Notes on Rayleigh scattering in lidar signals

Classical and quantum formulations are used to estimate Rayleigh scattering within lidar signals. Within the classical approach, three scenarios are used to characterize atmospheric molecular composition: 2-component atmosphere (N2 and O2), 4-component atmosphere (N2, O2, Ar, and CO2), and 5-component atmosphere (N2, O2, Ar, CO2, and water vapor). First, analysis focuses on Rayleigh scattering, showing the relative difference between the three scenarios within classical approach. The relative difference in molecular scattering between 2(4)-component atmosphere and 5-component atmosphere is below ~1%. The second analysis focuses on the lidar retrieval of aerosol backscatter and extinction coefficients showing the effect of different molecular formulations. A relative difference of ±3% was found between the molecular formulation of 2-component atmosphere and the molecular formulation of 5-component atmosphere. Consideration of the Raman rotational lines blocked by the interference filter is important for the elastic channels, but of little significance in the N2 Raman channel. For lidar retrieval of aerosol profiles, the 5-component approximation is the best when the water vapor profile is known, but 2-component is still adequate and quite accurate when water vapor is only poorly known.     

Differential Rayleigh scattering method for measurement of polarization and intermodal beat length in optical waveguides and fibers

We propose a modification of the Rayleigh scattering method, which allows for measurement of polarization and intermodal beat length in single-mode and few-mode channel waveguides and optical fibers. A significant sensitivity increase is achieved by taking two high-resolution photographs in oblique scattered light of π-shifted intensity distributions produced by interference of polarization or spatial modes and applying Fourier analysis to the differential image. In the case of polarization beat length measurements, the π-phase shift is obtained by switching the polarization state at the fiber input, while in intermodal measurements, the π-phase shifting is realized by changing the excitation conditions. The usefulness of the method for characterization of channel waveguides and optical fibers is demonstrated in several examples. Moreover, we show that the combination of the spectral interferometry method with the proposed method allows for broadband measurements of differential phase and group effective indices.     

Rayleigh scattering from ions near threshold

Theoretical studies of Rayleigh scattering of photons from neon atoms with different degrees of ionization, for energies both below and above the K-edges of the ions, are presented. Some unexpected structures both in Rayleigh scattering and in photoionization from neutral and weakly ionized atoms, very close to threshold, have been reported. It has recently been realized that some of the predicted structures may have a nonphysical origin and are due to the limitation of the independent-particle model and also to the use of a Coulombic Latter tail. Use of a K-shell vacancy potential — in which an electron is assumed to be removed from the K-shell — in calculating K-shell Rayleigh scattering amplitudes removes some of the structure effects near threshold. We present in this work a discussion of scattering angular distributions and total cross sections, obtained utilizing vacancy potentials, and compare these predictions with those previously obtained in other potential models.     

Rayleigh scattering in a ring system

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 28–29, October, 1991.     

Arbitrary three-dimensional polarization control based on cylindrical vector beams and binary phase coding

To obtain an arbitrary polarization in three dimensions is of significant interest for many applications. Here, we demonstrate a configuration to achieve it. After phase coding by binary phase plates, two cylindrical polarized beams are superposed and focused by a high-numerical aperture lens to obtain transversally and radially polarized components in the focus vicinity. By adjusting their intensity and phase difference, the desired three-dimensional polarization can be achieved. The proportion of the desired polarization is extremely high and the focus spot is smaller than the diffraction-limited spot size.     

Rayleigh scattering in elastic composite materials

This paper is devoted to long wave propagation in heterogeneous media. More specifically, we deal with Rayleigh diffraction in elastic materials with a periodic microstructure whose heterogeneities are in finite concentration or show great contrasts in properties.

This study is based on the homogenization method but contrary to the usual procedure in which only the first significant terms are used, the developments are established up to the third order. We demonstrate that the terms of a superior order successively introduce effects of polarization, of celerity dispersion and of attenuation and we thus bring to the fore a characteristic distance of mode conversion. Finally we demonstrate that the effect of dispersion alone appears in macroscopically isotropic materials.     

Calibration of laser-saturated fluorescence measurements using Rayleigh scattering

Calibration of laser-saturated fluorescence measurements using Rayleigh scattering is presented as an alternative to absorption. This new procedure is advantageous when measuring radical species at concentrations well below the corresponding detection limit for absorption. The calibration accounts for nonuniform laser irradiation by extracting the local fluorescence emission along the laser axis and works equally well for both saturated and near-saturated center-line conditions. The predicted error due to misfocusing of the collection optics is nearly negligible when the measured fluorescence is within 10% of its peak value. Number densities obtained using this method are within 15% of those obtained from absorption measurements.     

Hard X-ray polarimetry by means of Rayleigh scattering

A new linear polarimetry technique based on Rayleigh scattering is introduced. Its properties are compared to the Compton technique. Experimental verification was realized using a 5×5 segmented planar HPGe pixel detector. In the proof-of-principle experiment a measurement of Rayleigh scattering off lead atoms was performed for linearly polarized photons at two scattering angles.     

Comparison between measurements on Rayleigh scattering and form-factor theories for

From our measured differential cross section of Rayleigh scattering, the form factor for momentum transfers in the range was deduced. Data for U, Pb, Pt, W, Sn, Cd, Ag, Mo and Cu at energies from 60 to 662 keV and scattering angles ranging from 5° to 140° were used. In addition, for the region of momenta, experimental data from other authors at higher energies were analyzed. The experimental values obtained were compared with various form-factor theories and limits of validity are established. For the relativistic modified form factor G a good agreement always exists for θ ≤ 65°, independently of energy and atomic number.     

A polarization theory for the scattering of sound at imperfect interfaces

In a recent article the author gave a general theory of scattering by thin layers included in a continuous matrix. Such layers may be thought of as plates, shells, coatings, or interface layers depending on the particular physical context. It was shown that, in the general case, the scattering may be described in terms of the stress and momentum polarizations in the layer and that when the latter is thin compared with the wavelength of the incident sound, the through-thickness average polarizations satisfy certain boundary integral equations. In this article we develop the theory in the context of imperfect interfaces such as those which may occur in adhesive and diffusion bonds. The advantage of this approach is that it can account for general inhomogeneities and interfacial roughness provided that the root mean square thickness is small compared with the wavelength.     

Tip-enhanced Rayleigh scattering and photoluminescence from semiconductor nanoparticles

Tip-enhanced Rayleigh scattering images of Ge quantum dots grown on a Si substrate have been observed at room temperature. Changing the wavelength of the incidence light from 405 to 590 nm, the contrast of the images is reversed. It is found that the scattering intensity depends on the dielectric constants of the materials under the probe. By changing the wavelength of the incident light, we have obtained information about the dielectric constant dispersion of single Ge quantum dots. The spectral peak position of single Ge quantum dots is found to shift to higher energy, compared to that of bulk Ge. Tip-enhanced photoluminescence from an In0.25Ga0.75N film at room temperature has also been reported. The strong local enhancement of the photoluminescence of the localized excitons has been observed in the vicinity of a gold nano-particle attached to the end of the probe. A coupling to plasmons in the gold nano-particle yields strong enhancement of the photoluminescence.     

Spectral degree of polarization uniformity for polarization-sensitive OCT

Depolarization of light can be measured by polarization-sensitive optical coherence tomography (PS-OCT) and has been used to improve tissue discrimination as well as segmentation of pigmented structures. Most approaches to depolarization assessment for PS-OCT – such as the degree of polarization uniformity (DOPU) – rely on measuring the uniformity of polarization states using spatial evaluation kernels. In this article, we present a different approach which exploits the spectral dimension. We introduce the spectral DOPU for the pixelwise analysis of polarization state variations between sub-bands of the broadband light source spectrum. Alongside a comparison with conventional spatial and temporal DOPU algorithms, we demonstrate imaging in the healthy human retina, and apply the technique for contrasting hard exudates in diabetic retinopathy and investigating the pigment epithelium of the rat iris.     

Depolarization index and the average degree of polarization

Two single number metrics for depolarization of samples are contrasted: (1) the average degree of polarization of the exiting light averaged over the Poincaré sphere and (2) the depolarization index of Gill and Berbenau [Opt. Acta 32, 259-261 (1985); 33, 185-189 (1986)1. The depolarization index is a geometric measure that varies from 0 for the ideal depolarizer to 1 for nondepolarizing Mueller matrices. The average degree of polarization also varies from 0 to 1 and characterizes the typical level of depolarization. Although the depolarization index is very often close to the average degree of polarization, these two metrics can differ by more than 0.5 for certain Mueller matrices.     

Room-temperature phosphorescence chemosensor and Rayleigh scattering chemodosimeter dual-recognition probe for 2,4,6-trinitrotoluene based on manganese-doped ZnS quantum dots

Rayleigh scattering (RS) as an interference factor to detection sensitivity in ordinary fluorescence spectrometry is always avoided in spite of considerable efforts toward the development of RS-based resonance Rayleigh scattering (RRS) and hyper-Rayleigh scattering (HRS) techniques. Here, combining advantages of quantum dots (QDs) including chemical modification of functional groups and the installation of recognition receptors at their surfaces with those of phosphorescence such as the avoidance of autofluorescence and scattering light, l-cys-capped Mn-doped ZnS QDs have been synthesized and used for room-temperature phosphorescence (RTP) to sense and for RS chemodosimetry to image ultratrace 2,4,6-trinitrotoluene (TNT) in water. The l-cys-capped Mn-doped ZnS QDs interdots aggregate with TNT species induced by the formation of Meisenheimer complexes (MHCs) through acid-base pairing interaction between l-cys and TNT, hydrogen bonding, and electrostatic interaction between l-cys intermolecules. Although the resultant MHCs may quench the fluorescence at 430 nm, interdots aggregation can greatly influence the light scattering property of the aqueous QDs system, and therefore, dominant RS enhancement at defect-related emission wavelength was observed under the excitation of violet light of Mn-doped ZnS QDs, which was applied in chemodosimetry to image TNT in water. Meanwhile, Mn-doped ZnS QDs also exhibited a highly selective response to the quenching of the (4)T(1)-(6)A(1) transition emission (RTP) and showed a very good linearity in the range of 0.0025-0.45 μM TNT with detection limit down to 0.8 nM and RSD of 2.3% (n = 5). The proposed methods are well-suited for detecting the ultratrace TNT and distinguishing different nitro compounds.     

A volume-perturbation approach to the problem of Rayleigh wave scattering at a rectangular groove

The problem of scattering of Rayleigh waves at a rectangular groove is addressed. Grooves are known to excite bulk waves upon scattering and, hence, are potential sources (albeit secondary) in bulk-acoustic-wave (BAW) devices. The groove is formulated as a volume perturbation of the geometry. A modal method is used, and the results of Rayleigh wave reflection as well as bulk wave radiation are obtained and compared with the results available in the literature. The method is compared with the boundary perturbation formulation. The equivalence of the boundary perturbation method and the volume perturbation method is shown.     

Rayleigh scattering studies on inter-layer interactions in structure-defined individual double-wall carbon nanotubes

Although the inter-layer coupling in layered materials has attracted considerable interest due to its importance in determining physical properties of two-dimensional systems, studies on the inter-layer coupling in one-dimensional systems have so far been limited. Double-wall carbon nanotubes (DWCNTs) are one of the most fundamental and ideal model systems to study the inter-layer coupling in one-dimensional systems. In this work, Rayleigh scattering spectroscopy and transmission electron microscopy are used to characterize the electronic transition between inner-and outer-nanotubes of the exactly same individual DWCNT. We find that the inter-layer coupling is strong, leading to downshifts in most of the optical transition energies (up to ～0.2 eV) compared to isolated CNTs. We also find that the presence of metallic tubes lead to stronger shifts. The inter-layer screening of Coulomb interactions is one of the key factors in explaining the observed results.      

Mie and Rayleigh modeling of visible-light scattering in neonatal skin

Reduced-scattering coefficients of neonatal skin were deduced in the 450-750-nm range from integrating-sphere measurements of the total reflection and total transmission of 22 skin samples. The reduced-scattering coefficients increased linearly at each wavelength with gestational maturity. The distribution of diameters d and concentration ρ(A) of the skin-sample collagen fibers were measured in histological sections of nine neonatal skin samples of varying gestational ages. An algorithm that calculates Mie scattering by cylinders was used to model the scattering by the collagen fibers in the skin. The fraction of the reduced-scattering coefficient μ(s)' that was attributable to Mie scattering by collagen fibers, as deduced from wavelength-dependent analysis, increased with gestational age and approached that found for adult skin. An assignment of 1.017 for n(rel), the refractive index of the collagen fibers relative to that of the surrounding medium, allowed the values for Mie scattering by collagen fibers, as predicted by the model for each of the nine neonatal skin samples to match the values for Mie scattering by collagen fibers as expected from the measurements of μ(s)'. The Mie-scattering model predicted an increase in scattering with gestational age on the basis of changes in the collagen-fiber diameters, and this increase was proportional to that measured with the integrating-sphere method.     

Rayleigh scattering of silica core optical fiber after heat treatment

We investigated the Rayleigh scattering of silica core optical fibers, parts of which were heat treated at various temperatures, in relation to their fictive temperatures (T(f)). The scattering intensities from short fiber segments were clearly reduced by heat treatment compared with those of the unheated parts. The T(f) values of the heated parts of the fibers were determined by measuring the infrared reflection spectrum for cleaved end surfaces and were also reduced by controlling the heating temperature. The reduction in the scattering intensity correlates well with the reduction in T(f).     

Precision of moment-based estimation of the degree of polarization in coherent imagery without polarization device

We propose and analyze a statistical method to estimate the degree of polarization of light from a single speckle intensity image by analyzing the statistical distribution of the light intensity. The optimal precision of such an estimation method is evaluated by computing the Cramer-Rao bounds for several speckle degrees. Two moment-based estimators of the square degree of polarization are introduced and characterized. For the first time to our knowledge, it is shown theoretically and through simulations that the estimators are almost efficient for high orders of speckle. The robustness of the method is discussed for the case when the intensity fluctuations do not follow the standard speckle model.     

Simultaneous optical signal-to-noise ratio and differential group delay monitoring based on degree of polarization measurements in optical communications systems

We present a simultaneous optical signal-to-noise ratio (OSNR) and differential group delay (DGD) monitoring method based on degree of polarization (DOP) measurements in optical communications systems. For the first time in the literature (to our best knowledge), the proposed scheme is demonstrated to be able to independently and simultaneously extract OSNR and DGD values from the DOP measurements. This is possible because the OSNR is related to maximum DOP, while DGD is related to the ratio between the maximum and minimum values of DOP. We experimentally measured OSNR and DGD in the ranges from 10 to 30 dB and 0 to 90 ps for a 10 Gb/s non-return-to-zero signal. A theoretical analysis of DOP accuracy needed to measure low values of DGD and high OSNRs is carried out, showing that current polarimeter technology is capable of yielding an OSNR measurement within 1 dB accuracy, for OSNR values up to 34 dB, while DGD error is limited to 1.5% for DGD values above 10 ps. For the first time to our knowledge, the technique was demonstrated to accurately measure first-order polarization mode dispersion (PMD) in the presence of a high value of second-order PMD (as high as 2071 ps(2)).