Two-dimensional planar and crossover-free beamforming network architecture

1. An antenna system comprising:

an array of antennas disposed in a predetermined non-linear pattern, the array of antennas comprising a plurality of antennas and having a two-dimensional field of view; and

a two-dimensional beamforming network (BFN) disposed entirely on a single first surface, and having a one-dimensional array-side interface disposed on the first surface and a one-dimensional beam-side interface disposed on the first surface; wherein:

the antennas of the array of antennas are individually communicably coupled to the array-side interface, such that segments of the beam-side interface map to respective pixels in the two-dimensional field of view;

the predetermined non-linear pattern defines a second surface;

the array of antennas comprises a plurality of disjoint sets of antennas;

each disjoint set of antennas comprises a plurality of antennas of the array of antennas; and

for each disjoint set of antennas, each antenna of at least a non-empty subset of the disjoint set of antennas is perpendicularly displaced a respective distance along the second surface from a longitudinal axis of a hypothetical linear array of antennas disposed on the second surface.

2. An antenna system according to claim 1 , wherein the array of antennas and the two-dimensional beamforming network collectively form a true time delay system.

3. An antenna system according to claim 1 , wherein the one-dimensional array-side interface is segmented.

4. An antenna system according to claim 1 , wherein the one-dimensional beam-side interface is continuous.

5. An antenna system according to claim 1 , wherein the first surface is planar.

6. An antenna system according to claim 1 , wherein the first surface is non-planar.

7. An antenna system according to claim 1 , wherein the first surface is folded.

8. An antenna system according to claim 1 , wherein the predetermined non-linear pattern defines a second surface that extends smoothly from an edge of the first surface.

9. An antenna system according to claim 8 , wherein:

the predetermined non-linear pattern defines a second surface; and

the array of antennas is communicably coupled to the array-side interface via a crossover-free network disposed entirely on the first and/or second surface.

10. An antenna system according to claim 1 , wherein:

the antenna system has a design wavelength λ;

the plurality of disjoint sets of antennas comprises N disjoint sets of antennas; and

within each disjoint set of the antennas:

the antennas are spaced apart in a direction parallel to the longitudinal axis of the hypothetical linear array of antennas, wherein spacing between each pair of adjacent antennas is an integral multiple of about ½λ; and

the antennas are spaced apart in a direction perpendicular to the longitudinal axis of the hypothetical linear array of antennas.

11. An antenna system according to claim 10 , wherein:

the antenna system has a design wavelength λ; and

within each disjoint set of the antennas:

the antennas are spaced apart by respective integral multiples of (λ/2) in the direction parallel to the longitudinal axis; and

the antennas are spaced apart by respective integral multiples of (λ/2) in the direction perpendicular to the longitudinal axis.

12. An antenna system according to claim 1 , wherein:

the predetermined non-linear pattern defines a second surface;

the array of antennas comprises a plurality of disjoint sets of antennas;

each disjoint set of antennas comprises a plurality of antennas of the array of antennas; and

for each disjoint set of antennas, each antenna of at least a non-empty subset of the disjoint set of antennas is displaced a respective distance, measured along the second surface and parallel to one dimension of the two-dimensional field of view, from a longitudinal axis of a hypothetical linear array of antennas disposed on the second surface.

13. An antenna system according to claim 12 , wherein:

the antenna system has a design wavelength λ;

the plurality of disjoint sets of antennas comprises N disjoint sets of antennas; and

within each disjoint set of the antennas:

the antennas are spaced apart in a direction parallel to the longitudinal axis of the hypothetical linear array of antennas, wherein spacing between each pair of adjacent antennas is an integral multiple of about ½λ; and

the antennas are spaced apart in a direction perpendicular to the longitudinal axis of the hypothetical linear array of antennas.

14. An antenna system according to claim 12 , wherein:

the antenna system has a design wavelength λ; and

within each disjoint set of the antennas:

the antennas are spaced apart by respective integral multiples of (λ/2) in the direction parallel to the longitudinal axis; and

the antennas are spaced apart by respective integral multiples of (λ/2) in the direction perpendicular to the longitudinal axis.

15. An antenna system according to claim 1 , wherein the antenna system has a design wavelength between about 10 nanometers and about 1 millimeter.

16. An antenna system according to claim 1 , wherein the antenna system has a design wavelength between about 1 millimeter and about 100 meters.

17. An antenna system according to claim 1 , wherein:

the predetermined non-linear pattern defines a second surface; and

each antenna of the array of antennas comprises a grating coupler configured to optically couple to free space beyond the second surface with a coupling efficiency of at least about 25%.

18. An antenna system according to claim 1 , wherein the two-dimensional beamforming network comprises a Rotman lens.

19. An antenna system according to claim 1 , wherein the two-dimensional beamforming network comprises a Fourier transformer.

20. An antenna system according to claim 1 , wherein the two-dimensional beamforming network comprises a Butler matrix.

21. An antenna system according to claim 1 , wherein the two-dimensional beamforming network comprises a single-stage beamforming network.

22. An antenna system according to claim 1 , wherein the two-dimensional beamforming network comprises a single Rotman lens.

23. An antenna system according to claim 1 , wherein:

the array of antennas comprises N (N>1) disjoint sets of antennas;

each disjoint set of antennas comprises a plurality of antennas of the array of antennas; and

the two-dimensional beamforming network comprises:

N first beamforming networks, each first beamforming network being associated with a distinct set of the antennas and having a beam-side interface and a plurality of array-side ports, wherein the array-side ports of each first beamforming network are individually communicably coupled to respective antennas of the associated set of the antennas, the array-side ports of the N first beamforming networks thereby collectively forming the one-dimensional array-side interface of the two-dimensional beamforming network;

N second beamforming networks, each second beamforming network being associated with a distinct first beamforming network and having an array-side interface and a beam-side interface, wherein the beam-side interface of each second beamforming network is communicably coupled to the beam-side interface of the associated first beamforming network; and

a third beamforming network having an array-side interface and a plurality of beam-side ports, wherein the array-side interface of each second beamforming network is communicably coupled to a respective distinct portion of the array-side interface of the third beamforming network, and the plurality of beam-side ports of the third beamforming network collectively forms the one-dimensional beam-side interface of the two-dimensional beamforming network.

24. An antenna system according to claim 23 , wherein:

each first beamforming network consists essentially of a respective one-dimensional beamforming network;

each second beamforming network consists essentially of a respective one-dimensional beamforming network; and

the third beamforming network consists essentially of a distinct one-dimensional beamforming network.

25. An antenna system according to claim 23 , wherein:

each first beamforming network consists essentially of a respective Rotman lens;

each second beamforming network consists essentially of a respective Rotman lens; and

the third beamforming network consists essentially of a distinct Rotman lens.

26. An antenna system according to claim 23 wherein, for each first beamforming network:

the array-side ports of the first beamforming network are transversely ordered in a first order;

the antennas of the associated set of the antennas are transversely ordered in a second order; and

the antennas of the associated set of the antennas are individually communicably coupled to the respective array-side ports such that the first order is opposite the second order.

27. An antenna system according to claim 23 , wherein:

the antenna system has a design wavelength λ; and

the beam-side interface of each second beamforming network is communicably coupled to the beam-side interface of the associated first beamforming network by a respective associated first coupling, thereby collectively defining a plurality of first couplings, wherein each non-central first coupling is configured to delay signals of wavelength λ, propagating therethrough by a respective relative delay amount, such that the delay amount varies monotonically transversely across the non-central first coupling.

28. An antenna system according to claim 27 , wherein:

each first beamforming network is numbered with a unique integer j between

-

⌊

N

2

⌋

and

+

⌊

N

2

⌋

;

and

for each non-central first coupling, the delay amount varies monotonically transversely across the non-central first coupling between about

+

(

N

-

1

2

)

⁢

j

⁢

λ

and about

-

(

N

-

1

2

)

⁢

j

⁢

λ

29. An antenna system according to claim 28 wherein, for each central first coupling, the relative delay amount is about zero.

30. An antenna system according to claim 28 , wherein each first coupling comprises a respective plurality of discrete waveguides.

31. An antenna system according to claim 28 wherein, for each first beamforming network:

the set of the antennas associated with the first beamforming network comprises a respective number M of antennas; and

the associated first coupling comprises M discrete waveguides.

32. An antenna system according to claim 28 , wherein each non-central first coupling comprises a respective medium configured to delay signals propagating therethrough by a respective delay amount, such that the delay amount varies continuously transversely across the medium.

33. An antenna system according to claim 1 , wherein:

each dimension of a grating lobe-free two-dimensional field of view comprises a respective number of pixels;

the two-dimensional beamforming network comprises a plurality of distinct elementary components; and

the two-dimensional beamforming network is configured such that photons traverse, on average, a number of the distinct elementary components that is constant, with respect to the number of pixels along each dimension of the grating lobe-free field of view.