Optical force on a discrete invisibility cloak in time-dependent fields

We study, in time domain, the exchange of momentum between an electromagnetic pulse and a three-dimensional, discrete, spherical invisibility cloak. We find that a discrete cloak, initially at rest, would experience an electromagnetic force due to the pulse but would acquire zero net momentum and net displacement. On the other hand, we find that while the cloak may manage to conceal an object and shroud it from the electromagnetic forces associated with the pulse, the cloak itself can experience optomechanical stress on a scale much larger than the object would in the absence of the cloak. We also consider the effects of material dispersion and losses on the electromagnetic forces experienced by the cloak and show that they lead to a transfer of momentum from the pulse to the cloak.

Figure 1

Spectral (a) and time (b) profiles of the incident field. ${\widehat{\mathit{E}}}_{\mathrm{inc}}$ denotes the Fourier transform of ${\mathit{E}}_{\mathrm{inc}}$.

Figure 2

(a) Optical force experienced by the cloak vs time and its different contributions. (b) Momentum of the cloak vs time and its different contribution. (c) Position multiplied by the mass of the cloak of the center of mass of the cloak vs time.(d) Spectrum of the EM force and of its different contribution.

Figure 3

Normalized density of EM force (NDOF); (a)–(c) at time $t_A$ [see Fig. 2a] when the total EM force is strongest. (d)–(f) at time $t_B$ [see Fig. 2a] when the total EM force is weakest. First column ${\mathcal{F}}^{\mathrm{h}}$, middle column ${\mathcal{F}}^{\mathrm{p}}$, last column ${\mathcal{F}}^{\mathrm{t}}$. The scale for the NDOF is plotted in red in the bottom left-hand corner of the first figure in each row.

Figure 4

(a), (b), and (c) Spectra of the EM force and of its different contribution. The inserts give the real and imaginary parts of $f\left(\omega \right)$ in solid and dashed lines, respectively. (d), (e) and (f) momentum imparted to the cloak versus time.

Figure 5

Density of force on a test object located at the origin (center of the cloak). (a) Solid line: no cloak. dashed line: cloak with $d=\lambda /50$. Dot-dashed line with cloak and $d=\lambda /90$. (b) With dispersion parameters corresponding to Figs. 4a (dashed line), 4b (solid line), and 4c (dot-dashed line).