Abstract
In optical particle characterisation and aerosol science today light scattering simulations are regarded as an indispensable tool to develop new particle characterisation techniques or in solving inverse light scattering problems. Mie scattering and related computational methods have evolved rapidly during the past decade such that scattering computations for spherical scatterers a few order of magnitudes larger, than the incident wavelength can be easily performed. This significant progress has resulted from rapid advances in computational algorithms developed in this field and from improved computer hardware. In this chapter the history and a review of the recent progress of Mie scattering and Mie-related light scattering theories and available computational programs is presented. We will focus on Mie scattering theories but as there is much overlap to related scattering theories they will also be mentioned where appropriate. Short outlines of the various methods are given. This review is of course biased by my interest in optical particle characterisation and my daily reading.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M.I. Mishchenko, L.D. Travis, Bull. Am. Meteorol. Soc. 89(12), 1853 (2008)
M.I. Mishchenko, J. Quant. Spectrosc. Radiat. Transf. 110(14–16), 1210 (2009)
U. Kreibig, Physik in unserer Zeit 39(6), 281 (2008)
W. Hergert, T. Wriedt (eds.), Mie Theory 1908–2008 (Universität Bremen, Bremen, 2008)
T. Stübinger, U. Köhler, W. Witt, U. Köhler, W. Witt, in Particulate Systems Analysis 2008 (Stratford-upon-Avon, UK, 2008)
T. Wriedt, in Mie Theory 1908–2008, ed. by W. Hergert, T. Wriedt (Universität Bremen. Bremen, 2008), pp. 17–21
H. Horvath, J. Quant. Spectrosc. Radiat. Transf. 110(11), 783 (2009)
H. Horvath, J. Quant. Spectrosc. Radiat. Transf. 110(11), 787 (2009)
V. Garbin, G. Volpe, E. Ferrari, M. Versluis, D. Cojoc, D. Petrov, New J. Phys. 11(1), 013046 (2009)
M. Kolwas, Comput. Methods Sci. Technol. 16 Special Issue (2), 108 (2010)
T. Wriedt, Part.& Part. Syst. Charact. 15(2), 67 (1998)
F.M. Kahnert, J. Quant. Spectrosc. Radiat. Transf. 79–80, 775 (2003)
G. Veronis, S. Fan, in Surface Plasmon Nanophotonics (Springer, Dortrecht, 2007), pp. 169–182
G.A. Niklasson, W.E. Vargas, Encyclopedia of Surface and Colloid Science, 2nd edn. pp. 3346–3358 (2006)
J. Zhao, A.O. Pinchuk, J.M. McMahon, S. Li, L.K. Ausman, A.L. Atkinson, G.C. Schatz, Acc. Chem. Res. 41(12), 1710 (2008)
C.J. Bouwkamp, Rep. Prog. Phys. 17(1), 35 (1954)
V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A.M. Funston, C. Novo, P. Mulvaney, L.M. Liz-Marzán, F.J. F. Javier García de Abajo, Chem. Soc. Rev. (2008)
V. Veselago, L. Braginsky, V. Shklover, C. Hafner, J. Comput. Theor. Nanosci. 3, 189 (2006)
G. Mie, Annalen der Physik 330(3), 377 (1908)
R. Gans, Annalen der Physik 381(1), 29 (1925)
H. Blumer, Zeitschrift für Physik 32, 119 (1925)
N.A. Logan, Proc. IEEE pp. 773–785 (1965)
A. Clebsch, Journal für Mathematik, Band 61, Heft 3, 195 (1863)
L. Lorenz, Det Kongelige Danske Videnskabernes Selskabs Skrifter 6. Raekke, 6. Bind 1, 1 (1890)
L. Lorenz, Oeuvres scientifiques de L. Lorenz. Revues et annotées par H. Valentiner (Libraire Lehmann& Stage, Copenhague, 1898), chap. Sur la lumière réfléchie et réfractée par une sphère (surface) transparente., pp. 403–529
P. Debye, Annalen der Physik, Vierte Folge, Band 30. No. 1, 57 (1909)
W.T. Grandy, Scattering of waves from large spheres (Cambridge Univ. Press, Cambridge, 2000)
E. Davis, G. Schweiger, The Airborne Microparticle (Springer, Berlin, Heidelberg, 2002)
G. Burlak, The Classical and Quantum Dynamics of the Multispherical Nanostructures (Imperial College Press, London, 2004)
M. Kerker, The Scattering of Light, and Other Electromagnetic Radiation: and other electromagnetic radiation (Academic Press, New York, London, 1969)
P. Pesic, Sky in a bottle (MIT Press, Cambridge, 2005)
O. Keller, Prog. Opt. 43, 257 (2002)
H. Kragh, Appl. Opt. 30(33), 4688 (1991)
M. Cardona, W. Marx, Physik Journal 11, 27 (2004)
W. Marx, Phys. Unserer Zeit, pp. 34–39 (2007)
B.F. Bowman, www.biochem.mpg.de/iv/AgFN_Bibliometrie.pdf. accessed 15. Aug. 2008. (2008)
I. Fränz-Gotthold, M. von Laue, Annalen der Physik 425(3), 249 (1938)
H. Bateman, Cambridge University Press, 1915. http://www.archive.org/download/ mathematicalanal00baterich/mathematicalanal00baterich.pdf (1915)
G. Mie, Contributions to the optics of turbid media, particularly of colloidal metal solutions. Tech. Rep. Library Translation 1873, RAE-Lit-Trans-1873, Royal Aircraft Establishment (1976). http://diogenes.iwt.uni-bremen.de/vt/laser/papers/RAE-LT1873-1976-Mie-1908-translation.pdf
G. Mie, Contributions on the optics of turbid media, particularly colloidal metal solutions – Translation. Technical report. SAND78-6018. National Translation Center, Chicago, ILL, Translation 79–21946, Sandia Laboratories, Albuquerque, New Mexico (1978)
G. Mie, Consideraciones sobre la óptica de los medios turbios, especialmente soluciones coloidales. Traducción: Arturo Quirantes Sierra. Technical report http://www.ugr.es/aquiran/ciencia/mie/mie1908_spanish.pdf, Universidad de Granada (2007)
A. Quirantes, http://www.ugr.es/aquiran/mie.htm. (2007)
J.A. Stratton, Electromagnetic theory (McGraw-Hill, New York, 1941)
W.W. Hansen, Phys. Rev. 47, 139 (1935)
M. Born, E. Wolf, Principles of Optics, 7th edn. (Cambridge University Press, 1999)
H.C. van de Hulst, Light Scattering by Small Particles (Dover Publications, New York, 1981)
C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Berlin, 1983)
E.C.L. Ru, P.G. Etchegoin, Prinziples of surface-enhanced Raman spectroscopy and related plasmonic effects (Elsevier, Amsterdam, 2009)
S.V. (ed.), Thermal Nanosystems and Nanomaterials (Springer, Heidelberg, 2009) Mie Theory and the Discrete Dipole Approximation, Franck Enguehard, 2009
R.H. Giese, Elektron. Rechenanl. 3, 240 (1961)
J. Dave, Subroutines for computing the parameters of the electromagnetic radiation scattered by a sphere, Rep. No. 320–3237. Technical report, IBM Scientific Center, Palo Alto, Calif. (1968)
C.D. Cantrell, Numerical methods for the accurate calculation of spherical Bessel functions and the location of Mie resonances. Tech. Rep. http://www.utdallas.edu/cantrell/ee6481/lectures/bessres1.pdf, Center for Applied Optics, University of Texas at Dallas, Richardson, TX, USA (1988). http://www.utdallas.edu/cantrell/ee6481/lectures/bessres1.pdf
D. Deirmendjann, The Electromagnetic Scattering on Spherical Polydispersion (Elsevier, New York, 1969)
D. Deirmendjann, R. Clasen, W. Viezee, J. Opt. Soc. Am. 51(6), 620 (1961)
H.J. Metz, H.K. Dettmar, Kolloid-Zeitschrift und Zeitschrift für Polymere 192(1–2), 107 (1963)
B. Maguire, J. Aerosol Sci. 2(4), 417 (1971)
W. Wiscombe, Mie scattering calculations: Advances in technique and fast, vector-speed computer codes. Technical report, Technical Note NCAR/TN-140+STR, National Center for, Atmospheric Research (1979)
W.J. Wiscombe, Appl. Opt. 19(9), 1505 (1980)
W.J. Lentz, Appl. Opt. 15(3), 668 (1976)
G. Grehan, G. Gouesbet, Appl. Opt. 18(20), 3489 (1979)
A.R. Jones, J. Phys. D: Appl. Phys. 16(3), L49 (1983)
G.G. Siu, L. Cheng, J. Opt. Soc. Am. B 19(8), 1922 (2002)
H. Du, Appl. Opt. 43(9), 1951 (2004)
J. Shen, PIERS Online 1, 691 (2005)
A. Gogoi, A. Choudhury, G. Ahmed, J. Mod. Opt. 57, 2192 (2010)
W.C. Mundy, J.A. Roux, A.M. Smith, J. Opt. Soc. Am. 64(12), 1593 (1974)
C.F. Bohren, D.P. Gilra, J. Colloid Interface Sci. 72(2), 215 (1979)
M. Quinten, J. Rostalski, Part.& Parti. Syst. Charact. 13(2), 89 (1996)
I.W. Sudiarta, P. Chylek, J. Quant. Spectrosc. Radiat. Transf. 70(4–6), 709 (2001)
J.R. Frisvad, N.J. Christensen, H.W. Jensen, ACM Trans. Graph. 26 (2007)
W. Sun, N.G. Loeb, Q. Fu, J. Quant. Spectrosc. Radiat. Transf. 83(3–4), 483 (2004)
A.L. Aden, M. Kerker, J. Appl. Phys. 22(10), 1242 (1951)
A.Q. Sierra, http://www.ugr.es/aquiran/codigos.htm (2007)
O.B. Toon, T.P. Ackerman, Appl. Opt. 20(20), 3657 (1981)
T. Kaiser, G. Schweiger, Comput. Phys. 7(6), 682 (1993)
L. Kai, P. Massoli, Appl. Opt. 33(3), 501 (1994)
Z.S. Wu, L.X. Guo, K.F. Ren, G. Gouesbet, G. Gréhan, Appl. Opt. 36(21), 5188 (1997)
L. Liu, H. Wang, B. Yu, Y. Xua, J. Shen, China Part. 5, 230 (2007)
R.J. Martin, J. Mod. Opt. 40(12), 2467 (1993)
R. Martin, J. Mod. Opt. 42(1), 157 (1995)
M. Kerker, C.L. Giles, D.S.Y. Wang, J. Opt. Soc. Am. 72, 1826 (1982)
M. Kerker, D.S. Wang, C.L. Giles, J. Opt. Soc. Am. 73(6), 765 (1983)
M.E. Milham, Electromagnetic scattering by magnetic spheres: theory and algorithms. Technical report ERDEC-TR-207, ADA289798, Edgewood Research Development and Engineering Center (1994)
R.J. Tarento, K.H. Bennemann, P. Joyes, J. Van de Walle, Phys. Rev. E 69(2), 026606 (2004)
C. Mätzler, Matlab functions for mie scattering and absorption. Technical report, Research Report No. 2002–08, Institute of Applied Physics, University of Bern (2002)
A. Lakhtakia, V.K. Varadan, V.V. Varadan, Time-Harmonic Electromagnetic Fields in Chiral Media (Springer, Berlin, 1989)
W.S. Weiglhofer, A (Introduction to complex mediums for optics and electromagnetics (SPIE Press, Lakhtakia, 2003)
C.F. Bohren, Chem. Phys. Lett. 29, 458 (1974)
C.F. Bohren, J. Chem. Phys. 62(4), 1566 (1975)
C.F. Bohren, Light scattering by optically active particles (University of Arizona, Tucson 1975)
M. Hinders, B. Rhodes, Il Nuovo Cimento D 14, 575 (1992). 10.1007/BF02462344
B. Stout, M. Neviére, E. Popov, J. Opt. Soc. Am. A 23(5), 1111 (2006)
Y.L. Geng, X.B. Wu, L.W. Li, B.R. Guan, Phys. Rev. E 70(5), 056609 (2004)
C.W. Qiu, B. Luk’yanchuk, J. Opt. Soc. Am. A 25(7), 1623 (2008)
E. Kennaugh, Proc. Inst. Radio Eng. 49, 380 (1961)
A. Itoh, T. Hosono, IEICE Trans. Electron. E 75C(1), 107 (1992)
A. Itoh, T. Hosono, Electron. Commun. Japan (Part II: Electronics) 78(11), 10 (1995)
H. Bech, A. Leder, Optik—International Journal for Light and Electron Optics 117(1), 40 (2006)
H.E. Albrecht, H. Bech, N. Damaschke, M. Feleke, Optik 100, 118 (1995)
U. Kreibig, M. Vollmer, Opt. properties met. clust. (Springer, Berlin, 1995)
U. Kreibig, Appl. Phys. B: Lasers Opt. 93(1), 79 (2008)
M. Quinten, Optical Properties of Nanoparticle Systems, Mie and Beyond (Wiley-VCH, Berlin, 2011)
F. Möglich, Annalen der Physik 409(8), 825 (1933)
T. Evers, H. Dahl, T. Wriedt, Electron. Lett. 32(15), 1356 (1996)
A. Doicu, T. Wriedt, Opt. Commun. 136(1–2), 114 (1997)
G. Gouesbet, G (Gréhan, Generalized Lorenz-Mie Theories (Springer-Verlag Berlin Heidelberg, 2011)
A. Doicu, T. Wriedt, Y. Eremin, Light Scattering by Systems of Particles, Null-Field Method with Discrete Sources: Theory and Programs, vol. 124 (Springer, Berlin; New York, 2006)
J.A. Lock, Appl. Opt. 34(3), 559 (1995)
G. Gouesbet, G. Grehan, J. Opt. Pure Appl. Opt. 1(6), 706 (1999)
L. Mees, G. Gouesbet, G. Grehan, Opt. Commun. 282(21), 4189 (2009)
J.J. Wang, G. Gouesbet, Y.P. Han, G. Grehan, J. Opt. Soc. Am. Opt. Image Sci. Vis. 28(1), 24 (2011)
L. Mees, G. Gouesbet, G. Grehan, Appl. Opt. 40(15), 2546 (2001)
L.W. Davis, Phys. Rev. A 19(3), 1177 (1979)
G. Gouesbet, G. Grehan, B. Maheu, K.F. Ren, Electromagnetic scattering of shaped beams (Generalized Lorenz-Mie Theory). Technical report, LESP, CORIA, INSA de Rouen (1998). http://ren.perso.neuf.fr/ThesisHDRBooks/Livre_glmt.pdf
N.J. Moore, M.A. Alonso, Opt. Express 16(8), 5926 (2008)
P.W. Barber, S.C. Hill, Light scattering by particles: Computational methods (World Scientific Publishing, Singapore, 1990)
L. Mees. GLMT Champ Internes (2008). http://www.scattport.org/index.php/programs-menu/mie-type-codes-menu/130-glmt-champ-internes
M. Ringler, Plasmonische Nahfeldresonatoren aus zwei biokonjugierten Goldnanopartikeln. (2008)
G. Pellegrini, Modeling the optical properties of nanocluster-based functional plasmonic materials. Ph.D. thesis, Tesi di dottorato, Università degli Studi di Padova, Padova (2008)
L. Boyde, K.J. Chalut, J. Guck, Phys. Rev. E 83(2), 026701 (2011)
S. Lecler, Etude de la diffusion de la lumière par des particules sub-microniques. Ph.D. thesis, Thèse. l’Université Louis Pasteur, Strasbourg (2005)
R. Ruppin, Phys. Rev. B 11, 2871 (1975)
F. Borghese, P. Denti, R. Saija, Scattering from model nonspherical particles: theory and applications to environmental physics (Springer- Berlin, New York, 2007)
K. Travis, J. Guck, Biophys. Rev. Lett. 2, 179 (2006)
Y. Okada, in Light Scattering Reviews, ed. by A.A. Kokhanovsky, 5th edn. Springer Praxis Books (Springer Berlin, New York, 2010) pp. 3–35
W. Trinks, Annalen der Physik 414(6), 561 (1935)
S. Levine, G.O. Olaofe, J. Colloid Interface Sci. 27(3), 442 (1968)
J. Bruning, Y. Lo, IEEE Trans. Antennas Propag. 19(3), 378 (1971)
J. Bruning, Y. Lo, IEEE Trans. Antennas Propag. 19(3), 391 (1971)
K.A. Fuller, G.W. Kattawar, R.T. Wang, Appl. Opt. 25(15), 2521 (1986)
K.A. Fuller, G.W. Kattawar, Opt. Lett. 13(2), 90 (1988)
K.A. Fuller, G.W. Kattawar, Opt. Lett. 13(12), 1063 (1988)
D.W. Mackowski, J. Opt. Soc. Am. A 11(11), 2851 (1994)
D.W. Mackowski, M.I. Mishchenko, J. Opt. Soc. Am. A 13(11), 2266 (1996)
Y. lin Xu, Appl. Opt. 34(21), 4573 (1995)
Y.l. Xu, Appl. Opt. 36(36), 9496 (1997)
L. Liu, M.I. Mishchenko, W.P. Arnott, J. Quant. Spectrosc. Radiat. Transf. 109(15), 2656 (2008)
Y.l. Xu, J. Quant. Spectrosc. Radiat. Transf. 89(1–4), 385 (2004)
V. Schmidt, T. Wriedt, J. Quant. Spectrosc. Radiat. Transf. 110(14–16), 1392 (2009)
D. Mackowski, M. Mishchenko, J. Quant. Spectrosc. Radiat. Transf. 112, 2182 (2011)
M. Tagviashvili, Phys. Rev. A 81, 045802 (2010)
A.D. Ward, M. Zhang, O. Hunt, Opt. Express 16(21), 16390 (2008)
T. Grosges, A. Vial, D. Barchiesi, Opt. Express 13(21), 8483 (2005)
R.J. Zhu, J. Wang, G.F. Jin, Optik—Int. J. Light Electr. Opt. 116(9), 419 (2005)
C.G. Khoury, S.J. Norton, T. Vo-Dinh, Nanotechnology 21(31), 315203 (2010)
Y. Takano, K.N. Liou, Appl. Opt. 49(20), 3990 (2010)
A. Doicu, R. Schuh, T. Wriedt, in Light Scattering Reviews, 3 edn. by A.A. Kokhanovsky (Springer-Berlin, Germany, 2008), pp. 109–130
L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge Univ. Press, Cambridge, 2006)
T. Wriedt, http://www.scattport.org
J. Hellmers, T. Wriedt, J. Quant. Spectrosc. Radiat. Transf. 110(14–16), 1511 (2009)
P.J. Flatau, http://code.google.com/p/scatterlib/
T. Wriedt, J. Quant. Spectrosc. Radiat. Transf. 109(8), 1543 (2008)
Acknowledgments
I acknowledge the support of this work by Deutsche Forschungsgemeinschaft (DFG). I like to thank Jannis Saalfeld and Vincent Loke for lauguage editing.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wriedt, T. (2012). Mie Theory: A Review. In: Hergert, W., Wriedt, T. (eds) The Mie Theory. Springer Series in Optical Sciences, vol 169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28738-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-28738-1_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28737-4
Online ISBN: 978-3-642-28738-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)