System and method for extending path length of a wave signal using angle multiplexing

1. A system for extending a path length of an electromagnetic wave signal, the system comprising N arrays having M 1 through M N apertures, respectively,

wherein:

N≥2, M 1 ≥2, and each of M 2 through M N ≥1;

one or more apertures of the M 1 apertures in a first array is configured to send the electromagnetic wave signal to one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array;

the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array that receives the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traverses all or some of the paths between the N arrays.

2. The system of claim 1 , wherein the electromagnetic wave signal traverses all or some of the paths between the N arrays in a reconfigurable manner.

3. The system of claim 1 , wherein the one or more apertures of the M 1 apertures in the first array is further configured to send the electromagnetic wave signal to another aperture of the M 1 apertures in the first array after receiving the redirected electromagnetic wave signal from a M N -th aperture in the N-th array.

4. The system of claim 1 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array comprises each one of the M 2 apertures in the second array through the M N apertures in the N-th array.

5. The system of claim 1 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

6. The system of claim 5 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

7. The system of claim 6 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

8. The system of claim 1 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

9. The system of claim 1 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

10. The system of claim 1 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

11. A system for extending a path length of an electromagnetic wave signal, the system comprising N arrays having M 1 through M N apertures, respectively,

wherein:

N≥2, M 1 ≥2, and each of M 2 through M N≥ 1;

one or more apertures of the M 1 apertures in a first array is configured to send the electromagnetic wave signal to one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array;

the one or more apertures of a first aperture in the second array through a (M N −1)-th aperture in the N-th array, if M N >2, and through a M N-1 -th aperture in the (N−1)-th array, if M N =1, that receives the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traverses all or some of the paths between the N arrays.

12. The system of claim 11 , wherein the electromagnetic wave signal traverses all or some of the paths between the N arrays in a reconfigurable manner.

13. The system of claim 11 , wherein a M N -th aperture in the N-th array is configured to send the electromagnetic wave signal to another aperture of the M 1 apertures in the first array after receiving the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array.

14. The system of claim 11 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array comprises each one of the M 2 apertures in the second array through the M N apertures in the N-th array.

15. The system of claim 11 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

16. The system of claim 15 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

17. The system of claim 16 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

18. The system of claim 11 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

19. The system of claim 11 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

20. The system of claim 11 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

21. A system for extending a path length of an electromagnetic wave signal, the system comprising N arrays having M 1 through M N apertures, respectively,

wherein:

N>2, M 1 >2, and each of M 2 through M N >1;

a first aperture in the second array is configured to send the electromagnetic wave signal to a first aperture in the first array;

one or more apertures of the M 1 apertures in the first array is configured to send the electromagnetic wave signal to one or more apertures of the M 2 apertures in the second array through the M N apertures in a N-th array, except that the first aperture in the first array is configured not to send the electromagnetic wave signal to the first aperture in the second array;

the one or more apertures of the first aperture in the second array through a (M N −1)-th aperture in the N-th array, if M N >2, and through a M N-1 -th aperture in the (N−1)-th array, if M N =1, that receives the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traverses all or some of the paths between the N arrays.

22. The system of claim 21 , wherein the electromagnetic wave signal traverses all or some of the paths between the N arrays in a reconfigurable manner.

23. The system of claim 21 , wherein a M N -th aperture in the N-th array is configured to send the electromagnetic wave signal to another aperture of the M 1 apertures in the first array after receiving the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array.

24. The system of claim 21 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array comprises each one of the M 2 apertures in the second array through the MN apertures in the N-th array.

25. The system of claim 21 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

26. The system of claim 25 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

27. The system of claim 26 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

28. The system of claim 21 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

29. The system of claim 21 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

30. The system of claim 21 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

31. A method for extending a path length of an electromagnetic wave signal traversing between N arrays having M 1 through M N apertures, respectively, wherein N>2, M 1 >2, and each of M 2 through M N >1, the method comprising:

sending, by one or more apertures of the M 1 apertures in a first array, the electromagnetic wave signal to one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array;

receiving, by the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array, the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array;

redirecting, by the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array, the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traversing all or some of the paths between the N arrays.

32. The method of claim 31 , comprising the electromagnetic wave signal traversing all or some of the paths between the N arrays in a reconfigurable manner.

33. The method of claim 31 , further comprising after receiving, by the one or more apertures of the M 1 apertures in the first array, the redirected electromagnetic wave signal from a M N -th aperture in the N-th array, sending, by the one or more apertures of the M 1 apertures in the first array, the electromagnetic wave signal to another one of the M 1 apertures in the first array.

34. The method of claim 31 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array comprises each one of the M 2 apertures in the second array through the M N apertures in the N-th array.

35. The method of claim 31 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

36. The method of claim 35 , further comprising directing, by using a dispersion compensation device, substantially all of the plurality of signals from one aperture to another aperture.

37. The method of claim 36 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

38. The method of claim 31 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

39. The method of claim 31 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

40. The method of claim 31 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

41. A method for extending a path length of an electromagnetic wave signal traversing between N arrays having M 1 through M N apertures, respectively, wherein N>2, M 1 >2, and each of M 2 through M N >1, the method comprising:

sending, by one or more apertures of the M 1 apertures in a first array, the electromagnetic wave signal to one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array;

receiving, by the one or more apertures of a first aperture in the second array through a (M N −1)-th aperture in the N-th array, if M N >2, and through a M N-1 -th aperture in the (N−1)-th array, if M N =1, the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array;

redirecting, by the one or more apertures of the first aperture in the second array through the (M N −1)-th aperture in the N-th array, if M N >2, and through the M N-1 -th aperture in the (N−1)-th array, if M N =1, the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traversing all or some of the paths between the N arrays.

42. The method of claim 41 , comprising the electromagnetic wave signal traversing all or some of the paths between the N arrays in a reconfigurable manner.

43. The method of claim 41 , comprising after receiving, by a M N -th aperture in the N-th array, the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array, sending, by the M N -th aperture in the N-th array, the electromagnetic wave signal to another aperture of the M 1 apertures in the first array.

44. The method of claim 41 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in the second array through the M N apertures in the N-th array comprises each one of the M 2 apertures in the second array through the M N apertures in the N-th array.

45. The method of claim 41 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

46. The method of claim 45 , further comprising directing, by using a dispersion compensation device, substantially all of the plurality of signals from one aperture to another aperture.

47. The method of claim 46 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

48. The method of claim 41 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

49. The method of claim 41 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

50. The method of claim 41 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

51. A method for extending a path length of an electromagnetic wave signal traversing between N arrays having M 1 through M N apertures, respectively, wherein N>2, M 1 >2, and each of M 2 through M N >1, the method comprising:

sending, by a first aperture in the second array, the electromagnetic wave signal to a first aperture in the first array;

sending, by one or more apertures of the M 1 apertures in the first array, the electromagnetic wave signal to one or more apertures of the M 2 apertures in the second array through the M N apertures in a N-th array, except that the first aperture in the first array does not send the electromagnetic wave signal to the first aperture in the second array;

receiving, by the one or more apertures of the first aperture in the second array through a (M N −1)-th aperture in the N-th array, if M N >2, and through a M N-1 -th aperture in the (N−1)-th array, if M N =1, the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array, except that the first aperture in the second array does not receive the electromagnetic wave signal from the first aperture in the first array;

redirecting, by the one or more apertures of the first aperture in the second array through the (M N −1)-th aperture in the N-th array, if M N >2, and through the M N-1 -th aperture in the (N−1)-th array, if M N =1, the received electromagnetic wave signal back to the one or more apertures of the M 1 apertures in the first array; and

the electromagnetic wave signal traversing all or some of the paths between the N arrays.

52. The method of claim 51 , comprising the electromagnetic wave signal traversing all or some of the paths between the N arrays in a reconfigurable manner.

53. The method of claim 51 , comprising after receiving, by a M N -th aperture in the N-th array, the electromagnetic wave signal from the one or more apertures of the M 1 apertures in the first array, sending, by the M N -th aperture in the N-th array, the electromagnetic wave signal to another aperture of the M 1 apertures in the first array.

54. The method of claim 51 , wherein:

the one or more apertures of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the one or more apertures of the M 2 apertures in a second array through the M N apertures in a N-th array comprises each one of the M 2 apertures in the second array through the M N apertures in the N-th array.

55. The method of claim 51 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

56. The method of claim 55 , further comprising directing, by using a dispersion compensation device, substantially all of the plurality of signals from one aperture to another aperture.

57. The method of claim 56 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

58. The method of claim 51 , wherein the apertures in the first array and in at least one of the second array through the N-th array comprise volume holographic gratings, corner cube retroreflectors, diffraction gratings, mirrors, partial regenerators, or full regenerators.

59. The method of claim 51 , wherein:

the apertures in the first array are located in one or more sets of one or more satellites; and

the apertures in at least one of the second array through the N-th array are located in one or more sets of one or more satellites.

60. The method of claim 51 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.