Theory for absorption of ultrashort laser pulses by spheroidal metallic nanoparticles

The theory for the electric and magnetic fields energy absorption by small metallic particles subjected to the irradiation by ultrashort laser pulses of different duration in the region of surface plasmon excitation is developed. For the particles of the oblate or prolate spheroidal shape, there has been found the dependence of the absorbed energy on a number of factors, including a particle radius, a degree of the shape deviation from a spherical one, a pulse duration, the orientation of the magnetic field upon particle, the magnitude of carrier frequency, and the value of a shift of the carrier frequency of a laser ray from the frequency of the surface plasmon excitation in a spherical particle. An appreciable absorption grows at the length of free electron pass large compared to the particle size is established. The phenomenological and kinetic approach is compared with each other.

Figure 1

Dependence of the plasmon resonance frequencies on the form of gold nanoparticle.

Figure 2

Dependence of the energy absorbed by a spheroidal gold particle with $R={\left(R_{\perp }^2{R}_{\parallel }\right)}^{1/3}=200\text{Å}$ at the plasmon resonance frequency on the ratio between the spheroid semiaxes for different values of $\Gamma$, ${\text{s}}^{-1}$: (1)$2.637\times {10}^{15}$, (2) $1.582\times {10}^{15}$, (3) $1.13\times {10}^{15}$, and (4) $0.879\times {10}^{15}$. $\theta =\pi /4$.

Figure 3

The same as in Fig. 2, for the frequency ${\omega }_0=5.4\times {10}^{15}{\text{s}}^{-1}$.

Figure 4

The energy absorbed by a spheroidal gold particle with $R={\left(R_{\perp }^2{R}_{\parallel }\right)}^{1/3}=200\text{Å}$ as the function of the degree of its oblateness or prolateness for $\Gamma =0.879\times {10}^{15}{\text{s}}^{-1}$, at the frequencies ${\omega }_0$ higher than that of the plasmon resonance $\Omega$ of a spherical MN (a): (2) ${\omega }_0=8.8\times {10}^{15}{\text{s}}^{-1}$, (3) $9.7\times {10}^{15}{\text{s}}^{-1}$, and (4) $10.6\times {10}^{15}{\text{s}}^{-1}$ and lower than $\Omega$ (b): (2) ${\omega }_0=7.0\times {10}^{15}{\text{s}}^{-1}$, (3) $6.1\times {10}^{15}{\text{s}}^{-1}$, and (4) $5.2\times {10}^{15}{\text{s}}^{-1}$. $\theta =\pi /4$. Curves 1 in both parts of the figure correspond to the case ${\omega }_0=\Omega$.

Figure 5

Dependence of the energy absorbed by a prolate $\left(R_{\perp }/R_{\parallel }=0.7\right)$ gold particle with $R={\left(R_{\perp }^2{R}_{\parallel }\right)}^{1/3}=200\text{Å}$ on the frequency of a carrier wave for different values of $\Gamma$, ${\text{s}}^{-1}$: (1) $1.582\times {10}^{15}$, (2) $0.791\times {10}^{15}$, (3) $0.527\times {10}^{15}$, and (4) $0.396\times {10}^{15}$ (taken from Table ). $\theta =\pi /4$.

Figure 6

The energy absorbed by a prolate $\left(R_{\perp }/R_{\parallel }=0.7\right)$ gold particle with $R={\left(R_{\perp }^2{R}_{\parallel }\right)}^{1/3}=200\text{Å}$ as the function of the frequency of a carrier wave for $\Gamma =0.396\times {10}^{15}$, ${\text{s}}^{-1}$ and different angles of the laser pulse incidence: $\theta =\pi /4$—solid line, $\theta =\pi /3$—dotted line, and $\theta =\pi /6$—dashed line.

Figure 7

The energy absorbed by Au particle for polarization of a magnetic field longitudinal $(\parallel )$ to it axis of revolution vs degree of spheroid oblateness or prolateness. Curves are obtained at the frequency of the plasmon resonance ${\omega }_0=\Omega$, for different $R$, $\text{Å}$: 200 (curve 1), (2) 250, (3) 300. The phenomenological dependence for $R=200\text{Å}$ is given by triangles.

Figure 8

The same, as in Fig. 7 for $\perp$ polarization of magnetic field.