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;

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

the substantial number of the M 2 apertures in the second array through the M N apertures in the N-th array receiving the electromagnetic wave signal from the substantial number of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the substantial number of the M 1 apertures in the first array; and

the substantial number of the M 1 apertures in the first array is further configured to send the electromagnetic wave signal to another one 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.

2. The system of claim 1 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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.

3. 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.

4. The system of claim 3 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

5. The system of claim 4 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

6. 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.

7. 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.

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

9. 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 substantial number of the M 1 apertures in a first array is configured to send the electromagnetic wave signal to a substantial number of the M 2 apertures in a second array through the M N apertures in a N-th array;

the substantial number 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, receiving the electromagnetic wave signal from the substantial number of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the substantial number of the M 1 apertures in the first array; and

a M N -th aperture in the N-th array is configured to send the electromagnetic wave signal to another one of the M 1 apertures in the first array after receiving the electromagnetic wave signal from the substantial number of the M 1 apertures in the first array.

10. The system of claim 9 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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.

11. The system of claim 9 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

12. The system of claim 11 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

13. The system of claim 12 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

14. The system of claim 9 , 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.

15. The system of claim 9 , 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.

16. The system of claim 9 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

17. 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;

a substantial number of the M 1 apertures in a first array is configured to send the electromagnetic wave signal to a substantial number of the M 2 apertures in a 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 substantial number 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, receiving the electromagnetic wave signal from the substantial number of the M 1 apertures in the first array is configured to redirect the received electromagnetic wave signal back to the substantial number of the M 1 apertures in the first array; and

a M N -th aperture in the N-th array is configured to send the electromagnetic wave signal to another one of the M 1 apertures in the first array after receiving the electromagnetic wave signal from the substantial number of the M 1 apertures in the first array.

18. The system of claim 17 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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.

19. The system of claim 17 , wherein the electromagnetic wave signal comprises a plurality of signals each having a different wavelength in a multi-wavelength system.

20. The system of claim 19 , further comprising a dispersion compensation device configured to direct substantially all of the plurality of signals from one aperture to another aperture.

21. The system of claim 20 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

22. The system of claim 17 , 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.

23. The system of claim 17 , 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.

24. The system of claim 17 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

25. 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 substantial number of the M 1 apertures in a first array, the electromagnetic wave signal to a substantial number of the M 2 apertures in a second array through the M N apertures in a N-th array;

receiving, by the substantial number 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 substantial number of the M 1 apertures in the first array;

redirecting, by the substantial number 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 substantial number of the M 1 apertures in the first array; and

after receiving, by the substantial number 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 substantial number 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.

26. The method of claim 25 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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.

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

28. The method of claim 27 , further comprising directing, by using a dispersion compensation device, substantially all of the plurality of signals from one aperture to another aperture.

29. The method of claim 28 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

30. The method of claim 25 , 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.

31. The method of claim 25 , 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.

32. The method of claim 25 , wherein the apertures in the first array through the N-th array are located within a substantially sealed cavity.

33. 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 substantial number of the M 1 apertures in a first array, the electromagnetic wave signal to a substantial number of the M 2 apertures in a second array through the M N apertures in a N-th array;

receiving, by the substantial number 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 substantial number of the M 1 apertures in the first array;

redirecting, by the substantial number 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 substantial number of the M 1 apertures in the first array; and

after receiving, by a M N -th aperture in the N-th array, the electromagnetic wave signal from the substantial number 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 one of the M 1 apertures in the first array.

34. The method of claim 33 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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 33 , 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 33 , 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 33 , 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 33 , 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 a first aperture in the second array, the electromagnetic wave signal to a first aperture in the first array;

sending, by a substantial number of the M 1 apertures in a first array, the electromagnetic wave signal to a substantial number of the M 2 apertures in a 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 substantial number 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 substantial number 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 substantial number 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 substantial number of the M 1 apertures in the first array; and

after receiving, by a M N -th aperture in the N-th array, the electromagnetic wave signal from the substantial number 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 one of the M 1 apertures in the first array.

42. The method of claim 41 , wherein:

the substantial number of the M 1 apertures in the first array comprises each one of the M 1 apertures; and

the substantial number 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.

43. 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.

44. The method of claim 43 , further comprising directing, by using a dispersion compensation device, substantially all of the plurality of signals from one aperture to another aperture.

45. The method of claim 44 , wherein the dispersion compensation device comprises a multi-wavelength beam directing device using an achromatic Fourier transform lens.

46. 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.

47. 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.

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