Wireless energy transfer across variable distances with high-Q capacitively-loaded conducting-wire loops

1. A system, comprising:

at least one source resonator configured to be coupled to an energy source to generate an electromagnetic near field region; and

at least one device resonator located at a variable distance D from the at least one source resonator within the at least one source resonator's near-field region to enable resonant wireless energy transfer between the at least one source resonator and the at least one device resonator when the at least one source resonator is coupled to the energy source,

wherein at least two of the resonators comprise high-Q capacitively-loaded conducting-wire loops,

wherein the first high-Q capacitively-loaded conducting wire loop has a resonant frequency ω 1 and an intrinsic loss rate Γ 1 , and is capable of storing electromagnetic energy with an intrinsic quality factor Q 1 =ω 1 /(2Γ 1 ) greater than 100,

wherein the second high-Q capacitively-loaded conducting wire loop has a resonant frequency ω 2 and an intrinsic loss rate Γ 2 , and is capable of storing electromagnetic energy with an intrinsic quality factor Q 2 =ω 1 /(2Γ 2 ) greater than 100, and

wherein D is less than the wavelengths λ 1 =c/2πω 1 and λ 2 =c/2πω 2 corresponding to the resonant frequencies ω 1 and ω 2 , respectively, where c is the speed of light.

2. The system of claim 1 wherein the distance between the resonators is greater than 5 cm.

3. The system of claim 1 wherein the distance between the resonators is greater than 10 cm.

4. The system of claim 1 wherein that distance between the resonators is larger than the characteristic size of the smaller of the first resonator and the second resonator.

5. The system of claim 1 , wherein each resonator comprises an electrical conductor shaped into one or more loops wound in substantially a single plane circumscribing a substantially planar area.

6. The system of claim 5 , wherein the loops of the electrical conductors of each of the source and device resonators are in substantially the same plane.

7. The system of claim 5 , wherein a line drawn from the center of the source resonator to the center of the at least one device resonator is substantially normal to the circumscribed planar area of each resonator.

8. The system of claim 5 , wherein a line drawn from the center of the source resonator to the center of the at least one device resonator is substantially parallel to the circumscribed planar area of each resonator.

9. The system of claim 5 , wherein a line drawn from the center of the source resonator to the center of the at least one device resonator forms a different angle to the surface area circumscribed by the source resonator than to the circumscribed planar area of each resonator.

10. The system of claim 1 , further comprising an energy drain coupled to the at least one device resonator.

11. The system of claim 10 , wherein the energy drain comprises a robot, vehicle, computer, cell phone, or a portable electronic device.

12. The system of claim 1 , further comprising the energy source configured to be coupled to the first high-Q capacitively-loaded conducting wire loop and an energy drain configured to be coupled to the second high-Q capacitively-loaded conducting wire loop to provide useful power to the energy drain, and wherein the energy source is configured to provide energy to the first high-Q capacitively-loaded conducting wire loop at a rate that varies with a rate of wireless energy transfer κ between the first high-Q capacitively-loaded conducting wire loop and the second high-Q capacitively-loaded conducting wire loop.

13. The system of claim 12 , wherein the energy source is configured to provide energy to the first high-Q capacitively-loaded conducting wire loop at a rate that substantially minimizes the energy stored in the first high-Q capacitively-loaded conducting wire loop and the second high-Q capacitively-loaded conducting wire loop.

14. The system of claim 12 , wherein the energy source is configured to provide energy to the first high-Q capacitively-loaded conducting wire loop at a rate that substantially maximizes a ratio of the useful power to lost power from the energy source to the energy drain.

15. The system of claim 1 , wherein f 1 =ω 1 /(2π) and f 2 =ω 2 /(2π), and each of f 1 and f 2 is between about 5 MHz and 380 MHz.

16. The system of claim 1 , wherein each intrinsic loss rate comprises a resistive component and a radiative component.

17. The system of claim 1 , wherein Q 1 >200 and Q 2 >200.

18. The system of claim 1 , further comprising the energy source coupled to the source resonator and a vehicle having the device resonator, and wherein the system is configured to provide wireless power to the vehicle from the source resonator to the device resonator.

19. The system of claim 17 , further comprising the energy source coupled to the source resonator and a vehicle having the device resonator, and wherein the system is configured to provide wireless power to the vehicle from the source resonator to the device resonator.

20. The system of claim 1 , wherein κ/√{square root over (Γ 1 Γ 2 )}>1 for a range of the variable distance D in the near-field region, wherein κ is the wireless energy transfer rate.

21. The system of claim 20 , wherein the range of variable distance D includes distances greater than the characteristic size L 2 of the second high-Q capacitively-loaded conducting wire loop.

22. The system of claim 20 , wherein the range of variable distance D includes distances greater than twice the characteristic size L 2 of the second high-Q capacitively-loaded conducting wire loop.

23. A method, comprising:

providing at least one source resonator coupled to an energy source generating an electromagnetic near field region; and

providing at least one device resonator located at a variable distance D from the at least one source resonator within the at least one source resonator's near-field region to enable resonant wireless energy transfer between the at least one source resonator and the at least one device resonator,

wherein at least two of the resonators comprise high-Q capacitively-loaded conducting-wire loops,

wherein the first high-Q capacitively-loaded conducting wire loop has a resonant frequency ω 1 and an intrinsic loss rate Γ 1 , and is capable of storing electromagnetic energy with an intrinsic quality factor Q 1 =ω 1 /(2Γ 1 ) greater than 100,

wherein the second high-Q capacitively-loaded conducting wire loop has a resonant frequency ω 2 and an intrinsic loss rate Γ 2 , and is capable of storing electromagnetic energy with an intrinsic quality factor Q 2 =ω 1 /(2Γ 2 ) greater than 100, and

wherein D is less than the wavelengths λ 1 =c/2πω 1 and λ 2 =c/2πω 2 corresponding to the resonant frequencies ω 1 and ω 2 , respectively, where c is the speed of light.

24. The method of claim 23 wherein the distance between the resonators is greater than 5 cm.

25. The method of claim 23 wherein the distance between the resonators is greater than 10 cm.

26. The method of claim 23 wherein that distance between the resonators is larger than the characteristic size of the smaller of the first resonator and the second resonator.

27. The method of claim 23 , wherein each resonator comprises an electrical conductor shaped into one or more loops wound in substantially a single plane circumscribing a substantially planar area.

28. The method of claim 23 , wherein each intrinsic loss rate comprises a resistive component and a radiative component.

29. The method of claim 23 , wherein the energy source is coupled to the first high-Q capacitively-loaded conducting wire loop and an energy drain is coupled to the second high-Q capacitively-loaded conducting wire loop to provide useful power to the energy drain, and wherein the energy source provides energy to the first high-Q capacitively-loaded conducting wire loop at a rate that varies with a rate of wireless energy transfer κ between the first high-Q capacitively-loaded conducting wire loop and the second high-Q capacitively-loaded conducting wire loop.

30. The method of claim 29 , wherein the energy source provides energy to the first high-Q capacitively-loaded conducting wire loop at a rate that substantially maximizes a ratio of the useful power to lost power from the energy source to the energy drain.

31. The method of claim 29 , wherein the energy source provides energy to the first high-Q capacitively-loaded conducting wire loop at a rate that substantially minimizes the energy stored in the first high-Q capacitively-loaded conducting wire loop and the second high-Q capacitively-loaded conducting wire loop.

32. The method of claim 23 , wherein Q 1 >200 and Q 2 >200.

33. The method of claim 32 , wherein a vehicle carries the device resonator, and wherein the method provides wireless power to the vehicle from the source resonator to the device resonator.

34. The method of claim 23 , wherein a vehicle carries the device resonator, and wherein the method provides wireless power to the vehicle from the source resonator to the device resonator.

35. The method of claim 23 , wherein κ/√{square root over (Γ 1 Γ 2 )}>1 for a range of variable distance D in the near-field region, wherein κ is the wireless energy transfer rate.

36. The system of claim 35 , wherein the range of variable distance D includes distances greater than the characteristic size L 2 of the second high-Q capacitively-loaded conducting wire loop.

37. The system of claim 35 , wherein the range of variable distance D includes distances greater than twice the characteristic size L 2 of the second high-Q capacitively-loaded conducting wire loop.