Holographic mode conversion for transmission lines
The present disclosure provides systems and methods associated with mode conversion for electromagnetic field modification. A mode converting structure (holographic metamaterial) is formed with a distribution of dielectric constants chosen to convert an electromagnetic radiation pattern from a first mode to a second mode to attain a target electromagnetic radiation pattern that is different from the input electromagnetic radiation pattern. A solution to a holographic equation provides a sufficiently accurate approximation of a distribution of dielectric constants that can be used to form a mode converting device for use with one or more transmission lines, such as waveguides. One or more optimization algorithms can be used to improve the efficiency of the mode conversion.
1. An electromagnetic mode converting structure comprising:
a dielectric structure configured to modify a field pattern of a device from a first mode to a second mode, the dielectric structure divided into a plurality of sub-wavelength voxels,
wherein each voxel has a maximum dimension that is less than a wavelength for a specific frequency range, and each voxel is assigned one of a plurality of dielectric constants to approximate a distribution of the dielectric constants; and
a metamaterial with an effective dielectric constant less than 1 for at least a portion of a finite frequency range.
2. The electromagnetic mode converting structure of claim 1 , wherein the dielectric structure includes real and imaginary parts, each of the real and imaginary parts being individually optimizable variables.
3. The electromagnetic mode converting structure of claim 1 , wherein the approximation of the distribution of the dielectric constant further comprises modification of at least one dielectric constant and determine a cost function for the modification.
4. The electromagnetic mode converting structure of claim 1 , wherein the approximation of the distribution of the dielectric constants further comprises a holographic solution.
5. The electromagnetic mode converting structure of claim 1 , wherein the distribution of dielectric constants is a three-dimensional coordinate systems.
6. The electromagnetic mode converting structure of claim 5 , wherein the three-dimensional coordinate systems is one of a Cartesian coordinate system or a cylindrical coordinate system.
7. The electromagnetic mode converting structure of claim 1 , wherein the first mode is a TE 01 mode and the second mode is a TM 11 mode.
8. The electromagnetic mode converting structure of claim 1 , wherein the first mode is a TE 10 mode and the second mode is a TM 11 mode.
9. The electromagnetic mode converting structure of claim 1 , wherein the first mode is a TE 11 mode and the second mode is a TM 11 mode.
10. The electromagnetic mode converting structure of claim 1 , wherein the electromagnetic mode converting structure is dimensionally approximate to the device.
11. A method of generating an electromagnetic mode converting structure, the method comprising:
generating, using one or more materials having dielectric constants, the electromagnetic mode converting structure, the electromagnetic mode converting structure comprising:
a dielectric structure configured to modify a field pattern of a device from a first mode to a second mode, the dielectric structure divided into a plurality of sub-wavelength voxels, wherein each voxel has a maximum dimension that is less than a wavelength for a specific frequency range, and each voxel is assigned one of a plurality of dielectric constants to approximate a distribution of the dielectric constants; and
a metamaterial with an effective dielectric constant less than 1 for at least a portion of a finite frequency range.
12. The method of claim 11 , wherein the generation of the electromagnetic mode converting structure is performed by a three-dimensional printer.
13. The method of claim 11 , wherein the generation of the electromagnetic mode converting structure is performed by injection molding.
14. The method of claim 11 , wherein the generation of the electromagnetic mode converting structure is performed by one of chemical etching, chemical deposition, heating or ultrasonication.
15. The method of claim 11 , wherein the dielectric structure includes real and imaginary parts, each of the real and imaginary parts being individually optimizable variables.
16. The method of claim 11 , wherein the approximation of the distribution of the dielectric constant further comprises modification of at least one dielectric constant and determine a cost function for the modification.
17. The method of claim 11 , wherein the approximation the distribution of the dielectric constants further comprises a holographic solution.
18. The method of claim 11 , wherein the distribution of dielectric constants is a three-dimensional coordinate systems.
19. The method of claim 18 , wherein the three-dimensional coordinate systems is one of a Cartesian coordinate system or a cylindrical coordinate system.
20. The method of claim 11 , wherein the first mode is a TE 01 mode and the second mode is a TM 11 mode.
21. The method of claim 11 , wherein the first mode is a TE 10 mode and the second mode is a TM 11 mode.
22. The method of claim 11 , wherein the first mode is a TE 11 mode and the second mode is a TM 11 mode.
23. The method of claim 11 , wherein the electromagnetic mode converting structure is dimensionally approximate to the device.
24. A method comprising:
identifying a target functionality for a dielectric structure of an electromagnetic mode converting structure, wherein the target functionality comprises at least modifying a field pattern of a device from a first mode to a second mode, wherein the electromagnetic mode converting structure comprises a metamaterial with an effective dielectric constant less than 1 for at least a portion of a finite frequency range;
identifying dimensions to enclose the electromagnetic mode converting structure;
identifying a distribution of dielectric constants of the dielectric structure configured to modify the field pattern to an output field pattern that approximates the target functionality; and
generating the electromagnetic mode converting structure where the dielectric structure has a plurality of sub-wavelength voxels, wherein each voxel has a maximum dimension that is less than a wavelength for a specific frequency range, and each voxel is assigned one of a plurality of dielectric constants to approximate the distribution of the dielectric constants.
25. The method of claim 24 , wherein the dielectric structure includes real and imaginary parts, each of the real and imaginary parts being individually optimizable variables.
26. The method of claim 24 , wherein the approximation of the distribution of the dielectric constant further comprises modification of at least one dielectric constant and determine a cost function for the modification.
27. The method of claim 24 , wherein the approximation the distribution of the dielectric constants further comprises a holographic solution.
28. The method of claim 24 , wherein the distribution of dielectric constants is a three-dimensional coordinate systems.
29. The method of claim 28 , wherein the three-dimensional coordinate systems is one of a Cartesian coordinate system or a cylindrical coordinate system.
30. The method of claim 24 , wherein the first mode is a TE 01 mode and the second mode is a TM 11 mode.
31. The method of claim 24 , wherein the first mode is a TE 10 mode and the second mode is a TM 11 mode.
32. The method of claim 24 , wherein the first mode is a TE 11 mode and the second mode is a TM 11 mode.
33. The method of claim 24 , wherein the dimensions to enclose the electromagnetic mode converting structure are approximate dimensions of the device.
34. The method of claim 24 , further comprises a metamaterial with an effective dielectric constant less than 1 for at least a portion of the finite frequency range.