Enhancing Optical Gradient Forces with Metamaterials

We demonstrate how the optical gradient force between two waveguides can be enhanced using transformation optics. A thin layer of double-negative or single-negative metamaterial can shrink the interwaveguide distance perceived by light, resulting in a more than tenfold enhancement of the optical force. This process is remarkably robust to the dissipative loss normally observed in metamaterials. Our results provide an alternative way to boost optical gradient forces in nanophotonic actuation systems and may be combined with existing resonator-based enhancement methods to produce optical forces with an unprecedented amplitude.

Figure 1

The setup to enhance the optical gradient force between two dielectric slab waveguides. A metamaterial cladding indicated by the split-ring resonators is derived from a folding transformation to reduce the distance between the two dielectric waveguides (shown in plain gray) perceived by light. Since the optical gradient force decays with distance, the metamaterial slab allows enhancing the force.

Figure 2

Equivalence between the optical force in the traditional configuration of two silicon slab waveguides with $n=3.476$ and the transformed setup of silicon waveguides ($n=3.476$) with a metamaterial medium attached to it $n=-1$, $t=0.25a$). The solid blue line shows the optical force between two bare waveguides as a function of the gap distance $d_{\mathrm{w}/\mathrm{o}}$. The red circles represent the optical force generated in the transformed configuration as a function of the gap between the metamaterial slabs $d_{\mathrm{with}}$. The metamaterial slab is designed such that $d_{\mathrm{with}}=d_{\mathrm{w}/\mathrm{o}}+0.5a$. In these simulations, the fundamental TE modes are considered for $a/{\lambda }_0=0.39$, corresponding to a typical setup where ${\lambda }_0=1.55\mu \mathrm{m}$ and $a=600\mathrm{nm}$.

Figure 3

Electric field profiles of the fundamental mode in the waveguide pair. (a) The traditional configuration of two slab waveguides indicated by the gray rectangles. If the waveguides are placed close to each other, the evanescent tails interact with the waveguides, resulting in a gradient force between the two slabs. (b) The configuration with a metamaterial cladding as annihilating medium. In between the slab waveguides, we place a metamaterial slab that amplifies the evanescent tails. We demonstrate that this effect enhances the optical gradient force considerably.

Figure 4

The optical force on a $10\mu \mathrm{m}$-long waveguide section as a function of the gap distance between the waveguides for TM-polarized light (${\lambda }_0=1.55\mu \mathrm{m}$, $P_{\mathrm{input}}=1\mu \mathrm{W}$) for several metamaterial implementations of the annihilating slabs. (a) Some of the input power is lost because of reflection on the metamaterial layer and because of scattering in leaky modes. Note also the amplified evanescent waves clearly visible in the gap between the metamaterial slabs. (b) The black curve is the reference of bare silicon waveguides ($n=3.476$). The blue curve with squares corresponds to a waveguide pair with left-handed claddings ($\mathrm{Re}[ϵ]=\mathrm{Re}[\mu ]=-1$, loss $\mathrm{\text{tangent}}=10\%$). The red curves with circles, triangles, and diamonds show the resulting force for a poor man’s implementation of the annihilating slabs in which the permittivity equals $-1$ and the loss tangent is 10%, 5%, and 1%, respectively.