- Absorption
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- Chong YD and Stone 2011 showed theoretically that nearly perfect wave absorption can occur in a random scattering medium, even when the underlying material absorption is weak (i.e. the ratio of the transport scattering mean free path to the ballistic absorption length is small). Using a random matrix theoretical argument (based on the work of Bruce NA and Chalker JT 1996), they showed that the reflectance of an "extremal" incident wave (one corresponding to an extremal eigenvector of the reflectance matrix) vanishes on average as the inverse square of the number of scattering channels, whereas the average reflectance is independent of the number of scattering channels. Numerical simulations agreed with the analytical predictions to within 1% accuracy in the calculated reflectances, with no independently tunable degrees of freedom. In a simulation for 80 scattering channels, reflectances of less than 0.01 for the extremal incident wave were demonstrated, compared to an average reflectance of 0.85 or more. This theoretical analysis points to the possibility of enhancing the absorption of electromagnetic or acoustic waves in random media, by creating an optimally absorbed incident wave via wavefront shaping.
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- Chromatic monitoring
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- Complex characteristics of a process or material, such as absorption spectra, can be classified and differentiated by using a Gabor transform-based chromatic analysis (for example, Deakin AG et al 2008, Jones GR et al 2008, Jones GR et al 2000), which yields a representation of a spectrum by a low-dimensional set of parameters. This set is obtained by suitably combining outputs of several non-orthogonal spectral filters covering the wavelength range of the spectra. Such a parameter set can characterize the dominant wavelength, amplitude, and width of the spectrum (for example, see Deakin AG et al 2008). Sample application of chromatic analysis of absorption spectra to differentiate genuine liquor brands from their illicit preparations is discussed by Jones GR et al 2009. Chromatic analysis has also been used to characterize particulates (for example, Jones GR and Kolupala 2008)
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- Elementary volume of turbid medium
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- Conditions of the far-field modified uncorrelated single-scattering approximation (MUSSA) for the combined scattering of light by particles in a small volume (Mishchenko MI et al 2004b) are modified (Zhai Pen-Weng et al 2007). The modification replaces a limit on the average distance between any two particles by a more relaxed one: the largest dimension of that volume must be much greater than the wavelength of light.
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- Extinction paradox
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Berg MJ et al 2011 explain the extinction paradox by referring to the Ewald-Oseen theorem, which states that the incident wave is entirely cancelled inside the particle (for example, Fearn H et al 1996; see also Figure 1). They show the incompleteness of widely-accepted explanations (for example, van de Hulst 1981, section 8.22) and demonstrate that the extinction-paradox behavior occurs for small and large particles alike.
Fig. 1. The Ewald–Oseen (EO) extinction theorem (for example, Fearn H et al 1996) explains the extinction paradox for a water sphere in air (refractive index, m = 1.33 - 0i, phase shift parameter, ρ = 4). Equation numbers are those in Berg MJ et al 2011. Panels (a) and (b) show, in the equatorial plane of the sphere (coordinates are expressed relative to the sphere radius), the magnitude of the superposition of the incident field, Einc = Einc, 0 exp(ikz), and Eill (Eq. 29), as well as Einc and Esha (Eq. 30), respectively. Eill and Esha represent the contribution to the particle's scattered field due to the illuminated and shaded surfaces of the particle, respectively. Together, equations 29 and 30 are equivalent to the EO theorem, (Eq. 16). In (a), the illuminated particle side, Sill , which produces Eill , is denoted by the white arc. In (b), the shadow particle side, Ssha produces Esha , and is denoted likewise. If the integral in Eq. (16) is taken over the whole particle surface, which panels (a) and (b) together constitute, then the result is panel (c). The figure reproduced by permission from Berg MJ et al 2011.
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- Lambert law
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- Abitan H et al 2008 extend the Beer-Lambert law for any power density of the incoming light beam by accounting for spontaneous and stimulated emission in a medium with two energy levels. Their exact solution to the problem of change of the beam power with distance in a medium utilizes the Lambert W-function (Corless RM et al 1996).
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- Magnetism and scattering
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- A comment (Pallfy-Muhoray P 2007) and authors' reply (Oliveira SL and Rand 2007b) regarding "Intense non-linear magnetic dipole radiation at optical frequencies: Molecular scattering in a dielectric liquid" (Oliveira SL and Rand 2007a).
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- A ferrofluid containing small magnetic particles exhibits certain novel magneto-optical effects like zero transmission, enhanced coherent backscattering, trapping and controlled release of light as a function of an external magnetic field (Mehta RV et al 2006b, 2006a). See also a discussion regarding these results: Mehta RV et al 2008 vs Ramachandran H and Kumar 2008, and Mehta RV et al 2007 vs García-Cámara B et al 2007, as well as the original contribution by Kerker M et al 1983.
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- Negative refraction
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- McCall MW 2009 discusses physics of the backward wave phenomenon underlying the negative refraction and propagation of electromagnetic waves in negative index materials.
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- Optical binding
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- Simple analytical model for longitudinal optical binding of two spherical nanoparticles was presented by Karásek V and Zemánek 2007. Multiple scattering between two particles results in two basic forms of the dependency of the binding force on the distance between the particles depending on radii of studied Bessel beams.
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- The relationship of the stable-configuration distance between two optically bounded silica particles to the size and refractive index of the particles and the binding Gaussian beam diameter was estimated numerically by using the coupled dipole method (CDM) (Karásek V et al 2006). A comparison with measured distances for 1.28 and 3.00 µm particles is satisfactory with respect to the revealed sensitivity to the beam and particle characteristics.
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- Optical theorem
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- The measurement of the attenuation cross section is shown by Mishchenko MI et al 2009 to require a detector with an angular-diameter in the forward direction that is approximately greater than 200 √(λ / 2R), as viewed by the particle, where λ is the wavelength and R is the distance from the particle to detector. This condition yields agreement with the optical theorem (for example, Mishchenko 2006b) to within one percent. See also Berg MJ et al 2008b, Berg MJ et al 2008c.
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- Optical attenuation by multiple particles occurs in an angular range around the forward direction which is narrower than that for the single particle of the same type (Berg MJ et al 2008c).
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- Optical attenuation (extinction) caused by a single particle occurs over all directions - its commonly-perceived forward-angle nature is a consequence of the far-field limit (Berg MJ et al 2008b). Hence, a sufficiently large detector is crucial for the accurate measurement of the light attenuation by a particle. Moreover, attenuation does not necessarily cause a reduction of the energy flow along the exact forward direction.
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- Optical theorem is once again validated by showing that the attenuation of electromagnetic radiation by a particle is caused by the interference of the incident and the forward-scattered field (Mishchenko MI 2006b).
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- Polarization
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- A study of the Cartesian reflection symmetries of the electromagnetic field within a homogeneous sphere interacting with a plane wave (Berg MJ et al 2008a) shows that the sphere cannot change the (vertical) linear polarization state of the incident wave upon scattering it into any direction contained in the horizontal and vertical scattering planes. However, the scattered wave's polarization state is, in general, elliptical for any other scattering direction.
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- Partially polarized light beam: conditions for it to be considered a sum of a completely polarized and a completely unpolarized components (Wolf E 2008).
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- Scattering
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Currie M et al 2009 examined both experimentally and theoretically scattering by a glass fiber of broadband light pulses (25 and 100 nm FWHM) produced by a model-locked laser. Wavelength filtering of the scattered light removed the short temporal nature of the pulses and allowed one to observe the broadband effects in angular scattering patterns obtained by rotating a point detector (1D pattern: scattered irradiance vs. scattering angle) and an optical spectrometer input (2D pattern: scattered irradiance at a wavelength vs. scattering angle) about the axis of 9 µm and 50 µm diameter glass fibers (Fig. 1). Angular oscillations of the scattered light for each wavelength of the 2D patterns are similar to those produced by monochromatic steady-output (cw) light sources. In contrast, a wavelength-filtered optical pulse may significantly dampen these oscillations.
Fig. 1. A pattern of peaks (in false color: dark = low, bright = high) appear in the 2-D data obtained by measuring the spectrum of light scattered by a 9 µm diameter glass fiber as a function of the scattering angle. The fiber is illuminated by a broadband coherent light source (a mode-locked pulsed laser). The slope and periodicity of the experimental pattern of peaks (top panel) match well those of a calculated pattern (bottom panel). The source's spectral envelope is impressed upon the experimental data while the calculations are based on a uniform excitation spectrum. Small differences in the periodicities of the two patterns may arise from (1) experimental uncertainty in the refractive index and geometry of the fiber, and in the angle of incidence, and/or (2) the difficulty of finding the peak's centroid (e.g. the peak near 760 nm and 33 degrees in the bottom panel). The figure reproduced by permission from Currie M et al 2009 with minor modifications.
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- The relationship between the asymptotic far field and the near field in the Lorenz-Mie theory and the T-matrix formulation is explicitly established through the Kirchhoff surface integral (Bi L et al 2010).
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- Like many other properties of water, such as density and isothermal compressibility, scattering by water is also "anomalous", exhibiting a minimum at 24.64 °C (Zhang X and Hu 2010). The minimum temperature increases with salinity, reaching 27.49 °C for a salinity of 40 (see figure).
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- Sea salts (see seawater, composition) with different ionic weight and sizes affect the concentration fluctuation differently. Thus, solutions of sea salts, even at the same concentration, exhibit different scattering coefficients (Zhang X et al 2009b): the scattering coefficients of NaCl solutions are consistently about 6.7% or 4% lower than seawater of the same NaCl mass concentration or of the same refractive index. This implies consistent errors in measuring optical properties of seawater, such as attenuation and absorption of light, with instruments calibrated by using salt solutions as surrogates of seawater.
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- A new model of light scattering by pure seawater, in which the Gibbs function of seawater (Feistel R 2008) was used exclusively to derive the thermodynamic parameters associated with fluctuations of refractive index (RI) with density and salt concentration, was proposed by Zhang X and Hu 2009b. According to this model, light scattering by seawater increases non-linearly over an extended range of salinity (up to 120 g kg-1) at temperature ranging from 0 to 80 °C. The linear extrapolation would significant overestimate scattering by up to 30% at a salinity of 120 g kg-1, while underestimating it at lower salinities.
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- The effect of sea salts on the volume scattering function of light by pure seawater at 90°, i.e. β(90°)sw, was deduced from thermodynamic principles (Zhang Xiaodong et al 2009a). A non-linear increase with salinity, S, in β(90°)sw, by ~33% at S = 40 ppt, is due to the salt concentration fluctuations, which more than compensate for the decreasing contribution of the density fluctuations. The results agree with Morel's measurements (Morel A 1968, 1966) within his experimental error of 2%. The power-law slope of the wavelength spectrum of β(90°)sw in the visible increases from -4.286 to -4.306 for salinity ranging from 0 to 40 ppt.
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- The volume scattering function of light by pure water at 90° was evaluated from an expression for the density-dependent fluctuations of the refractive index (dn2/dρ), where n is the refractive index and ρ is the density of water (Zhang Xiaodong and Hu 2009). That expression was deduced from the general Lorentz-Lorenz equation (for example, Born M and Wolf 1980). The results agree with Morel's measurements (Morel A Morel A 1968) well within his experimental error of 2% (an average difference of -0.67%).
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- Gustav Mie and the evolving discipline of electromagnetic scattering by particles (Mishchenko MI and Travis 2008d).
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- Scattering in an absorbing medium
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- Electromagnetic scattering by an arbitrary finite object embedded in a homogeneous absorbing medium is analyzed theoretically using the volume integral equation (Mishchenko MI 2007d). The author points out that the solution of this problem is only meaningful in the context of defining and considering direct optical observables, such as the phase matrix.
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- Scattering minimization
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García-Cámara B et al 2011 proposed corrected and generalized expressions for zero scattering by a small homogeneous sphere (Kerker's null scattering case, Kerker M et al 1983) in the forward and backward directions:
| εr = [π (4 - µr) - iVk3(µr - 1)] / [π (2µr + 1) - iVk3(µr - 1)] |
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| εr = µr |
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respectively, where εr is the relative electric permittivity, µr is the magnetic permeability, V is the sphere volume, and k is the wavenumber of the incident radiation in the medium surrounding the sphere. Figure 1 shows sample scattering patterns for spheres satisfying such conditions. These substantially corrected expressions, which satisfy the optical theorem, are built upon inclusion of the radiative correction (for example, Draine BT 1988) and account for the effect of the sphere size. See also related VBA.
Figure 1. Angular scattering patterns of a homogeneous nanosphere with a diameter of 9.92 nm (volume, V, of 511.13 nm3) and the relative electric permittivity, εr , and magnetic permeability, µr , that together satisfy either the generalized zero-forward [(εr , µr) = (2, 0.4 – 3.88x10−5i); red] or the zero-backward [(εr , µr) = (2, 2); blue] conditions (García-Cámara B et al 2011) at a wavelength of 500 nm (wavenumber, k, of 0.01257 nm-1). The arrow represents the direction of the incident field. The figure reproduced by permission from García-Cámara B et al 2011 with minor modifications.
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- Electromagnetic transparency by coated spheres with radial anisotropy (Gao L et al 2008).
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- Single emitter optics
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- Exploring the limits of single emitter detection in fluorescence and extinction (Wrigge G et al 2008).
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- Zumofen G et al 2008 show theoretically that a single oscillating dipole under focused illumination by a directional dipolar electromagnetic field can perfectly reflect light.
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- Thermal emission from particles
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- Strong thermal emission from carbon nanoparticles is observed upon their illumination by low-power (milliwatts) laser light commonly used in Raman spectroscopy (Osswald S et al 2008). This emission results from heating the nanoparticles up to 3000 °C due to high light absorption cross sections of and a poor thermal conduction between the nanoparticles. Such a heating may result in phase transformation, extensive graphitization, and even evaporation of the nanoparticles.
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- See also Turbid media optics
