Subpixel smoothing finite-difference time-domain method for material interface between dielectric and dispersive media

Using high-resolution microscopy data to generate realistic structures for electromagnetic FDTD simulations from complex biological models

Finite-difference time-domain (FDTD) electromagnetic simulations are a computational method that has seen much success in the study of biological optics; however, such simulations are often hindered by the difficulty of faithfully replicating complex biological microstructures in the simulation space. Recently, we designed simulations to calculate the trajectory of electromagnetic light waves through realistically reconstructed retinal photoreceptors and found that cone photoreceptor mitochondria play a substantial role in shaping incoming light. In addition to vision research and ophthalmology, such simulations are broadly applicable to studies of the interaction of electromagnetic radiation with biological tissue. Here, we present our method for discretizing complex 3D models of cellular structures for use in FDTD simulations using MEEP, the MIT Electromagnetic Equation Propagation software, including subpixel smoothing at mesh boundaries. Such models can originate from experimental imaging or be constructed by hand. We also include sample code for use in MEEP. Implementation of this algorithm in new code requires understanding of 3D mathematics and may require several weeks of effort, whereas use of our sample code requires knowledge of MEEP and C++ and may take up to a few hours to prepare a model of interest for 3D FDTD simulation. In all cases, access to a facility supercomputer with parallel processing capabilities is recommended. This protocol offers a practical solution to a significant challenge in the field of computational electrodynamics and paves the way for future advancements in the study of light interaction with biological structures.

Tensor-conductance model for reducing the computational artifact in target tissue for low-frequency dosimetry

Objective.In protecting human from low-frequency (<100 kHz) exposure, an induced electric field strength is used as a physical quantity for assessment. However, the computational assessment suffers from a staircasing error because of the approximation of curved boundary discretized with cubic voxels. The international guidelines consider an additional reduction factor of 3 when setting the limit of external field strength computed from the permissible induced electric field. Here, a new method was proposed to reduce the staircasing error considering the tensor conductance in human modeling for low-frequency dosimetry.Approach.We proposed a tensor-based conductance model, which was developed on the basis of the filling ratio and the direction of the tissue interface to satisfy the electric field boundary condition and reduce staircasing errors in the target tissue of a voxel human model.Main results.The proposed model was validated using two-layer nonconcentric cylindrical and spherical models with different conductivity contrasts. A comparison of induced electric field strengths with solutions obtained using an analytical formula and finite element method simulation indicated that for a wide range of conductivity ratios, staircasing errors were reduced compared with a conventional scalar-potential finite-difference method. The induced electric field in a simple anatomical head model using our approach was in good agreement with finite element method for exposure to uniform magnetic field exposure and that from coil, simulating transcranial magnetic stimulation.Significance.The proposed tensor-conductance model demonstrated that the staircasing error in an inner target tissue of a voxel human body can be reduced. This finding can be used for the electromagnetic compliance assessment and dose evaluation in electric or magnetic stimulation at low frequencies.

Finite-difference Time-domain (FDTD) Optical Simulations: A Primer for the Life Sciences and Bio-Inspired Engineering

Light influences most ecosystems on earth, from sun-dappled forests to bioluminescent creatures in the ocean deep. Biologists have long studied nano- and micro-scale organismal adaptations to manipulate light using ever-more sophisticated microscopy, spectroscopy, and other analytical equipment. In combination with experimental tools, simulations of light interacting with objects can help researchers determine the impact of observed structures and explore how variations affect optical function. In particular, the finite-difference time-domain (FDTD) method is widely used throughout the nanophotonics community to efficiently simulate light interacting with a variety of materials and optical devices. More recently, FDTD has been used to characterize optical adaptations in nature, such as camouflage in fish and other organisms, colors in sexually-selected birds and spiders, and photosynthetic efficiency in plants. FDTD is also common in bioengineering, as the design of biologically-inspired engineered structures can be guided and optimized through FDTD simulations. Parameter sweeps are a particularly useful application of FDTD, which allows researchers to explore a range of variables and modifications in natural and synthetic systems (e.g., to investigate the optical effects of changing the sizes, shape, or refractive indices of a structure). Here, we review the use of FDTD simulations in biology and present a brief methods primer tailored for life scientists, with a focus on the commercially available software Lumerical FDTD. We give special attention to whether FDTD is the right tool to use, how experimental techniques are used to acquire and import the structures of interest, and how their optical properties such as refractive index and absorption are obtained. This primer is intended to help researchers understand FDTD, implement the method to model optical effects, and learn about the benefits and limitations of this tool. Altogether, FDTD is well-suited to (i) characterize optical adaptations and (ii) provide mechanistic explanations; by doing so, it helps (iii) make conclusions about evolutionary theory and (iv) inspire new technologies based on natural structures.

Generalized tensor FDTD method for sloped dispersive interfaces and thin sheets

We present a modified formulation of the Finite-Difference Time-Domain (FDTD) technique that facilitates the accurate modeling of curved plasmonic interfaces. These interfaces appear in structures of interest for the design of optical metamaterials, such as arrays of plasmonic nanorods. Our approach uses the standard rectangular FDTD mesh and tensor effective permittivities for the interface cells, implicitly enforcing field boundary conditions, and is readily applicable to thin curved dispersive layers. We demonstrate the accuracy and effectiveness of our approach with the periodic analysis of a silver nanorod array and the computation of scattering parameters from a thin dispersive ring in a waveguide.

Review and accuracy comparison of various permittivity-averaging schemes for material discontinuities in the two-dimensional FDFD method: implementation using efficient computer graphics techniques

Several known and widely used averaging techniques aiming to improve the accuracy of the two-dimensional finite-difference frequency-domain (FDFD) method, in the presence of material discontinuities, are reviewed, numerically tested, and compared with respect to their accuracies. Furthermore, all averaging techniques are rigorously and efficiently implemented using the Supercover Digital Differential Analyzer algorithm and a modified Liang-Barsky algorithm suitably adapted from computer graphics applications. The FDFD with Gaussian blurring; the FDFD with volume-polarized effective permittivity; the FDFD with volume-polarized effective permittivity on shifted cells; and the FDFD with anisotropic smoothing [FDFD (AS)] are compared with respect to their accuracies (for both TE and TM polarization), in the case of scattering by an infinite homogeneous cylinder (for which analytical solution exists) comprising a lossless dielectric, a high-index, low-loss dielectric, or a metal. Sample plots of the relative errors are presented for various field components. Absolute error norms (L₂ and L_∞) are also presented for both polarizations and for two grid-cell sizes for quantitative comparisons. The results show that the FDFD (AS) prevails in accuracy mainly because it satisfies the boundary conditions at the cylinder's boundary the best. However, for the high-index dielectrics and metals, even the FDFD without any averaging gives very good results for the field components parallel to the uniformity direction. However, the FDFD (AS) is always more accurate when the in-plane field components are sought.