Xiang’e Han

Debye series for light scattering by a multilayered sphere

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.

Scattering of a shaped beam by a spherical particle with an eccentric spherical inclusion

Based on the generalized Lorenz–Mie theory (GLMT), a method of describing a Gaussian beam scattering by an eccentric sphere is developed. For a general case, the eccentric sphere is arbitrarily located and arbitrarily oriented with respect to the illuminating Gaussian beam. The simulations are validated for plane wave scattering by an eccentric sphere and shaped beam scattering by a coated sphere. The far-field scattering and extinction efficiency factors of scattering of a Gaussian beam by an eccentric sphere in the general case of oblique illumination are discussed.

Optical absorption analysis and optimization of gold nanoshells

Gold nanoshells, consisting of a nanoscale dielectric core coated with an ultrathin gold shell, have wide biomedical applications due to their strong optical absorption properties. Gold nanoshells with high absorption efficiencies can help to improve these applications. We investigate the effects of the core material, surrounding medium, core radius, and shell thickness on the absorption spectra of gold nanoshells by using the light-scattering theory of a coated sphere. Our results show that the position and intensity of the absorption peak can be tuned over a wide range by manipulating the above-mentioned parameters. We also obtain the optimal absorption efficiencies and structures of hollow gold nanoshells and gold-coated SiO(2) nanoshells embedded in water at wavelengths of 800, 820, and 1064 nm. The results show that hollow gold nanoshells possess the maximum absorption efficiency (5.42) at a wavelength of 800 nm; the corresponding shell thickness and core radius are 4.8 and 38.9 nm, respectively. They can be used as the ideal photothermal conversation particles for biomedical applications.

Debye series analysis of radiation pressure force exerted on a multilayered sphere

On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.

Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model

The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder.

Geometrical-optics approximation of forward scattering by gradient-index spheres.

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

Scattering from an elliptical cylinder by using the vectorial complex ray model

The vectorial complex ray model (VCRM) is applied to the light scattering of an elliptical cylinder illuminated by a plane wave. In the VCRM, all waves are described by vectorial complex rays, and the scattering intensities are computed by the superposition of the complex amplitudes of the vectorial rays. The significant merit of this approach is that the wave properties are integrated in the ray model such that the divergence/convergence of the wave each time it encounters a dioptric surface is deduced by the wavefront curvature equation, and the phase shifts due to the focal lines are determined directly by the curvature of the wavefront. The approach is particularly suitable for a large cylinder with an elliptical cross section.

On Characteristics of a Spheroidal Particle by Use of Debye Series

We derive the formula of the Debye series decomposition for axially incident plane wave scattering by a spheroidal particle. The Debye series writes each term of the Mie infinite series as another infinite series, and clarifies the physical origins of many effects that occur in electromagnetic scattering, which is of great importance to the study of characteristics of light scattering. The characteristics of a spheroidal particle can be studied within the framework of physical origin by use of the Debye series.

Computation of on-axis Gaussian beam scattering by nonuniform glass microbeads using a geometrical-optics approach

Within the framework of geometrical optics, we obtain the on-axis Gaussian beam scattering of nonuniform glass microbeads. The phase shift due to the optical path is deduced and the scattering angles of the p ray are given. On the basis of this work, the scattering intensity distribution is calculated and compared with that obtained by the generalized Lorenz–Mie theory. As indicated by the comparison, the surface wave effect of this gradient index (GRIN) microbead is smaller than that of a homogeneous microbead. The calculation time of the geometrical-optics approximation (GOA) is much less than that of generalized Lorenz–Mie theory (GLMT).

A Faster Approximation of Forward Scattering by Gradient-index Particles

By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0 - {60 - ) for gradient-index particles illuminated by acollimated ted incident beam. The incident angle of the re∞ected light is derived from the scattering angle to improve the approximation precision. This method proves efiective for transparent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. With the given index model, the geometrical optics approximation is efiective only for forward small angles, typically less than 10 - or so when the refractive index difierence of a particle is greater than a certain value. DOI: 10.2529/PIERS061023013549