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Dr. Hoang Thanh Xuan - "Multipole and Plane Wave Expansions for Solving Electromagnetic Boundary Value Problems"

Singapore-MIT Alliance for Research and Technology Centre, Singapore 138602, Singapore


Plane wave and multipole expansions are the two most common mode expansions of the general solution of Maxwell’s equations. Exploiting their unique properties enables us to rigorously modeling interactions of light with planar and spherical boundary surfaces. In the first part of this talk, I will discuss how to represent the optical field of a structured light beam in terms of these two expansions. I then solve the light-surface interactions in solid immersion and microsphere-based microscopies. Experimentally, I present how one can obtain sub-surface images of an integrated circuit with resolution of 120 nm by tailoring the amplitude, phase, and polarization of the illumination beam in the solid immersion microscopy operating with the illumination wavelength of 1.342 mm.

In the second part, I focus on light propagation and coupling in the systems of optically coupled microspheres. I highlight the similarity between the behavior of electrons in atoms and that of resonant light in microspheres. Inspired by the concept of the Fano resonance in atomic physics, I discuss the spectral responses of the systems illuminated with simple dipole radiation. Based on the multipole expansion approach, multipolar interference is shown to play a crucial role in molding the flow of light in the coupled-resonator systems. Using this exact solution of Maxwell’s equations instead of coupled-mode theory not only enables more accurate quantification of guided modes in the systems, but also facilitates a more intuitive understanding of the underlying physics. Furthermore, I will also discuss how to combine the two mode expansions for rigorously modeling light-particle interactions near the surface of a substrate.