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Published in Luis Liz-Marzán, Colloidal Synthesis of Plasmonic Nanometals, 2020
Andrés Guerrero-Martinez, José Lorenzo Alonso-Gómez, Baptiste Auguie, M. Magdalena Cid, Luis M. Liz-Marzán
Further studies will probably call for more accurate modeling tools that extend beyond the limitations of the coupled-dipole approach. In particular, multipole expansions are necessary to acknowledge the contribution of higher-order modes which are typically encountered in larger particles or short particle-particle distances. In this regard, we point out the T-matrix method as a promising framework, with flexibility in the description of particles of arbitrary shape [137], and, perhaps as importantly, the efficient treatment of multiple-scattering [138] and orientation-averaging [139]. Another elegant approach recently proposed by Giessen and co-workers considers the extension of the hybridization picture to more complex structures with strong multipolar and magnetic response, such as coupled split-ring resonators [140]. We conclude by noting that complex nanostructures may not only be produced to present exotic optical activity properties through optimized coupling of meta-atoms, but also in shaping the intrinsic chirality of the exciting field itself [141, 142].
FDTD Simulation of Trapping Microspheres and Nanowires with Optical Tweezers
Published in Sarhan M. Musa, Computational Nanotechnology Using Finite Difference Time Domain, 2017
Jing Li, Chunli Zhu, Xiaoping Wu
In recent years, this has become the main way that the comprehensive electrodynamics theory and Maxwell stress tensor method are employed to calculate the strongly focused laser beam and the force exerted on the particle with size between λ/10 and 10λ. It requires that six components of the electromagnetic field on the surface of the particle be calculated. Usually, the numerical methods for solving electromagnetic field distribution include the finite element method (FEM) [23], the T-matrix method [24, 25], and the finite-difference time-domain (FDTD) method [26–30]. Among them, the use of the finite-element method is limited by the minimum of the space grid and time interval, and the T-matrix method is appropriate for highly symmetric particles. Nevertheless, the FDTD method can solve problems, such as the electromagnetic scattering, radiation, etc., for objects with complicated shapes. Meanwhile, it can give the time evolution process of the electromagnetic field. Thus, this method is adopted to get the optical trapping force exerted on microparticles of this dimension.
Computational Biophotonics
Published in Vadim Backman, Adam Wax, Hao F. Zhang, A Laboratory Manual in Biophotonics, 2018
Vadim Backman, Adam Wax, Hao F. Zhang
The key feature of the T-matrix method is that it separates all properties of the incident field and those of the scattering particle. In other words, the scattering properties of the object are completely determined by the T-matrix, while the incident field is fully described by vector a. Therefore, one needs to calculate the T-matrix for a given scattering particle only once. After that, the matrix can be used to predict the scattered field for any configuration of the illumination as long as illumination vector a is known.
Aerosol optical properties calculated from size distribution measurements: An uncertainty study
Published in Aerosol Science and Technology, 2023
Hagen Telg, Don R. Collins, Allison McComiskey
A common technique to calculate optical properties of particles of arbitrary shape is the transition matrix (T-matrix) method (Waterman 1965). In the presented study we use a formulation of the T-matrix method that approximates particles as randomly oriented oblate and prolate spheroids (Leinonen 2014; Mishchenko 1991), where the asphericity is quantified by the ratio, ξ, of the equatorial to polar radius. The model further requires the particle’s complex refractive index and the wavelength of the scattered light, where the latter is kept constant throughout this study at a value of 550 nm. As ξ increases, calculations become too costly to be carried out for every possible combination of random input parameters in the Monte Carlo analysis. Therefore, we compiled a four-dimensional look-up table (LUT) for the scattering coefficient as a function of particle diameter, shape parameter, real, and imaginary part of the refractive index. We linearly interpolate the LUT to the random input values. Note, the T-matrix code exhibits increasing difficulties in computing larger particle shape parameters with increasing particle diameter. For particles larger than 2 μm extrapolation was required for large Φ.
Enhanced near-field thermal radiation between black phosphorus with high electron density by BP/hBN heterostructures
Published in Nanoscale and Microscale Thermophysical Engineering, 2023
Huadong Huang, Shiquan Shan, Zhijun Zhou
The dispersion relation can be obtained by setting the denominator in Eq. (4) [37]. This method of calculating the electromagnetic field relationship between the surfaces through the transfer matrix is also called the T-matrix method. Like the S-matrix method by calculating the scattering matrix, it is widely used to calculate the Fresnel reflection and transmission coefficients of complex structures, such as multilayer anisotropic materials [38].