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• Resonant States(RSs)/Quasi-normal modes(ANMs) Resonant States, also known as Quasi-Normal Modes are a means for describing the response of a system almost exclusively in terms of its resonant response. These states solutions to a system's equations of motion that satisfy outgoing boundary conditions, and that consequently have complex eigenvalues. These serve as an elegant means of characterizing the system's response function since real part of the RS eigenmodes tells us the frequency at which a resonance occurs and its imaginary part tells the rate at which this excitation decays in time.
  
  
• Optical Antennas can be seen as the optical analogues of the more familiar radio and microwave antennas. Like their larger wavelength counterparts, optical antennas have approximately the same size as the electromagnetic wavelength that they receive/emit.
  Despite this analogy, there are notable differences between optical antennas and their radio frequency anologues stemming from difference in light-matter interactions at even good conductors have high losses at light frequencies. Other differences arise from the fact the emitter and receiver elements in optical antennsas are either quantum or specifically designed mesoscopic systems without analogs of the coaxial feed elements of lower frequency antennas 59 , 58 , 56 , 55 , 53 , 51 , 50 , 49 , 47 , 46 , 45 .
  
  
• Photonic jets are regions of high field intensity that can be formed by incident beams impinging on dielectric spheres. Photonic jets offer a cost effective means of producing essentially diffraction limited spots with applications to single molecule detection, lithography, confined heating, and more. Extended Mie theory methods allowed us to readily design the conditions for producing photonic jets and study their properties. 57 , 42 , 41 , 40 , 39 , 37 , 34 .
  
  
• Multiple Scattering T-matrix theory
  
  
• Light diffusion and abosrption in multiple scattering systems Poster PDF
  
  
• Theoretical modeling of optical tweezers Poster PDF
  
  
• Improvements in the modeling of light transport in dense heterogeneous systems
  
  
• Enhancement of non-linear effects in heterogeneous systems
  
  
• Effective media theory