Holographic mode conversion for electromagnetic radiation
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 input electromagnetic field pattern from a first mode to a second mode to attain a target electromagnetic field pattern (near or far) that is different from the input electromagnetic field pattern. A solution to a holographic equation provides a sufficiently accurate approximation of a distribution of dielectric constants that can be used in conjunction with an electromagnetic radiation device with a known output field pattern to attain a target field pattern. A voxel-based discretization of the distribution of dielectric constants can be used to generate the mode converting structure and/or to facilitate the optimization algorithms. One or more optimization algorithms can be used to improve the efficiency of the mode conversion.
1. An apparatus, comprising:
a mode converting structure with a volumetric distribution of dielectric constants configured to be positioned relative to an electromagnetic radiation (EMR) device, to modify a field pattern of the EMR device for a finite frequency range from a first mode to a second mode,
wherein the mode converting structure is divided into a plurality of sub-wavelength voxels,
wherein each voxel has a length, width, and height, with a maximum dimension that is less than half of a wavelength of a frequency within the finite frequency range, and
wherein each voxel is assigned one of a plurality of dielectric constants to approximate the distribution of dielectric constants of the mode converting structure.
2. The apparatus of claim 1 , wherein the EMR device comprises a radio frequency (RF) antenna.
3. The apparatus of claim 1 , wherein the first mode comprises a near-field distribution corresponding to one of: a short electric dipole, a magnetic dipole, a crossed dipole, a half-wave dipole antenna, a Yagi-Uda antenna, a rectangular patch antenna, a patch over ground plane, an un-shorted rectangular waveguide opening, an open termination of a coaxial cable, an un-shorted terminus of a transmission line, a rectangular horn, a circular horn, a horn with a parabolic dish, an aperture antenna, an MSAT antenna, an aperture antenna array, an endfire antenna array, a passive phased array, an active phased array, a directional antenna, a floodlight, a spotlight, a light emitting diode (LED), an LED array, and a directional LED array.
4. The apparatus of claim 1 , wherein the second mode comprises a near-field distribution corresponding to one of: a short electric dipole, a magnetic dipole, a crossed dipole, a half-wave dipole antenna, a Yagi-Uda antenna, a rectangular patch antenna, a patch over ground plane, an un-shorted rectangular waveguide opening, an open termination of a coaxial cable, an un-shorted terminus of a transmission line, a rectangular horn, a circular horn, a horn with a parabolic dish, an aperture antenna, an MSAT antenna, an aperture antenna array, an endfire antenna array, a passive phased array, an active phased array, a directional antenna, a floodlight, a spotlight, a light emitting diode (LED), an LED array, and a directional LED array.
5. The apparatus of claim 1 , wherein the volumetric distribution is approximately homogeneous in one spatial dimension in a coordinate system, such that the volumetric distribution of the mode converting structure is effectively two-dimensional.
6. The apparatus of claim 5 , wherein the coordinate system is Cartesian, such that the volumetric distribution corresponds to a uniform extrusion of a planar two-dimensional distribution perpendicular to its plane.
7. The apparatus of claim 5 , wherein the coordinate system is cylindrical, such that the volumetric distribution corresponds to a uniform rotation of a two-dimensional planar cross section around a selected axis of revolution.
8. The apparatus of claim 1 , wherein the volumetric distribution of dielectric constants is selected based on an equation for a holographic solution.
9. The apparatus of claim 8 , wherein the volumetric distribution of dielectric constants is selected using the equation:
∈ hol ( x,y,z )−1=β E goal ·E in */|E in | 2 ,
wherein ∈ hol (x,y,z) is the volumetric distribution of dielectric constants in an x, y, z coordinate system,
wherein β is a selectable normalization constant,
wherein E in is the input field distribution of electromagnetic radiation from the EMR device on the surface of the mode converting structure relative to the x, y, z coordinate system, and
wherein E goal is the output field distribution of electromagnetic radiation from the mode converting structure relative to the x, y, z coordinate system.
10. The apparatus of claim 8 , wherein the volumetric distribution of dielectric constants is selected using the equation:
∈ hol ( x,y,z )−1=β| E goal +E in | 2 /|E in | 2 ,
wherein ∈ hol (x,y,z) is the volumetric distribution of dielectric constants in an x, y, z coordinate system,
wherein β is a selectable normalization constant,
wherein E in is the input field distribution of electromagnetic radiation from the EMR device on the surface of the mode converting structure relative to the x, y, z coordinate system, and
wherein E goal is the output field distribution of electromagnetic radiation from the mode converting structure relative to the x, y, z coordinate system.
11. The apparatus of claim 8 , wherein the volumetric distribution of dielectric constants is selected using the equation:
∈ hol ( x,y,z )−α+β E goal ·E in */|E in | 2 ,
wherein ∈ hol (x,y,z) is the volumetric distribution of dielectric constants in an x, y, z coordinate system,
wherein α and β are selectable constants,
wherein E in is the input field distribution of electromagnetic radiation from the EMR device on the surface of the mode converting structure relative to the x, y, z coordinate system,
wherein E goal is the output field distribution of electromagnetic radiation from the mode converting structure relative to the x, y, z coordinate system.
12. The apparatus of claim 11 , wherein for values of ∈ hol below a minimum threshold, the volumetric distribution of dielectric constants is set to a predetermined minimum value, ∈ min .
13. The apparatus of claim 11 , wherein for values of ∈ hol above a maximum threshold, the volumetric distribution of dielectric constants is set to a predetermined maximum value, ∈ max .
14. The apparatus of claim 1 , wherein the volumetric distribution of dielectric constants is selected using an optimization algorithm in which the dielectric constants are treated as optimizable variables.
15. The apparatus of claim 1 , wherein the mode converting structure includes a metamaterial.
16. The apparatus of claim 1 , wherein the mode converting structure comprises at least two metamaterials, wherein each of the metamaterials has a different dielectric constant.
17. The apparatus of claim 16 , wherein at least one of the metamaterials has an effective dielectric constant less than 1 for the finite frequency range.
18. The apparatus of claim 16 , wherein at least one of the metamaterials has a complex permittivity value.
19. The apparatus of claim 18 , wherein the at least one metamaterial with the complex permittivity value functions as an effective gain medium for the finite frequency range.
20. The apparatus of claim 18 , wherein the effective dielectric constant of the at least one metamaterial with the complex permittivity value has a negative imaginary part for the finite frequency range.
21. The apparatus of claim 1 , wherein at least some of the voxels are rectangular parallelepipeds.
22. The apparatus of claim 1 , wherein at least some of the voxels have more than six planar faces.