Phase-Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity

The principle of the dual burst technique (DBT) based on phase-Doppler anemometry (PDA) is proposed for simultaneous particle refractive index, size and velocity measurements. This technique used the trajectory effects in PDA systems to separate the two contributions of the different scattering processes. In the case of forward scattering and refracting particles, it is shown that from the phase of the reflected contribution, the particle diameter can be deduced, whereas from the refracted contribution the particle refractive index and velocity can be obtained. Furthermore, the intensity ratio of these two scattering processes can be used for absorption measurements. Simulations based on generalized Lorenz-Mie theory and experimental tests using monodispersed droplets of different refractive indices and absorption coefficients have validated this technique.     

光在光轴取向任意条件下的晶体表面透射率

为了分析一束光在晶体表面的能量损失以及两束折射光的能量比,给出了一种求解反射率和透射率的方法。讨论了光从各向同性介质入射到单轴晶体表面时的折射和反射,注意到了e光线与e光波方向的不同,e光折射率与e光波法线折射率的不同,得出了在界面处应该满足的边界方程。在晶体光轴取向任意的条件下,给出了表明各光束间能量关系的折射率和反射率的理论表达式,为晶体器件特性的研究提供了有力的理论工具。数值模拟表明:得到的结果满足能量守恒;反射到各向同性介质中的光的电场(或磁场)与原入射光的电场(或磁场)不再平行;光轴的取向和入射角的大小对折射的o光、e光的能量比有很大的影响。     

Geometrical optics approximation for light scattering by absorbing spherical particles

By means of geometrical optics, an approximation method is presented to compute the light scattering intensity of absorbing spherical particles illuminated by a plane wave. For absorbing particles, the effective refractive index and the effective refractive angle are related to the complex refractive index and incident angle. The formulas for calculation of the break of phases of reflection and refraction, which are different from the case of transparent particles, are exactly derived. Verification of the geometrical optics approximation (GOA) was performed by case studies and comparison of the present results with the Mie scattering. It is found that agreement between the GOA and the Mie theory is excellent in forward directions for weakly/moderately absorbing particles. Differently, for strongly absorbing particles, good agreement between the calculation methods is in the forward directions and large scattering angles. The agreement between the GOA and the Mie theory is better for larger particles.     

光在双轴晶体表面的反射与折射

介绍了光在双轴晶体表面反射、折射问题的求解方法.用该方法可以方便精确地计算晶体任意取向下光从任意方向入射时折射光的折射率、偏振态、波矢方向、能流方向. 推导了反射光、折射光的振幅和能量的计算公式. 并以KTP晶体为例，给出了数值计算的结果. 关键词： 双轴晶体 双折射 菲涅耳公式 布儒斯特角     

Optical properties of grooved silicon microstructures: Theory and experiment

The reflection spectra of grooved silicon structures consisting of alternating silicon walls and grooves (air channels) with a period of a = 4–6 μm are studied experimentally and theoretically in the mid-IR spectral range (2–25 μm) upon irradiation of samples by normally incident light polarized along and perpendicular to silicon layers. The calculation is performed by the scattering matrix method taking into account Rayleigh scattering losses in a grooved layer by adding imaginary parts to the refractive indices of silicon and air in grooved regions. The experimental and calculated reflection spectra are in good agreement in the entire spectral range studied. The analysis of experimental and calculated spectra gave close values of the effective refractive indices and birefringence of the studied structures in the long-wavelength spectral region. The values calculated in the effective medium model in the long-wavelength approximation (λ ≫ a) gave considerably understated values. The obtained results confirm the efficiency of the scattering matrix method for describing the optical properties of silicon microstructures.     

Optical colours and polarization of a model reflection nebula

Simple models of a reflection nebula in the form of a plane-parallel slab containing smooth spherical solid particles in submicron size range have been considered. Single scattering has been assumed. The effect of varying the composition and size distribution function of the grains have been brought out in the calculations using Mie theory of scattering. The analytical part of the geometry of the problem has been treated quite rigorously and the resulting expression for nebular intensity has been presented in a somewhat new form. In this paper, the case of the star behind the nebula has been examined. A comparison of the theoretical results with the observations of the Merope nebula shows that the dirty ice grains with index of refraction about 1·3–0·1i and size parametera ₀ = 0·5μ give reasonable agreement with the colours. Simultaneously, the polarization in the visual and blue wavelength bands agree approximately up to offset angle of 6 minutes of arc. The larger offset angles pose an intriguing problem. The general trends of nebular colours and polarization with variation of real and imaginary parts of index of refraction and the size distribution parameter have been tabulated to serve as a guide for further study of reflection nebulae with the star in the rear. A part of this work was presented at the first scientific meeting of the Astronomical Society of India, held on 27 and 28 February 1974 at Hyderabad. An erratum to this article is available at .     

Some Far-Field Scattering Characteristics of Radially Inhomogeneous Particles

The finely stratified sphere model was used to calculate scattered electromagnetic fields from radially inhomogeneous spherical particles illuminated by electromagnetic plane waves. The calculation results show that radial gradients of the real part of the refractive indices change the ray paths into curved lines inside large spherical particles, resulting in fluctuations of rainbow positions for droplets during heat transfer processes. The light intensity in the forward scattering region is found to be useful to infer information about the profile of the imaginary part of the refractive index.     

An “exact” geometric-optics approach for computing the optical properties of large absorbing particles

Based on the principles of geometric optics, the ray-tracing technique has been extensively used to compute the single-scattering properties of particles whose sizes are much larger than the wavelength of the incident wave. However, the inhomogeneity characteristics of internal waves within an absorbing particle, which stem from a complex index of refraction, have not been fully taken into consideration in the geometric ray-tracing approaches reported in the literature for computing the scattering properties of absorbing particles. In this paper, we first demonstrate that electromagnetic fields associated with an absorbing particle can be decomposed into the TE and TM modes. Subsequently, on the basis of Maxwell's equations and electromagnetic boundary conditions for the TE-mode electric field and the TM-mode magnetic field, we derive generalized Fresnel reflection and refraction coefficients, which differ from conventional formulae and do not involve complex angles. Additionally, a recurrence formulism is developed for the computation of the scattering phase matrix of an absorbing particle within the framework of the conventional geometric ray-tracing method. We further present pertinent numerical examples for the phase function and the degree of linear polarization in conjunction with light scattering by individual absorbing spheres, and discuss the deviation of the geometric optics solutions from the exact Lorenz-Mie results with respect to size parameter and complex refractive index.     

Development of an optical refractometer by analysis of one-dimensional photonic bandgap structures with defects

A theoretical analysis of an optical fiber photonic-bandgap-based refractometer is presented. The design is based on a quarter-wave reflector with one defect. By modifying both the real and the imaginary parts of the index of refraction of the defects we begin to change either the frequency or the amplitude of the localized optical mode. So we could fabricate a specific optical fiber refractometer by combining all the variables: index of refractive index of the defects and the rest of layers, thickness of the defect, number of layers, etc. to yield a large set of design possibilities, for example, detecting wider or thinner ranges of refractive indices, or controlling the detection accuracy. Some rules for the practical implementation of the refractometer are given.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.     

On geometric optics and surface waves for light scattering by spheres

A geometric optics approach including surface wave contributions has been developed for homogeneous and concentrically coated spheres. In this approach, a ray-by-ray tracing program was used for efficient computation of the extinction and absorption cross sections. The present geometric-optics surface-wave (GOS) theory for light scattering by spheres considers the surface wave contribution along the edge of a particle as a perturbation term to the geometric-optics core that includes Fresnel reflection–refraction and Fraunhofer diffraction. Accuracies of the GOS approach for spheres have been assessed through comparison with the results determined from the exact Lorenz–Mie (LM) theory in terms of the extinction efficiency, single-scattering albedo, and asymmetry factor in the size–wavelength ratio domain. In this quest, we have selected a range of real and imaginary refractive indices representative of water/ice and aerosol species and demonstrated close agreement between the results computed by GOS and LM. This provides the foundation to conduct physically reliable light absorption and scattering computations based on the GOS approach for aerosol aggregates associated with internal and external mixing states employing spheres as building blocks.     

气溶胶粒子散射和吸收特性对复折射率依赖性的数值研究

利用米散射理论数值计算分析了尺度参数为0.1~100时球形典型气溶胶粒子的散射和吸收特性对复折射率的依赖性关系。气溶胶粒子复折射率的实部和虚部是一个有机的整体,粒子复折射率的实部和虚部可以分别影响其散射和吸收特性。若实际大气气溶胶粒子大多是成核模态和积聚模态的小粒子,基于气溶胶的散射和吸收特性可以获得其复折射率的唯一解。但是,如果大气中存在大量的粗模态粒子时,气溶胶散射和吸收特性对其复折射率的依赖性较为复杂,只有选择有限的合适复折射率库区间,才有可能获得更合适的有效复折射率。     

Soft X‐ray refractive index by reconciling total electron yield with specular reflection: experimental determination of the optical constants of graphite

The complex refractive index of many materials is poorly known in the soft X‐ray range across absorption edges. This is due to saturation effects that occur there in total‐electron‐yield and fluorescence‐yield spectroscopy and that are strongest at resonance energies. Aiming to obtain reliable optical constants, a procedure that reconciles electron‐yield measurements and reflection spectroscopy by correcting these saturation effects is presented. The procedure takes into account the energy‐ and polarization‐dependence of the photon penetration depth as well as the creation efficiency for secondary electrons and their escape length. From corrected electron‐yield spectra the absorption constants and the imaginary parts of the refractive index of the material are determined. The real parts of the index are subsequently obtained through a Kramers–Kronig transformation. These preliminary optical constants are refined by simulating reflection spectra and adapting them, so that measured reflection spectra are reproduced best. The efficacy of the new procedure is demonstrated for graphite. The optical constants that have been determined for linearly polarized synchrotron light incident with p‐ and s‐geometry provide a detailed and reliable representation of the complex refractive index of the material near π‐ and σ‐resonances. They are also suitable for allotropes of graphite such as graphene.     

Numerical approach for depth profiling with GE‐XRF

The atomic percentage of implanted particles on the sample surface was estimated from the peak position of angle dependency of the experimental grazing exit X‐ray fluorescence (GE‐XRF) intensity profile. An algorithm for constructing three‐parametric Gaussian‐type depth profiles of atoms implanted in a substrate was developed. The position of the maximum and its value of the implanted particles distribution as well as a dispersion of that distribution were considered in the calculations. The model was applied to the intensity of the As Kα line emitted from As atoms implanted in a Si wafer. The least‐square method was used to minimize the overall difference between experimental and calculated GE‐XRF intensity. Optimum parameters of the particle distribution were determined in this procedure. Using that profile, the depth dependencies of effective real and imaginary parts of atomic scattering factor and complex index of refraction of the sample material were evaluated. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermally tempered glass surface stress measurement by critical ray

A critical ray was excited along the glass surface by laser beam incidence. Part of the critical ray was refracted during propagation. The angle of refraction depended on the refractive index of the glass sirface. When the glass surface was birefringent due to the photoelastic effect, the angles of refraction differed from each other between two linearly polarized beams. This difference allows surface stress determination.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

The Phase-Doppler-Difference-Method,a New-Laser-Doppler Technique for Simultaneous Size and Velocity Measurements. Part 2: Optical particle characteristics as a base for the new diagnostic technique

Simultaneous size and velocity measurements can be obtained by using photodetector positions of different off-axis-angles. But not for all of these positions one receives unambiguous results for the correlation between the phase difference and the particle diameter. This can be clearly demonstrated by the plots of the numerical calculations of the complete Mie's scattering equations. These plots show that for transparent particles which exceed the continuous phase in density at special off-axis-angles the situation of light refraction changes into a situation of additional light reflection or vice versa. On the other hand for transparent particles which are less dense compared with the continuous phase and for totally absorbing materials these plots confirm the simplified equations for reckoning the particle diameter by the laws of geometrical optics. The good agreement between these results can also be verified for the backscatter mode for measurements of metallic spheres with an imaginary refractive index.     

On a characteristic feature of electromagnetic wave attenuation by a spherical particle in absorbing medium

We analyze attenuation of a plane electromagnetic wave by a homogeneous spherical particle in absorbing medium. Relations between the values of imaginary and real parts of the complex refractive index of the medium, which result in negative values of attenuation in the Rayleigh approximation, are obtained for the particular case of a nonabsorbing spherical cavity in a medium with absorption. We given an example of negative attenuation due to small air bubbles in water in the range of centimeter waves. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 12, pp. 1489–1494, December, 1997.     

Reflexion und Brechung an optisch einachsigen Medien in Richtung fehlender Doppelbrechung

Reflection and Refraction at Uniaxial Media in Directions of Vanishing Double Refraction The amplitude relations for the reflection and refraction of plane monochromatic waves by uniaxial media in the case of vanishing double refraction of the refracted respectively reflected waves in the uniaxial medium are obtained by a limiting process from generalized Fresnel formulae earlier derived. The incidence both from the isotropic and from the uniaxial medium is considered. The boundary conditions may be fulfilled in the case considered only by addition of refracted respectively reflected waves with amplitudes varying linearly with the distance from the boundary plane in the uniaxial medium. The requirement of vanishing double refraction restricts the possible choice of the common tangential components of all refraction vectors and consequently also of the refraction vectors of incident waves from a primarily twodimensional complex manifold to onedimensional complex manifolds, which are determined in this paper.     

Diffraction and external reflection by dielectric faceted particles

The scattering of light by dielectric particles much larger than the wavelength of incident light is attributed to diffraction, external reflection and outgoing refracted waves. This paper focuses on diffraction and external reflection by faceted particles, which can be calculated semi-analytically based on physical optics. Three approximate methods; the surface-integral method (SIM), the volume-integral method (VIM), and the diffraction plus reflection pattern from ray optics (DPR) are compared. Four elements of the amplitude scattering matrix in the SIM and the VIM are presented in an explicit form. Of interest is that diffraction and external reflection are separable in the SIM, whereas they are combined in the VIM. A feature of zero forward reflection is noticed in the SIM. The applicability of the DPR method is restricted to particles with random orientations. In the manner of van de Hulst, we develop a new technique to compute the reflection pattern of randomly oriented convex particles using spheres with the same refractive index, resulting in an improvement in the precision of the reflection calculation in near-forward and near-backward directions. The accuracy of the aforementioned three methods is investigated by comparing their results with those from the discrete-dipole-approximation (DDA) method for hexagonal particles at the refractive index of 1.3+i1.0. For particles with fixed orientations, it is found that the SIM and the VIM are comparable in accuracy and applicable when the size parameter is on the order of 20. The ray-spreading effect on the phase function is evident from the results of various size parameters. For randomly oriented particles, the DPR is more efficient than the SIM and the VIM.