Wireless energy transfer with high-Q sub-wavelength resonators
Described herein are embodiments of transferring electromagnetic energy that includes a first electromagnetic resonator structure receiving energy from an external power supply, said first resonator structure may have a first mode with a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , and a first Q-factor Q 1 =ω 1 L 1 /R 1ohm +R 1rad ). A second electromagnetic resonator structure being positioned distal from said first resonator structure and not electrically wired to the first resonator structure, said second resonator structure having a second mode with a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ). The electromagnetic energy may be transferred from said first resonator structure to said second resonator structure over a distance D that is smaller than each of the resonant wavelengths λ 1 and λ 2 corresponding to the resonant frequencies ω 1 and ω 2 , respectively, where the characteristic sizes of the resonator structures are less than the resonant wavelengths and where Q1>100, Q2>100, R 1ohm >R 1rad , and R 2ohm >R 2rad .
1. A system of transferring electromagnetic energy comprising:
a first electromagnetic resonator receiving energy from a power supply, said first electromagnetic resonator having a first mode with a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , an inductance L 1 , and a first Q-factor Q 1 =ω 1 L 1 /(R 1ohm +R 1rad ), wherein R 1ohm is the ohmic component of resistance in the first electromagnetic resonator and R 1rad is the radiative component of resistance in the first resonator;
a second electromagnetic resonator being positioned distal from said first electromagnetic resonator and not electrically wired to the first electromagnetic resonator, said second electromagnetic resonator having a second mode with a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , and inductance L 2 , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ), wherein R 2ohm is the ohmic component of resistance in the second electromagnetic resonator and R 2rad is the radiative component of resistance in the second electromagnetic resonator; and
wherein electromagnetic energy is wirelessly transferred from said first electromagnetic resonator to said second electromagnetic resonator over a distance D that is smaller than each of the resonant wavelengths λ 1 and λ 2 corresponding to the resonant frequencies ω 1 and ω 2 , respectively,
wherein √{square root over (Q 1 Q 2 )}>100, R 1ohm >R 1rad , and R 2ohm >R 2rad .
2. The system of claim 1 , further comprising an energy drain coupled to the second electromagnetic resonator.
3. The system of claim 2 , wherein the energy drain comprises a robot, vehicle, computer, cell phone, or a portable electronic device.
4. The system of claim 1 , wherein Q 1 >100.
5. The system of claim 1 , wherein Q 2 >100.
6. The system of claim 1 , wherein Q 1 >100 and Q 2 >100.
7. The system of claim 1 , further comprising a third electromagnetic resonator, coupled to an energy drain, located at a variable distance from the first electromagnetic resonator, and wherein the first electromagnetic resonator and the third electromagnetic resonator are coupled to wirelessly transfer electromagnetic energy from the first electromagnetic resonator to the third electromagnetic resonator.
8. The system of claim 7 , further comprising the energy drain coupled to the third electromagnetic resonator.
9. The system of claim 1 , further comprising a third electromagnetic resonator, coupled to another power supply, located at a variable distance from the second electromagnetic resonator, and wherein the third electromagnetic resonator and the second electromagnetic resonator are coupled to wirelessly transfer electromagnetic energy from the third electromagnetic resonator to the second electromagnetic resonator.
10. The system of claim 1 , wherein at least one of the electromagnetic resonators is a tunable electromagnetic resonator.
11. The system of claim 1 , wherein the electromagnetic resonators are movable relative to one another and wherein the wireless energy transfer occurs over a range of distances.
12. The system of claim 11 , wherein the range of distances includes 5 cm.
13. The system of claim 11 , wherein the range of distances includes 10 cm.
14. The system of claim 11 , wherein the range of distances includes 30 cm.
15. The system of claim 11 , wherein κ/√{square root over (Γ 1 Γ 2 )}>0.2 over the range of distances.
16. The system of claim 15 , wherein κ/√{square root over (Γ 1 Γ 2 )}>0.5 over the range of distances.
17. The system of claim 15 , wherein κ/√{square root over (Γ 1 Γ 2 )}>1 over the range of distances.
18. The system of claim 11 , wherein an efficiency of the wireless energy transfer is at least 20% over the range of distances.
19. The system of claim 1 , wherein the resonant frequencies f 1 =ω 1 /2π and f 2 =ω 2 /2π are each at least 5 MHz.
20. The system of claim 1 , further comprising a feedback mechanism coupled to at least one of the electromagnetic resonators to correct for detuning.
21. The system of claim 1 , wherein an energy drain is coupled to the second electromagnetic resonator, and wherein the power supply and the energy drain are configured to be driven to increase a ratio of useful-to-lost power for varying wireless energy transfer rates κ between the first electromagnetic resonator and the second electromagnetic resonator.
22. The system of claim 1 , wherein the first electromagnetic resonator and second electromagnetic resonator are configured to be adjustably tuned to increase a ratio of useful-to-lost power for varying wireless energy transfer rates κ between the first electromagnetic resonator and the second electromagnetic resonator.
23. The system of claim 1 , wherein the first electromagnetic resonator and the second electromagnetic resonator have different characteristic sizes.
24. The system of claim 1 , wherein characteristic sizes of the electromagnetic resonators are less than the resonant wavelengths of the electromagnetic resonators, respectively.
25. A method of transferring electromagnetic energy comprising:
providing a first electromagnetic resonator receiving energy from a power supply, said first electromagnetic resonator having a first mode with a resonant frequency ω 1 , an intrinsic loss rate Γ 1 , an inductance L 1 , and a first Q-factor Q 1 =ω 1 L 1 /(R 1ohm +R 1rad ), wherein R 1ohm is the ohmic component of resistance in the first electromagnetic resonator and R 1rad is the radiative component of resistance in the first electromagnetic resonator;
providing a second electromagnetic resonator being positioned distal from said first electromagnetic resonator and not electrically wired to the first electromagnetic resonator, said second electromagnetic resonator having a second mode with a resonant frequency ω 2 , an intrinsic loss rate Γ 2 , and inductance L 2 , and a second Q-factor Q 2 =ω 2 L 2 /(R 2ohm +R 2rad ), wherein R 2ohm is the ohmic component of resistance in the second electromagnetic resonator and R 2rad is the radiative component of resistance in the second electromagnetic resonator; and
transferring electromagnetic energy wirelessly from said first electromagnetic resonator to said second electromagnetic resonator over a distance D that is smaller than each of the resonant wavelengths λ 1 and λ 2 corresponding to the resonant frequencies ω 1 and ω 2 , respectively,
wherein √{square root over (Q 1 Q 2 )}>100, R 1ohm >R 1rad , and R 2ohm >R 2rad .
26. The method of claim 25 , wherein an energy drain is coupled to the second electromagnetic resonator.
27. The method of claim 26 , wherein the energy drain comprises a robot, vehicle, computer, cell phone, or a portable electronic device.
28. The method of claim 25 , wherein Q 1 >100.
29. The method of claim 25 , wherein Q 2 >100.
30. The method of claim 25 , wherein Q 1 >100 and Q 2 >100.
31. The method of claim 25 , wherein a third electromagnetic resonator, coupled to an energy drain, is located at a variable distance from the first electromagnetic resonator, and wherein the first electromagnetic resonator and the third electromagnetic resonator are coupled to wirelessly transfer electromagnetic energy from the first electromagnetic resonator to the third electromagnetic resonator.
32. The method of claim 31 , wherein the energy drain is coupled to the third electromagnetic resonator.
33. The method of claim 25 , wherein a third electromagnetic resonator, coupled to another power supply, is located at a variable distance from the second electromagnetic resonator, and wherein the third electromagnetic resonator and the second electromagnetic resonator are coupled to wirelessly transfer electromagnetic energy from the third electromagnetic resonator to the second electromagnetic resonator.
34. The method of claim 25 , wherein at least one of the electromagnetic resonators is a tunable resonator.
35. The method of claim 25 , wherein the electromagnetic resonators are movable relative to one another and wherein the wireless energy transfer occurs over a range of distances.
36. The method of claim 35 , wherein the range of distances includes 5 cm.
37. The method of claim 35 , wherein the range of distances includes 10 cm.
38. The method of claim 35 , wherein the range of distances includes 30 cm.
39. The method of claim 35 , wherein κ/√{square root over (Γ 1 Γ 2 )}>0.2 over the range of distances.
40. The method of claim 39 , wherein κ/√{square root over (Γ 1 Γ 2 )}>0.5 over the range of distances.
41. The method of claim 39 , wherein κ/√{square root over (Γ 1 Γ 2 )}1 over the range of distances.
42. The method of claim 35 , wherein an efficiency of the wireless energy transfer is at least 20% over the range of distances.
43. The method of claim 25 , wherein resonant frequencies f 1 =ω 1 /2π and f 2 =ω 2 /2π are each at least 5 MHz.
44. The method of claim 25 , wherein a feedback mechanism is coupled to at least one of the electromagnetic resonators to correct for frequency detuning.
45. The method of claim 25 , wherein an energy drain is coupled to the second electromagnetic resonator, and wherein the power supply and the energy drain are driven to increase a ratio of useful-to-lost power for varying wireless energy transfer rates κ between the first electromagnetic resonator and the second electromagnetic resonator.
46. The method of claim 25 , wherein the first electromagnetic resonator and second electromagnetic resonator are adjustably tuned to increase a ratio of useful-to-lost power for varying wireless energy transfer rates κ between the first electromagnetic resonator and the second electromagnetic resonator.
47. The method of claim 25 , wherein the first electromagnetic resonator and the second electromagnetic resonator have different characteristic sizes.
48. The method of claim 25 , wherein characteristic sizes of the electromagnetic resonators are less than the resonant wavelengths of the electromagnetic resonators, respectively.