Theoretical Physics

• Computational & Analytical Classical Electrodynamics:

• Modeling electromagnetic scattering from wavelength-sized dielectric objects of arbitrary shape.
  
I have developed computer simulations to model the interaction of electromagnetic (EM) radiation with matter.  The simulations are based on the Discrete Dipole Approximation (DDA) model.  This model was first established by Purcell & Pennypacker in 1973 and models an object as an array of polarizable points (dipoles) that respond to an incident light wave and to each other.  The DDA model is one of many computational models for  EM scattering, but is one of only a few such models that can handle "realistic" complex-shaped objects (like snow flakes, sand & dust particles for example).   The DDA model is also especially unique in that it is an intuitively-based model; it represents an object as it really is - an assembly of discrete points (atoms/molecules). 


• Microscopic optics: Atomic/Molecular model of reflection & refraction from surfaces. 
  
Usually reflection and refraction is explained from a macroscopic perspective; the discrete atomic nature of a medium is neglected in favor of a continuous description utilizing the concept of a refractive index.  Neglecting the discrete nature of a material is often justified since the wavelength of the light (especially optical wavelengths) is much greater than the atomic features of a medium's material and hence it appears continuous to the field.  This work explores the canonical problem of reflection and refraction of an electromagnetic plane wave from objects only several wavelengths in size.   The objects are modeled as an array of polarizable coupled electric-dipoles in order to best represent the discrete nature of the actual objects.  The results show that Snell's law and the laws of reflection and refraction still apply to objects of this size.  


• Patterns in EM scattering
  
The scattering of EM radiation (light) from an object can be of substantial practical use as it provides a way to study the physical properties of objects in situ. Often measurement of the light scattered from an object is conducted and interpreted in terms of the scattering angle.  This is the "natural choice" since it is the scattering angle that is physically varied in a scattering measurement.  However, the appearance of the scattering data as a function of the scattering angle can be complicated and not amenable to any simple analysis.  Recent work has found that analyzing the scattering data in terms of the scattering wave vector in place of the scattering angle causes patterns to appear in the data.  These patterns relate to specific aspects of the scattering object's physical character and hence become useful in interpreting the data.  For more info see the paper, "Patterns in Mie Scattering: Normalization by the Rayleigh Cross Section" and references therein.


• Extinction & the Optical Theorem
  
Scatterers  both spherical and nonspherical in shape, are often encountered in the natural environment.  Examples include atmospheric clouds and aerosols.  The scattering of sun light by these particles produces radiative forcing effects that influence the Earth's climate.   Extinction is the process by which radiant energy is removed from an incident wave due to the scattering and absorption of the wave by a scatterer.  The extinction cross section  measures the total power removed from the incident wave, and hence, is a quantity of interest in many electromagnetic scattering applications.  A well-known relationship, called the optical theorem, relates the cross section to the amplitude of the scattered wave in the exact forward direction.  This work explicitly demonstrates the origin of the forward character of the optical theorem  using computer simulations of  simple scattering systems.  The conclusion is that the optical theorem derives its forward character from the behavior of the energy flows created by the interference of the incident and scattered waves.  This energy flow consists of opposing directions of flow that cancel each other in all but the forward direction when integrated in the far-field to yield the cross section.   For more info, see "Extinction and the optical theorem. Part I. Single particles.," and "Extinction and the optical theorem. Part II. Multiple partilces."

• Electromagnetic Scattering by Cubes in Fixed Orientations
  
This report presents results of a computational study of electromagnetic scattering from a cubic scatterer in fixed orientations.  The Discrete Dipole Approximation (DDA) is used to solve the scattering problem numerically providing the electromagnetic wave inside the cube and scattered by it.  The main objective is to use the results from the DDA to anticipate the major features of photoelectron emission measurements from cubic sodium chloride crystals exposed to Vacuum Ultraviolet (VUV) radiation.  The VUV light is generated by the synchrotron Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory.  A major result of this work shows that the symmetry of the arrangement formed by the illumination geometry and the orientation of the cube strongly influences both the structure of the fields and the character of the photoelectron emission.  Distinct features appear in the electron distributions that are qualitatively similar to those seen in previous experimental measurements in  addition to new features that seem to be related to the cubic geometry of the scatterers.  

Experimental Physics

• Scattering from a Freezing Polymer Drop:

Experimental collaboration with  Richard Flagan and Adam Olsen in the Department of Chemical Engineering at the California Institute of Technology.  A ~100 micron sized liquid polymer drop was levitated in an electrostatic trap.  A laser with an emission of 532nm is scattered from the liquid drop and the scattered light intensity is collected over an angular range of ~24 degrees.  The temperature of the drop's surroundings is decreased until it begins to freeze.  As the drop freezes, its structure changes which causes the way that it scatters light to change, supplying the possibility to analyze the scattering data to study how the drop's structure changes as it freezes.  We applied our scattering models to the measurements and developed a possible sequence of changes in the drops structure.

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