The discrete dipole approximation: an overview and recent developments

We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.

[1]  Kun-mu Chen,et al.  Electromagnetic Fields Induced Inside Arbitrarily Shaped Biological Bodies , 1974 .

[2]  G. Niklasson,et al.  Coupled multipolar interactions in small-particle metallic clusters. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  S. O'Brien,et al.  Scattering by irregular inhomogeneous particles via the digitized Green's function algorithm. , 1988, Applied optics.

[4]  Three-dimensional reconstruction of dielectric objects by the coupled-dipole method. , 2000, Applied optics.

[5]  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.

[6]  B. Gustafson,et al.  Comparison between Multisphere Light-scattering Calculations: Rigorous Solution and Discrete-Dipole Approximation , 1999 .

[7]  Larry D. Travis,et al.  Light scattering by nonspherical particles : theory, measurements, and applications , 1998 .

[8]  Kamal Belkebir,et al.  Three-dimensional optical imaging in layered media. , 2006, Optics express.

[9]  B. Draine,et al.  Application of fast-Fourier-transform techniques to the discrete-dipole approximation. , 1991, Optics letters.

[10]  Erik Jorgensen,et al.  Method of moments solution of volume integral equations using higher‐order hierarchical Legendre basis functions , 2004 .

[11]  H. Kimura,et al.  Light scattering by large clusters of dipoles as an analog for cometary dust aggregates , 2004 .

[12]  Modeling light scattering from Diesel soot particles. , 2004, Applied optics.

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

[14]  Edward K. N. Yung,et al.  Analysis of electromagnetic scattering of three-dimensional dielectric bodies using Krylov subspace FFT iterative methods , 2003 .

[15]  A. T. Hoop Convergence criterion for the time-domain iterative Born approximation to scattering by an inhomogeneous, dispersive object , 1991 .

[16]  Peter M. A. Sloot,et al.  Coupled Dipole Simulations of Elastic Light Scattering on Parallel Systems , 1995 .

[17]  B. T. Draine,et al.  Radiative Torques on Interstellar Grains: I. Superthermal Spinup , 1996 .

[18]  J. Kong,et al.  Scattering of Electromagnetic Waves, Numerical Simulations , 2001 .

[19]  Light Scattering by Clusters: the Al-Term Method , 1995 .

[20]  B. Draine,et al.  Discrete-Dipole Approximation For Scattering Calculations , 1994 .

[21]  Edward K. N. Yung,et al.  The application of iterative solvers in discrete dipole approximation method for computing electromagnetic scattering , 2006 .

[22]  Z. Laczik Discrete-dipole-approximation-based light-scattering calculations for particles with a real refractive index smaller than unity. , 1996, Applied optics.

[23]  Akhlesh Lakhtakia,et al.  On Two Numerical Techniques for Light Scattering by Dielectric Agglomerated Structures , 1993, Journal of research of the National Institute of Standards and Technology.

[24]  Yu-lin Xu,et al.  Scattering mueller matrix of an ensemble of variously shaped small particles. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[25]  Doyle,et al.  Optical properties of a suspension of metal spheres. , 1989, Physical review. B, Condensed matter.

[26]  T. Lemaire Coupled-multipole formulation for the treatment of electromagnetic scattering by a small dielectric particle of arbitrary shape , 1997 .

[27]  B. Dembart,et al.  The accuracy of fast multipole methods for Maxwell's equations , 1998 .

[28]  A. R. Jones Electromagnetic wave scattering by assemblies of particles in the Rayleigh approximation , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[29]  J. M. Greenberg,et al.  A model for the optical properties of porous grains , 1990 .

[30]  Bruno Torrésani,et al.  Some approximate methods for computing electromagnetic fields scattered by complex objects , 1998 .

[31]  P. Flatau Fast solvers for one dimensional light scattering in the discrete dipole approximation. , 2004, Optics express.

[32]  J. Rahola,et al.  Light Scattering by Porous Dust Particles in the Discrete-Dipole Approximation , 1994 .

[33]  Bruce T. Draine,et al.  The discrete-dipole approximation and its application to interstellar graphite grains , 1988 .

[34]  D. Mackowski Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles. , 1995, Applied optics.

[35]  Alfons G. Hoekstra,et al.  The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength , 2007 .

[36]  Michiel Min,et al.  Infrared extinction by homogeneous particle aggregates of SiC, FeO and SiO2 : Comparison of different theoretical approaches , 2006 .

[37]  H. V. Hulst Light Scattering by Small Particles , 1957 .

[38]  Clifton E. Dungey,et al.  Light scattering by nonspherical particles : a refinement to the coupled-dipole method , 1991 .

[39]  Static Polarizabilities of Dielectric Nanoclusters , 2005, cond-mat/0508360.

[40]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[41]  A G Hoekstra,et al.  Radiation forces in the discrete-dipole approximation. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[42]  Anne Sentenac,et al.  Three-dimensional subwavelength optical imaging using the coupled dipole method , 2004 .

[43]  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.

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

[45]  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.

[46]  Eric Darve,et al.  The Fast Multipole Method I: Error Analysis and Asymptotic Complexity , 2000, SIAM J. Numer. Anal..

[47]  J. Blum,et al.  Optical properties of dust aggregates. II: Angular dependence of scattered light , 1993 .

[48]  Jouni I. Peltoniemi,et al.  Variational volume integral equation method for electromagnetic scattering by irregular grains , 1996 .

[49]  Bruce T. Draine,et al.  Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation. [electromagnetic scattering and absorption by interstellar grains] , 1992 .

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

[51]  Polymer dispersed liquid crystal droplets: methods of calculation of optical characteristics , 1998 .

[52]  Akhlesh Lakhtakia,et al.  STRONG AND WEAK FORMS OF THE METHOD OF MOMENTS AND THE COUPLED DIPOLE METHOD FOR SCATTERING OF TIME-HARMONIC ELECTROMAGNETIC FIELDS , 1992 .

[53]  Sencer Koc,et al.  Multilevel Fast Multipole Algorithm for the Discrete Dipole Approximation , 2001 .

[54]  Thomas Wriedt,et al.  Light scattering by single erythrocyte: Comparison of different methods , 2006 .

[55]  J Rahola,et al.  Accuracy of internal fields in volume integral equation simulations of light scattering. , 1998, Applied optics.

[56]  G. Salzman,et al.  The scattering matrix for randomly oriented particles , 1986 .

[57]  P. Chaumet,et al.  Superresolution in total internal reflection tomography. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[58]  Graeme L. Stephens,et al.  Microwave radiative transfer through clouds composed of realistically shaped ice crystals , 1995 .

[59]  J. Blum,et al.  Optical properties of dust aggregates : I. Wavelength dependence , 1992 .

[60]  Olivier J. F. Martin,et al.  Efficient Scattering Calculations in Complex Backgrounds , 2004 .

[61]  Hajime Okamoto,et al.  Modeling of backscattering by non-spherical ice particles for the interpretation of cloud radar signals at 94 GHz. An error analysis , 1995 .

[62]  Anthony J. Illingworth,et al.  Error analysis of backscatter from discrete dipole approximation for different ice particle shapes , 1997 .

[63]  D. Mackowski,et al.  Scattering by two spheres in contact: comparisons between discrete-dipole approximation and modal analysis. , 1993, Applied optics.

[64]  O. Martin,et al.  A library for computing the filtered and non-filtered 3D Green"s tensor associated with infinite homogeneous space and surfaces , 2002 .

[65]  Joshua E. Barnes,et al.  Error Analysis of a Tree Code , 1989 .

[66]  N. Khlebtsov An approximate method for calculating scattering and absorption of light by fractal aggregates , 2000 .

[67]  E. Zubko,et al.  Discrete dipole approximation simulations of scattering by particles with hierarchical structure. , 2005, Applied optics.

[68]  Anne Sentenac,et al.  Coupled dipole method for scatterers with large permittivity. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  L. Tsang,et al.  A sparse matrix iterative approach for modeling tree scattering , 2003 .

[70]  Thomas Wriedt,et al.  A Review of Elastic Light Scattering Theories , 1998 .

[71]  N B Piller Influence of the edge meshes on the accuracy of the coupled-dipole approximation. , 1997, Optics letters.

[72]  Roland W. Freund,et al.  Conjugate Gradient-Type Methods for Linear Systems with Complex Symmetric Coefficient Matrices , 1992, SIAM J. Sci. Comput..

[73]  William H. Press,et al.  Numerical recipes in C , 2002 .

[74]  S. Amini,et al.  Multi-level fast multipole solution of the scattering problem , 2003 .

[75]  S B Singham Theoretical factors in modeling polarized light scattering by arbitrary particles. , 1989, Applied optics.

[76]  D. Mackowski,et al.  Calculation of total cross sections of multiple-sphere clusters , 1994 .

[77]  C F Bohren,et al.  Light scattering by an arbitrary particle: a physical reformulation of the coupled dipole method. , 1987, Optics letters.

[78]  Jussi Rahola,et al.  On the Eigenvalues of the Volume Integral Operator of Electromagnetic Scattering , 1999, SIAM J. Sci. Comput..

[79]  Akhlesh Lakhtakia,et al.  General theory of the Purcell-Pennypacker scattering approach and its extension to bianisotropic scatterers , 1992 .

[80]  B. Torrésani,et al.  Multidipole formulation of the coupled dipole method for electromagnetic scattering by an arbitrary particle , 1992 .

[81]  A. Jones Scattering efficiency factors for agglomerates for small spheres , 1979 .

[82]  Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies. , 2002, Optics letters.

[83]  B. T. Draine,et al.  Propagation of Electromagnetic Waves on a Rectangular Lattice of Polarizable Points , 2004 .

[84]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[85]  Andrew A. Lacis,et al.  Scattering, Absorption, and Emission of Light by Small Particles , 2002 .

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

[87]  Hiroshi Kimura,et al.  Applicability of the discrete-dipole approximation to light-scattering simulations of large cosmic dust aggregates , 2006 .

[88]  Peter M. A. Sloot,et al.  Large Scale Simulations of Elastic Light Scattering by a Fast Discrete Dipole Approximation , 1998 .

[89]  C Acquista,et al.  Light scattering by tenuous particles: a generalization of the Rayleigh-Gans-Rocard approach. , 1976, Applied optics.

[90]  J. Hovenier Light scattering by non-spherical particles. Proceedings. Workshop, Amsterdam (Netherlands), 2 - 3 May 1995. , 1996 .

[91]  T. Charalampopoulos,et al.  On the electromagnetic scattering and absorption of agglomerated small spherical particles , 1994 .

[92]  Anne Sentenac,et al.  Efficient computation of optical forces with the coupled dipole method. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[93]  M. Mishchenko,et al.  Reprint of: T-matrix computations of light scattering by nonspherical particles: a review , 1996 .

[94]  Neil V. Budko,et al.  Spectrum of the Volume Integral Operator of Electromagnetic Scattering , 2006, SIAM J. Sci. Comput..

[95]  P. Chaumet,et al.  On the Importance of Local-Field Corrections for Polarizable Particles on a Finite Lattice: Application to the Discrete Dipole Approximation , 2004 .

[96]  P. Chiappetta Multiple scattering approach to light scattering by arbitrarily shaped particles , 1980 .

[97]  J. Rahola,et al.  Light Scattering by Dense Clusters of Spheres , 1997 .

[98]  Alan R. Jones,et al.  Light scattering for particle characterization , 1999 .

[99]  Alfons G. Hoekstra,et al.  New computational techniques to simulate light scattering from arbitrary particles , 1993 .

[100]  D T Venizelos,et al.  Development of an algorithm for the calculation of the scattering properties of agglomerates. , 1996, Applied optics.

[101]  A G Hoekstra,et al.  Dipolar unit size in coupled-dipole calculations of the scattering matrix elements. , 1993, Optics letters.

[102]  Ching-Chuan Su,et al.  Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anisotropy , 1989 .

[103]  Bruce T. Draine,et al.  The Discrete Dipole Approximation for Light Scattering by Irregular Targets , 2000 .

[104]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[105]  Jussi Rahola,et al.  Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems , 1995 .

[106]  G. Videen,et al.  Chaotic light scattering from a system of osculating, conducting spheres , 1997 .

[107]  Vadim A. Markel,et al.  Small-particle composites. I. Linear optical properties. , 1996, Physical review. B, Condensed matter.

[108]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[109]  T. Wriedt,et al.  Comparison of scattering calculations for aggregated particles based on different models , 1999 .

[110]  D. Mackowski,et al.  Discrete dipole moment method for calculation of the T matrix for nonspherical particles. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[111]  Vadim A. Markel Coupled-dipole Approach to Scattering of Light from a One-dimensional Periodic Dipole Structure , 1993 .

[112]  B. Draine,et al.  User Guide for the Discrete Dipole Approximation Code DDSCAT (Version 5a10) , 2000, astro-ph/0008151.

[113]  F.Michael Kahnert,et al.  Numerical methods in electromagnetic scattering theory , 2003 .

[114]  E. Purcell,et al.  Scattering and Absorption of Light by Nonspherical Dielectric Grains , 1973 .

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

[116]  B. V. Bronk,et al.  Internal and scattered electric fields in the discrete dipole approximation , 1999 .

[117]  E. Zubko,et al.  Optimizing the discrete-dipole approximation for sequences of scatterers with identical shapes but differing sizes or refractive indices , 2006 .

[118]  Kirk A. Fuller,et al.  Light Scattering by Agglomerates: Coupled Electric and Magnetic Dipole Method , 1994 .

[119]  A. Hoekstra Computer Simulations of Elastic Light Scattering , 1994 .

[120]  A. Samokhin,et al.  A Generalized Overrelaxation Method for Solving Singular Volume Integral Equations in Low-Frequency Scattering Problems , 2005 .

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

[122]  J. Ku Comparisons of coupled-dipole solutions and dipole refractive indices for light scattering and absorption by arbitrarily shaped or agglomerated particles , 1993 .

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

[124]  N. Khlebtsov Orientational averaging of integrated cross sections in the discrete dipole method , 2001 .

[125]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[126]  Vadim A. Markel,et al.  Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions , 2004 .

[127]  Takashi Kozasa,et al.  Optical Properties of Dust Aggregates , 1991 .

[128]  H. Y. Chen,et al.  Optical scattering and absorption by branched chains of aerosols. , 1989, Applied optics.

[129]  Damon A. Smith,et al.  Discrete dipole approximation for magneto-optical scattering calculations. , 2006, Optics express.

[130]  Modelling the optical properties of composite and porous interstellar grains , 2004, astro-ph/0409457.

[131]  F. Teixeira,et al.  Fast algorithm for matrix–vector multiply of asymmetric multilevel block‐Toeplitz matrices in 3‐D scattering , 2001 .

[132]  D. A. Dunnett Classical Electrodynamics , 2020, Nature.

[133]  Caicheng Lu A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes , 2003 .

[134]  W. M. McClain,et al.  Elastic light scattering by randomly oriented macromolecules: Computation of the complete set of observables , 1986 .

[135]  Nicolas B. Piller Coupled-dipole approximation for high permittivity materials , 1999 .

[136]  M. Mishchenko,et al.  Calculation of the amplitude matrix for a nonspherical particle in a fixed orientation. , 2000, Applied optics.

[137]  C F Bohren,et al.  Light scattering by an arbitrary particle: the scattering-order formulation of the coupled-dipole method. , 1988, Journal of the Optical Society of America. A, Optics and image science.

[138]  P. Chaumet,et al.  Numerical simulations of the electromagnetic field scattered by defects in a double-periodic structure , 2005 .

[139]  B. Draine,et al.  Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

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

[141]  Jun Q. Lu,et al.  Systematic comparison of the discrete dipole approximation and the finite difference time domain method , 2007 .

[142]  M. Quante,et al.  Comment on error analysis of backscatter from discrete dipole approximation for different ice particle shapes [Liu, C.-L., Illingworth, A.J., 1997, Atmos. Res. 44, 231-241.] , 1998 .

[143]  Light scattering by needle-type and disk-type particles , 2006 .

[144]  P. Flatau,et al.  Improvements in the discrete-dipole approximation method of computing scattering and absorption. , 1997, Optics letters.

[145]  P. Chaumet,et al.  Generalization of the Coupled Dipole Method to Periodic Structures , 2003, physics/0305051.

[146]  A. Yaghjian Electric dyadic Green's functions in the source region , 1980 .

[147]  G. Schatz,et al.  Discrete dipole approximation for calculating extinction and Raman intensities for small particles with arbitrary shapes , 1995 .

[148]  Shao-Liang Zhang,et al.  GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems , 1997, SIAM J. Sci. Comput..

[149]  Gorden Videen,et al.  Discrete-dipole analysis of backscatter features of agglomerated debris particles comparable in size with wavelength , 2006 .

[150]  Kirk A. Fuller,et al.  Electromagnetic Scattering by Compounded Spherical Particles , 2000 .