Calculating coherent light-wave propagation in large heterogeneous media

Abstract

Understanding the interaction of light with a highly scattering material is essential for optical microscopy of optically thick and heterogeneous biological tissues. Ensemble-averaged analytic solutions cannot provide more than general predictions for relatively simple cases. Yet, biological tissues contain chiral organic molecules and many of the cells' structures are birefringent, a property exploited by polarization microscopy for label-free imaging. Solving Maxwell's equations in such materials is a notoriously hard problem. Here we present an efficient method to determine the propagation of electro-magnetic waves in arbitrary anisotropic materials. We demonstrate how the algorithm enables large scale calculations of the scattered light field in complex birefringent materials, chiral media, and even materials with a negative refractive index.

Fast Computation of Scattering by Isolated Defects in Periodic Dielectric Media

“…The efficiency arises for two reasons: (a) the reduction in the number of numerical solutions to Maxwell's equations, and (b) the reduction in the problem size for each solution. If we associate a unit cost 𝐶 to compute the solution for a single source using any method such as FDTD or other approaches [11], then the cost to compute 𝑛 𝑑 columns of the S-matrix is essentially 𝑛 𝑑 𝐶. The efficiency gain in (a) arises from replacing 𝑛 𝑑 by a much smaller number.…”

“…Therefore, the efficiency gain is independent of how fast the underlying near field solver works, and depends only on how many times it must be run. A faster solver such as [11] would simply reduce 𝐶, but (a) will reduce the product 𝑛 𝑑 𝐶 as discussed above, and in more detail below.…”

“…Furthermore, since by definition 𝜒 (𝑑) (𝒓) = 0 for 𝒓 outside the volume of the defect, successive iteration of (11) shows that Γ (𝑑) 𝑖 𝑗 (𝒓, 𝒓 ) is non-zero only when both its arguments lie inside the defect volume as well, i.e. 𝒓, 𝒓 ∈ defect.…”

“…Recent work by Vettenburg et al [11] introduces a method that derives from the same formalism discussed in this paper, but proceeds to an efficient calculation of near fields. This advancement in solving Maxwell equations will clearly benefit the first step of the computational strategy described in this work, and as discussed briefly in the paragraph above.…”

Towards single-photon deep-tissue microscopy

“…A novel class of modified Born-series methods was recently discovered and put forward to bridge this gap [9]. We show that this type of method can be extended to Maxwell's electromagnetic vector fields [6], and applied to very general materials, including biological tissues and metamaterials [13]. Figure 3 shows how this can be used to study how structured illumination is refracted and scattered by the heterogeneities within a model specimen.…”