Shape and size effects on the energy absorption by small metallic particles

The electric and magnetic light absorption by small metallic particles of an ellipsoidal shape has been studied theoretically in frequency regions that are higher and lower than the characteristic frequency of an electron free path between walls of the particle. The assumption of diffuse reflection of electrons from an inner surface of the particle is taken as boundary conditions of the problem. Analytical expressions for the absorbed power are obtained provided that the thickness of a skin layer is large enough compared with a particle size. Size and shape effects on the absorption are investigated for three polarizations of an incident radiation. The particles may be either larger or smaller than the electron free path. The dependence of the relative contribution of the electric and magnetic absorption on the degree of particle asymmetry is discussed in detail for different wave polarizations. Similar dependence for the ratio of longitudinal and transverse components of the conductivity tensor are studied as well.

Figure 1

Ratio between transverse ${\sigma }_{\perp }$ and longitudinal ${\sigma }_{\Vert }$ components of the electric conductivity of the spheroidal SMP as a function of the ratio between minor and major spheroid’s semiaxes, at low $\omega ⪡v_F∕\left(2R\right)$ (1) and high $\omega ⪢v_F∕\left(2R\right)$ (2) light frequencies.

Figure 2

Ratio between transverse and longitudinal components of tensor ${\sigma }_m$ of the spheroidal SMP versus the ratio between minor and major axes of the spheroid, at low $\omega ⪡v_F∕\left(2R\right)$ (1) and high $\omega ⪢v_F∕\left(2R\right)$ (2) light frequencies.

Figure 3

Dependence of the ratio between magnetic and electric energy absorbed by SMP on the ratio between minor and major spheroid’s semiaxes, at light frequencies $\omega ⪡v_F∕\left(2R\right)$ and for two polarizations of the incident wave: EL-MT (curves 1 and 3) and ET-ML (2 and 4). Curves (1) and (2) are for a particle with $R=75\mathrm{\AA }$, and curves (3) and (4) for $R=50\mathrm{\AA }$. The results for a particle with $R=300\mathrm{\AA }$ at frequencies $\omega ⪢v_F∕\left(2R\right)$ are shown for the EL-MT polarization by crosses (×) and for the ET-ML polarization by circles (엯) [they are coincident with the curve (2)]. The insets show the polarization of the EM wave with regard to the spheroid’s axes.

Figure 4

Dependence of the ratio between magnetic and electric energy absorbed by SMP on the ratio between minor and major spheroid’s semiaxes, for $\omega ⪡v_F∕\left(2R\right)$ and for the orientation of the electric field along the minor axes of the spheroid and the MT polarization of the magnetic vector. Curve (1) corresponds to the particle with $R=75\mathrm{\AA }$ and curve (2) to a particle with $R=50\mathrm{\AA }$. The results for a particle with $R=300\mathrm{\AA }$ at light frequencies $\omega ⪢v_F∕\left(2R\right)$ in the same polarization of the electric and magnetic vectors are shown by circles (엯).

Figure 5

Dependence of the ratio between magnetic and electric energy absorbed by SMP on the ratio between minor and major semiaxes of the spheroid, at light frequencies $\omega =2\times {10}^{14}{\mathrm{s}}^{-1}⪢v_F∕\left(2R\right)$ and for three polarizations of the incident wave: EL-MT (1), ET-ML (2), and ET-MT (3). Curves (1)–(3) are for a particle with $R=300\mathrm{\AA }$. The results for particles with $R=75\mathrm{\AA }$ and $=50\mathrm{\AA }$ at frequencies $\omega =4\times {10}^{13}{\mathrm{s}}^{-1}⪡v_F∕\left(2R\right)$ are shown for the ET-ML polarization by circles (엯) [they are coincident with curve (2)] and by crosses (×), accordingly.