In this paper, we present MieLab, a free computational package for simulating the scattering of electromagnetic radiation by multilayered spheres or an ensemble of particles with normal size distribution. It has been designed as a virtual laboratory, including a friendly graphical user interface (GUI), an optimization algorithm (to fit the simulations to experimental results) and scripting capabilities. The paper is structured in five different sections: the introduction is a perspective on the importance of the software for the study of scattering of light scattering. In the second section, various approaches used for modeling the scattering of electromagnetic radiation by small particles are discussed. The third and fourth sections are devoted to provide an overview of MieLab and to describe the main features of its architectural model and functional behavior, respectively. Finally, several examples are provided to illustrate the main characteristics of the software. 1. Introduction The scattering and absorption of electromagnetic (EM) radiation by small particles are important issues for a surprisingly large number of disciplines: solid-state physics, electrical engineering, meteorology, chemistry, biophysics, astronomy, and medicine are just a few of them [1, 2]. The optical properties of such small particles are closely related to their physical and geometrical parameters such as composition, size, shape, and embedding medium [3]. Hence, a quantitative knowledge of the EM scattering as a function of the particle parameters is required if we want to understand the optical phenomena occurring in them, as well as for developing remote sensing and laboratory techniques for particle characterization. However, obtaining such quantitative knowledge is not an easy task in many cases. Fortunately, in spite of the enormous amount of particle shapes and configurations which can be found in nature or in laboratory synthesis processes, it is often sufficient to study simpler systems not only for understanding the elementary phenomena occurring in them but also for practical applications. An excellent example of such kind of particle, which is both simple and of great interest for many applications, is the multilayered sphere (Figure 1). In the field of atmospheric science, light absorption by aerosols has a heating effect in the atmosphere, which is of great interest to study several climatic effects. Their optical properties can be successfully modeled using a core-shell type particle [4, 5]. Moreover, in the field of nanotechnology, applications of
References
[1]
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley-Interscience, New York, NY, USA, 1998.
[2]
M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, Cambridge University Press, Cambridge, UK, 1st edition, 2002.
[3]
K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” Journal of Physical Chemistry B, vol. 107, no. 3, pp. 668–677, 2003.
[4]
J. V. Martins, P. Artaxo, C. Liousse, J. S. Reid, P. V. Hobbs, and Y. J. Kaufman, “Effects of black carbon content, particle size, and mixing on light absorption by aerosols from biomass burning in Brazil,” Journal of Geophysical Research D, vol. 103, no. 24, pp. 32041–32050, 1998.
[5]
P. Chylek, V. Ramaswamy, and R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” Journal of the Atmospheric Sciences, vol. 41, no. 21, pp. 3076–3084, 1984.
[6]
F. Tihay, G. Pourroy, M. Richard-Plouet, A. C. Roger, and A. Kiennemann, “Effect of Fischer-Tropsch synthesis on the microstructure of Fe-Co-based metal/spinel composite materials,” Applied Catalysis A, vol. 206, no. 1, pp. 29–42, 2001.
[7]
P. Mazzoldi, G. W. Arnold, G. Battaglin, F. Gonella, and R. F. Haglund, “Metal nanocluster formation by ion implantation in silicate glasses: nonlinear optical applications,” Journal of Nonlinear Optical Physics and Materials, vol. 5, no. 2, pp. 285–330, 1996.
[8]
C. S？nnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Letters, vol. 5, no. 2, pp. 301–304, 2005.
[9]
C. Loo, A. Lowery, N. Halas, J. West, and R. Drezek, “Immunotargeted nanoshells for integrated cancer imaging and therapy,” Nano Letters, vol. 5, no. 4, pp. 709–711, 2005.
[10]
A. M. Gobin, M. H. Lee, N. J. Halas, W. D. James, R. A. Drezek, and J. L. West, “Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy,” Nano Letters, vol. 7, no. 7, pp. 1929–1934, 2007.
[11]
K. Zhu and M. Popovi？, “Spectral response of a multi-layered sphere applied in microwave breast imaging,” in Proceedings of the 4th European Conference on Antennas and Propagation (EuCAP '10), pp. 1–4, 2010.
[12]
W. Yang, “Improved recursive algorithm for light scattering by a multilayered sphere,” Applied Optics, vol. 42, no. 9, pp. 1710–1720, 2003.
[13]
T. Wriedt, “Light scattering theories and computer codes,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 110, no. 11, pp. 833–843, 2009.
[14]
O. Pe？a and U. Pal, “Scattering of electromagnetic radiation by a multilayered sphere,” Computer Physics Communications, vol. 180, no. 11, pp. 2348–2354, 2009.
[15]
G. Mie, “Beitr？ge zur optik trüber medien, speziell kolloidaler metall？sungen,” Annals of Physics, vol. 330, pp. 377–445, 1908.
[16]
A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” Journal of Applied Physics, vol. 22, no. 10, pp. 1242–1246, 1951.
[17]
P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Physical Review, vol. 127, no. 5, pp. 1837–1843, 1962.
[18]
P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Physical Review, vol. 134, p. AB1, 1964.
[19]
R. Bhandari, “Scattering coefficients for a multilayered sphere: analytic expressions and algorithms,” Applied Optics, vol. 24, pp. 1960–1967, 1985.
[20]
J. R. Wait, “Electromagnetic scattering from a radially inhomogeneous sphere,” Applied Scientific Research B, vol. 10, no. 5-6, pp. 441–450, 1963.
[21]
J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Canadian Journal of Physics, vol. 33, pp. 189–195, 1955.
[22]
C. S. Kim and C. Yeh, “Scattering of an obliquely incident wave by a multilayered elliptical lossy dielectric cylinder,” Radio Science, vol. 26, no. 5, pp. 1165–1176, 1991.
[23]
S. Asano and G. Yamamoto, “Light scattering by a spheroidal particle,” Applied Optics, vol. 14, no. 1, pp. 29–49, 1975.
[24]
Z. S. Wu and Y. P. Wang, “Electromagnetic scattering for multilayered sphere. Recursive algorithms,” Radio Science, vol. 26, no. 6, pp. 1393–1401, 1991.
[25]
B. R. Johnson, “Light scattering by a multilayer sphere,” Applied Optics, vol. 35, no. 18, pp. 3286–3296, 1996.
[26]
Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, and G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Applied Optics, vol. 36, no. 21, pp. 5188–5198, 1997.
[27]
L. Kai and P. Massoli, “Scattering of electromagnetic plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Applied Optics, vol. 33, no. 3, pp. 501–511, 1994.
[28]
J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Mathematics of Computation, vol. 35, pp. 773–782, 1980.
[29]
P. Lu, J. Nocedal, C. Zhu, R. H. Byrd, and R. H. Byrd, “A limited-memory algorithm for bound constrained optimization,” The SIAM Journal on Scientific Computing, vol. 16, pp. 1190–1208, 1994.
[30]
O. Pe？a, L. Rodríguez-Fernández, V. Rodríguez-Iglesias et al., “Determination of the size distribution of metallic nanoparticles by optical extinction spectroscopy,” Applied Optics, vol. 48, no. 3, pp. 566–572, 2009.
[31]
O. Pe？a, U. Pal, L. Rodríguez-Fernández, and A. Crespo-Sosa, “Linear optical response of metallic nanoshells in different dielectric media,” Journal of the Optical Society of America B, vol. 25, no. 8, pp. 1371–1379, 2008.
[32]
E. M. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophysical Journal, vol. 186, pp. 705–714, 1973.
[33]
B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophysical Journal, vol. 333, p. 848, 1988.
