Mie Scattering by a Charged Dielectric Particle

We study for a dielectric particle the effect of surplus electrons on the anomalous scattering of light arising from the transverse optical phonon resonance in the particle’s dielectric function. Excess electrons affect the polarizability of the particle by their phonon-limited conductivity, either in a surface layer (negative electron affinity) or the conduction band (positive electron affinity). We show that surplus electrons shift an extinction resonance in the infrared. This offers an optical way to measure the charge of the particle and to use it in a plasma as a minimally invasive electric probe.

Figure 1

Dimensionless surface conductivity $\tau ={\tau }^{\prime }+i{\tau }^{\prime \prime }$ for MgO for $n_s={10}^{13}{\mathrm{cm}}^{-2}$ (left) and polarizability of excess electrons $\alpha ={\alpha }^{\prime }+i{\alpha }^{\prime \prime }$ for ${\mathrm{Al}}_2{\mathrm{O}}_3$ for $n_b=3\times {10}^{17}{\mathrm{cm}}^{-3}$ (right) as a function of the inverse wavelength ${\lambda }^{-1}$.

Figure 2

Dielectric constant $ϵ={ϵ}^{\prime }+i{ϵ}^{\prime \prime }$, refractive index $N=n+ik$ (top), and extinction efficiency $Q_t$ (bottom) depending on the particle radius $a$ for MgO and ${\mathrm{Al}}_2{\mathrm{O}}_3$ as a function of the inverse wavelength ${\lambda }^{-1}$.

Figure 3

Magnification of the extinction resonances depending on ${\lambda }^{-1}$ and $a$. Crosses indicate their maxima (from left to right) for $n_s=0$ (red), $2\times {10}^{13}$ (green), and $5\times {10}^{13}{\mathrm{cm}}^{-2}$ (blue) at $T=300\mathrm{K}$ for MgO (left panel) and for $n_b=3n_s/a$ for ${\mathrm{Al}}_2{\mathrm{O}}_3$ (right panel). Open circles indicate the maxima for free electrons.

Figure 4

Middle: Extinction efficiency $Q_t$ as a function of the inverse wavelength ${\lambda }^{-1}$ and the radius $a$ for a MgO particle with $n_s={10}^{13}{\mathrm{cm}}^{-2}$ and $T=300\mathrm{K}$. The dotted lines indicate the extinction maximum for $n_s=0$ (black), $2\times {10}^{12}$ (green), $5\times {10}^{12}$ (red), and ${10}^{13}{\mathrm{cm}}^{-2}$ (blue) obtained from (8). Top and bottom: Extinction efficiency $Q_t$ as a function of ${\lambda }^{-1}$ for $a=0.2\mu \mathrm{m}$ (top) and $a=0.05\mu \mathrm{m}$ (bottom) for different surface electron densities.

Figure 5

Position of the extinction resonance depending on the surface charge $n_s$ for LiF, MgO, and ${\mathrm{Al}}_2{\mathrm{O}}_3$ (for equivalent bulk charge $n_b=3n_s/a$) particles with different radii $a$. Solid (dashed) lines are obtained from the Mie contour [Eq. (8)].