Effective Complex Refractive Index Research Articles

Optical simulation and experimental investigation of the crystalline silicon/black silicon/perovskite tandem structures

The use of a black silicon (b-Si) interlayer is a promising solution for improving the optical properties of crystalline Si/perovskite solar cells. Optical numerical simulation of the crystalline Si/b-Si/perovskite structures can efficiently optimize their parameters at the initial tandem solar cell design stage. In this work, the optical properties of these structures were modeled using the transfer matrix method, where an array of cone-like nanoneedles of the b-Si interlayer is approximated as a homogeneous optical medium, for which the effective complex refractive index is the weighted average of those for Si and perovskite. Analytical equations are obtained for tandem structures' reflection, transmission, and absorption. The simulated reflectance spectra of the structures were compared with those of structures without the b-Si layer, as well as with experimental data. Numerical calculations and experiments confirm that nanotexturing significantly improves the optical properties of tandem structures. In addition, the nanotextured tandem structures have a wide-angle antireflective characteristic at incidence angles less than 60°, indicating their omnidirectional light-trapping capability. The proposed simulation model satisfactorily describes the optical behavior of crystalline Si/b-Si/perovskite tandem structures and can be used to estimate their optical properties depending on various parameters. As a demonstration, a numerical analysis was performed to study the effect of the b-Si interlayer thickness on the reflection of the tandem structure.

A novel theoretical method to determine the effective optical properties of high refractive index nanocomposites.

The continuous development of advanced optical devices towards high performance, miniaturization and integration has led to an increasing demand for high refractive index optical materials. Nanocomposites - made from high refractive index inorganic nanoparticles and good processability polymers - combine the advantages of both materials to create a synergistic effect. However, the diversity and complexity of the composites make laboratory preparation less efficient. Therefore, to prepare composites that meet the refractive index requirements, it is essential to predict the effective optical properties at different wavelengths. This study proposes a finite element parametric retrieval (FEPR) method to calculate the effective complex refractive index of nanocomposites (meff). The effects of the ratio of film thickness to particle diameter, particle arrangement, particle volume fraction (fv) and particle diameter (d) on meff are considered. The results demonstrate that changing the spatial arrangement, volume fraction and diameter of the particles can cause changes in the scattering effect of particles or the interaction between the electromagnetic waves and the particles, resulting in changes in the meff. Compared with effective medium theory (EMT), the FEPR method can be used to characterise the meff values in complex cases through finite element parametric modelling. The FEPR method is an efficient and accurate method for predicting the effective optical properties of nanocomposites, and can also be applied to the design and development of materials to discover the factors influencing the properties and variation patterns from large amounts of data, and to obtain predictive models that can guide the design of new materials.

Extremely low effective impedance in stratified graphene-dielectric metamaterials

The periodic reflections in frequency were observed in a stack of graphene layers and generally reported as a series of mini photonic bandgaps owing to the multiple interference by the graphene layers. In this research, the Floquet-Bloch theory was employed to obtain the effective refractive index and Bloch impedance for understanding the wave propagation characteristic therein. Interestingly, the periodic reflections were found to occur in the frequency band having drastic variation in complex Bloch impedance and effective refractive index as well, wherein a Floquet-Bloch mode having pure real effective refractive index and extremely low Bloch impedance exists.

Determination of the refractive index and wavelength-dependent optical properties of few-layer CrCl within the Fresnel formalism.

SummaryBased on previous reports on the optical microscopy contrast of mechanically exfoliated few layer CrCl3 transferred on 285 nm and 270 nm SiO2 on Si(100), we focus on the experimental determination of an effective mean complex refractive index via a fitting analysis based on the Fresnel equations formalism. Accordingly, the layer and wavelength‐dependent absorbance and reflectance are calculated. Layer and wavelength‐dependent optical contrast curves are then evaluated demonstrating that the contrast is significantly high only around well‐defined wavelength bands. This is validated a posteriori, by experimental UV‐Vis absorbance data. The present study aims to show the way towards the most reliable determination of thickness of the 2D material flakes during exfoliation.

Plasmonic effect of diffused Ag nanoparticles in EB evaporated Ag/TiO2 bilayer thin films and role of oxygen pressure

Oxygen pressure mediated interfacial diffusion of silver up to top surface of thick (∼120 nm) TiO2 layer in e-beam evaporated Ag/TiO2 bilayer thin films has been observed. This effect has been investigated in oxygen pressure range of 5.9 × 10−5-5.8 × 10−4 mbar during evaporation. The amount of Ag diffusion (5–24%) has been found to be correlated with the induced porosity of TiO2 layer. Both compositional and structural characterizations confirm Ag0 chemical state of diffused silver. Scanning Electron Microscopy revealed Ag aggregates having an approximate average diameter of ∼4 nm and ∼24 nm on top surface. Spectroscopic ellipsometry analysis demonstrates that plasmonic absorption caused by these Ag nanoparticles manifests significant modulation of effective complex refractive indices (ECRI) of TiO2 layer. Specifically, the imaginary part of ECRI of TiO2 exhibits substantial non-zero value (∼6.5 × 10−2) in the visible wavelength range which is otherwise close to zero (<10−5) for intrinsic TiO2 thin film. Finally, the optical role of diffused silver on wavelength and peak of interference absorption in Ag/TiO2 bilayer thin film system has been demonstrated. This investigation gives insight on plasmonic contribution of diffused Ag nanoparticles and its consequence on ECRI of dielectric thin film due to in-situ e-beam evaporation without any post deposition treatment.

Large-Area Virus Coated Ultrathin Colorimetric Sensors with a Highly Lossy Resonant Promoter for Enhanced Chromaticity.

Acclimatable colors in response to environmental stimuli, which are naturally endowed with some living things, can provide an opportunity for humans to recognize hazardous substances without taking empirical risks. Despite efforts to create artificial responsive colors, realistic applications in everyday life require an immediate/distinct colorimetric realization with wide chromatic selectivity. A dynamically responsive virus (M‐13 phage)‐based changeable coloring strategy is presented with a highly lossy resonant promoter (HLRP). An ultrathin M‐13 phage layer for rapid response to external stimuli displays colorimetric behavior, even in its subtle swelling with strong resonances on HLRP, which is modeled using the complex effective refractive index. Optimal designs of HLRP for several material combinations allow selective chromatic responsivity from the corresponding wide color palette without modification of the dynamic responsive layer. As a practical demonstration, the spatially designed colorimetric indicator, which is insensitive/sensitive to external stimuli, provides an intuitive perception of environmental changes with hidden/revealed patterns. Furthermore, the proposed colorimetric sensor is tested by exposure to various volatile organic chemicals and endocrine disrupting chemicals for versatile detectability, and is fabricated in a wafer‐scale sample for large‐area scalability.

Flexible, Large‐Area Covert Polarization Display Based on Ultrathin Lossy Nanocolumns on a Metal Film

AbstractCovert polarization displays provide a barrier to the inadvertent viewing of stored optical information. For security and anti‐counterfeiting purposes, access to concealed information without compromising packaging aesthetics is required in certain situations. However, optical conversion with polarized light typically requires sophisticated nanostructures only possible with limited materials, which are not appropriate for application to objects requiring flexibility or conformability, and color selectivity. A flexible, large‐area covert polarization display based on ultrathin lossy nanocolumns with wide color selectivity is presented. Self‐aligned porous nanocolumns (PNCs) fabricated by glancing angle deposition are a facile approach to polarization distinguishable structures. PNCs deposited on metal are designed to switch color in accordance with polarization by ultrathin resonance, which is modeled using the complex effective refractive index. Several combinations of material and thickness are presented to extend color selectivity with the standard red green blue gamut and color palette. As a demonstration, covert polarization display labels are attached to daily objects with curved and wrinkled surfaces, and hidden quick response codes are revealed by polarization adjustment in indoor and outdoor environments. Moreover, a multifunctional water contact detection covert polarization display is demonstrated based on the sensitivity of PNCs to the refractive index of the analyte.

Characterization of optically effective complex refractive index of black carbon composite aerosols

Black carbon aerosols, always existing as complicated mixtures of various species, have important impacts on the global and regional climate, whereas their effective aerosol complex refractive index (ACRI) is a must for modeling their radiative effects. Retrieval of optically effective ACRI from accurately calculated scattering and absorption properties of an internal-mixed aerosol model with BC and dust coated with sulfate, roughly representing ambient aged multicomponent BC particles, are performed. The sensitivities of retrieved optically effective ACRI to particle size distribution and composition ratio are explored, and the popular volume weighted average (VWA) method and Bruggeman effective medium (BEM) theory are also considered for comparison. The optically effective ACRIs depicts dramatic variation for monodisperse size parameter larger than π, as opposed to almost a constant for size parameter less than π, whereas the VWA and BEM can hardly provide acceptable effective ACRIs for coarse BC composite particles. The retrieved optically effective ACRI are sensitive to both size distribution and composition ratio, and becomes more sensitive to particle size distribution with aerosols containing more BC content. As BC volume content reaches ~4%, the VWA overestimates the imaginary part of effective ACRI with significant bias when compared with the optically effective ACRI, indicating overestimated aerosol absorption in most atmospheric environments in aerosol-climate models employing the VWA. We suggest that the optically effective ACRI, rather than the ACRI given by the VWA, should be applied to account for coarse BC-containing particles in the state-of-the-art aerosol-climate models.

Analytical approximation to the complex refractive index of nanofluids with extended applicability.

Currently, there are available a few simple analytical approximations to the complex effective refractive index that may be used for nanofluids. Namely, the Maxwell Garnett mixing formula with scattering corrections, the Maxell Garnett Mie approximation, the Foldy-Lax approximation and the small particle limit of the quasi-crystalline approximation. These approximations are valid either for very small nanoparticles (below a few nanometers in radius) or for very dilute nanofluids (below about 1% in particles' volume fractions) and therefore, do not cover the whole domain of particle suspensions referred to as nanofluids. Here we propose a new simple analytical approximation based on local field corrections to the Foldy-Lax approximation. The new mixing formula coincides with the mentioned approximations when they are expected to be valid and provides physically sound predictions when the mentioned approximations are no longer valid, within the realm of nanofluids. We compare predictions of the analytical approximations considered in this work with experimental data published earlier for nanofluids of polystyrene in water.

Optical sizing of nanoparticles in thin films of nonabsorbing nanocolloids.

We study an optical method to infer the size of nanoparticles in a thin film of a dilute nonabsorbing nanocolloid. It is based on determining the contribution of the nanoparticles to the complex effective refractive index of a suspension from reflectivity versus the angle of incidence curves in an internal reflection configuration. The method requires knowing only approximately the particles' refractive index and volume fraction. The error margin in the refractive index used to illustrate this technique was 2%. The method is applicable to sizing nanoparticles from a few tens of nanometers to about 200nm in radius and requires a small volume of the sample, in the range of a few microliters. The method could be used to sense nanoparticle aggregation and is suitable to be integrated into microfluidic devices.

Does optically effective complex refractive index of internal-mixed aerosols have a physically-based meaning?

It is documented that some unreasonable low real parts of aerosol complex refractive index (ACRI) are retrieved from measured particle optical properties, and whether the optically effective ACRI has a physically-based sense is still an open question. Numerical determination of the optically effective ACRI from accurately calculated scattering and absorption properties of polydisperse coated BC particles by the core-shell Mie, representing some internal-mixed aged BC particles under polluted urban environments, is performed with a Mie theory based data analysis scheme. After getting rid of retrieval uncertainties (such as altered shapes), the look-up tables without limiting ACRI ranges based on known particle compositions could theoretically result in some unreasonable extreme real parts of optically effective ACRI of coarse coated BC with some shell/core ratios. Based on limited look-up tables with aerosol compositions considered, the retrieved imaginary parts of optically effective ACRIs of coarse coated BC, showing smooth as a function of shell/core ratio, are significantly lower than those approximated by the volume weighted average (VWA) method by a factor of nearly 3. Although the VWA shows acceptable performances for coated BC in the Aitken or accumulation modes, it could overestimate the absorption of coarse coated BC by a factor of ~2 for large shell/core ratio. This may be one of the reasons why modelled aerosol optical depth is 20% larger than observed. Our study indicates that the optically effective ACRI of internal-mixed BC particles does have a physically-based meaning like real ACRI, unless limited ACRI look-up tables considering aerosol compositions are applied for retrieval. We suggest that the optically effective ACRI, rather than the ACRI given by the VWA, should be considered for coarse internal-mixed particles in the state-of-the-art aerosol-climate models.

Optically effective complex refractive index of coated black carbon aerosols: from numerical aspects

Abstract. Aerosol complex refractive index (ACRI) is an important microphysical parameter used for the studies of modeling their radiative effects. With considerable uncertainties related to retrieval based on observations, a numerical study is a powerful method, if not the only one, to provide a better and more accurate understanding of retrieved optically effective ACRIs of aged black carbon (BC) particles. Numerical investigations of the optically effective ACRIs of polydisperse coated BC aggregates retrieved from their accurate scattering and absorption properties, which are calculated by the multiple-sphere T-matrix method (MSTM), without overall particle shape variations during retrieval, are carried out. The aim of this study is to evaluate the effects of aerosol microphysics, including shell∕core ratio Dp∕Dc, BC geometry, BC position inside coating, and size distribution, on retrieved optically effective ACRIs of coated BC particles. At odds with expectations, retrieved optically effective ACRIs of coated BC particles in coarse mode are not merely impacted by their chemical compositions and shell∕core ratio, being highly complicated functions of particle microphysics. However, in accumulation mode, the coated BC optically effective ACRI is dominantly influenced by particle chemical compositions and the shell∕core ratio. The popular volume-weighted average (VWA) method and effective medium theory (EMT) provide acceptable ACRI results for coated BC in accumulation mode, and the resulting uncertainties in particle scattering and absorption are both less than approximately 10 %. For coarse coated BC, the VWA and EMT, nevertheless, produce dramatically higher imaginary parts than those of optically effective ACRIs, significantly overestimating particle absorption by a factor of nearly 2 for heavily coated BC with a large BC fractal dimension or BC close to the coating boundary. Using the VWA could introduce significant overestimation in aged BC absorption analysis studies, and this may be one of the reasons why modeled aerosol optical depth is 20 % larger than observed, since it is widely employed in the state-of-the-art aerosol–climate models. We propose a simple new ACRI parameterization for fully coated BC with Dp/Dc≥2.0 in coarse mode, which can serve as a guide for the improvement of ACRIs of heavily coated BC, and its scattering and absorption errors are reduced by a factor of nearly 2 compared to the VWA. Our study indicates that a reliable estimate of the radiative effects of aged BC particles in coarse mode would require accounting for the optically effective ACRI, rather than the ACRI given by the VWA, in aerosol–climate models.

Determining the Complex Refractive Index of Neat CdSe/CdS Quantum Dot Films

Understanding how structural and synthetic factors influence the complex refractive index of quantum dot (QD) solids is crucial to tailoring the light–matter interactions of QD-containing photonic and optoelectronic devices. However, neat QD films are challenging to accurately model as they are a mixture of inorganic core/shell materials and surrounding organic ligands. Furthermore, both the QD film morphology and the complex refractive index vary due to particle size, ligand chain length, and the deposition process. Here, we study the complex refractive index of neat CdSe/CdS core/shell QD films by using variable-angle spectroscopic ellipsometry to derive the effective complex refractive index using Kramers–Kronig consistent dispersion models. We use this information in conjunction with intrinsic refractive index data of CdSe and CdSe/CdS QDs extracted from solution-state absorption data and effective medium approximations (EMA) to describe neat QD films. We find that EMAs can successfully be used as a t...

Controlling Nonreciprocity Using Enhanced Brillouin Scattering

The properties of space-time modulated media operating in the sub-sonic regime are discussed based on rigorous Bloch-Floquet theory. A geometrical description in the frequency-wavenumber plane is developed to provide insight into the possible interactions and their nature. It is shown that the secular equation has a singularity, which results in a weak/passive second harmonic generation process. Additionally bandgaps arising from the strong/active parametric interaction between an incident wave and its space-time harmonic, result in an inelastic Brillouin like scattering process. Hence when the incident frequency is inside a forward (backward) bandgap, a Stokes' (Anti-Stokes') scattered wave bounces back to the source. Although the forward and backward bandgaps do not generally occur at the same frequency bands, the insertion loss and gap width are equal. Requiring that both gaps do not overlap, enforces a lower bound on the modulation speed. It is shown that although an increase in the modulation index is desirable, as it enhances the non-reciprocal behaviour, it also limits the range of possible modulation speeds. The effective complex refractive index is calculated over a wide frequency range. It is shown that peaks appear in the extinction coefficient, indicating scattering to Stokes' and Anti-Stokes' waves. Finally, a comprehensive numerical analysis based on the Finite Difference Time Domain method is developed to verify and demonstrate the intriguing properties of space-time modulated media.

On the extinction coefficient of light in non-absorbing nanoparticle suspensions.

We assess the validity and possible use of a simple formula for the complex effective refractive index of a colloidal suspension of very small particles obtained from the quasi-crystalline approximation. This approximation takes into account the so-called dependent scattering effects, which are strongest, in relative terms, in suspensions of non-absorbing nanometer-sized particles. We test experimentally the predictions of the model for the extinction of light in dispersions of sodium dodecyl sulfate micelles in tri-distilled water. We find that the theoretical model can be fitted to the experimental data and provide estimates of the micelles' size and the minimum distance between each other in suspension.

Mechanism of large optical nonlinearity in gold nanoparticle films.

The Z-scan technique, using femtosecond (fs) laser pulses at 1480nm laser pulses, was used to measure the nonlinear optical properties of gold (Au) nanoparticle (NP) films made by both nanosecond (ns) and fs pulsed laser deposition (PLD) in vacuum. At irradiance levels of 1×1012 Wm-2, the ns-PLD films displayed induced absorption with β=4×10-5 mW-1, and a negative lensing effect with n2=-4.7×10-11 m2 W-1 with somewhat smaller values for the fs-PLD films. These values of n2 imply an unphysically large change in the real part of the refractive index, demonstrating the need to take account of nonlinear changes of the Fresnel coefficients and multiple beam interference in Z-scan measurements on nanoscale films. Following this approach, the Z-scan observations were analyzed to determine the effective complex refractive index of the NP film at high irradiance. It appears that at high irradiance the NP film behaves as a metal, while at low irradiance it behaves as a low-loss dielectric. Thus, it is conjectured that, for high irradiance near the waist of the Z-scan laser beam, laser driven electron tunneling between NPs gives rise to metal-like optical behavior.

Ultra-fast transient plasmonics using transparent conductive oxides

During the last decade, plasmonic- and metamaterial-based applications have revolutionized the field of integrated photonics by allowing for deep subwavelength confinement and full control over the effective permittivity and permeability of the optical environment. However, despite the numerous remarkable proofs of principle that have been experimentally demonstrated, few key issues remain preventing a widespread of nanophotonic technologies. Among these fundamental limitations, we remind the large ohmic losses, incompatibility with semiconductor industry standards, and largely reduced dynamic tunability of the optical properties. In this article, in the larger context of the new emerging field of all-dielectric nanophotonics, we present our recent progresses towards the study of large optical nonlinearities in transparent conducting oxides (TCOs) also giving a general overview of the most relevant and recent experimental attainments using TCO-based technology. However, it is important to underline that the present article does not represent a review paper but rather an original work with a broad introduction. Our work lays in a sort of ‘hybrid’ zone in the middle between high index contrast systems, whose behaviour is well described by applying Mie scattering theory, and standard plasmonic elements where optical modes originate from the electromagnetic coupling with the electronic plasma at the metal-to-dielectric interface. Beside remaining in the context of plasmonic technologies and retaining all the fundamental peculiarities that promoted the success of plasmonics in the first place, our strategy has the additional advantage to allow for large and ultra-fast tunability of the effective complex refractive index by accessing the index-near-zero regime in bulk materials at telecom wavelength.

Broadband optical properties of biomass‐burning aerosol and identification of brown carbon chromophores

AbstractThe radiative effects of biomass‐burning aerosols on regional and global scales can be substantial. Accurate modeling of the radiative effects of smoke aerosols requires wavelength‐dependent measurements and parameterizations of their optical properties in the UV and visible spectral ranges along with improved description of their chemical composition. To address this issue, we used a recently developed approach to retrieve the time‐ and spectral‐dependent optical properties of ambient biomass‐burning aerosols from 300 to 650 nm wavelengths during a regional nighttime bonfire festival in Israel. During the biomass burning event, the overall absorption at 400 nm increased by about 2 orders of magnitude, changing the single scattering albedo from a background level of 0.95 to 0.7. Based on the new retrieval method, we provide parameterizations of the wavelength‐dependent effective complex refractive index from 350 to 650 nm for freshly emitted and slightly aged biomass‐burning aerosols. In addition, PM2.5 filter samples were collected for detailed offline chemical analysis of the water‐soluble organics that contribute to light absorption. Nitroaromatics were identified as major organic species responsible for the increased absorption at 400 to 500 nm. Typical chromophores include 4‐nitrocatechol, 4‐nitrophenol, nitrosyringol, and nitroguaiacol; oxidation‐nitration products of methoxyphenols; and known products of lignin pyrolysis. Our findings emphasize the importance of both primary and secondary organic aerosols from biomass burning in absorption of solar radiation and in effective radiative forcing.

Reducing light-scattering losses in nanocolloids by increasing average inter-particle distance

First, we present a brief review of the theory of the complex effective refractive index of a disordered suspension of nanoparticles that take into account the effects of scattering by the particles. We present numerical examples of the dependence of the scattering losses in nanocolloids with the concentration of non-absorbing and weakly absorbing nanoparticles. Then, we explore a way to reduce scattering losses in colloidal suspensions of non-absorbing nanoparticles. Finally, we provide some physical insight into the dependence of scattering losses with the particle concentration.

A new approach for retrieving the UV–vis optical properties of ambient aerosols

Abstract. Atmospheric aerosols play an important part in the Earth's energy budget by scattering and absorbing incoming solar and outgoing terrestrial radiation. To quantify the effective radiative forcing due to aerosol–radiation interactions, researchers must obtain a detailed understanding of the spectrally dependent intensive and extensive optical properties of different aerosol types. Our new approach retrieves the optical coefficients and the single-scattering albedo of the total aerosol population over 300 to 650 nm wavelength, using extinction measurements from a broadband cavity-enhanced spectrometer at 315 to 345 nm and 390 to 420 nm, extinction and absorption measurements at 404 nm from a photoacoustic cell coupled to a cavity ring-down spectrometer, and scattering measurements from a three-wavelength integrating nephelometer. By combining these measurements with aerosol size distribution data, we retrieved the time- and wavelength-dependent effective complex refractive index of the aerosols. Retrieval simulations and laboratory measurements of brown carbon proxies showed low absolute errors and good agreement with expected and reported values. Finally, we implemented this new broadband method to achieve continuous spectral- and time-dependent monitoring of ambient aerosol population, including, for the first time, extinction measurements using cavity-enhanced spectrometry in the 315 to 345 nm UV range, in which significant light absorption may occur.