Refractive Index Of Substrate Research Articles

Generation of conventional and reflective photonic nanojets and improving intensity enhancement with their superposition

Herein, we report the theoretical investigation on photonic nanojets (PNJs) of substrate-supported single-spherical dielectric microparticles. Conventional and reflective PNJs (CPNJs and RPNJs) are observed in the case of metal and dielectric substrates. The dependence of the maximum electric field intensity enhancement (ηmax) of the CPNJs and RPNJs on the nanogap between the metal substrate and dielectric microsphere, the metal substrate's refractive indices, and the incident light's wavelength is studied. More importantly, the spatial separation between the CPNJs and RPNJs is found to be strongly dependent upon the angle of incidence (θ). A significant improvement in the EFIE is observed for the grazing incidence upon the superposition of CPNJ and RPNJ. The theoretical investigation is also performed by replacing the metal substrate with a dielectric substrate, and the results obtained are reported here for comparison. Finally, this investigation is extended for the dielectric microsphere placed on a thin metal film deposited on a dielectric substrate and studied the role of θ on the characteristic parameters of the CPNJs and RPNJs.

Reply to Comment on “Fast and accurate electromagnetic field calculation for substrate-supported metasurfaces using the discrete dipole approximation”

Abstract The recent comment on our previously published article questioned the novelty and computational efficiency of our work. Here we respond by restating the novelty and scientific value of our work as well as showing why the specific alternative methods stated in the comment are unlikely to outperform the methods we compare for metasurface applications involving high refractive index particles near high refractive index substrates.

Defocus-integration interferometric scattering microscopy for speckle suppression and enhancing nanoparticle detection on a substrate.

Direct optical detection and imaging of single nanoparticles on a substrate in wide field underpin vast applications across different research fields. However, speckles originating from the unavoidable random surface undulations of the substrate ultimately limit the size of the decipherable nanoparticles by the current optical techniques, including the ultrasensitive interferometric scattering microscopy (iSCAT). Here, we report a defocus-integration iSCAT to suppress the speckle noise and to enhance the detection and imaging of single nanoparticles on an ultra-flat glass substrate and a silicon wafer. In particular, we discover distinct symmetry properties of the scattering phase between the nanoparticle and the surface undulations that cause the speckles. Consequently, we develop the defocus-integration technique to suppress the speckles. We experimentally achieve an enhancement of the signal-to-noise ratio by 6.9 dB for the nanoparticle detection. We demonstrate that the technique is generally applicable for nanoparticles of various materials and for both low and high refractive index substrates.

Tackling the inverse problem in ellipsometry: analytic expressions for supported coatings with nonuniform refractive index profiles in the thin film and weak contrast limits

Ellipsometry is a powerful tool for the evaluation of the refractive index profile of a film or coating supported on a solid substrate. A well-acknowledged problem, however, is the inverse problem: Given a set of data, under what conditions can a refractive index profile be determined unambiguously? To this end, a series expansion of the Abeles matrix method has been applied to an arbitrary refractive index profile to determine analytic expressions of the ellipsometric ratio ρ. Two types of expressions are found: The thin film limit in which the film thickness L is much less than the wavelength of the incident light beam ( L≪λ ) and the weak contrast limit in which the refractive index of the coating is very near the refractive index of the supporting substrate. In the thin film limit, the first two terms in the series expansion are relatively straight-forward, and they depend on two types of integrals involving the difference between the dielectric profile of the coating and the dielectric constant of the substrate. While higher order terms are possible, they are quite convoluted and do not assist in the inverse problem. In the weak contrast limit, however, the series expansion of ρ depends on the moments of the difference between the dielectric profile of the coating and the dielectric constant of the substrate, allowing an analytic expression that applies to coatings that are even much larger than the incident light beam. The expressions associated with both limits are verified through comparison to the numerical evaluation of ρ with the Abeles matrix method. The results demonstrate that through judicious selection of the substrate refractive index and incident wavelength, conditions can be created that permit critical insights into the inverse problem for either thin coatings or for coatings that are very near the refractive index of the substrate.

Formation of optical planar waveguides on fused quartz by MeV ion implantation

AbstractThe optical losses and the refractive index change of optical planar waveguides formed by MeV ion implantation were correlated with the experimental ion implantation parameters. Direct ion implantation was performed by means of carbon, silicon and copper ion beams impinging on the substrate surface at normal incidence. The ions were accelerated at energies ranging from 3 to 12 MeV with fluences varying from 1 × 1012 to 2 × 1016 ion/cm2, according to the type of implanted ion. The modification of the substrate refractive index due to the ion irradiation‐induced damage was evaluated using the prism coupler method, and the refractive index profiles were determined by means of a reconstruction method using a multilayer structure approximation. The guiding properties of the waveguides were analysed using the fibre‐coupling technique to determine both the optical transmission and transversal modes at 635 nm. The main practical relevance of our research is the obtention of high‐quality waveguides at low current density MeV ion implantation (≤80 nA/cm2) without post‐implantation annealing.

Giant and tunable 2D-chiroptical response in few-layer borophene metasurfaces

The 2D-chiroptical response in few-layer borophene metasurfaces (FBMs) is studied theoretically. By stacking borophene metasurfaces with the same physical parameters near the topological transition for the borophene metasurface, it is found that there exists strong 2D chirality, which can be controlled by the incident angle and the twist angle between the metasurfaces. When the borophene metasurfaces with different electron densities are stacked, the strong circular conversion dichroism (CCD) is found near the corresponding topological transition frequency for each borophene metasurface, resulting in the formation of the multiband CCD spectra. It is demonstrated that in the FBM there exists an ultrahigh sensitivity of the CCD to the substrate refractive index.

Dynamic Nonlocal Dielectric Metasurfaces: Tuning Collective Lattice Resonances via Substrate–Superstrate Permittivity Contrast

Contrary to local resonances of single nanostructures, collective (or nonlocal) resonances in periodic metasurfaces, such as surface lattice resonances (SLRs), can significantly enhance light–matter interaction, leading to higher spectral selectivity. The dynamic control of such nonlocal response represents an emerging field of research. While tuning of SLRs has been demonstrated in plasmonic metasurfaces, the use of dielectric metasurfaces provides additional conditions to control both reflectance and transmittance, with minimum absorption effects. A close‐to‐homogeneous environment is usually required to guarantee the excitation of SLRs. Here, we propose theoretically and demonstrate experimentally a practical strategy for the tuning of SLRs in dielectric metasurfaces when an arbitrary index mismatch is considered between substrate and superstrate. The approach is based on a generalized lattice sum theory that accounts for the presence of a substrate. Dynamic tuning of the SLRs in silicon metasurfaces placed on a substrate is achieved with a changeable superstrate via an optofluidic process. Two tuning mechanisms are revealed corresponding to shifting and damping of the SLR, depending on the superstrate–substrate refractive index contrast. The demonstrated dynamic manipulation of transmission and reflection may be exploited in dielectric metasurfaces for tunable spectral selectivity, sensing, or novel display technologies.

Tunable optical chirality of twisted light with graphene

Twisted light carrying orbital angular momentum is inherently chiral. To promote the application of such twisted light in chiral science, it is highly desirable to control its optical chirality in a flexible way. We report here an approach to control the chirality of twisted light by taking advantage of tunable optical properties of graphene. A full vector theoretical model is developed to investigate the chirality of twisted light with Laguerre-Gaussian mode reflected from a graphene-substrate interface. It is revealed that the chirality of twisted light upon reflection is very sensitive to the incident angle. The greater the incident angle, the greater the maximum value of the chirality density. Moreover, the chirality of twisted light can be flexibly tuned by modulating the Fermi energy of the graphene and the substrate refractive index. In addition, the chirality of twisted light can be tuned from positive to negative values by changing the sign of the topological charge. Such tunable optical chirality has potential applications in chiral molecular recognition, chiral structure detection, and chiral micromanipulation.

Two Decades of Arrayed Imaging Reflectometry for Sensitive, High-Throughput Biosensing.

Arrayed imaging reflectometry (AIR), first introduced in 2004, is a thin-film interference sensor technique that optimizes optical properties (angle of incidence, polarization, substrate refractive index, and thickness) to create a condition of total destructive interference at the surface of a silicon substrate. The advantages of AIR are its sensitivity, dynamic range, multiplex capability, and high-throughput compatibility. AIR has been used for the detection of antibodies against coronaviruses, influenza viruses, Staphylococcus aureus, and human autoantigens. It has also shown utility in detection of cytokines, with sensitivity comparable to bead-based and ELISA assays. Not limited to antibodies or antigens, mixed aptamer and protein arrays as well as glycan arrays have been employed in AIR for differentiating influenza strains. Mixed arrays using direct and competitive inhibition assays have enabled simultaneous measurement of cytokines and small molecules. Finally, AIR has also been used to measure affinity constants, kinetic and at equilibrium. In this review, we give an overview of AIR biosensing technologies and present the latest AIR advances.

High sensitivity lossy-mode resonance refractometer using low refractive index PFA planar waveguide

In this work a new strategy to improve the sensitivity of refractometers based on lossy-mode resonances has been proved. The proximity of the PFA (tetrafluoroethylene-perfluoro polymer) substrate refractive index to that of water has permitted to implement an optical refractometer with a sensitivity of 41,034 nm per refractive index unit (nm/RIU) for refractive indices ranging from 1.3318 to 1.3347. The work is supported with both theoretical and experimental results. This high sensitivity can be used for the development of LMR based chemical sensors and biosensors, where a low limit of detection is required, with the additional advantage of a simple disposable planar configuration.

Structure‐Induced Tunable Multipolar Moments and the Associated Purcell Enhancement in Silicon‐Like Metasurfaces

The recent breakthrough in integrating single quantum emitters to dielectric metasurfaces opens up avenues in quantum technologies with the possibility to obtain on‐demand single photon sources and efficient spin–photon interface. All‐dielectric metasurfaces with unprecedented possibilities of generating directional light scattering instigated a novel concept of the Kerker effect that led to applications in nanophotonics. Here, an all‐dielectric metasurface consisting of silicon‐like nanodisks with square lattice symmetry that exhibits Kerker condition governed by constructive interference of multipoles optimized for the zero‐phonon line (ZPL) of negatively charged nitrogen‐vacancy (NV‐) center at a wavelength of 640 nm is discussed. The phase and amplitude of excited multipolar moments are manipulated by varying the geometrical parameters of the metasurfaces. The constructive interference between multipolar moments generates a Kerker condition, which is tunable by varying the diameter, thickness, refractive index of nanodisks, and substrate refractive index. The Kerker condition is further used to control the emission from a single NV‐ center and a Purcell enhancement of 300 times is achieved at 640 nm. The study profoundly explores new insights into quantum metasurfaces and paves a new way to utilize dielectric resonators with emitters as on‐chip quantum light sources at Kerker condition.

Detour-phased perovskite ultrathin planar lens using direct femtosecond laser writing

Perovskite-enabled optical devices have drawn intensive interest and have been considered promising candidates for integrated optoelectronic systems. As one of the important photonic functions, optical phase modulation previously was demonstrated with perovskite substrate and complex refractive index engineering with laser scribing. Here we report on the new scheme of achieving efficient phase modulation by combining detour phase design with 40 nm ultrathin perovskite films composed of nanosized crystalline particles. Phase modulation was realized by binary amplitude patterning, which significantly simplifies the fabrication process. Perovskite nanocrystal films exhibit significantly weak ion migration effects under femtosecond laser writing, resulting in smooth edges along the laser ablated area and high diffractive optical quality. Fabrication of a detour-phased perovskite ultrathin planar lens with a diameter of 150 μm using femtosecond laser scribing was experimentally demonstrated. A high-performance 3D focus was observed, and the fabrication showed a high tolerance with different laser writing powers. Furthermore, the high-quality imaging capability of perovskite ultrathin planar lenses with a suppressed background was also demonstrated.

Structural coloration and ultraviolet protective fabrication on fabrics coated with SiO2/TiO2 multilayer films via a magnetron sputtering method

Interference structural colors and excellent ultraviolet (UV) protection performance were prepared by coating SiO2/TiO2 composite multilayer film on polypropylene non-woven fabrics (PP-NW) and polyester woven fabrics (PET-W) via a magnetron sputtering method. The colors on the coated structured film of “substrate/[TiO2/SiO2]k/air” (TSk) and “substrate/[SiO2/TiO2]k/air” (STk) (k=2, 3, 4, 5) was confirmed to be the interference structural colors. The positions and numbers of the strongest reflection peaks of the reflection-reducing type of TSk film and the reflection-enhancing type of STk film were consistent with theoretical calculations. The optical properties obtained from depositing the same STk film on PP-NW and PET-W were different. The reflectivity of the STk film was greater than the TSk film. The STk-coated samples with the PET substrate have a higher reflectivity than samples with the PP substrate because of the higher refractive index of PET. The reflection-enhancing film structure and higher refractive index substrate improved the film reflectivity. This research offered a theoretical basis and practical guidance for structural coloration and functional fabrication on fabric substrates.

Analytical Investigation and Systematic Design Approach for High-Sensitivity Guided Mode Resonance Sensors With Graphene-Enabled Tunability

The high quality factor of guided mode resonance (GMR) structures and their sensitivity to the adjacent media’s refractive index (RI) make them excellent candidates for sensing applications. In this study, we derive analytical sensitivity equations for the GMR structures for the first time, which can be utilized to better understand and optimize their behavior. The simulated structures (based on the finite element method) show excellent agreement with the analytical sensitivities for both the transverse electric and magnetic (TE and TM) modes. The effects of waveguide height, working wavelength, and material RIs on the obtained sensitivities were surveyed, which helped achieve a design approach based on the analytical equations. The substrate RI should be as low as possible for any application. For analytes, the RI of the waveguide thin film should be low, whereas this trend is different for gas sensors; there is an optimum RI for the waveguide in the TE mode, and in the TM mode, the waveguide should have a higher possible RI. Moreover, the TM-mode gas sensors exhibit optimum sensitivity for a specified waveguide height. The design approach was used for a gas sensor operating at methane resonance wavelength (1653.7 nm), which can be tuned using a double-layer graphene sheet. A linear tunability of up to 5 nm was achieved using 1 eV chemical potential adjustment, whereas the device sensitivity remains between 291.9 to 295.5 nm/RIU. Moreover, higher sensitivities up to 950 nm/RIU can be obtained for analyte sensors at 1550 nm.

Stability of symmetry-protected BICs in dielectric metasurfaces

Optical metasurfaces with high Q -factors have attracted much attention due to their sharp spectral features and significant field enhancement. The excitation of symmetry-protected bound states in the continuum (SP-BICs) is an efficient way to achieve a high Q -factor resonator. The experimental Q -factors of resonant quasi-SP-BIC metasurfaces are currently not high. In this work, we numerically demonstrate the stability of SP-BICs in silicon metasurfaces. The two SP-BICs are transformed into quasi-SP-BICs by breaking the in-plane symmetry of the structure, and their resonance properties are discussed by far-field radiation and near-field distribution. Moreover, the effects of different periods, sizes, substrate refractive indices, and shape factors on the SP-BICs are explored, and the Q -factors of quasi-SP-BICs always exhibit the same inverse quadratic dependence on asymmetry parameters, which demonstrates the stability of the SP-BIC. Our results may provide theoretical support for the experimental realization of ultrahigh Q -factor quasi-SP-BICs.

On the terahertz response of metal-gratings on anisotropic dielectric substrates and its prospective application for anisotropic refractive index characterization

This paper discusses the terahertz electromagnetic response of metallic gratings on anisotropic dielectric substrates. The metallic gratings consist of parallel gold stripes. Utilizing numerical simulations, we observe that it is possible to excite a series of resonant modes in these structures. These modes are affected differently by the different indices on the anisotropic substrate. An analytical model is discussed to show that modes associated with transmission peaks are due to the excitation of (a) Fabry–Pérot modes with polarization along the grating and/or (b) waveguide modes with polarization perpendicular to the grating. It is observed that the resonance associated with the TM1,1 mode is a narrow linewidth resonance which, in some particular circumstances, becomes nearly independent of substrate thickness. Therefore, from the spectral position of this resonance, it is possible to extract the out-of-plane component of the substrate refractive index with very small uncertainty. Based on this observation, we demonstrate the refractive index characterization of several lossless semiconductor substrates through frequency-domain polarized terahertz transmission measurements in the frequency range of 0.2–0.6 THz at normal incidence. The reliability of the technique is demonstrated on well-known materials, such as high-resistivity silicon and sapphire substrates. This technique is also applied for the characterization of a Fe-doped β-Ga2O3 single-crystal substrate.

Optical and magneto-optical properties of ferromagnetic monolayer CrBr3 : A first-principles GW and GW plus Bethe-Salpeter equation study

The discovery of atomically thin two-dimensional (2D) magnetic semiconductors has triggered enormous research interest recently. In this work, we use first-principles many-body perturbation theory to study a prototypical 2D ferromagnetic semiconductor, monolayer chromium tribromide (CrBr$_3$). With broken time-reversal symmetry, spin-orbit coupling, and excitonic effects included through the full-spinor $GW$ and $GW$ plus Bethe-Salpeter equation ($GW$-BSE) methods, we compute the frequency-dependent layer polarizability tensor and dielectric function tensor that govern the optical and magneto-optical properties. In addition, we provide a detailed theoretical formalism for simulating magnetic circular dichroism, magneto-optical Kerr effect, and Faraday effect, demonstrating the approach with monolayer CrBr$_3$. Due to reduced dielectric screening in 2D and the localized nature of the Cr $d$ orbitals, we find strong self-energy effects on the quasiparticle band structure of monolayer CrBr$_3$ that give a 3.8 eV indirect band gap. Also, excitonic effects dominate the low-energy optical and magneto-optical responses in monolayer CrBr$_3$ where a large exciton binding energy of 2.3 eV is found for the lowest bright exciton state with excitation energy at 1.5 eV. We further find that the magneto-optical signals demonstrate strong dependence on the excitation frequency and substrate refractive index. Our theoretical framework for modeling optical and magneto-optical effects could serve as a powerful theoretical tool for future study of optoelectronic and spintronics devices consisting of van der Waals 2D magnets.

Investigation of directivity of the nanoantenna by its inherent resonant states

We present a quasinormal mode (QNM) approach for modeling the nanoantenna and describe the response of localized dielectric cylinder resonators. The inherent resonant states of the dielectric cylinder nanocavity are investigated for modified and reduced geometrical symmetry. We find some modes contributing mainly to the directivity and have a high-quality factor. The variation of the eigenmodes with cylinder height and substrate refractive index has also been investigated.

Structure-induced broadband tunable resonances in soft material based dielectric metasurfaces

The dielectric metasurfaces using soft materials have generated opportunities in metamaterials by manipulating light interaction at a sub-wavelength scale. Here, we study the low-index dielectric metasurface consisting of a monolayer of dielectric micro-spheres in the visible region. The metasurface exhibits optical resonances, which appear as dips in the reflectivity spectra measured using the state-of-the-art micro-reflectivity facility. The origin of resonances is due to the diffraction of light on the corrugated surface, which appears as a grating mode or due to the light trapped within the micro-spheres termed as the leaky mode. The tunability of resonant modes is discussed as a function of the lattice constant and the effective refractive index of the metasurface. The experimental results are validated using the finite-difference time-domain simulations and theoretical calculations. The impact of the substrate refractive index is studied which shows higher refractive index contrast between the sample and the substrate, more light is confined within the metasurface. The proposed soft material-based metasurfaces can be used as a mask for making more complex photonic structures, generating structural coloration, and material base for rapid sensing.

Retrieval of Optical Constants of Undoped Flash-Evaporated Lead Iodide Films from an Analysis of Their Normal Incidence Transmission Spectra Using Swanepoel’s Transmission Envelope Theory of Non-Uniform Films

Abstract: Normal-incidence transmission-wavelength (T_exp (λ)-λ) spectra of 1 and 1.2 m thick flash-evaporated lead iodide (PbI2) films on 1.1 mm thick glass slides held at 200 ℃ display well-spaced several interference-fringe maxima and minima in the λ-range 520-900 nm, without exhibiting a transparent region and with the maxima lying well below the substrate transmission. Below 520 nm, these T_exp (λ)-λ curves drop steeply to zero (at λ ≼ 505 nm), signifying crystalline-like PbI2 film absorption. As corrections of measured (PbI2 film/substrate) transmittance data for substrate absorption and spectrometer slit-width effect were marginal over the studied λ-range, the observed low transmittance of (PbI2 film/substrate) system was related to PbI2 film thickness non-uniformity (∆d), which causes shrinkage of both maxima and minima and leads to significant film optical absorption that reduces both maxima and minima. The McClain ENVELOPE algorithm was utilized, with a minor modification, to construct maxima T_M (λ_max/λ_min) and minima T_m (λ_min/λ_max) envelope curves, which were analyzed by Swanepoel’s envelope method of non-uniform films using an approach that takes account of dispersive substrate refractive index n_s (λ) and circumvents the non-availability of a high-λ transparency region. In such analytical approach, ∆d was varied till a re-generated T_gen (λ)-λ curve matches the T_exp (λ)-λ curve. An average thickness d ̅ of the film, besides its refractive index n(λ) and absorption coefficient α(λ) in the weak, medium and strong absorption regions, were then obtained. The energy-dependence of α(λ) is discussed in view of interband electronic transition models. The obtained results are consistent with other literature studies on similar flash-evaporated PbI2 films. Keywords: PbI2, Optical constants and bandgap, Swanepoel's transmission envelope method, Non-uniform films.