Electrostriction enhancement in metamaterials

We demonstrate a controllable enhancement in the electrostrictive properties of a medium using dilute composite artificial materials. Analytical expressions for the composite electrostriction are derived and used to show that enhancement, tunability, and suppression can be achieved through a careful choice of constituent materials. Numerical examples with Ag, ${\mathrm{As}}_2{\mathrm{S}}_3$, Si, and ${\mathrm{SiO}}_2$ demonstrate that even in a nonresonant regime, artificial materials can bring more than a threefold enhancement in the electrostriction.

Figure 1

Schematic view of the metamaterial geometry investigated; a primitive cubic array of spheres in a host medium. Inset: fundamental unit cell for a cubic lattice of spheres.

Figure 2

Contour plots of (a) ${log}_{10}\left|\mathrm{Re}\left(\gamma \right)\right|$ from (25), and (b) ${log}_{10}\left|\mathrm{Re}\left({\varepsilon }_{\mathrm{r}}\right)\right|$ from (8), for an array of Ag spheres embedded in a ${\mathrm{SiO}}_2$ matrix, against filling fraction $f$ and wavelength $\lambda$. A diluteness threshold of $f=15\%$ (dashed white curve) and an attenuation length threshold of ${\alpha }_{\mathrm{L}}=0.1\mathrm{mm}$ (solid white curve) are also shown.

Figure 3

Contour plots of (a) ${log}_{10}\left|\mathrm{Re}\left(\gamma \right)\right|$ from (25), and (b) ${log}_{10}\left|\mathrm{Re}\left({\varepsilon }_{\mathrm{r}}\right)\right|$ from (8), for an array of Ag spheres embedded in a ${\mathrm{As}}_2{\mathrm{S}}_3$ matrix, against filling fraction $f$ and wavelength $\lambda$. A diluteness threshold of $f=15\%$ (dashed white curve) and an attenuation length threshold of ${\alpha }_{\mathrm{L}}=0.1\mathrm{mm}$ (solid white curve) are also shown.

Figure 4

Contour plots of (a) ${log}_{10}\left|\mathrm{Re}\left(\gamma \right)\right|$ from (19), and (b) ${log}_{10}\left|\mathrm{Re}\left({\varepsilon }_{\mathrm{r}}\right)\right|$ from (8), for an array of ${\mathrm{SiO}}_2$ spheres embedded in a Si matrix, against filling fraction $f$ and wavelength $\lambda$. A diluteness threshold of $f=15\%$ (dashed white curve) and an attenuation length threshold of ${\alpha }_{\mathrm{L}}=0.1\mathrm{mm}$ (solid white curve) are also shown.

Figure 5

Composite electrostriction $\mathrm{Re}\left(\gamma \right)$ from (19) at $\lambda =1550$ nm for an array of (a) ${\mathrm{SiO}}_2$ spheres embedded in a Si matrix, and (b) ${\mathrm{As}}_2{\mathrm{S}}_3$ spheres embedded in a ${\mathrm{SiO}}_2$ matrix. The electrostriction for the inclusion ${\gamma }_{\mathrm{i}}$ (dashed black line) and matrix ${\gamma }_{\mathrm{m}}$ (dashed red line) materials are also given.