Light scattering from small spherical particles has applications in a vast number of disciplines including astrophysics, meteorology optics and particle sizing. Mie theory provides an exact analytical characterization of plane wave scattering from spherical dielectric objects. There exist many variants of the Mie theory where fundamental assumptions of the theory has been relaxed to make generalizations. Notable such extensions are generalized Mie theory where plane waves are replaced by optical beams, scattering from lossy particles, scattering from layered particles or shells and scattering of partially coherent (non-classical) light. However, no work has yet been reported in the literature on modifications required to account for scattering when the particle or the source is in motion relative to each other. This is an important problem where many applications can be found in disciplines involving moving particle size characterization. In this paper we propose a novel approach, using special relativity, to address this problem by extending the standard Mie theory for scattering by a particle in motion with a constant speed, which may be very low, moderate or comparable to the speed of light. The proposed technique involves transforming the scattering problem to a reference frame co-moving with the particle, then applying the Mie theory in that frame and transforming the scattered field back to the reference frame of the observer.
2. Reid, J. P. and L. Mitchem, "Laser probing of single-aerosol droplet dynamics," Annu. Rev. Phys. Chem., Vol. 57, 245-271, 2006.
3. Konig, G., K. Anders, and A. Frohn, "A new light-scattering technique to measure the diameter of periodically generated moving droplets ," J. Aerosol. Sci., Vol. 17, 157-167, 1986.
4. Beuthan, J., O. Minet, J. Helfmann, M. Herrig, and G. Muller, "The spatial variation of the refractive index in biological cells," Phys. Med. Biol., Vol. 41, 369-382, 1996.
5. Kelly, K. L., E. Coronado, L. L. Zhao, and G. C. Schatz, "The optical properties of metal nanoparticles: The influence of size, shape and dielectric environment," J. Phys. Chem. B, Vol. 107, 668-677, 2003.
6. Quinten, M. and J. Rostalski, "Lorenz-Mie theory for spheres immersed in an absorbing host medium," Part. Part. Syst.Charact., Vol. 13, 89-96, 1996.
7. Gouesbet, G., "Generalized Lorenz-Mie theory and applications," Part. Part. Syst. Charact., Vol. 11, 22-34, 1994.
8. Purcell, E. M. and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," The Astrophys. J., Vol. 186, 705-714, 1973.
9. Acquista, C., "Validity of modifying Mie theory to describe scattering by nonspherical particles," Appl. Opt., Vol. 17, 3851-3852, 1978.
10. Censor, D., "Non-relativistic scattering in the presence of moving objects: The Mie problem for a moving sphere," Progress In Electromagnetics Research, Vol. 46, 1-32, 2004.
11. Park, S. O. and C. A. Balanis, "Analytical technique to evaluate the asymptotic part of the impedance matrix of Sommerfeld-Type integrals ," IEEE Trans. Antennas Propag., Vol. 45, 798-805, 1997.
12. Felderhof, B. U. and R. B. Jones, "Addition theorems for spherical wave solutions of the vector Helmholtz equation," J. Math. Phys., Vol. 28, 836-839, 1987.
13. Zutter, D. D., "Fourier analysis of the signal scattered by three-dimensional objects in translational motion-I," Appl. Sci. Res., Vol. 36, 241-256, 1980.
14. Chu, W. P. and D. M. Robinson, "Scattering from a moving spherical particle by two crossed coherent plane waves," Appl. Opt., Vol. 16, 619-626, 1977.
15. Borowitz, S. and L. A. Bornstein, A Contemporary View of Elementary Physics, McGraw-Hill, 1968.
16. Rothman, M. A., Discovering the Natural Laws: The Experimen-tal Basis of Physics, Dover Publications Inc., New York, 1989.
17. Einstein, A., Relativity: The Special and General Theory, Methuen & Co. Ltd., 1924.
18. Lee, A. R. and T. M. Kalotas, "Lorentz transformations from the first postulate," Am. J. Phys., Vol. 43, 434-437, 1975.
19. Bohren, C. F. and D. R. Huffman, Absorption and Scattering by of Light by Small Particles, John Wiley & Sons Inc., United States of America, 1983.
20. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1972.
21. McCall, M. and D. Censor, "Relativity and mathematical tools:Waves in moving media," Am. J. Phys., Vol. 75, 1134-1140, 2007.
22. Jackson, J. D., Classical Electrodynamics, John Wiley, New York, 1965.
23. Bachman, R. A., "The converse relativistic Doppler theorem," Am. J. Phys., Vol. 64, 493-494, 1995.
24. Wang, Z. B., B. S. Luk'yanchuk, M. H. Hong, Y. Lin, and T. C. Chong, "Energy flow around a small particle investigated by classical Mie theory," Phys. Rev. B, Vol. 70, 035418, 2004.