James A. Lock

Improved Gaussian beam-scattering algorithm.

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Enhanced Coupling to Microsphere Resonances with Optical Fibers

Morphology-dependent resonances (MDRs) of polystyrene microspheres were excited by an optical fiber coupler. For optical elimination of the air–cladding interface at the optical fiber coupler surface, the microsphere was immersed in an index-matching oil. MDRs were observed, even though the relative refractive index between the microsphere and the oil was only 1.09. The observed MDR spectra are in good agreement with the generalized Lorenz–Mie theory and the localization principle. The scattering efficiency into each MDR is estimated as a function of the impact parameter by means of generalized Lorenz–Mie theory.

Partial-Wave Representations of Laser Beams for Use in Light-Scattering Calculations

In the framework of generalized Lorenz-Mie theory, laser beams are described by sets of beam-shape coefficients. The modified localized approximation to evaluate these coefficients for a focused Gaussian beam is presented. A new description of Gaussian beams, called standard beams, is introduced. A comparison is made between the values of the beam-shape coefficients in the framework of the localized approximation and the beam-shape coefficients of standard beams. This comparison leads to new insights concerning the electromagnetic description of laser beams. The relevance of our discussion is enhanced by a demonstration that the localized approximation provides a very satisfactory description of top-hat beams as well.

Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle

I review the theory of the scattering of a Gaussian laser beam by a dielectric spherical particle and give the details for constructing a computer program to implement the theory. Computational results indicate that if the width of the laser beam is much less than the diameter of the particle and if the axis of the beam is incident near the edge of the particle, the fifth-, sixth-, and ninth-order rainbows should be evident in the far-field scattered intensity. I performed an experiment that yielded tentative evidence for the presence of the sixth-order rainbow.

Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. II. On-axis trapping force

The efficiency of trapping an on-axis spherical particle by use of laser tweezers for a particle size from the Rayleigh limit to the ray optics limit is calculated from generalized Lorenz-Mie light-scattering theory and the localized version of a Gaussian beam that has been truncated and focused by a high-numerical-aperture lens and that possesses spherical aberration as a result of its transmission through the wall of the sample cell. The results are compared with both the experimental trapping efficiency and the theoretical efficiency obtained from use of the localized version of a freely propagating focused Gaussian beam. The predicted trapping efficiency is found to decrease as a function of the depth of the spherical particle in the sample cell owing to an increasing amount of spherical aberration. The decrease in efficiency is also compared with experiment.

Calculation of the radiation trapping force for laser tweezers by use of generalized Lorenz-Mie theory. I. Localized model description of an on-axis tightly focused laser beam with spherical aberration

Calculation of the radiation trapping force in laser tweezers by use of generalized Lorenz-Mie theory requires knowledge of the shape coefficients of the incident laser beam. The localized version of these coefficients has been developed and justified only for a moderately focused Gaussian beam polarized in the x direction and traveling in the positive z direction. Here the localized model is extended to a beam tightly focused and truncated by a high-numerical-aperture lens, aberrated by its transmission through the wall of the sample cell, and incident upon a spherical particle whose center is on the beam axis. We also consider polarization of the beam in the y direction and propagation in the negative z direction to be able to describe circularly polarized beams and reflected beams.

Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder

I expand the radiation potential of an arbitrary monochromatic electromagnetic wave in the cylindrical coordinate eigenfunctions of the scalar Helmholtz equation. Since the resulting beam shape coefficients are found to be an inverse Fourier transform of the z component of the beam fields, the incident Gaussian beam is parameterized by a Fourier angular spectrum of plane waves. The beams partial-wave coefficients are then obtained, as well as the scattered fields produced by the interaction of the beam with an infinitely long homogeneous circular cylinder. The fields are evaluated analytically in the far zone by the method of stationary phase, and the physical interpretation of the results are discussed extensively.

Cooperative effects among partial waves in Mie scattering

Observations of an illuminated water droplet at a close distance are described mathematically by the Fourier transform of the Mie-scattering amplitude convolved with the aperture function of the observer’s eye. Most of the sharp enhancements found in the Fourier transform correspond to geometrical rays associated with the various terms in the Debye-series expansion of the Mie amplitude. However, there are some enhancements that cannot be ascribed to any individual Debye-series term. Instead, they arise from a constructive interference cooperation of the phase of a scattering resonance in a single partial wave with the region of the stationary phase corresponding to geometrical orbiting in the m-internal-reflection portion of the Fourier transform of the scattering amplitude. This phase cooperation amplifies the contribution that the scattering resonance makes to the Fourier-transform amplitude.

Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder

We derive the Debye-series expansion of the partial-wave scattering and interior amplitudes for the interaction of a diagonally incident beam of arbitrary profile with an infinitely long homogeneous dielectric circular cylinder. We then discuss the physical interpretation of the various terms of the series. We also consider the one-internal-reflection Debye-series terms for diagonal plane-wave incidence and examine the first-order rainbow extinction transition as a function of the tilt angle of the incident plane wave. We experimentally observe the first-order rainbow extinction transition and compare our observations with the Debye-series predictions.

Rayleigh–Brillouin scattering to determine one-dimensional temperature and number density profiles of a gas flow field

Rayleigh-Brillouin spectra for heated nitrogen gas were measured by imaging the output of a Fabry-Perot interferometer onto a CCD array. The spectra were compared with the theoretical 6-moment model of Rayleigh-Brillouin scattering convolved with the Fabry-Perot instrument function. Estimates of the temperature and a dimensionless parameter proportional to the number density of the gas as functions of position in the laser beam were calculated by least-squares deviation fits between theory and experiment.