Thermal undercut structure for metasurface tuning

1. A metasurface comprising:

a number of periodically-repeated unit cells arranged on a substrate, each of the unit cells including:

a high-index dielectric block;

a heat source positioned to selectively modulate heat applied to the high-index dielectric block; and

an insulating undercut region at an interface between the high-index dielectric block and the substrate, wherein the metasurface receives light through the substrate and reflects the light out through the substrate after the light is phase-shifted by the high-index dielectric block.

2. The metasurface of claim 1 , wherein the heat source includes an electrode separated from the high-index dielectric block by a spacer layer.

3. The metasurface of claim 2 , wherein the spacer layer is diamond-like carbon.

4. The metasurface of claim 1 , wherein the insulating undercut region is filled with air.

5. The metasurface of claim 1 , wherein each cell is insulated on a bottom surface by the insulating undercut region and wherein each of the periodically-repeated unit cells has side surfaces insulated from adjacent unit cells.

6. The metasurface of claim 1 , further comprising:

an index modulation controller that selectively changes an index of the high-index dielectric block by regulating heat supplied by the heat source.

7. The metasurface of claim 1 , wherein the high-index dielectric block includes silicon.

8. The metasurface of claim 1 , wherein the substrate is a low-index dielectric substrate.

9. The metasurface of claim 1 , wherein the insulating undercut region has a diameter that is equal to or greater than a corresponding diameter of the high-index dielectric block.

10. A method comprising:

selectively modulating heat applied to a high-index dielectric block in each cell of a plurality of periodically-repeated unit cells arranged on a substrate, each cell in the plurality of periodically-repeated unit cells being separated from the substrate by an insulating undercut region, wherein light is received through the substrate and reflected out of the substrate after light is phase-shifted by the high-index dielectric block.

11. The method of claim 10 , wherein selectively modulating the heat further comprises selectively modulating voltage applied to an electrode separated from the high-index dielectric block by a spacer layer.

12. The method of claim 11 , wherein the spacer layer is diamond-like carbon.

13. The method of claim 10 , wherein the insulating undercut region is a cavity filled with air.

14. The method of claim 10 , wherein each cell of the plurality of periodically-repeated unit cells is insulated on a bottom surface by the insulating undercut region and wherein each of the of the periodically-repeated unit cells has sides has side surfaces insulated from adjacent unit cells.

15. The method of claim 10 , wherein selectively modulating the heat changes an index of the high-index dielectric block.

16. The method of claim 10 , wherein the high-index dielectric block includes silicon.

17. The method of claim 10 , wherein the substrate is a low-index dielectric substrate.

18. The method of claim 10 , wherein the insulating undercut region has a diameter that is equal to or greater than a corresponding diameter of the high-index dielectric block.

19. A system comprising:

a high-index dielectric block;

an electrode thermally coupled to the high-index dielectric block through a spacer layer;

an insulating undercut region at an interface between the high-index dielectric block and an adjacent substrate; and

an index modulation controller that modulates a voltage applied to the electrode to controllably alter an index of the high-index dielectric block, wherein light is received through the adjacent substrate and reflected out of the adjacent substrate once the light has been phase shifted by the high-index dielectric block.