Topics in Particle and Dispersion Science

Mie theory: Optical resonances and ripple

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Light scattering and absorption properties of spheres exhibit in some cases a distinctive fine structure in the particle size- or wavelength-dependent patterns (see a comment on the equivalence of the particle size and wavelength in Mie theory: Algorithms for functions of the sphere size and refractive index). The coarse mode of the fine structure for dielectric spheres (referred to as the ripple, for example, Bohren CF and Huffman 1983) has long been predicted and observed (Barnes MD and La Mer 1946, Barnes MD et al 1947). It took some 30 more years to predict (Chılek P et al 1976) and observe (for example, Szymanski WW et al 1982, Ashkin A and Dziedzic 1981) the fine structure. Some or all of this structure is frequently referred to as optical resonances.

Features in the particle size- or wavelength-dependent patterns of spheres, that are referred to as optical resonances, range from extremely sharp peaks with linewidths on the order of 10^-4 and smaller (for example, Bohren CF and Huffman 1983, p. 301) to much broader features, for example relatively wide peaks (tens of nanometers) in spectra of optical properties of metallic nanoparticles and metallodielectric nanoshells. See Fig. 1 for a sample of such features in the attenuation efficiency of a water droplet in air. These features occur at relative particle size and refractive index of the sphere for which the denominators of a_n and b_n functions of Mie theory exhibit local minima (Bohren CF and Huffman 1983). We will refer to all such features as optical resonances.

Optical resonances, also referred to as morphology dependent resonances (MDR) and whispering gallery modes (WGM), have been observed in light scattering properties (for example, Ashkin A and Dziedzic 1981), absorption efficiency (for example, Bennet HS and Rosasco 1978), and fluorescence emission (see Mie theory: Fluorescence emission resonances). The sharp optical resonance peaks (the narrowest MDRs) in the absorption efficiency have recently been postulated to significantly contribute to absorption of sunlight by water droplets in clouds in limited wavelength bands on the order of 10 nm wide, relevant to remote-sensing, but not in wider wavelength ranges (Zender CS and Talamantes 2006, Cappa CD et al 2004). However, given that departures from sphericity that are as small as 1/100 of the wavelength extinguish these resonances (for example, Mischenko MI and Lacis 2003, the validity of that postulate has been recently doubted (Mishchenko MI 2009).

Optical resonances are absent in the light scattering characteristic of spherical air bubbles in water (refractive index, m < 1) (the bottom curve in Fig. 1; see also Marston PL et al 1982). Strong absorption of light by the sphere material, such as in the case of a carbon sphere (the middle curve in Fig. 1) also suppresses oscillations, except perhaps the first peak, in the particle-size spectra of the scattering/absorption properties.

Optical resonances also occur in light scattering by cylindrical particles (for example, Owen JF et al 1982). They can be observed in elastic light scattering, i.e. in a scattering process that does not affect the wavelength of the scattered light, as well as in fluorescence, and Raman scattering.

CITATION: Jonasz M. 2006. Mie theory: Optical resonances and ripple (www.tpdsci.com/Tpc/MieOptRes.php). In: Top. Part. Disp. Sci. (www.tpdsci.com).

HISTORY: Published: 21-Mar-2006 Modified: 01-Mar-2010 Peer-reviewed: 07-Dec-2006

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