To achieve better accuracy in their investigations, biologists have recently been using three-dimensional models as intermediates between two-dimensional cell culture and the in vivo study of tissues. Some of these models are based on spheroids, which are cellular aggregates retaining many characteristics of in vivo behaviors while being still easy to use and implement in labs. To study such objects, multiple observation techniques can be used according to the objective of the study, including those using electromagnetic waves as nondestructive, noninvasive, and label-free analysis. Low-frequency (<1 MHz) ones are currently under investigation as electrochemical impedance spectroscopy. However, unlike microwaves (from 300 MHz to 60 GHz), they cannot penetrate the cell. Furthermore, most of the devices dedicated to microwave dielectric characterization are only focusing on cellular scales lower than spheroids (single cell, cell mats, or suspensions) or on tissues and organs. In this article, a microwave spectroscopy device using a coplanar waveguide adapted to the study of spheroids is presented with the dielectric characterization of fixed spheroids, with capacitance and conductance measurements from 0.5 to 20 GHz, aiming at filling the scale gap in the state of the art.

Scattering of electromagnetic (EM) waves by small (ka ≪ 1) impedance particleD of anarbitrary shape, embedded in a homogeneous medium, is studied. Analytic, closed form,formula for the scattered field is derived. The scattered field is of the orderO(a2 −κ), where κ ∈ [ 0,1)is a number. This field is much larger than in the case of Rayleigh-type scattering. Thenumerical results demonstrate a wide range of applicability of the analytic formula forthe scattered field. Comparison with Mie-type solution is carried out for various boundaryimpedances and radii of the particle.

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectricstructure mounted on a perfectly conducting plate in three dimensions. Given thatuniqueness of solution holds, existence of solution follows from a well-known Fredholmframework for the variational formulation of the problem in a suitable Sobolev space. Inthis paper, we derive a Rellich identity for a solution to this variational problem undersuitable smoothness conditions on the material parameter. Under additional non-trappingassumptions on the material parameter, this identity allows us to establish uniqueness ofsolution for all positive wave numbers.

Inverse scattering problem is discussed for the Maxwell’s equations. A reduction of theMaxwell’s system to a new Fredholm second-kind integral equation with a scalarweakly singular kernel is given for electromagnetic (EM) wave scattering. Thisequation allows one to derive a formula for the scattering amplitude in which only ascalar function is present. If this function is small (an assumption that validates aBorn-type approximation), then formulas for the solution to the inverse problem areobtained from the scattering data: the complex permittivityϵ′(x) in a bounded regionD ⊂ R3 is found from the scattering amplitudeA(β,α,k) known for a fixed k = ω √ϵ0μ0 >0 and allβ,α ∈ S2, whereS2 is the unit sphere in R3,ϵ0 and μ0 are constantpermittivity and magnetic permeability in the exterior regionD′ = R3\D. The novel pointsin this paper include: i) A reduction of the inverse problem for vectorEM waves to a vector integral equation with scalar kernelwithout any symmetry assumptions on the scatterer, ii) A derivation of thescalar integral equation of the first kind for solving the inversescattering problem, and iii) Presenting formulas for solving this scalar integralequation. The problem of solving this integral equation is an ill-posed one. A method fora stable solution of this problem is given.