Beam pattern synthesis for metamaterial antennas
A determined object wave can be approximately formed by applying a modulation pattern to metamaterial elements receiving RF energy from a feed network. For example, a desired object wave at a surface of an antenna is selected to be propagated into a far-field pattern. A computing system can compute an approximation of the object wave by calculating a modulation pattern to apply to metamaterial elements receiving RF energy from a feed network. The approximation can be due to a grid size of the metamaterial elements. Once the modulation pattern is determined, it can be applied to the metamaterial elements and the RF energy can be provided in the feed network, causing emission of the approximated object wave from the antenna.
1. A method for beam shaping using a metamaterial surface antenna technology (MSA-T) system, the method comprising: determining a modulation pattern based at least in part on a reference wave from a feed network of an antenna multiplied by an antenna-plane pattern; forming an aperture modulation pattern based at least in part on a magnitude of an aperture taper function multiplied with the modulation pattern and a lower bound of an element modulation range of an aperture and an upper bound of the element modulation range of the aperture; and determining a modulation function of the aperture based at least in part on a product of the aperture modulation pattern and the reference wave, and
discarding a phase portion of the aperture taper function multiplied with the modulation pattern.
2. The method of claim 1 , wherein the method further comprises applying the modulation function of the aperture to an antenna system aperture.
3. The method of claim 2 , wherein applying the modulation function to the aperture further comprises modulating an impedance of the aperture in electromagnetic contact with the reference wave.
4. The method of claim 1 , wherein the method further comprises selecting the antenna-plane pattern.
5. The method of claim 4 , wherein selecting the antenna-plane pattern further comprises receiving the antenna-plane pattern from an external system.
6. The method of claim 4 , wherein selecting the antenna-plane pattern further comprises:
defining a two-dimensional far-field beam pattern; and
back-propagating the two-dimensional far-field beam pattern to an antenna plane.
7. The method of claim 4 , wherein selecting the antenna-plane pattern further comprises determining the antenna-plane pattern based on a selected projected beam pattern.
8. The method of claim 7 , wherein the method further comprises causing a set of radiating elements coupled to the aperture to emit a beam pattern based on the selected projected beam pattern.
9. The method of claim 7 , wherein the method further comprises approximating the selected projected beam pattern.
10. The method of claim 1 , wherein the method further comprises causing the reference wave to propagate through a parallel-plate waveguide, a rectangular waveguide or a microstrip line.
11. The method of claim 1 , wherein the reference wave further comprises a set of fields in the feed network.
12. The method of claim 1 , further comprising controlling an antenna system comprising a set of radiating elements coupled to the aperture.
13. The method of claim 12 , wherein the set of radiating elements comprises sub-wavelength antenna elements, each configured to emit an electromagnetic emission in response to received electromagnetic energy, wherein each of the sub-wavelength antenna elements comprises at least one electromagnetically resonant element, and wherein a physical diameter of individual sub-wavelength antenna elements is less than an effective wavelength of the electromagnetic emission.
14. The method of claim 1 , wherein applying the modulation function of the aperture to an antenna causes a sampled approximation of the antenna-plane pattern.
15. The method of claim 1 , wherein forming the aperture modulation pattern further comprises:
forming the aperture modulation pattern by shifting or scaling the magnitude of the aperture taper function multiplied with the modulation pattern to fit within a lower bound of the element modulation range of the aperture and an upper bound of the element modulation range of the aperture.
16. A method of constructing a modulation function for an aperture in a metamaterial surface antenna technology (MSA-T) system, the method comprising:
receiving a spatial-domain antenna-plane pattern;
determining a set of fields based at least in part on energy from a feed network coupled to the aperture that couples energy to a set of radiating elements, each field corresponding to a radiating element in an antenna plane, the set of fields forming a reference wave;
computing a modulation pattern based at least in part on multiplying the reference wave by the spatial-domain antenna-plane pattern;
multiplying an aperture taper function with the modulation pattern and discarding a phase portion of a result to form a real modulation pattern;
shifting and scaling the elements of the real modulation pattern to lie within upper and lower bounds of an element modulation range to form an aperture modulation pattern; and
determining the modulation function of the aperture based at least in part on a product of the aperture modulation pattern and the reference wave.
17. The method of claim 16 , wherein receiving the spatial-domain antenna-plane pattern further comprises receiving the spatial-domain antenna-plane pattern from an external system.
18. The method of claim 16 , wherein receiving the spatial-domain antenna-plane pattern further comprises determining the spatial-domain antenna-plane pattern based on a selected projected beam pattern.
19. The method of claim 18 , further comprising causing the set of radiating elements to emit a beam pattern based on the selected projected beam pattern.
20. The method of claim 18 , further comprising approximating the selected projected beam pattern.
21. The method of claim 16 , further comprising propagating the reference wave through a parallel-plate waveguide, a rectangular waveguide or a microstrip line.
22. The method of claim 16 , wherein the set of radiating elements comprises sub-wavelength antenna elements, each configured to emit an electromagnetic emission in response to received electromagnetic energy, wherein each of the sub-wavelength antenna elements comprises at least one electromagnetically resonant element, and wherein a physical diameter of individual sub-wavelength antenna elements is less than an effective wavelength of the electromagnetic emission.
23. The method of claim 16 , wherein discarding the phase portion of the result further comprises keeping a magnitude part of the result.
24. The method of claim 16 , further comprising applying the modulation function to the aperture.
25. The method of claim 16 , further comprising computing the aperture taper function based at least in part on a sampled approximation of the aperture.
26. The method of claim 16 , further comprising computing the modulation function of the aperture based at least in part on a sampled approximation of an ideal modulation function of the aperture.
27. The method of claim 16 , further comprising applying the modulation function of the aperture to the aperture to cause a sampled approximation of the spatial-domain antenna-plane pattern.
28. The method of claim 16 , wherein receiving an antenna-plane pattern further comprises:
defining a two-dimensional far-field beam pattern; and
back-propagating the two-dimensional far-field beam pattern to the antenna plane to form the spatial-domain antenna-plane pattern.
29. A method for beam shaping using a metamaterial surface antenna technology (MSA-T) system, the method comprising:
defining a field description of a far-field beam pattern;
determining an object wave at an antenna plane that causes the far-field beam pattern based on a transfer function of free space;
computing a modulation function to apply to radiating elements of an antenna to form the object wave, including discarding a phase portion of an ideal modulation pattern to form a magnitude modulation pattern; and
causing the modulation function to be applied to the radiating elements of the antenna.
30. The method of claim 29 , wherein the radiating elements comprise sub-wavelength antenna elements, each configured to emit an electromagnetic emission in response to received electromagnetic energy, wherein each of the sub-wavelength antenna elements comprises at least one electromagnetically resonant element, and wherein a physical diameter of individual sub-wavelength antenna elements is less than an effective wavelength of the electromagnetic emission.
31. The method of claim 29 , wherein computing the modulation function further comprises:
determining a modulation pattern based at least in part on a reference wave from a feed network of the antenna multiplied by the object wave;
forming an aperture modulation pattern based at least in part on an aperture taper function, modulation pattern, a lower bound of an element modulation range of an aperture and an upper bound of the element modulation range of the aperture;
discarding the phase portion of the modulation pattern to form the magnitude modulation pattern; and
determining the modulation function of the aperture based at least in part on a product of the aperture modulation pattern and the reference wave.
32. The method of claim 29 , further comprising:
converting the field description from a spatial domain into a frequency domain to form a k-space field description; and
back-propagating the k-space field description to the antenna plane to form the object wave.
33. The method of claim 29 , wherein defining the field description of a far-field pattern further comprises:
receiving a two-dimensional beam profile projection located in a far-field of the antenna; and
defining the field description based on a two-dimensional beam profile on a two-dimensional planar grid located in the far-field of the antenna, the grid corresponding to a set of radiating element locations at an aperture plane of the antenna.
34. The method of claim 29 , wherein causing the modulation function to be applied to the radiating elements of the antenna further comprises modulating an impedance of an aperture of the antenna in electromagnetic contact with a reference wave.
35. The method of claim 29 , wherein the method further comprises selecting the far-field beam pattern.
36. The method of claim 29 , wherein the method further comprises causing a set of radiating elements coupled to an aperture of the antenna to emit a beam pattern based on the far-field beam pattern.
37. The method of claim 29 , wherein causing the modulation function to be applied to the radiating elements of the antenna further comprises approximating the far-field beam pattern.