Determination of size, refractive index, and dispersion of single droplets from wavelength-dependent scattering spectra

Intensities of light scattered in the planes parallel and perpendicular to the polarization plane of the incident light are used to determine the size, refractive index, and dispersion of a single droplet suspended in an electrodynamic balance. Wavelengths of TE- and TM-mode resonances are determined independently with high precision when a ring dye laser is scanned. Resonating wavelengths are matched with theoretical intensity peaks to determine the constants of a dispersion formula and the size that minimizes the difference between observed and calculated wavelengths. The procedure permits the determination of the size and refractive index with relative errors of 3 × 10(-5) and dispersion with an absolute error 2 × 10(-5) over the experimental spectral range.     

Analysis of time-dependent scattering spectra for studying processes associated with microdroplets

Techniques are presented for analysis of time-dependent scattering spectra from single droplets undergoing physical changes. Times of appearance of resonances in experimental spectra are aligned with theoretical resonances, and the size and refractive index of a droplet as functions of time are determined from the minimum errors in alignment between observed and theoretical resonances. The techniques have been applied to time-dependent elastic scattering spectra obtained from single droplets evaporating under quasi-steady conditions and during unsteady growth. The results of quasi-steady evaporation data show that size and refractive index can be determined with relative errors of 1 x 10(-4). The quasi-steady evaporation data of a droplet are used to identify the resonances observed during the unsteady growth of the same droplet, and the size and refractive index at each resonance are calculated from the identity of the resonance.     

Optical properties of graphene based annular photonic crystals

The optical properties of a graphene based annular photonic crystal (APC) are theoretically investigated. The proposed structure is a hollow core cylindrical shell consists of the alternate dielectric layer and graphene monolayer immersed in free space. In order to study the photonic band structures of the APC, we obtained the optical spectra of the graphene based APC by employing the transfer matrix method in the cylindrical waves for both TE and TM polarizations. In this work we study the effect of different geometrical and optical parameters of the structure on the low loss high reflectance graphene induced band gap. It is found that the graphene induced band gap which appeared in the frequency below 10 THz is polarization independent and remains almost invariant with the change in the period number, the radius of the inner core region and the refractive indices of the inner core region and the surrounding medium. However, its width increases by increasing the azimuthal mode number and the chemical potential of the graphene monolayers and decreases by increasing the refractive index and the thickness of the dielectric layers.     

Observation of sudden temperature jumps in optically levitated microdroplets due to morphology-dependent input resonances

During the slow evaporation of an optically levitated microdroplet of a glycerol-water mixture (3:1) (approximately 12.44 μm in radius) several morphology-dependent input resonances have been observed in its Raman spectrum. These resonances yield sudden temperature jumps of approximately 10 °C in the microdroplet as evidenced by sudden shifts in the output (Raman) resonance spectra. The latter effects could be explained by a simple energy balance calculation and the dependence of droplet refractive index and density on temperature.     

氧化锌/二氧化硅复合膜的结构色研究

采用静电自组装技术,以氧化锌（ZnO）和二氧化硅（SiO2）溶胶颗粒为前驱体,通过控制双组分膜层的不同厚度,制备出结构色鲜艳的ZnO/SiO2复合膜,并利用分光测色仪、多角度分光光度仪及扫描电子显微镜等研究复合膜的颜色、微观结构和形态特征。研究结果发现,ZnO/SiO2复合膜的亮度和色度均较单一组分薄膜的高,复合薄膜的颜色仍随厚度和观察角度的变化而变化。通过对薄膜的微观结构分析,结合其厚度随周期数的变化规律,发现复合薄膜的厚度随着自组装循环次数的增加而增加,薄膜中的纳米粒子并没有形成明显的高低折射率交替分布的双层结构,可能形成的是高折射率层（H层）、有效折射率层（eff层）和低折射率层（L层）的多层微观结构。这种特殊的多层结构与光作用发生干涉,形成了鲜亮度和饱和度更高的结构色。     

Light scattering by a coated sphere illuminated with a Gaussian beam

The intensity of light scattered by a coated sphere illuminated with an off-axis Gaussian beam is calculated. Results are shown for different beam positions with respect to the sphere. As the beam is shifted further away from the surface of the sphere, the higher-Q morphology-dependent resonances become increasingly important in the backscatter spectra, and the angular scattering intensity becomes smoother.

The scattered intensity depends on the beam position, the refractive indices of the core and coat, the radius of the core, and the thickness of the coat. As the beam is moved further away from the sphere, the effect of the core on the scattering intensity decreases. When the incident Gaussian beam is focused outside of a particle with a relatively small core, the scattering spectra and angular scattering patterns become similar to those of a homogeneous sphere having the refractive index of the coat. These calculated results suggest that measurements of spectral scattering and angular scattering patterns for several Gaussian beam positions could be useful for the characterization of coated spheres.

     

Core and shell sizing of small silver-coated nanospheres by optical extinction spectroscopy

Silver metal nanoparticles (Nps) are extensively used in different areas of research and technology due to their interesting optical, thermal and electric properties, especially for bare core and core-shell nanostructures with sizes smaller than 10?nm. Since these properties are core-shell size-dependent, size measurement is important in manipulating their potential functionalization and applications. Bare and coated small silver Nps fabricated by physical and chemical methods present specific characteristics in their extinction spectra that are potentially useful for sizing purposes. This work presents a novel procedure to size mean core radius smaller than 10?nm and mean shell thickness of silver core-shell Nps based on a comparative study of the characteristics in their optical extinction spectra in different media as a function of core radii, shell thickness and coating refractive index. From the regularities derived from these relationships, it can be concluded that plasmon full width at half-maximum (FWHM) is sensitive to core size but not to coating thickness, while plasmon resonance wavelength (PRW) is related to shell thickness and mostly independent of core radius. These facts, which allow sizing simultaneously both mean core radius and shell thickness, can also be used to size bare silver Nps as a special case of core-shell Nps with zero shell thickness. The proposed method was applied to size experimental samples and the results show good agreement with conventional TEM microscopy.     

Accuracy of internal fields in volume integral equation simulations of light scattering

We studied the accuracy of volume integral equation simulations of internal fields in small particles illuminated by a monochromatic plane wave as well as the accuracy of the scattered fields. We obtained this accuracy by considering scattering by spheres and comparing the simulated internal and scattered fields with those obtained by Mie theory. The accuracy was measured in several error norms (e.g., mean and root mean square). Furthermore, the distribution of the errors within the particle was obtained. The accuracy was measured as a function of the size parameter and the refractive index of the sphere and as a function of the cube size used in the simulations. The size parameter of the sphere was as large as 10, and three refractive indices were considered. The errors in the internal field are located mostly on the surface of the sphere, and even for fine discretizations they remain relatively large. The errors depend strongly on the refractive index of the particle. If the discretization is kept constant, the errors depend only weakly on the size parameter. We also examined the case of sharp internal field resonances in the sphere. We show that the simulation is able to reproduce the resonances in the internal field, although at a slightly larger refractive index.     

Method to reduce errors of droplet sizing based on the ratio of fluorescent and scattered light intensities (laser-induced fluorescence/Mie technique)

The droplet sizing accuracy of the laser technique, based on the ratio of laser-induced fluorescence (LIF) and scattered light (Mie) intensities from droplets, is examined. We develop an analytical model of the ratio of fluorescent to scattered light intensities of droplets, which shows that the LIF/Mie technique is susceptible to sizing errors that depend on the mean droplet size and the spread of the droplet size distribution. The sizing uncertainty due to the oscillations of the scattered light intensity as a function of droplet size is first quantified. Then, a new data processing method is proposed that can improve the sizing uncertainty of the technique for the sprays that were examined in this study by more than 5% by accounting for the size spread of the measured droplets, while improvements of 25% are possible when accounting for the mean droplet size. The sizing accuracy of the technique is evaluated in terms of the refractive index of liquid, scattering angle, and dye concentration in the liquid. It is found that the proposed approach leads to sizing uncertainty of less than 14% when combined with light collection at forward scattering angles close to 60° and the lowest fluorescent dye concentration in the liquid for all refractive indices.     

Microphysical aerosol parameters from multiwavelength lidar

The hybrid regularization technique developed at the Institute of Mathematics of Potsdam University (IMP) is used to derive microphysical properties such as effective radius, surface-area concentration, and volume concentration, as well as the single-scattering albedo and a mean complex refractive index, from multiwavelength lidar measurements. We present the continuation of investigations of the IMP method. Theoretical studies of the degree of ill-posedness of the underlying model, simulation results with respect to the analysis of the retrieval error of microphysical particle properties from multiwavelength lidar data, and a comparison of results for different numbers of backscatter and extinction coefficients are presented. Our analysis shows that the backscatter operator has a smaller degree of ill-posedness than the operator for extinction. This fact underlines the importance of backscatter data. Moreover, the degree of ill-posedness increases with increasing particle absorption, i.e., depends on the imaginary part of the refractive index and does not depend significantly on the real part. Furthermore, an extensive simulation study was carried out for logarithmic-normal size distributions with different median radii, mode widths, and real and imaginary parts of refractive indices. The errors of the retrieved particle properties obtained from the inversion of three backscatter (355, 532, and 1064 nm) and two extinction (355 and 532 nm) coefficients were compared with the uncertainties for the case of six backscatter (400, 710, 800 nm, additionally) and the same two extinction coefficients. For known complex refractive index and up to 20% normally distributed noise, we found that the retrieval errors for effective radius, surface-area concentration, and volume concentration stay below approximately 15% in both cases. Simulations were also made with unknown complex refractive index. In that case the integrated parameters stay below approximately 30%, and the imaginary part of the refractive index stays below 35% for input noise up to 10% in both cases. In general, the quality of the retrieved aerosol parameters depends strongly on the imaginary part owing to the degree of ill-posedness. It is shown that under certain constraints a minimum data set of three backscatter coefficients and two extinction coefficients is sufficient for a successful inversion. The IMP algorithm was finally tested for a measurement case.     

Absolute refractometry of dry gas to ±3 parts in 10⁹

We present a method of measuring the refractive index of dry gases absolutely at 632.8 nm wavelength using a Fabry-Perot cavity with an expanded uncertainty of <3×10?? (coverage factor k=2). The main contribution to this uncertainty is how well vacuum-to-atmosphere compression effects (physical length variation) in the cavities can be corrected. This paper describes the technique and reports reference values for the refractive indices of nitrogen and argon gases at 100 kPa and 20 °C with an expanded uncertainty of <9×10?? (coverage factor k=2), with the additional and larger part of this uncertainty coming from the pressure and temperature measurement.     

Optimisation of distributed feedback laser biosensors

A new integrated optical sensor chip is proposed, based on a modified distributed- feedback (DFB) semiconductor laser. The semiconductor layers of different refractive indices that comprise a laser form the basis of a waveguide sensor, where changes in the refractive index of material at the surface are sensed via changes in the evanescent field of the lasing mode. In DFB lasers, laser oscillation occurs at the Bragg wavelength. Since this is sensitive to the effective refractive index of the optical mode, the emission wavelength is sensitive to the index of a sample on the waveguide surface. Hence, lasers are modelled as planar waveguides and the effective index of the fundamental transverse electric mode is calculated as a function of index and thickness of a thin surface layer using the beam propagation method. We find that an optimised structure has a thin upper cladding layer of ~0.15 mum, which according to this model gives detection limits on test layer index and thickness resolution of 0.1 and 1.57 nm, respectively, a figure which may be further improved using two lasers in an interferometer-type configuration.     

Refractive indices and thicknesses of optical waveguides fabricated by silicon ion implantation into silica glass

Planar optical waveguides formed by Si ion implantation into PECVD SiO₂ have been characterized by the dark mode spectroscopy method at a wavelength of 0.6328 μm. The measured effective index values of the guided modes have been used to investigate the optical properties of the core layers of the waveguides after different pre-implantation treatments. It was found that annealing the specimens before implantation, affected both the refractive index and thickness of the core layers. In the annealed specimens a thicker core layer and a larger relative refractive index difference between the core and the buffer layer resulted.     

Optical-constant calculation of non-uniform thickness thin films of the Ge10As15Se75 chalcogenide glassy alloy in the sub-band-gap region (0.1–1.8 eV)

Optical-transmission spectra are very sensitive to inhomogeneities in thin films. In particular, a non-uniform thickness produces a clear shrinking in the transmission spectrum at normal incidence. If this deformation is not taken into account, it may lead to serious errors in the calculated values of the refractive index and film thickness. In this paper, a method first applied by Swanepoel for enabling the transformation of an optical-transmission spectrum of a thin film of wedge-shaped thickness into the spectrum of a uniform film, whose thickness is equal to the average thickness of the non-uniform layer, has been employed. This leads subsequently to the accurate derivation of the refractive index in the subgap region (0.1–1.8 eV), the average thickness, as well as a parameter indicating the degree of film-thickness uniformity. This optical procedure is applied to the particular case of freshly-prepared films of the Ge₁₀As₁₅Se₇₅ ternary chalcogenide glassy alloy. The dispersion of the refractive index is discussed in terms of the Wemple–DiDomenico single-oscillator model. The optical-absorption edge is described using the ‘non-direct transition' model proposed by Tauc, and the optical energy gap is calculated by Tauc's extrapolation. Finally, the photo-induced and thermally induced changes in the optical properties of the a-Ge₁₀As₁₅Se₇₅ layers are also studied.     

Rainbow refractometry: simultaneous measurement of temperature, refractive index, and size of droplets

The capabilities and limitations of rainbow refractometry, specifically the minimum measurable droplet size and the errors in the refractive index (temperature), have been studied. We evaluate what we believe is a new method of indirectly applying the Lorenz-Mie theory to rainbow refractometry. The results show that this new method reduces the errors and eliminates the biases that may occur if the Airy theory is used. A more precise method to filter the high-frequency oscillations associated with the measurement signals was developed. Finally, it was discovered that the errors associated with rainbow refractometry are such that a single droplet measurement is unreliable. A mean refractive index should be determined on the basis of multiple droplet measurements.     

Refractive-index measurements of natural air-hydrate crystals in an Antarctic ice sheet

The refractive index of air-hydrate crystals found in a deep Antarctic ice sheet was measured for the first time, as far as we know, using a Mach-Zehnder interferometer. A small difference between the refractive indices of the air-hydrate crystals and the matrix ice crystal was measured by the fringe-shift method. It was found that the refractive indices of all air-hydrate crystals were larger than those of ice, and the average difference was 5.3 × 10(-3), even considering the refractive-index anisotropy of ice crystals. Because the refractive indices depend on the occupancy ratio of cagelike cavities by air molecules, we compared the experimental results with the calculated values using the Onsager cavity model. We determined that the present method is useful for estimation of the cavity occupancy ratio of air-hydrate crystals and also of the amount of air molecules in polar ice cores.     

Simulation and optimization of polymer-coated microsphere resonators in chemical vapor sensing

This study presents a chemical vapor sensor based on polymer-coated microsphere resonators. A theoretical simulation of the sensor response is performed, and optimization of the polymer layer thickness is investigated. Results show that the sensor exhibits a good linearity and a low detection limit of the refractive index change. Especially at the thermostable thickness of the polymer layer, the refractive index detection limit of the wavelength around 780 nm can be as low as ~2×10?? refractive index unit for a spectral resolution of 10 fm, without any temperature control. Because of the good sensing performance and simple manipulation, the proposed sensor is a very promising platform for chemical vapor detections.     

Long-period grating refractive index sensor with a modified cladding structure for large operational range and high sensitivity

What is believed to be a novel long-period grating (LPG) refractive index sensor with a modified cladding structure is proposed and studied. In the proposed structure, the cladding of the fiber has a two-layer structure, i.e., a cladding layer of low refractive index with a reduced radius and an overlay of high refractive index. The sensitivity of the structure-modified LPG sensor to the ambient refractive index change as a function of the cladding layer and overlay parameters is investigated by way of modeling. It is found that an increase of the ambient refractive index causes a field redistribution of the cladding mode into the overlay when the parameters of the overlay are properly selected. It is shown that by reducing the radius of the cladding layer, the operational range of the LPG refractive index sensor can be as large as 0.195 (from 1.244 to 1.440) with a minimum sensitivity of 660 nm/refractive index, which represents a 31% increase of operational range in comparison with the operational range obtained from the reported structure. The design guidelines for achieving this large operation range and high sensitivity are explained by investigating the dependence of the cladding modes on the radius of the cladding layer.     

Heterodyne polariscope for sequential measurements of the complete optical parameters of a multiple-order wave plate

A new heterodyne polariscope for sequential measurements of the complete optical parameters of linearly birefringent materials is proposed. A multiple-order crystalline quartz quarter-wave plate used as a sample was tested in two sequential setups. In the first setup we used an electro-optic modulator to modulate the circular heterodyne polariscope and then applied a phase-locking technique to measure the principal axis angle precisely. In the second setup, removing the first quarter-wave plate, resulted in a linear heterodyne polariscope, and again we used the phase-locking technique to extract the apparent retardance. Furthermore, by tilting the sample and placing a material of known thickness into the second setup, we determined the order, thickness, and refractive indices (ne and no) of a multiple-order wave plate by using the new algorithm. The proposed method has average absolute errors of 0.2167 degrees and 0.15% with respect to the principal axis angle and the apparent retardance, respectively. The order, thickness, and refractive indices are also in good agreement with the known sample data. In contrast to the conventional measurement schemes that could not measure more than two parameters, the proposed heterodyne polariscope uniquely measures six parameters.     

A simple method for fabricating a Mach-Zehnder type waveguide using sol-gel derived photopatternable hybrid materials for optical biosensors

In this work, we report on a simple method to fabricate a Mach-Zehnder type waveguide pattern using photopatternable sol-gel organic-inorganic hybrid materials. The refractive indices and propagation losses of the gel films were measured using the prism coupling method. The refractive indices of the resulting films were significantly influenced by the 3-trimethoxysilylpropylmethacrylate (TMSPM) concentration, and the average propagation loss was 0.32-0.52 dB/cm at the wavelength of 632.8 nm. The waveguides were fabricated using spin-coating and a photolithography technique. The Y-branch and straight pattern of the Mach-Zehnder waveguide were well-defined and had high transparency (> 97%) in the visible region. The average thickness of the gel films was 10 microm, and the average width of the Mach-Zehnder pattern was 10 microm. The structural and optical properties of the fabricated patterns were analyzed using scanning electron microscopy (SEM), atomic force microscopy (AFM), near-infrared (IR) spectroscopy, and ultraviolet (UV)-visible spectroscopy.