High contrast gradient index lens antennas

1. A silicon film comprising:

a first plurality of voids, wherein respective ones of the first plurality of voids have a regular n-gon geometry, and

the first plurality of voids are arranged on a regular n-gon lattice having a first size;

wherein:

the silicon film has an effective permittivity between about 1.0 and about 11.8 based on the size of the respective voids having a regualr n-gon geometry;

the effective permittivity is a function of a measured fill factor of the respective voids having a regular n-gon geometry, where the effective permittivity decreases as the measured fill factor increases; and

the respective voids having a regular n-gon geometry comprise a characteristic dimension from about 25 μm to about 175 μm.

2. The film of claim 1 , wherein n equals 3, 4, or 6.

3. The film of claim 1 , wherein the film has a minimum effective permittivity less or equal to about 1.25.

4. The film of claim 1 , wherein the first plurality of voids are formed by a deep reactive ion etch process.

5. The film of claim 1 , wherein a refractive index of the film varies based on a location along the film.

6. The film of claim 1 , further comprising:

a second plurality of voids, wherein respective ones of the second plurality of voids have a regular n-gon geometry, and

the second plurality of voids are arranged on a regular n-gon lattice having a second size different from the first size.

7. An optical element comprising:

a first silicon film including a first plurality of voids; and

a second silicon film disposed on the first silicon film, the second silicon film including a second plurality of voids, wherein respective ones of the first plurality of voids have a regular m-gon geometry,

the first plurality of voids are arranged on a regular m-gon lattice,

respective ones of the second plurality of voids have a regular n-gon geometry,

the second plurality of voids are arranged on a regular n-gon lattice, and

the first silicon film has a first refractive index and the second silicon film has a second refractive index;

wherein:

the first silicon film and the second silicon film have an effective permittivity between about 1.0 and about 11.8 based on the size of the respective voids having a regular m-gon or n-gon geometry;

the effective permittivity is a function of a measured fill factor of the respective voids having a regular m-gon or n-gon geometry, where the effective permittivity decreases as the measured fill factor increases; and

the respective voids having a regular m-gon or n-gon geometry comprise a characteristic dimension from about 25 μm to about 175 μm.

8. The optical element of claim 7 , wherein m equals 3, 4, or 6 and n equals 3, 4, or 6.

9. The optical element of claim 8 , wherein m and n are equal to one another.

10. The optical element of claim 7 , wherein the first refractive index is different from the second refractive index.

11. The optical element of claim 7 , wherein the first refractive index varies based on a first location along the first film and the second refractive index varies based on a second location along the second film.

12. A method of manufacturing a silicon film, comprising:

providing a silicon wafer; and

forming a first plurality of voids in the silicon wafer, wherein respective ones of the first plurality of voids have a regular n-gon geometry, and

the first plurality of voids are arranged on a regular n-gon lattice having a first size;

wherein:

the silicon film has an effective permittivity between about 1.0 and about 11.8 based on the size of the respective voids having a regular n-gon geometry;

the effective permittivity is a function of a measured fill factor of the respective voids having a regualr n-gon geometry, where the effective permittivity decreases as the measured fill factor increases; and

the respective voids having a regular n-gon geometry comprise a characteristic dimension from about 25 μm to about 175 μm.

13. The method of claim 12 , wherein forming the first plurality of voids includes a photolithographic drilling process.

14. The method of claim 12 , wherein forming the first plurality of voids includes a deep reactive ion etch process.

15. The method of claim 12 , wherein n equals 3, 4, or 6.

16. The method of claim 12 , wherein the silicon film has a minimum effective permittivity less than or equal to about 1.25.

17. The method of claim 14 , wherein a refractive index of the film varies based on a location along the film.

18. The method of claim 12 , further comprising:

forming a second plurality of voids in the silicon wafer, wherein respective ones of the second plurality of voids have a regular n-gon geometry, and

the second plurality of voids are arranged on a regular n-gon lattice having a second size different from the first size.