Optical Momentum Transfer to Absorbing Mie Particles

The momentum transfer to absorbing particles is derived from the Lorentz force density without prior assumption of the momentum of light in media. We develop a view of momentum conservation rooted in the stress tensor formalism that is based on the separation of momentum contributions to bound and free currents and charges consistent with the Lorentz force density. This is in contrast with the usual separation of material and field contributions. The theory is applied to predict a decrease in optical momentum transfer to Mie particles due to absorption, which contrasts the common intuition based on the scattering and absorption by Rayleigh particles.

Figure 1

Integration path for (5) applied to a lossy particle with radius $a$ and ($ϵ$, $\mu$) in a background of (${ϵ}_0$, ${\mu }_0$). (a) An integration path that completely encloses the particle gives the total Lorentz force $\overline{F}$. (b) The integration path just inside the boundary gives the force on the free carriers ${\overline{F}}_c$.

Figure 2

Lorentz force density on bound currents (arrows) overlain on electric field intensity $|E_z{|}^2$ $[(V/m{)}^2]$ resulting from a $\widehat{z}$ polarized plane wave of unit amplitude incident from free space with wavelength ${\lambda }_0=1064\mathrm{nm}$ onto a dielectric cylinder. (a) The lossless cylinder is defined by $ϵ=16{ϵ}_0$. ($\max (|f_b|)=1.25\times {10}^{-6}[\mathrm{N}/{\mathrm{m}}^3]$) (b) The lossy cylinder, described by $ϵ=(16+10i){ϵ}_0$, contains an additional force density on free currents. $(\max (|f_b|)=3.00\times {10}^{-9}\mathrm{N}/{\mathrm{m}}^3$).

Figure 3

Forces on a $2\mu \mathrm{m}$ diameter sphere due to a plane wave of unit amplitude. The wave is incident from free space with wavelength ${\lambda }_0=1064\mathrm{nm}$ onto a nonmagnetic sphere with (a) $ϵ=2{ϵ}_0+i{ϵ}_I$ and (b) $ϵ=16{ϵ}_0+i{ϵ}_I$.

Figure 4

Force versus diameter for a dielectric sphere ($ϵ/{ϵ}_0=16+i$) incident by a unit amplitude plane wave. The free-space wavelength of the incident wave is ${\lambda }_0=1064\mathrm{nm}$.