Modulation of rolling K vectors of angled gratings

1. A grating forming method, comprising:

projecting an ion beam toward a substrate at ion beam angle ϑ relative to a surface normal of the substrate, wherein:

a first portion of a grating to be formed on the substrate is positioned at a first rotation angle ϕ 1 between the ion beam and a first grating vector of one or more first fins to be formed by the ion beam contacting the first portion;

the first rotation ϕ 1 angle is selected to form the one or more first fins with a first slant angle ϑ′ 1 ;

a second portion of the grating to be formed on the substrate is positioned at a second rotation angle ϕ 2 between the ion beam and a second grating vector of one or more second fins to be formed by the ion beam contacting the second portion; and

the second rotation angle ϕ 2 is selected to form the one or more second fins of the grating with a second slant angle ϑ′ 2 different than the first slant angle ϑ′ 1 .

2. The method of claim 1 , wherein the ion beam angle ϑ for the forming the one or more first fins and the one or more second fins is the same.

3. The method of claim 2 , wherein forming the one or more first fins and the one or more second fins comprises moving the platen along an x-axis thereof.

4. The method of claim 1 , wherein forming the one or more first fins and the one or more second fins comprises moving the platen in an x-direction and/or a z-direction.

5. The method of claim 1 , wherein forming the one or more first fins and the one or more second fins comprises tilting the platen relative to a z-direction.

6. The method of claim 1 , further comprising bending the ion beam relative to the platen.

7. The method of claim 6 , wherein bending the ion beam comprises moving one or more pairs of electrodes relative to the ion beam.

8. The method of claim 7 , wherein the one or more electrodes comprises:

a plurality of entrance electrodes;

a plurality of suppression electrodes positioned downstream of the entrance electrodes; and

a plurality of exit electrodes positioned downstream of the suppression electrodes.

9. The method of claim 1 , wherein the ion beam is produced by an ion beam source having a plurality of electrodes positioned along a beam path of the ion beam, and wherein a first beam angle α and a second beam angle α are provided by varying voltages to electrodes.

10. A grating forming method, comprising:

projecting an ion beam toward a substrate at ion beam angle ϑ relative to a surface normal of the substrate, a first portion of a grating to be formed on the substrate is positioned at a first rotation angle ϕ 1 between the ion beam and a first grating vector of one or more first fins to be formed by the ion beam contacting the first portion, the first rotation ϕ 1 angle is selected to form the one or more first fins with a first slant angle ϑ′ 1 ;

rotating the substrate such that a second portion of the grating to be formed on the substrate is positioned at a second rotation angle ϕ 2 between the ion beam and a second grating vector of one or more second fins to be formed by the ion beam contacting the second portion, the second rotation angle ϕ 2 is selected to form the one or more second fins of the grating with a second slant angle ϑ′ 2 different than the first slant angle ϑ′ 1 .

11. The method of claim 10 , wherein the ion beam angle ϑ remains static.

12. The method of claim 10 , wherein forming the one or more first fins and the one or more second fins comprises moving the platen in an x-direction and/or a z-direction.

13. The method of claim 10 , wherein forming the one or more first fins and the one or more second fins comprises tilting the platen relative to a z-direction.

14. The method of claim 10 , wherein the first tilt angle β and the second tilt angle β are provided by moving the platen relative to the ion beam.

15. The method of claim 14 , wherein the ion beam angle ϑ remains static.

16. The method of claim 15 , wherein forming the one or more first fins and the one or more second fins comprises moving the platen in an x-direction and/or a z-direction.

17. The method of claim 15 , wherein forming the one or more first fins and the one or more second fins comprises tilting the platen relative to a z-direction.

18. A grating forming method, comprising:

positioning a first portion of a substrate retained on a platen in a path of an ion beam, the substrate having a grating material disposed thereon, the ion beam configured to contact the grating material at an ion beam angle ϑ relative to a surface normal of the substrate and form one or more first fins in the grating material;

rotating the substrate retained on the platen about an axis of the platen resulting in a first rotation angle ϕ between the ion beam and a grating vector of the one or more first fins, the one or more first fins having a first slant angle ϑ′ relative to the surface normal of the substrate;

positioning a second portion of the substrate in the path of the ion beam configured to form one or more second fins in the grating material; and

rotating the substrate about the axis of the platen resulting in a second rotation angle ϕ between the ion beam and the grating vector of the one or more second fins, the one or more second fins having a second slant angle ϑ′ relative to the surface normal of the substrate.

19. The method of claim 18 , wherein a first beam angle α and a second beam angle α are at least partially provided by bending the ion beam relative to the platen.

20. The method of claim 19 , wherein the ion beam is produced by an ion beam source having a plurality of electrodes positioned along a beam path of the ion beam, and wherein the first beam angle α and the second beam angle α are provided by one or both of varying voltages to the electrodes and moving one or more pairs of electrodes positioned about the ion beam relative to the ion beam.