Scott A. Schaub

Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam

Series expressions for the net radiation force and torque for a spherical particle illuminated by an arbitrarily defined monochromatic beam are derived utilizing the spherical‐particle/arbitrary‐beam interaction theory developed in an earlier paper. Calculations of net force and torque are presented for a 5‐μm‐diam water droplet in air optically levitated by a tightly focused (2 μm beam waist diameter) TEM00‐mode argon‐ion (λ=0.5145 μm) laser beam for on and off propagation axis, and on and off structural resonance conditions. Several features of these theoretical results are related to corresponding experimental observations.

Internal and near‐surface electromagnetic fields for a spherical particle irradiated by a focused laser beam

Theoretical expressions for the internal and external electromagnetic fields for an arbitrary electromagnetic beam incident upon a homogeneous spherical particle are derived, and numerical calculations based upon this theoretical development are presented. In particular, spatial distributions of the internal and near‐surface electric field magnitude (source function) for a focused fundamental (TEM00 mode) Gaussian beam of 1.06 μm wavelength and 4 μm beam waist diameter incident upon a 5‐μm‐diam water droplet in air are presented as a function of the location of the beam focal point relative to the sphere center. The calculations indicate that the internal and near‐surface electric field magnitude distribution can be strongly dependent upon relative focal point positioning and may differ significantly from the corresponding electric field magnitude distribution expected from plane‐wave irradiation.

Internal fields of a spherical particle illuminated by a tightly focused laser beam: Focal point positioning effects at resonance

The spherical particle/arbitrary beam interaction theory developed in an earlier paper is used to investigate the dependence of structural resonance behavior on focal point positioning for a spherical particle illuminated by a tightly focused (beam diameter less than sphere diameter), linearly polarized, Gaussian‐profiled laser beam. Calculations of absorption efficiency and distributions of normalized source function (electric field magnitude) are presented as a function of focal point positioning for a particle with a complex relative index of refraction of n=1.33+5.0×10−6i and a size parameter of α≊29.5 at both nonresonance and resonance conditions. The results of the calculations indicate that structural resonances are not excited during the on‐center focal point positioning of such a tightly focused beam but structural resonances can be excited by proper on‐edge focal point positioning. Electric wave resonances were found to be excited by moving the focal point from on‐center towards the edge of the...

Electromagnetic field for a beam incident on two adjacent spherical particles

Through an application of our previously derived single spherical particle-arbitrary beam interaction theory, an iterative procedure has been developed for the determination of the electromagnetic field for a beam incident on two adjacent spherical particles. The two particles can differ in size and composition and can have any positioning relative to each other and relative to the focal point and propagation direction of the incident beam. Example calculations of internal and near-field normalized source function ( approximately |E|(2)) distributions are presented. Also presented are calculations demonstrating the effect of the relative positioning of the second adjacent particle on far-field scattering patterns.

Theoretical analysis of the effects of particle trajectory and structural resonances on the performance of a phase-Doppler particle analyzer.

A generalized theoretical model for the response of a phase-Doppler particle analyzer (PDPA) to homogeneous, spherical particles passing at arbitrary locations through a crossed beam measurement volume is presented. The model is based on the arbitrary beam theory [J. Appl. Phys. 64, 1632 (19

Simplified scattering coefficient expressions for a spherical particle located on the propagation axis of a fifth-order Gaussian beam

8)] and is valid for arbitrary particle size and complex refractive index. In contrast to classical Lorenz-Mie theory, the arbitrary beam approach has the added capability of accounting for effects that are due to the presence of the finite-size crossed incident beams that are used in the PDPA measurement technique.The theoretical model is used to compute phase shift as a function of both the particle position within the measurement volume and particle diameter (1.0 µm < diameter water droplets < 10.0 µm for both resonant and nonresonant sizes) for 30° off-axis receiver configuration. Results indicate that trajectory effects are most pronounced for particle trajectories through the edge of the crossed beam measurement volume on the side opposite the detector. Trajectories through the center of the probe volume gave phase shifts that are nearly identical to those obtained with Lorenz-Mie plane-wave theory. Phase shifts calculated for particle diameters corresponding to electric-wave resonances showed the largest deviation from the corresponding nonresonance diameter phase shifts. Phase shifts for droplets at magnetic wave resonance conditions showed smaller effects, closely following. the behavior of nonresonant particle sizes. The major influence of aerosol trajectory on actual particle size determination (for both resonant and nonresonant particle sizes) is that the measured aerosol size distributions will appear broader than the actual size distribution that exists within a spray.

Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment

Expanding on developments presented in an earlier paper, theoretical expressions for the scattering coefficients of a homogeneous, absorbing, spherical particle irradiated by a fifth‐order Gaussian beam are presented for the special case of the particle center located on the propagation axis of the beam. For this case, evaluation of two‐dimensional surface integrals, required in computing the scattering coefficients for the most general particle location, is reduced to a computationally more efficient one‐dimensional integral. For a typical size parameter α=πd/λ=17, the CPU time required for calculation of scattering coefficients is reduced by a factor of ∼1500 by using the simplified coefficient expressions. In addition, computation of electromagnetic field components is reduced from double summation to single summation expressions, further simplifying the field calculations.

Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing

A simple theoretical model is presented that allows calculation of the image produced by a spherical absorbing particle illuminated by monochromatic, coherent laser light. Results presented in this paper are restricted to a single-lens imaging system, although generalization to more complex imaging system configurations would be straightforward. The method uses classic Lorenz-Mie scattering theory to obtain the electro-magnetic field external to an absorbing spherical particle and a Fourier optics approach to calculate the intensities in the image plane. Experimental results evaluating focus characteristics are examined for 50 um diameter water droplets using an N2 laser imaging system in conjunction with a digital image processor, and the experimental images are compared to the results of the theoretical model. Comparative focus criteria results are particularly useful in aerosol science research involving dynamic particle size measurements in which criteria for focus and depth of field must be established.

Effects Of Non-Spherical Drops On A Phase Doppler Spray Analyzer

A theoretical model is presented for the formation of small-particle shadow images in a single-lens laser-imaging system. The model uses a modification of classical Lorenz-Mie theory, presented by the authors in an earlier paper, to calculate the external electromagnetic fields resulting from the interaction of a Gaussian laser beam with a finite absorbing spherical particle. Propagation of the electric field through the imaging system components is developed from a scalar viewpoint using the thin-lens transformation and the Fresnel approximation to the Huygens-Fresnel propagation equation. The theoretical model is valid for either transparent or absorbing spheres and has no restrictions on the allowable degree or direction of aerosol defocus. Direct comparisons between theoretical calculations and experimental observations are reported for 53-microm-diameter transparent water droplets and 66-microm-diameter absorbing nickel spheres for defocus ranging from -2 mm (toward the lens) to +2 mm (away from the lens). Theory and experiment showed good agreement in the boundary edge gradient and the location of the external peaks, while observable differences existed in the magnitude of the central spots. Theoretical results, comparing water and nickel aerosols, showed observable differences in the calculated average internal intensity (AII). In contrast, the boundary edge gradient showed less dependence on changes in the optical properties of the particle. These results indicate that criteria, such as the AII, used in focus determination must be reevaluated when applying in-focus sizing algorithms to aerosols with significantly different optical properties.

Interactions of intense ultraviolet laser radiation with solid aerosols

A Phase Doppler Spray Analyzer (P/DSA) and a laser imaging system (LIS) was used to study the response of a P/DSA to non-spherical particles. Methanol particles with an aspect ratio ranging from 0.7 to 1.4 were used in this investigation. Results indicated that the P/DSA was quite sensitive to particle shape. A Berglund-Liu generator was used to produce particles of 98 um (volumetric diameter). The P/DSA instrument measured particle sizes ranging from 142 μm for a particle of aspect ratio 0.7 to 84 μm for an aspect ratio of 1.4. Particle diameters based on averaged x and y diameters for the laser imaging system ranged from 95 μm to 92 μm over the same range of aspect ratios.