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1. (WO2017095878) BEAM PATTERN SYNTHESIS AND PROJECTION FOR METAMATERIAL ANTENNAS
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CLAIMS

1. A method of constructing a modulation pattern for an aperture in a metamaterial surface antenna technology (MSA-T) system, the method comprising:

defining a far-field pattern based on a beam profile projected onto a two-dimensional reference surface located in a far-field of an antenna;

converting the far- field pattern sampled on the two-dimensional reference surface from a two-dimensional spatial domain into a Fourier domain to form a two-dimensional k-space field representation;

back-propagating the two-dimensional k-space field representation from the two-dimensional reference surface to an aperture plane of the antenna using a transfer function of free space to form a k-space aperture field representation;

converting the k-space aperture field representation from a two-dimensional Fourier domain to the two-dimensional spatial domain to form an object wave that represents an emission from the antenna that forms the far-field pattern;

determining a reference wave comprising a set of fields in a feed network at each radiating element resulting from energy distributed from one or more feed input ports;

forming an ideal holographic modulation pattern from the reference wave and the object wave;

multiplying an aperture taper function to the ideal holographic modulation pattern to form a tapered ideal hologram modulation pattern;

retaining a magnitude of the tapered ideal hologram modulation pattern and discarding a phase part of the tapered ideal hologram modulation pattern to form a magnitude pattern; shifting and scaling elements of the magnitude pattern to lie within an upper bound and a lower bound of an element modulation range to form an aperture modulation pattern; and

applying the aperture modulation pattern to a set of radiating elements of the aperture of the antenna during activation of the one or more feed input ports to cause a radiated emission that approximates the far-field pattern in the far- field of the antenna.

2. The method of claim 1, wherein each of a set of grid elements of a two-dimensional planar grid on the reference surface directly corresponds to a radiating element from the set of radiating elements at the aperture plane.

3. The method of claim 1, wherein back- propagating the two-dimensional k-space field representation further comprises constructing the transfer function of free space between the far- field pattern and the aperture plane of the antenna.

4. The method of claim 1 , wherein the reference wave is propagating through a transmission line structure.

5. The method of claim 4, wherein the transmission line structure is a substrate integrated waveguide, a parallel-plate waveguide, a rectangular waveguide or a microstrip line.

6. The method of claim 1 , 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.

7. The method of claim 1 , wherein applying the aperture modulation pattern further comprises modulating an impedance of the aperture in electromagnetic contact with the reference wave.

8. The method of claim 1, wherein the aperture modulation pattern causes a sampled approximation of the beam profile projected onto the two-dimensional reference surface.

9. An antenna system comprising:

an aperture coupled to a feed network and approximated by an aperture taper function, the aperture comprising:

a set of radiating aperture elements having an element modulation range and configured to selectively transfer energy from a reference wave, the set of radiating aperture elements configured to radiate a beam pattern based on energy received from the reference wave; and

a control system comprising a processor configured to:

define a desired beam profile projected onto a two-dimensional plane located in a far-field of an antenna;

convert the desired beam profile from a spatial domain far-field pattern into a frequency domain field description;

construct the transfer function of free space;

back-propagate the frequency domain field description in the far-field back to an antenna plane to form an antenna plane frequency domain field description;

convert the antenna plane frequency domain field description into a spatial domain to form an object wave;

compute a modulation function to apply to radiating elements of the antenna to form the object wave, including discarding a phase portion of an ideal modulation pattern to form a magnitude modulation pattern; and

apply the modulation function to the set of radiating aperture elements of the antenna to form an approximation of the desired beam profile.

10. The system of claim 9, wherein to compute the modulation function to apply to the radiating elements of the antenna to form the object wave further comprises:

determine the ideal modulation pattern based at least in part on the reference wave multiplied by the object wave, wherein the feed network comprising a feed input port is configured to provide the reference wave to the set of radiating aperture elements;

discard the phase portion of the ideal modulation pattern to form the magnitude modulation pattern;

form a tapered modulation pattern multiplying the aperture taper function with elements of the magnitude modulation pattern;

normalize the tapered modulation pattern based at least in part on an upper bound and lower bound of the element modulation range of the aperture from an aperture modulation pattern; and

apply the modulation function to the aperture to approximate the desired beam profile based at least in part on the aperture modulation pattern and the reference wave.

11. The system of claim 10, wherein the reference wave is propagating through a transmission line structure.

12. The system of claim 11, wherein the transmission line structure is a substrate integrated waveguide, a parallel-plate waveguide, a rectangular waveguide or a microstrip line.

13. The system of claim 9, wherein the antenna system further comprises

metamaterial surface antenna technology (MSA-T).

14. The system of claim 13, wherein the set of radiating aperture 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.

15. A device for beam shaping, the system comprising:

storage configured for storing an aperture taper function and an element modulation range of an aperture of an antenna;

circuitry configured to interface with the antenna and provide a modulation function to apply to radiating elements of the aperture; and

a processor configured to:

receive a two-dimensional beam profile projection located in a far- field of the antenna;

back-propagate a representation of the two-dimensional beam profile projection to an antenna plane to form an object wave;

compute the modulation function to form the object wave, including discarding a phase portion of an ideal modulation pattern to form a magnitude modulation pattern; and

transmit the modulation function to the antenna for application to the radiating elements of the antenna to radiate an approximation of the object wave which results in an approximation of the two-dimensional beam profile projection.

16. The device of claim 15, wherein to compute the modulation function to form the object wave further comprises:

determine the ideal modulation pattern based at least in part on a reference wave from a feed network of the antenna multiplied by the object wave;

discard the phase portion of the ideal modulation pattern to form the magnitude modulation pattern; and

form the modulation function based at least in part on an aperture taper function, magnitude modulation pattern, a lower bound of the element modulation range of the aperture and an upper bound of the element modulation range of the aperture.

17. The device of claim 16, wherein the reference wave is propagating through a transmission line such as a parallel-plate waveguide, a rectangular waveguide or a microstrip line.

18. The device of claim 16, wherein to form the modulation function further comprises:

form a product pattern by scaling and multiplying elements of the aperture taper function with elements of the magnitude modulation pattern; and

normalize the product pattern based at least in part on the upper bound and the lower bound of the element modulation range of the aperture to form the modulation function.

19. The device of claim 16, wherein to form the modulation function further comprises causing modulation function values to lie within the element modulation range of the aperture.

20. The device of claim 15, wherein to back-propagate the representation of the two-dimensional beam profile projection to the antenna plane to form the object wave further comprises converting the two-dimensional beam profile projection from a spatial domain into a frequency domain to form a k-space field description.

21. The device of claim 15, wherein to back-propagate the representation of the two-dimensional beam profile projection to the antenna plane further comprises constructing the transfer function of free space between the two-dimensional beam profile projection and an aperture plane of the antenna.

22. The device of claim 15, wherein to receive the two-dimensional beam profile projection located in the far- field of the antenna further comprises defining a far-field pattern based on the two-dimensional beam profile projection 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.

23. The device of claim 15, wherein the processor is configured to control an antenna system comprising a set of radiating elements coupled to the aperture.

24. The device of claim 23, 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.

25. 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.

26. The method of claim 25, 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.

27. The method of claim 25, 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.

28. The method of claim 27, wherein the method further comprises causing the reference wave to propagate through a parallel-plate waveguide, a rectangular waveguide or a microstrip line.

29. The method of claim 27, wherein forming the aperture modulation pattern further comprises:

forming a product pattern by scaling and summing elements of the aperture taper function with elements of the magnitude modulation pattern to make elements of the product pattern greater than a lower bound of the element modulation range of the aperture; and

normalizing the product pattern based at least in part on an upper bound of the element modulation range of the aperture to form the aperture modulation pattern.

30. The method of claim 25, 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.

31. The method of claim 30, wherein back-propagating the k-space field description to the antenna plane further comprises constructing the transfer function of free space between the far-field beam pattern and an aperture plane of the antenna.

32. The method of claim 25, 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.

33. The method of claim 25, 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.

34. The method of claim 25, wherein the method further comprises selecting the far-field beam pattern.

35. The method of claim 25, 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.