Light scattering by a cube: Accuracy limits of the discrete dipole approximation and the T-matrix method

We simulated light-scattering by small and wavelength-sized cubes with three largely different values of the refractive index using the discrete dipole approximation (DDA) and the T-matrix method. Our main goal was to push the accuracy of both methods to the limit. For the DDA we used an earlier developed extrapolation technique based on simulation results for different levels of discretization. For the T-matrix method we developed a procedure to estimate a confidence range for the simulated value, using results for different values of the truncation index (number of multipoles). In most cases this confidence range was reliable, enclosing the corresponding DDA result. We present benchmark results by both methods, including estimated uncertainties, for selected integral and angle-resolved scattering quantities. Estimated relative uncertainties of the DDA result are unprecedentedly small (from 10(-7) to 10(-3)), while relative differences between the T-matrix and DDA results are larger (from 10(-4) to 0.2) in accordance with estimated T-matrix uncertainties.

[1]  M. Kahnert,et al.  Light scattering by particles with small-scale surface roughness: comparison of four classes of model geometries , 2012 .

[2]  Thomas Wriedt,et al.  T-matrix method for biaxial anisotropic particles , 2009 .

[3]  Maxim A Yurkin,et al.  Convergence of the discrete dipole approximation. II. An extrapolation technique to increase the accuracy. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  Younan Xia,et al.  Chemical synthesis of novel plasmonic nanoparticles. , 2009, Annual review of physical chemistry.

[5]  Alfons G. Hoekstra,et al.  The discrete-dipole-approximation code ADDA: Capabilities and known limitations , 2011 .

[6]  M. Mishchenko,et al.  Light scattering by size-shape distributions of randomly oriented axially symmetric particles of a size comparable to a wavelength. , 1993, Applied optics.

[7]  P. Martin,et al.  A new method to calculate the extinction properties of irregularly shaped particles , 1993 .

[8]  W. Steen.  Absorption and Scattering of Light by Small Particles , 1999 .

[9]  J J Stamnes,et al.  Application of the extended boundary condition method to particles with sharp edges: a comparison of two surface integration approaches. , 2001, Applied optics.

[10]  Y. Shkuratov,et al.  An analytical solution to the light scattering from cube-like particles using Sh-matrices , 2010 .

[11]  R. T. Wang,et al.  Scattering from arbitrarily shaped particles: theory and experiment. , 1991, Applied optics.

[12]  M. Kahnert.  T-matrix computations for particles with high-order finite symmetries , 2013 .

[13]  O. Martin,et al.  Increasing the performance of the coupled-dipole approximation: a spectral approach , 1998 .

[14]  J. Pollack,et al.  Light scattering by randomly oriented cubes and parallelepipeds. , 1983, Applied optics.

[15]  Maxim A Yurkin,et al.  Application of the discrete dipole approximation to very large refractive indices: Filtered coupled dipoles revived. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  D. Langbein.  Normal modes at small cubes and rectangular particles , 1976 .

[17]  Alfons G. Hoekstra,et al.  Comparison between discrete dipole implementations and exact techniques , 2007 .

[18]  Alfons G. Hoekstra,et al.  Accuracy of the discrete dipole approximation for simulation of optical properties of gold nanoparticles , 2010 .

[19]  P. Kaye,et al.  Modelling diffraction by facetted particles , 2012 .

[20]  Alfons G. Hoekstra,et al.  The discrete dipole approximation: an overview and recent developments , 2007 .

[21]  Michael Kahnert,et al.  Irreducible representations of finite groups in the T-matrix formulation of the electromagnetic scattering problem. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[22]  J J Stamnes,et al.  Application of the extended boundary condition method to homogeneous particles with point-group symmetries. , 2001, Applied optics.

[23]  M. Mishchenko,et al.  Scattering of light by polydisperse, randomly oriented, finite circular cylinders. , 1996, Applied optics.

[24]  Y. Shkuratov,et al.  Scattering matrix calculated in geometric optics approximation for semitransparent particles faceted with various shapes , 2003 .

[25]  A volume and surface source integral formulation for electromagnetic scattering from printed circuit antennas , 1991 .

[26]  M. Kahnert,et al.  Modeling optical properties of particles with small-scale surface roughness: combination of group theory with a perturbation approach. , 2011, Optics express.

[27]  A. Sihvola,et al.  Polarizability analysis of cubical and square-shaped dielectric scatterers , 2001 .

[28]  Thomas Wriedt,et al.  Comparison of computational scattering methods , 1998 .

[29]  M. Kahnert,et al.  A case study on the reciprocity in light scattering computations. , 2012, Optics express.

[30]  L. Shafai,et al.  Numerical solution of integral equations for dielectric objects of prismatic shapes , 1991 .

[31]  Jussi Rahola,et al.  Solution of Dense Systems of Linear Equations in the Discrete-Dipole Approximation , 1996, SIAM J. Sci. Comput..

[32]  T. Wriedt,et al.  Improving the numerical stability of T-matrix light scattering calculations for extreme particle shapes using the nullfield method with discrete sources , 2011 .

[33]  Maxim A Yurkin,et al.  Convergence of the discrete dipole approximation. I. Theoretical analysis. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[34]  B. Auguié,et al.  Severe loss of precision in calculations of T-matrix integrals , 2012 .

[35]  J. Rahola,et al.  Computations of scattering matrices of four types of non-spherical particles using diverse methods , 1996 .

[36]  Konstantin V Gilev,et al.  Comparison of the discrete dipole approximation and the discrete source method for simulation of light scattering by red blood cells. , 2010, Optics express.

[37]  R. Fuchs,et al.  Theory of the optical properties of ionic crystal cubes , 1975 .

[38]  Graeme L. Stephens,et al.  Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the Block–Toeplitz structure , 1990 .

[39]  A. Kokhanovsky.  Modeling of light depolarization by cubic and hexagonal particles in noctilucent clouds , 2006 .