Annotation of the results obtained in 2022
In third year of the project, the research was performed in several directions in accordance with the proposed plan. All problems were considered and the corresponding results were obtained. The main theoretical results are as follows. The conditions for the realization of polarizing switching between resonant and nonresonant states of anisotropic metasurfaces are theoretically determined. The analysis of the building block in the form of Si disk with a hole shifted from the disk’s center, which leads to the excitation of bianisotropic longitudinal components of the magnetic dipole moment in the disk irradiated by electromagnetic wave with a magnetic field vector oriented along the direction of the hole shift, was fulfilled. Tuning of the aspect ratios for the disk and the hole was performed in order to obtain (a) the values of the bianisotropic component of the excited dipole that are close to the maximum values in the infrared (IR) region and (b) the spectral positions of resonances of the dipole’s minor component far from the main resonances of the disk with a hole. This allows to excite the solitary resonances of the reflection coefficient of the metasurface against almost zero background, which are wide enough for the experimental detection. The strategy for solving the inverse problem of determining the characteristics of a single disk for a given QTM wavelength in a metasurface was developed. In addition, we obtained the general relationships between the refractive index of the substrate, metasurface’s period and QTM wavelength, for which the destruction of the QTM regime due to the diffraction into the substrate does not occur. The conditions for the practical observation of QTM resonances on dielectric substrates with different refractive indices are determined. It was found that switching the polarization of the incident wave to the orthogonal one leads to the disappearance of the bianisotropy of the required type and the QTM effect is violated. Based on the characteristics of the designed silicon metasurfaces, theoretical models of high-gradient near-field optical fields, arising in the metasurface/substrate system, were proposed and their magnitudes and directions were estimated depending on the parameters of external irradiation. We determined the intensity of the electric component of the near field in the disk at the QTM wavelength, which exceeds the intensity of the incident wave by 110 times, while the calculated amplification of the intensity of magnetic field in the considered metasurface was about of 1000 times. The estimated value of the sensitivity of QTM resonance to the environment is about of 150 nm/RIU (refractive index unit). On the basis of the developed models, the influence of the optical near field of the metasurface on the luminescence of quantum dots located in the metasurface under the conditions of QTM resonance was determined. Based on the study of the characteristics of various semiconductor materials, InSb QDs with diameter of about 13 nm excited by near-field pumping from QTM at wavelength 1450 nm were selected as optimal QDs for observing photoluminescence. Simulation of various regimes of functioning of the Si metasurface loaded with InSb QDs in the absence and presence of graphene was carried out. At the same time, a change in the electrochemical potential of graphene placed above the metasurface allows to modulate the narrow peak of the reflection coefficient in the regime of QTM excitation. The functional layout of an optical chip, intended for the conversion and amplification of the electromagnetic energy, based on a metasurface loaded with semiconductor quantum dots and externally controlled by a voltage applied to the graphene layer is presented. The main experimental results are as follows. The experimental verification and demonstration of the effect of polarization switching between resonant and nonresonant states of anisotropic metasurfaces were carried out. Using the strategy of tuning the parameters of Si disks with a hole, 2 designs of metasurfaces on SiO2 substrates were developed and 2 structures with 6 metasurfaces in each structure were fabricated by means of electron-beam lithography method. Three metasurfaces with different parameters were chosen from them for full characterization. For the first two metasurfaces, the QTM resonance was observed at wavelengths close to the telecom wavelength. To verify the observation of the QTM effect for the experimentally fabricated metasurfaces, their reflection spectra were compared with the calculated ones for different polarization types of incident wave. It was found that the narrowband spectral resonances are excited in the telecom wavelength range nearby the predicted wavelengths for the silicon metasurfaces on a SiO2 substrate irradiated by a wave with the calculated type of polarization. Change in the polarization of the incident wave to the orthogonal one results in the complete suppression of the spectral feature of the QTM resonance for both the experimentally measured and numerically calculated curves. In addition, we experimentally demonstrated metasurfaces for narrowband polarization filtering of optical radiation and for polarizing control of the generation of strong electric and magnetic fields in the area of metasurfaces. To accomplish this goal, two types of different metasurfaces with different building block geometries were fabricated. In particular, for narrowband polarization filtering, the metasurface was fabricated from placed on a SiO2 substrate silicon cuboids with one radially cut edge. It was found that minor components of the excited dipole (electric and magnetic), oriented perpendicular to the wave vector of the incident wave, appear in the scattering spectra of the cuboid with a defect at the wavelengths close to the wavelengths of the main components’ resonances. A weak dependence of the position of minor components’ resonances for a cuboid from the metasurface on its period and sufficiently accurate agreement between their wavelengths and the wavelengths of resonances for a single cuboid were found. Simple strategy for the design and fabrication of polarization metasurfaces is proposed. 1) At the first stage, it is necessary to choose Si cuboid of the regular shape so that dipole resonances are excited at given wavelengths. 2) At the second stage, it is necessary to introduce a small defect into such a cuboid and obtain the resonant response of the minor dipole components at the wavelengths corresponding to the wavelengths of the main components. 3) At the third stage, by assembling the cuboids with a defect into a metasurface with a period allowing one to neglect the collective effects between cuboids, it possible to significantly enhance the response of the minor component and obtain the cross-polarization effect, namely, the conversion of the incident wave energy into the orthogonal component of the scattered light. Comparison of the measured reflectance spectra for the fabricated metasurfaces with the numerically calculated ones showed the good agreement between them. It was found that the cross-polarization component is observed in the reflectance spectra when metasurface composed of cuboids with defects is irradiated by linearly polarized wave. In this case, the resonances at the wavelengths 680 nm and 800 nm are associated with the excitation of minor component of the magnetic and electric dipole, respectively. The second type of experimentally fabricated metasurfaces based on the disks with a shifted hole was utilized to demonstrate the polarizing control of the generation of strong electric and magnetic fields in the QTM regime. The angular dependences for the reflection coefficient of the metasurface were experimentally measured and numerically calculated. The rotation of the polarization plane from 0 to 90 degrees resulted in the smooth changing of the reflection coefficient from 73% to 2%. At the same time, the experimentally measured spectra are well in agreement with the calculated ones, and the values of the reflection coefficient experimentally measured at the wavelength of QTM excitation are well in agreement with the calculated polarization dependence of the reflection coefficient.

 

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Annotation of the results obtained in 2020
The project is devoted to fundamental research aimed at the development of the methods for concentrating electromagnetic energy in the optical wavelength range at a small spatial scale in order to implement new ultra-thin elements of integrated optics, tunable sources of optical radiation, as well as nanodevices allowing to control the parameters of light radiation at subwavelength scales. The project's idea is related to the possibility of resonant excitation of quasi-trapped modes in nanostructures and metasurfaces with bianisotropic properties using external electromagnetic waves with linear polarization. In the first year of the project, the ongoing research was aimed at creating analytical models of the optical response for metasurfaces consisting of particles with bianisotropic properties, as well as on the determination of the conditions for the formation of quasi-trapped modes in such systems. A nonlocal optical response theory was developed, which allows describing the origin of the bianisotropic properties of dielectric particles. This theory is based on the expansion of the external electric field in a Taylor series with the subsequent calculation of the contributions from each term of the expansion to the induced dipole moments of the particle. Using the reciprocity property of the dielectric susceptibility, symmetry ratios for direct (electric and magnetic) and bianisotropic (electromagnetic and magneto-electric) dipole polarizability tensors were obtained in explicit form, which is fully consistent with Onsager's theory of kinetic coefficients. The conditions for the appearance of a bianisotropic response of particles depending on their symmetry are formulated. It includes a) the condition for bianisotropy of longitudinal type (if the direction of the wave vector of the incident wave does not coincide with the rotational symmetry axis of the particle, then nonzero longitudinal components of the particle dipole moments arise, which are oriented along the incidence direction of the external wave); b) the condition for bianisotropy of transverse type: if longitudinal bianisotropy is realized in the system, then additional contributions to the transverse components of the particle dipole moments, which are not related to the diagonal elements of the polarizability tensor, arise if the external wave is incident along a direction that is not perpendicular to the plane of mirror symmetry. Thus, it has been determined that one of the possibilities for the formation of a bianisotropic response of a particle is the introduction of a symmetry-breaking defect into its structure. To analyze the bianisotropic response of particles with arbitrary shape, a two-stage investigation scheme was developed. It includes a numerical multipole analysis of the spectra of scattering cross-sections in a given frequency range, as well as a subsequent procedure for optimization of the particle parameters to implement the required bianisotropic response at a given wavelength. In particular, using the model of a silicon cylinder with an off-center cutout, the conditions for quadrupole bianisotropy were determined. The obtained result can be used to develop metasurfaces with resonant optical properties based on quadrupole response for its constituent particles. Next, the analytical models were proposed for calculating the dipole moments of a particle in both infinite and finite-size arrays of particles exhibiting bianisotropic properties. In the case of the infinite metasurface, the model allows calculating the transmission and reflection coefficients of plane electromagnetic waves. For finite arrays, their extinction and scattering cross-sections, as well as the collective multipole moments of the entire system, are calculated. Using the proposed models, the mechanism of quasi-trapped modes excitation in metasurfaces consisting of particles with bianisotropic properties was explicitly revealed. It also allows the development of an algorithm for tuning and optimizing of metasurfaces supporting the resonance of quasi-tripped modes in a given spectral range. It was found that the completely trapped mode corresponded to dipole moments of individual particles phased in a certain way and directed perpendicular to the metasurface plane. Additionally, it was shown that the spectral position of the trapped mode is determined by the period of the metasurface and the individual polarizabilities of the particles. In the case of silicon prisms with a base in the form of an isosceles triangle, the conditions for the occurrence of quasi-trapped modes in metasurfaces consisting of them were determined. Calculation of the corresponding fields inside the metasurface’s unit cells was fulfilled. It was found that under the condition of a quasi-trapped mode, the intensities of the electric and magnetic fields in such a metasurface can reach values three and four orders of magnitude greater than the incident fields' intensities, respectively. It was shown that the fields are localized both inside the particles and above the metasurface creating "hot spots" outside the particles. The selection of parameters corresponding to polarization switching (at a certain wavelength) between quasi-trapped modes of the electric and magnetic type in the metasurface was carried out. It is proposed to use such metasurfaces for pumping control of especially embedded active centers. Experimentally, the technology of deposition of silicon films on silicon dioxide substrates, followed by their characterization using ellipsometry, was developed. Next, using the method of ion-beam lithography, the arrays of silicon disks were manufactured and then characterized by scanning and optical microscopy. А comprehensive study of the features of the surface plasmon polaritons excitation in graphene by means of highly efficient energy transfer from semiconductor quantum dots located near its surface, which can be pumped by quasi-trapped modes of the metasurface of bianisotropic dielectric particles, was performed. A theoretical model was proposed for the analysis of the features arising in plasmonic V-scheme of interaction for a semiconductor quantum dot simultaneously excited by an optical pumping field and a surface plasmon polariton mode at very different frequencies. Optimization of the parameters for the system, including graphene and InSb quantum dot placed above it, was fulfilled. Under the excitation of the InSb quantum dot by an optical field at a wavelength of 1.55 μm, the near-field response occurring at 5.24 μm leads to the efficient excitation of surface plasmon polaritons. The use of collective resonance with surface plasmon polaritons in the metalayer of quantum dots, placed near graphene surface, allowed to realize constructive interference of responses of individual quantum dots. It can provide significant enhancement of the near field in the entire system. The possibility of generating slow/long-lived plasmon polaritons was shown in the considered system. Such long-lived plasmon polaritons can be an alternative to long-range ones and can be used to create the bright near-field sources of surface waves on graphene. Experimentally, the technology for transferring graphene onto an unstructured substrate was worked out. Additionally, a technique for the direct generation of surface plasmon polaritons in graphene was developed. For the subsequent use of graphene for a plasmonic platform, the graphene areas with defects were identified to generate surface plasmon polaritons. To detect plasmon polaritons, a method based on recording their conversion into waves propagating from the surface was proposed. The results of the project can be found on the Internet, links to resources: https://zanauku.mipt.ru/2020/10/29/oboshlos-bez-poter-uchenye-nakachali-grafen-svetom/ https://www.photonics.com/Articles/Extra_Level_Helps_Convert_Light_Energy_into/a66400

 

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Annotation of the results obtained in 2021
In the second year of the implementation of the project devoted to fundamental research of the possibilities of concentrating electromagnetic energy in the optical range on small spatial scales due to the resonant excitation of quasi-trapped modes in nanostructures and metasurfaces, a number of important results were obtained. In accordance with the proposed plan, the research was carried out in several directions. The theoretical block included tasks 1) to optimize the geometric and material parameters of dielectric, hybrid and layered nanoparticles to obtain a resonant anisotropic or bianisotropic optical response in a given spectral range, 2) study the effect of a inhomogeneous environment in the form of a substrate on the resonance response of individual particles and the resonance of trapped modes of metasurfaces , 3) study of the influence of electromagnetic fields excited in inhomogeneous systems with quantum dots on the development of cooperative optical effects and on the change in their luminescence spectra. All tasks were considered and the corresponding results were obtained. In the experimental block, methods for creation of silicon particle arrays were developed, and their geometric and optical properties were characterized. The main theoretical results are as follows. The scattering and extinction cross sections were calculated with the inclusion of multipole decomposition for hybrid particles (silicon + gold) of a cuboid shape. It was shown that the main mechanism of interaction of light with hybrid particles (silicon + gold) with sizes of about 100 nm is absorption. The bianisotropic response in scattering induced due to the "material" asymmetry is weak and, against the background of suppressive absorption, will not be able to ensure the realization of the observed quasi-trapped modes in metasurfaces composed of such hybrid particles. Under these conditions, the metasurface will exhibit the properties of a set of independent absorbers of light energy. When studying purely silicon particles, it was found that such particles in the form of a parallelepiped have an isotropic resonant optical response when the particle is irradiated along the rotational symmetry axis. In the near infrared, extinction is mainly determined by scattering. The introduction of a special defect in the shape of a particle that destroys its rotational symmetry leads to the appearance of an anisotropic and bianisotropic optical responses. In this case, bianisotropic properties are much less pronounced than anisotropic ones. To reveal the role of the substrate, we performed a comparative analysis of the bianisotropic optical response of dielectric disk particles under conditions of a homogeneous environment, dielectric, and mirror substrates. In the case of a dielectric substrate, it was found that the presence of a transparent substrate does not lead to the disappearance of the bianisotropic response of the dielectric particle. In this case, the properties of bianisotropy in the presence of a substrate retain all the features of bianisotropy of a particle in free space. The presence of a mirror substrate enhances the longitudinal bianisotropic effect, leading to a blue shift of its resonance. An increase in the longitudinal bianisotropy is accompanied by an increase in the near fields in the system. With an increase in the distance from the particle to the substrate, bianisotropy decreases, approaching its value in a homogeneous space. When studying the influence of the substrate on the excitation of trapped modes in metasurfaces, disk particles of molybdenum disulfide, characterized by a high anisotropic refractive index, were considered. To obtain a bianisotropic response in the metasurface, it was assumed that each disc has a through hole offset from its center. To obtain the resonance of the quasi-trapped mode in a given spectral region, the operation of numerical optimization of the particle size and adjustment of the metasurface period was performed. The study showed that with an increase in the refractive index of the substrate, the spectral position of the resonances of the quasi-trapped modes shifts to the red side with a change in their figure of merit. Analysis of the near fields under resonance conditions showed that strong magnetic fields are concentrated in the holes of the discs, and electric fields in their immediate environment. An analysis of the sensitivity of the spectral position of the resonances of quasi-locked modes to the refractive index of the environment has shown their high practicality for sensory applications. Using the example of trimeric clusters (blocks) of dielectric disk particles, it was found that an increase in the near fields in metasurfaces composed of such blocks can be obtained under the condition that an anapole state is excited in them. To assess the influence of quantum objects on the development of cooperative optical effects in inhomogeneous structures, a model of quantum dots (QDs) loaded into the center of a plasmon waveguide consisting of two graphene sheets was constructed. In this model, QDs were used to pump surface plasmon polaritons (SPPs). Based on the compiled model, a numerical simulation of SPP propagation in the presence and absence of Ag2Se QDs in a hybrid graphene-gold waveguide was carried out. It was found that it is possible to use the SPP wavelength, directly obtained from the dispersion equation for an empty waveguide, to determine the distance between QDs in order to tune the system for the required type of interference. In the future, this approach will be used to observe collective effects and quasi-trapped modes in metasurfaces based on quantum dots and dielectric nanoparticles. Based on the QD model in systems with SPP, it was also demonstrated that the amplification and concentration of the near-field energy localized in a combined system of a metasurface with quantum dots and graphene layers in the form of a plasmon waveguide can be realized due to the synchronization of QD responses, which is achieved by changing the period of the QD array and adjusting the additional voltage applied to graphene. The main experimental results are as follows. Experimental methods of creating single particles and metasurfaces were mastered and applied. To obtain the samples, silicon films deposited on a transparent glass substrate were used. Lithographic methods based on these films were used to obtain arrays of nanoparticles with different sizes, shapes, and periods. Several designs of metasurfaces have been developed, in particular, consisting of individual cuboids, including options without a defect and containing a cut on one of the edges of the cuboid in the form of a specific sector. An additional design was developed to create through-hole silicon disc metasurfaces. Analysis of the quality of the formed metasurfaces showed its high level. Individual nanoparticles in the form of cuboids and cuboids with a cut are distinguished by a high repeatability of the shape factor. In the course of manufacturing, the options for obtaining metasurfaces both from pure silicon and with metallization of nanoparticles with a thin metal film were tested. The centrifugation method was chosen to integrate semiconductor colloid quantum dots with a metasurface. Based on the results of preliminary experiments, a technique was developed for applying colloidal PbS quantum dots on a nanostructured metasurface. In order to obtain the optimal quality of the application of quantum dots, studies were carried out in order to determine the optimal parameters of centrifugation, in order to exclude the influence of the speed and time of rotation of the centrifuge on the properties of the obtained systems. In what follows, it is assumed that the optimal centrifugation parameters in all cases will remain unchanged for all subsequent experiments. It is shown that when nanoparticles are deposited and distributed over the surface of a nanostructured metasurface, due to the action of capillary and other forces, larger particles disintegrate, followed by selection of smaller ones, which, as expected, should lead to a change in their luminescent response. The analysis of the optical properties of metasurfaces composed of silicon cuboids on a glass substrate was carried out on a spectrophotometer in the frequency range 450–1250 nm upon excitation of the samples with a broadband quartz lamp. Metasurfaces were irradiated both by unpolarized normally incident waves and using polarizers. The signal reflected from the metasurface was detected both in the absence of analyzers and in their presence. It was experimentally established that metasurfaces composed of defect cuboids have the properties of a polarizer for incident light. Measurement of the reflection spectra demonstrated their resonance character associated with the excitation of dipole resonances of the metasurface particles. Comparison of the experimental results with theoretical and numerical simulations showed their adequate agreement.

 

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