Magnetic control of surface states

1. A method comprising:

inducing a surface state at a first input location;

defining a propagation path for the surface state by imposing a first spatially-varying magnetic field having a first non-zero magnitude B 1 at a first magnetic field location r 1 on the propagation path and a second non-zero magnitude B 2 at a second magnetic field location r 2 on the propagation path, the first spatially-varying magnetic field being configured to produce a spatially-varying permittivity, the propagation path extending from the first input location to a first output location spatially separated from the first input location; and

varying the propagation path by changing the first spatially-varying magnetic field to a second magnetic field having a third non-zero magnitude B 3 at the first magnetic field location r 1 and a fourth non-zero magnitude B 4 at the second magnetic field location r 2 , and wherein the ratio of B4/B3 is different from the ratio of B2/B1.

2. The method of claim 1 wherein the first spatially-varying magnetic field varies along one direction.

3. The method of claim 1 wherein the first spatially-varying magnetic field varies along two orthogonal directions.

4. The method of claim 1 wherein the first spatially-varying magnetic field varies along three orthogonal directions.

5. The method of claim 1 wherein the first spatially-varying magnetic field varies substantially monotonically.

6. The method of claim 1 wherein the first spatially-varying magnetic field varies non-monotonically.

7. The method of claim 1 wherein the first spatially-varying magnetic field is substantially quasi-static.

8. The method of claim 1 wherein varying the propagation path by changing the first spatially-varying magnetic field includes steering the surface state by changing the first spatially-varying magnetic field.

9. The method of claim 1 wherein the propagation path is substantially two-dimensional.

10. The method of claim 1 wherein the propagation path is substantially three-dimensional.

11. The method of claim 1 further comprising generating the first spatially-varying magnetic field.

12. The method of claim 1 wherein the spatially-varying permittivity varies in a first frequency range, and wherein the surface state has a second frequency range, and wherein the first frequency range overlaps at least in part with the second frequency range.

13. The method of claim 12 wherein the first frequency range includes optical frequencies.

14. The method of claim 12 wherein the second frequency range includes optical frequencies.

15. The method of claim 1 wherein the surface state includes a photonic crystal surface state.

16. The method of claim 1 wherein the surface state includes plasmon energy.