Description of Research Expertise:
All my research is devoted, in one way or another, to studying the interaction of light with matter or to using light to probe the structure and properties of matter. This intersects with the areas of condensed matter physics, chemical physics, atomic and molecular spectroscopy, nano-optics and biomedical optical imaging. The latter has been my main focus for the past ten years. The problems that arise in biomedical imaging with light are often very mathematical in nature. This naturally brought me to the fields of radiative transport and inverse problems. In the past, I was very interested in the interplay between the geometrical and optical properties of physical objects. In biomedical imaging, I am still looking at the same problem, but from a different point of view. While in the past I was seeking to determine the optical properties of samples whose geometry is known (this is often referred to as the forward problem), now I am interested in using optical measurements to deduce information about the sample geometry (the inverse problem).
I have used numerical computing throughout my entire career and it still plays a very important role in my research. I enjoy writing code and have more than 20 years of programming experience.
H.Y.Ban, D.R.Busch, S.Pathak, F.A.Moscatelli, M.Machida, J.C.Schotland V.A.Markel, and A.G.Yodh: Diffuse optical tomography in the presence of a chest wall
Journal of Biomedical Optics 18 (2): 026016,2013.
X.Y.Z.Xiong, L.J.Jiang, V.A.Markel and I.Tsukerman: Surface waves in three-dimensional electromagnetic composites and their effect on homogenization Optics Express 21 (9): 10412-10421,2013.
V.A.Markel and J.C.Schotland
: Homogenization of Maxwell's equations in periodic composites: Boundary effects and dispersion relations
Physical Review E 85 (6): 066603,2012.
V.A.Markel and A.K.Sarychev: Comment on "Green's function theory for infinite and semi-infinite particle chains"
Physical Review B 86 (3): 037401,2012.
L.Florescu, V.A.Markel and J.C.Schotland: Inversion formulas for the broken-ray Radon transform Inverse Problems 27 : 025002,2011.
A.A.Govyadinov, G.Y.Panasyuk, J.C.Schotland and V.A.Markel: Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles
Physical Review B 84 (15): 155461,2011.
A.E.Ershov, I.L.Isaev, P.N.Semina, V.A.Markel, and S.V.Karpov: Effects of size polydispersity on the extinction spectra of colloidal nanoparticle aggregates
Physical Review B 85 (4): 045421,2011.
G.Y.Panasyuk, J.C.Schotland and V.A.Markel: Quantum theory of the electromagnetic response of metal nanofilms
Physical Review B 84 (5): 155460,2011.
L.Florescu, V.A.Markel and J.C.Schotland: Single-scattering optical tomography: Simultaneous reconstruction of scattering and absorption
Physical Review E 81 (1): 016602,2010.
V.A.Markel: Comment on "What is negative refraction"
Journal of Modern Optics 57 (20): 2098-2102; ibid 2109-2110 (rejoinder),2010.