Spherical Dielectric Particles Research Articles

Magnetic dipole radiation tailored by substrates: numerical investigation.

Nanoparticles of high refractive index materials can possess strong magnetic polarizabilities and give rise to artificial magnetism in the optical spectral range. While the response of individual dielectric or metal spherical particles can be described analytically via multipole decomposition in the Mie series, the influence of substrates, in many cases present in experimental observations, requires different approaches. Here, the comprehensive numerical studies of the influence of a substrate on the spectral response of high-index dielectric nanoparticles were performed. In particular, glass, perfect electric conductor, gold, and hyperbolic metamaterial substrates were investigated. Optical properties of nanoparticles were characterized via scattering cross-section spectra, electric field profiles, and induced electric and magnetic moments. The presence of substrates was shown to have significant impact on particle's magnetic resonances and resonant scattering cross-sections. Variation of substrate material provides an additional degree of freedom in tailoring optical properties of magnetic multipoles, important in many applications.

Negative azimuthal force of nanofiber-guided light on a particle

We calculate the force of a quasicircularly polarized guided light field of a nanofiber on a dielectric spherical particle. We show that the orbital parts of the axial and azimuthal components of the Poynting vector are always positive while the spin parts can be either positive or negative. We find that, for appropriate values of the size parameter of the particle, the azimuthal component of the force is directed oppositely to the circulation direction of the energy flow around the nanofiber. The occurrence of such a negative azimuthal force indicates that the particle undergoes a negative torque.

Interaction of two dielectric macroparticles

The electrostatic interaction of two charged dielectric spherical particles with a nonuniform freecharge distribution over their surfaces in an external homogeneous electric field is considered. An exact solution for the electric field potential is obtained, and an analytical expression for the interaction force between these two particles is found. The case of a uniform free-charge distribution is considered in detail, and the region of parameters in the plane “the ratio of the radii vs. the ratio of the charges,” where repulsion between two like-charged particles turns into attraction as the interparticle distance decreases is established.

Numerical study of the properties of optical vortex array laser tweezers

Chu et al. constructed a kind of Ince-Gaussian modes (IGM)-based vortex array laser beams consisting of p x p embedded optical vortexes from Ince-Gaussian modes, IG(e)(p,p) modes [Opt. Express 16, 19934 (2008)]. Such an IGM-based vortex array laser beams maintains its vortex array profile during both propagation and focusing, and is applicable to optical tweezers. This study uses the discrete dipole approximation (DDA) method to study the properties of the IGM-based vortex array laser tweezers while it traps dielectric particles. This study calculates the resultant force exerted on the spherical dielectric particles of different sizes situated at the IGM-based vortex array laser beam waist. Numerical results show that the number of trapping spots of a structure light (i.e. IGM-based vortex laser beam), is depended on the relation between the trapped particle size and the structure light beam size. While the trapped particle is small comparing to the beam size of the IGM-based vortex array laser beams, the IGM-based vortex array laser beams tweezers are suitable for multiple traps. Conversely, the tweezers is suitable for single traps. The results of this study is useful to the future development of the vortex array laser tweezers applications.

Thermodynamics of a liquid wetting film on a spherical particle with an adsorbed ion

A thermodynamic description has been formulated for a wetting film formed on a spherical solid dielectric particle with a discrete electric charge adsorbed on its surface. The description is based on differential equations for the equilibrium nonspherical profile of the film and electric potentials in the particle, film, and a vapor-gas medium. By combining these equations and taking into account the action of disjoining pressure in the film, the film shape in a noncentral electric field has been determined and an expression has been derived for the chemical potential of condensate molecules in the film as a function of the effective curvature radius of the film external surface, this radius being predetermined by the number of condensate molecules in the film. The magnitude of the adsorbed electric charge, its characteristic size and its location with respect to the center of the solid particle, dielectric permittivities of the liquid in the film and the material of the particle, particle size, and the characteristics of the isotherm of the disjoining pressure represent parameters of the problem. Three characteristic disjoining pressure isotherms corresponding to films that wet and partly wet the particle in the absence of the electric charge have been considered. It has been shown that the noncentral position of an adsorbed ion at small particle sizes strongly affects the surface profile of a thin film and the chemical potential of its molecules.

Designing photonic structures of nanosphere arrays on reflectors for total absorption

By means of full electrodynamic simulations, we investigate structures that can totally absorb light minimizing all reflections. Such efficient absorbers of visible and infrared light are useful in photovoltaic and sensor applications. Our study provides a simple and transparent analysis of the optical properties of structures comprising a resonant cavity and a reflector, which are the basic ingredients of a resonant absorber, based on general principles of scattering theory. We concentrate on periodic arrays of metallic or dielectric spherical particles in front of metallic or dielectric mirrors and show that tuning the material absorption could turn resonances in the structures into total absorption bands. Perfect absorption is predicted in metallic sphere arrays but also for Si spheres on a metallic substrate, moreover, by replacing the substrate below the Si spheres with a lossless dielectric Bragg mirror an all-dielectric-perfect-absorber is designed.

Temporal dynamics of a “Photonic Jet” from a dielectric microparticle illuminated by a laser pulse

Transient response in the near-field of light wave scattering by micron spherical dielectric particles under laser pulse irradiation is considered. A region of space constituting a photonic jet is theoretically investigated, and the temporal dynamics of the jet size and peak intensity are analyzed. The jet evolution scenario is shown to include generally the non-resonant and resonant temporal phases; a photonic jet can change its spatial form and intensity during each phase.

Optical trapping forces depending on size of dielectric polystyrene microspheres

A single-beam gradient force trap or an optical laser tweezer has been a powerful tool to accurately measure pico-newton to femto-newton forces in a variety of fields, such as biology, colloid/polymer physics, and rheology. When an appropriate refractive index mismatch between an object and a medium is provided, the laser beam can hold the object of which its size ranges from a few nanometers to tens of micrometer scale. The optical trapping mechanism depends on the relative length scale between an object and the wavelength of a light. In the Rayleigh regime where the diameter of the object is smaller than the wavelength of the light ( ), the trap stiffness increases with the particle size, as the number of rays incident on the particle increases. On the contrary, all rays hit an object in the ray optics regime ( ) such that Ashkin expected the trapping force to be independent of its size without quantitative calculations. Similarly, Wright et al. predicted that the size dependence on the axial and radial trapping forces are negligible in the ray optics regime, based on calculating the dimensionless efficiency of the optical trapping force for a single ray. Using the generalized LorenzMie theory, Lock also suggested that the trapping force in the axial direction does not change with the particle size. However, Simmons et al. reported the experimental results in which the trap stiffness for dielectric particles decreases as the size increases when the particle size is larger than the wavelength of a light. More recently, Mazolli et al. used an explicit partial-wave representation to extend the force expression from the Rayleigh regime (i.e., electromagnetic force model) to the GOA. In the ray optics regime, they reported that the trap stiffness is inversely proportional to the particle radius. Tlusty et al. also calculated the trapping force of highly localized fields on dielectric particles in which the trapping force in the ray optics regime decreases as their size increases. In this communication, we aim to address such contradiction, regarding the dependence of the optical trapping force on the particle size in the ray optics regime. Based on the GOA, we analytically calculate the optical trapping force with varying the particle size. Then, we compare the analytical calculations to the drag experiments in which a particle trapped by the laser tweezers is subjected to the Stokes drag force. We also provide a schematic explanation, based on drawing the ray propagation and finding the magnitude of the momentum change. Before we report our results, experimental materials and method are briefly described. We use polystyrene (PS, Interfacial Dynamics Corporation) latex particles with different radii, a=1.4, 1.7, and 3.7 μm. The refractive index of these particles is np=1.57. In order to obtain the trap stiffness (κt), which is the ratio of the Stokes drag force (Fs=6πaηu) to the lateral displacement (∆y) from the center of the particle, it is held in the aqueous phase (refractive index, nm=1.326) by the laser tweezers, and subjected to drag forces by translating the microscope stage at several constant velocities between u=3 and 7 μm/s. The viscosity of the aqueous solution is η=1 cP. We use particle tracking to measure the particle displacement during applying the Stokes flow around the particle. A movie captured on a CCD camera (Hitachi KP-M1) is saved at a frame rate of 29.97 frames/s. The digitized image sequences are imported to image processing software (ImageJ) to find the particle displacement (∆y) from the equilibrium position in the optical trap. The laser tweezer apparatus is constructed around the inverted microscope. The laser is generated by a 4-Watt CW Nd:YAG laser (λ0=1,064 nm, Coherent Compass 1064-400M). A water immersion objective (63×, NA 1.2, Zeiss C-Apochromat) is used to provide a high convergence angle (φmax), which is a maximum half angle of the conelike laser beam, given by φmax=sin(NA/nm)≈64.5. We refer the reader to Pantina and Furst for a more detailed description of the laser tweezer setup. In order to quantitatively calculate the optical trapping force in the ray optics regime, we consider the first reflection and the successive refractions of a single incident ray with power (P) hitting a dielectric spherical particle, the dimensionless efficiency (Q) of the trapping force is given by,

Optical trapping map of dielectric spheres

Many applications use a focused Gaussian laser beam to manipulate spherical dielectric particles. The axial trapping efficiency of this process is a function of (i) the particle radius r, (ii) the ratio of the refractive index of particle over the medium, and (iii) the numerical aperture of the delivered light beam. During what we believe is the first comprehensive simulation of its kind, we uncovered optical trapping regions in the three-dimensional (3D) parameter space forming an iso-surface landscape with ridge-like contours. Using specific points in the parameter space, we drew attention to difficulties in using the trapping efficiency and stiffness metrics in defining how well particles are drawn into and held in the trap. We have proposed an alternative calculation based on the maximum forward and restoration values of the trapping efficiency in the axial sense, called the trapping quality. We also discuss the manner in which the ridge regions may be harnessed for effective particle sorting, how the optical trapping blind spots can be used in applications that seek to eschew photothermal damage, and how trapping can proceed when many parameters change, such as when swelling occurs.

Casimir force between composite materials containing nonspherical particles

The Casimir force between metal-dielectric composite slabs containing nonspherical particles is investigated. The composite slab may have the symmetric (the nonspherical metal particles and spherical dielectric particles are randomly distributed) or asymmetric microstructure (the nonspherical metal particles are randomly embedded in the dielectric host medium), and the corresponding effective permittivity is described by the generalized Bruggeman effective medium approximation or generalized Maxwell-Garnett approximation. As a consequence, the Casimir force can be controlled by the volume fraction and the particles' shape. It is found that the Casimir force achieves a minimal value for spherical particles, and the magnitude of Casimir force can become strong for nonspherical particles. In addition, the Casimir force for the metal-dielectric composites with the symmetric microstructure shows a fast change at the shape-dependent percolation threshold, above (below) which the composite slab is metallic (dielectric). Our study may be of great interest for making precise comparisons between theoretical and experimental results on the Casimir force.

Liquid-crystal-enabled electrophoresis of spheres in a nematic medium with negative dielectric anisotropy

We describe electrophoresis of spherical dielectric particles in a uniformly aligned nematic medium with a negative dielectric anisotropy. A spherical particle that orients the liquid crystal (LC) perpendicularly to its surface moves under the application of a uniform direct current or alternating current electric field. The electric field causes no distortions of the LC director far away from the sphere. Electrophoresis in the nematic LC shows two types of nonlinearity in the velocity versus field dependence. The velocity component parallel to the applied electric field grows linearly with the field, but when the field is high enough, it also shows a cubic dependence. The most interesting is the second type of nonlinear electrophoresis that causes the sphere to move perpendicularly to the applied field. This perpendicular component of velocity is proportional to the square of the field. The effect exists only in an LC and disappears when the material is melted into an isotropic fluid. The quadratic effect is caused by the dipolar symmetry of director distortions around the sphere and is classified as an LC-enabled electrophoresis (LCEEP). The nonlinear electrophoretic mobility of particles in LCEEP offers a rich variety of control parameters to design three-dimensional trajectories of particles for microfluidic and optofluidic applications.

Photonic jet shaping of mesoscale dielectric spherical particles: Resonant and non-resonant jet formation

A descriptive analysis of the morphological shapes of photonic jets (PJs) these being a specific spatially localized and high-intensity area formed near micron-sized transparent spherical dielectric particles illuminated by a visible laser radiation, is presented. The PJ shape characterization is based on the numerical calculations of the near-field distribution according to the Mie theory and accounts for jet dimensions and shape complexity. The special situation of the morphology-dependent resonances excitation in the internal field of the particle is also considered.

Photonic jets from resonantly excited transparent dielectric microspheres

We report on the theoretical investigations of the near-field diffraction patterns from micrometer-sized spherical dielectric particles illuminated by a light wave upon the excitation of morphology-dependent resonances in the internal field. The specific spatial area, which constitutes the so-called photonic jet (PJ), is studied. The longitudinal and transverse dimensions of the PJ are calculated along with its peak intensity as a function of the distance from a particle. The numerical calculations show that at a resonance depending on its quality factor, the PJ can “stick” to the particle; its intensity can increase to a several orders of magnitude, and its width can decrease but mostly near the microsphere surface. The average length of the PJ remains nearly unchanged.

Numerical study of random lasing in three dimensional amplifying disordered media

In this paper, the lasing action in three-dimensional active random systems has been numerically investigated. Here, random systems of spherical dielectric particles imbedded in an active medium are considered. The quasi steady state approximation for the population inversion of the active medium is applied to solve three dimensional governing equations. Results show that when the density of particles increases to an upper limit, the intensity of lasing modes is enhanced. Also, the effects of pumping rate and particle size on the number of lasing modes and their intensity are studied. Lasing threshold of laser modes in different disordered systems is calculated and it is shown that by an appropriate selection of the central frequency of gain line-shape, the output power intensity of random lasers increases. These results are in agreement with the experimental results observed by others.

Transparent uniaxial anisotropic spherical particles designed using radial anisotropy

Based on Mie scattering theory and the assumption that the particle is electrically small in size (k(t)a≪1,k(m)a≪1), an analytic relationship between radial and tangential permittivity parameters has been established for achieving minimal scattering from an arbitrary rotationally uniaxial anisotropic spherical object incident by a plane wave. Analysis of fields in both the far- and near-field zones indicates that the derived relation is not only valid for electrically small particles, but also applicable to larger ones whose sizes are comparable with the free space wavelength after slight adjustments in parameters. Furthermore, it is observed that the dielectric spherical particle of reduced tangential permittivity yields better transparency performance than the design using a plasmonic cover by Alu and Engheta [Phys. Rev. E 72, 016623 (2005)]. As such, particles with carefully engineered radial anisotropy are transparent without using any coating and are ideal for applications with space constraint and stringent transparency criteria.

Photonic nanojet calculations in layered radially inhomogeneous micrometer-sized spherical particles

A photonic nanojet (PNJ) corresponds to the specific highly localized spatial region of electromagnetic near-field distribution in the vicinity of a transparent micrometer-sized particle illuminated by a light wave. Here we consider dielectric spherical composite particles consisting of a core and several concentric shells having different refractive indices. The longitudinal and latitudinal sizes of a PNJ and its peak intensity depending on the optical contrast variation of shells are numerically investigated. We show that by properly changing the refractive indices of neighboring shells, it is possible to manipulate the PNJ shape and, in particular, extend its longitudinal size or increase its peak intensity.

Mie scattering in the time domain Part 1 The role of surface waves

We computed the Debye series p=1 and p=2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p=1,2 surface wave glory in the time domain.

Perturbation between two traps in dual-trap optical tweezers

Dual-trap optical tweezers are widely used in biological sciences and many other areas. The two traps are generally considered to be independent of each other in most situations. But when they are close and even touch side by side, the influence may not be negligible. We calculate the optical force of dielectric spherical particles trapped in dual-trap optical tweezers by means of the discrete dipole approximation method and analyze the perturbation effect between the two traps. We find that the electric field does not change much when it is scattered by the trapped particles. As a result, the scattering light from one sphere has a little perturbation effect on the trapping force upon the other sphere. The perturbation mainly comes from the other trap and is thus affected by the distance between the two traps. In the experiment, the displacement of the sphere trapped in an immovable trap is observed when another trap is moving close. The experiment data of relative displacement match qualitatively with the calculation data.

Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime

Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.

Optical forces on arbitrary shaped particles in optical tweezers

Discrete dipole approximation (DDA) method is an efficient method for computing electromagnetic (EM) field of nanometer/micrometer-sized dielectric particles with arbitrary geometric shape and topology. In this work we employ the DDA method to calculate the optical force of dielectric shaped particles embedded in optical tweezers made from focused Gaussian laser beams. The EM force is calculated based on the self-consistent solution of EM field distribution and discrete dipole moment distribution within the particles. The DDA method agrees well with the Mie theory for spherical dielectric particles and this supports the effectiveness of the DDA method in handling optical forces in optical tweezers. The optical force for shaped particles such as cubes, rectangles, cylinders, and core-shell composite particles shows many interesting features. The force strongly depends on the orientation of the particle with respect to the laser beam propagation and polarization direction and the aspect ratio of the anisotropic particle. For a core-shell composite particle the zero-force balance point shifts from the particle center to its two sides. When an additional particle comes close a trapped particle, the perturbation effect strongly depends on the relative location of the center of the focused laser beam with respect to the two particles. Furthermore, the geometry of shaped particles not only affects the magnitude of the optical force but also influences the optical trap stiffness.