toroidal electric field phasor into a poloidal electric field phasor, or vice versa, and a consequence of this source invariance is the polarization-state invariance of the differential scattering efficiency when the irradiating field is a plane wave. Both the total scattering and forward-scattering efficiencies of an ellipsoid composed of the simplest Lorentz-nonreciprocal medium are maximum when the plane wave is incident in a direction coparallel (but not antiparallel) to Γ, and the backscattering efficiency is minimum when Γ is parallel to the incidence direction. The total scattering and forward-scattering efficiencies are maximum when the incidence direction is parallel to the largest semi-axis of the ellipsoid if the incidence direction is coparallel (but not antiparallel) to Γ. Lorentz nonreciprocity in an object is thus intimately connected to the shape of that object in affecting the scattered field.

Chiral sculptured thin films for circular polarization of mid-wavelength infrared light.

Being an assembly of identical upright helices, a chiral sculptured thin film (CSTF) exhibits the circular Bragg phenomenon and can therefore be used as a circular polarization filter in a spectral regime called the circular Bragg regime. This has been already demonstrated in the near-infrared and short-wavelength infrared regimes. If two CSTFs are fabricated in identical conditions to differ only in the helical pitch, and if both are made of a material whose bulk refractive index is constant in a wide enough spectral regime, then the center wavelengths of the circular Bragg regimes of the two CSTFs must be in the same ratio as their helical pitches by virtue of the scale invariance of the frequency-domain Maxwell postulates. This theoretical result was confirmed by measuring the linear transmittance spectra of two zinc-selenide CSTFs with helical pitches in the ratio 1:7.97. The center wavelengths were found to be in the ratio 1:7.1, and the deviation from the ratio of helical pitches is explainable at least in part because the bulk refractive index of zinc selenide decreases a little with wavelength. We concluded that CSTFs can be fabricated to function as circular polarization filters in the mid-wavelength infrared regime.

Bicontrollable terahertz metasurface with subwavelength scattering elements of two different materials.

Transmission of a normally incident plane wave through a metasurface with bicontrollable subwavelength scattering elements was simulated using a commercial software. Some pixels composing the H-shaped scattering elements were made of a magnetostatically controllable material whereas the remaining pixels were made of a thermally controllable material, the metasurface designed to operate in the terahertz spectral regime. The copolarized transmission coefficients were found to exhibit stopbands that shift when either a magnetostatic field is applied or the temperature is increased or both. Depending on spectral location of the stopband, either the magnetostatic field gives coarse control and temperature gives fine control or vice versa. The level of magnetostatic control depends on the magnetostatic-field configuration.

Time-domain electromagnetic scattering by a sphere in uniform translational motion.

Scattering by a uniformly translating sphere of a pulse that modulates the amplitude of a linearly polarized plane wave was formulated using the frame-hopping method involving a laboratory inertial reference frame and the sphere's comoving inertial reference frame. The incident signal was defined in the laboratory frame and transformed to the comoving frame with the Lorentz transformation, thereby altering the incident signal's spectrum, direction of propagation of the carrier plane wave, and the direction of the incident electric field, depending on the sphere's velocity. In the comoving frame, the incident signal was Fourier-transformed to the frequency domain, and the scattered field phasors were computed in all directions using the constitutive parameters of the material of the sphere at rest. The scattered signal in the comoving frame was obtained using the inverse Fourier transform. Finally, the scattered signal in the laboratory frame was obtained by inverting the original Lorentz transformation. The backscattered signal was found to depend strongly on the sphere's velocity, when the sphere's speed is an appreciable fraction of the speed of light in free space. The change in the backscattered signal compared with the backscattered signal from a stationary sphere is the greatest when the sphere's velocity is either parallel or antiparallel to the direction of propagation of the incident signal. The backscattered signal is also affected by motion transverse to the incident signal's direction of propagation; then, the backscattered signal depends on whether or not the motion is aligned with the direction of the incident electric field.