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Disclosed is an apparatus for use in wireless energy transfer, which includes a first resonator structure configured to transfer energy non-radiatively with a second resonator structure over a distance greater than a characteristic size of the second resonator structure. The non-radiative energy tra

Disclosed is an apparatus for use in wireless energy transfer, which includes a first resonator structure configured to transfer energy non-radiatively with a second resonator structure over a distance greater than a characteristic size of the second resonator structure. The non-radiative energy transfer is mediated by a coupling of a resonant field evanescent tail of the first resonator structure and a resonant field evanescent tail of the second resonator structure.

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What is claimed is: 1. An apparatus for use in wireless energy transfer, the apparatus comprising: a first resonator structure configured for energy transfer with a second resonator structure, over a distance D larger than a characteristic size L1 of said first resonator structure or larger than a

What is claimed is: 1. An apparatus for use in wireless energy transfer, the apparatus comprising: a first resonator structure configured for energy transfer with a second resonator structure, over a distance D larger than a characteristic size L1 of said first resonator structure or larger than a characteristic size L2 of said second resonator structure, wherein the energy transfer has a rate κ and is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, wherein said resonant field of the first resonator structure has a resonance angular frequency ω1, a resonance frequency-width Γ1, and a resonance quality factor Q1=ω1/2Γ1 at least larger than 100, and said resonant field of the second resonator structure has a resonance angular frequency ω2, a resonance frequency-width Γ2 , and a resonance quality factor Q2 =ω2/2Γ2 at least larger than 100, wherein the absolute value of the difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1, and Γ2. 2. The apparatus of claim 1, wherein the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 0.2. 3. The apparatus of claim 1, wherein D/L2 is at least larger than 1, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 0.5. 4. The apparatus of claim 1, wherein D/L2 is at least larger than 5, Q1 is at least larger than 200, Q2 is at least larger than 200, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 5. The apparatus of claim 1, wherein D/L2 is at least larger than 5, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 6. The apparatus of claim 1, wherein D/L2 is at least larger than 5, Q1 is at least larger than 300, Q2 is at least larger than 300, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 7. The apparatus of claim 1, wherein the quantity κ/√{square root over (Γ1Γ2)} is maximized at an angular frequency {tilde over (ω)} with a frequency width {tilde over (Γ)}, and the absolute value of the difference of the angular frequencies ω1 and {tilde over (ω)} is smaller than the width {tilde over (Γ)}, and the absolute value of the difference of the angular frequencies ω2 and {tilde over (ω)} is smaller than the width {tilde over (Γ)}. 8. The apparatus of claim 1, further comprising the second resonator structure. 9. The apparatus of claim 1, wherein a device coupled to the first or second resonator structure with a coupling rate Γwork receives from the resonator structure, to which it is coupled, a usable power Pwork at least larger than 0.03 Watt. 10. The apparatus of claim 9, wherein Pwork is at least larger than 1 Watt. 11. The apparatus of claim 9, wherein Pwork is at least larger than 30 Watt. 12. The apparatus of claim 9, wherein, if the device is coupled to the first resonator, the quantity [(Γwork/Γ1)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than 2, and if the device is coupled to the second resonator, the quantity [(Γwork /Γ2)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than 2. 13. The apparatus of claim 9, wherein the device comprises at least one of a robot, a mobile electronic device, a computer, a sensor, a vehicle, a medical device configured to be implanted in a patient, a television screen, a wireless keyboard, and a wireless mouse. 14. The apparatus of claim 9, further comprising the device. 15. The apparatus of claim 9, wherein, during operation, a power supply coupled to the first or second resonator structure with a coupling rate Γsupply drives the resonator structure, to which it is coupled, at a frequency f and supplies power Ptotal, wherein the absolute value of the difference of the angular frequencies ω=2π f and ω1 is smaller than the resonant width Γ1, and the absolute value of the difference of the angular frequencies ω=2π f and ω2 is smaller than the resonant width Γ2. 16. The apparatus of claim 15, wherein, if the power supply is coupled to the first resonator, the quantity [(Γsupply/Γ1)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than 2, and if the power supply is coupled to the second resonator, the quantity [(Γsupply/Γ2)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than 2. 17. The apparatus of claim 15, further comprising the power supply. 18. The apparatus of claim 15, wherein, during the energy exchange, power Prad is radiated and the radiation loss ηrad=Prad/Ptotal is less that 10%. 19. The apparatus of claim 15, wherein, during the energy exchange, power Prad is radiated and the radiation loss ηrad=Prad/Ptotal is less that 1%. 20. The apparatus of claim 1, wherein the resonant fields are electromagnetic. 21. The apparatus of claim 20, wherein f is at least larger than 100 kHz and smaller than 500 MHz. 22. The apparatus of claim 20, wherein f is at least larger than 1 MHz and smaller than 50 MHz. 23. The apparatus of claim 20, wherein f is within one of the frequency bands specially assigned for industrial, scientific, and medical (ISM) equipment. 24. The apparatus of claim 20, wherein the resonant fields are primarily magnetic at a distance Dp from the center of the closest resonant object, whose characteristic size is LR, and the ratio of the average electric field energy density to the average magnetic field energy density is smaller than 0.1 for Dp/LR less than 3. 25. The apparatus of claim 20, wherein the resonant fields are primarily magnetic at a distance Dp from the center of the closest resonant object, whose characteristic size is LR, and the ratio of the average electric field energy density to the average magnetic field energy density is smaller than 0.01 for Dp/LR less than 3. 26. The apparatus of claim 20, wherein at least one of the first and second resonator structures comprises a self resonant coil of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon. 27. The apparatus of claim 26, wherein the resonator structure receiving energy from the other resonator structure comprises a self resonant coil of conducting wire, wherein said coil is helical, the radius of said coil is about 10 cm, the height of said coil is about 3 cm, the number of turns of said coil is about 6, and the radius of said conducting wire is about 2 mm. 28. The apparatus of claim 26, wherein the resonator structure receiving energy from the other resonator structure comprises a self resonant coil of conducting wire, wherein said coil is helical, the radius of said coil is about 30 cm, the height of said coil is about 20 cm, the number of turns of said coil is about 5.25, and the radius of said conducting wire is about 3 mm. 29. The apparatus of claim 20, wherein at least one of the first and second resonator structures comprises a capacitively loaded loop or coil of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon. 30. The apparatus of claim 29, wherein the resonator structure receiving energy from the other resonator structure comprises a capacitively loaded loop of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said loop is less than 10 cm and the width of said conducting wire or Litz wire or ribbon is less than 1 cm. 31. The apparatus of claim 29, wherein the resonator structure receiving energy from the other resonator structure comprises a capacitively loaded loop of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said loop is less than 30 cm and the width of said conducting wire or Litz wire or ribbon is less than 5 cm. 32. The apparatus of claim 20, wherein at least one of the first and second resonator structures comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon. 33. The apparatus of claim 32, wherein the resonator structure receiving energy from the other resonator structure comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said rod is less than 10 cm and the width of said conducting wire or Litz wire or ribbon is less than 1 cm. 34. The apparatus of claim 32, wherein the resonator structure receiving energy from the other resonator structure comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said rod is less than 30 cm and the width of said conducting wire or Litz wire or ribbon is less than 5 cm. 35. The apparatus of claim 1, further comprising a feedback mechanism for maintaining the resonant frequency of one or more of the resonant objects. 36. The apparatus of claim 35, wherein the feedback mechanism comprises an oscillator with a fixed frequency and is configured to adjust the resonant frequency of the one or more resonant objects to be about equal to the fixed frequency. 37. The apparatus of claim 35, where the feedback mechanism is configured to monitor an efficiency of the energy transfer, and adjust the resonant frequency of the one or more resonant objects to maximize the efficiency. 38. An apparatus for use in wireless energy transfer, the apparatus comprising: a first resonator structure configured for energy transfer with a second resonator structure, over a distance D larger than a characteristic thickness T1 of said first resonator structure or larger than a characteristic size L2 of said second resonator structure, wherein the energy transfer has a rate κ and is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, wherein said resonant field of the first resonator structure has a resonance angular frequency ω1, a resonance frequency-width Γ1, and a resonance quality factor Q1=ω1/2Γ1 at least larger than 100, and said resonant field of the second resonator structure has a resonance angular frequency ω2, a resonance frequency-width Γ2, and a resonance quality factor Q2=ω2/2Γ2 at least larger than 100, wherein the absolute value of the difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1 and Γ2. 39. The apparatus of claim 38, wherein the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 0.2. 40. The apparatus of claim 38, wherein D/L2 is at least larger than 1, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 0.5. 41. The apparatus of claim 38, wherein D/L2 is at least larger than 5, Q1 is at least larger than 200, Q2 is at least larger than 200, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 42. The apparatus of claim 38, wherein D/L2 is at least larger than 5, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 43. The apparatus of claim 38, wherein D/L2 is at least larger than 5, Q1 is at least larger than 300, Q2 is at least larger than 300, and the quantity κ/√{square root over (Γ1Γ2)} is at least larger than 1. 44. The apparatus of claim 38, wherein the quantity κ/√{square root over (Γ1Γ2)} is maximized at an angular frequency {tilde over (ω)} with a frequency width {tilde over (Γ)}, and the absolute value of the difference of the angular frequencies ω1 and {tilde over (ω)} is smaller than the width {tilde over (Γ)}, and the absolute value of the difference of the angular frequencies ω2 and {tilde over (ω)} is smaller than the width {tilde over (Γ)}. 45. The apparatus of claim 38, further comprising the second resonator structure. 46. The apparatus of claim 38, wherein a device coupled to the first or second resonator structure with a coupling rate Γwork receives from the resonator structure, to which it is coupled, a usable power Pwork at least larger than 0.03 Watt. 47. The apparatus of claim 46, wherein Pwork is at least larger than 1 Watt. 48. The apparatus of claim 46, wherein Pwork is at least larger than 30 Watt. 49. The apparatus of claim 46, wherein, if the device is coupled to the first resonator, the quantity [(Γwork/Γ1)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than about 2, and if the device is coupled to the second resonator, the quantity [(Γwork/Γ2)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than about 2. 50. The apparatus of claim 46, wherein the device comprises at least one of a robot, a mobile electronic device, a computer, a sensor, a vehicle, a medical device configured to be implanted in a patient, a television screen, a wireless keyboard, and a wireless mouse. 51. The apparatus of claim 46, further comprising the device. 52. The apparatus of claim 46, wherein, during operation, a power supply coupled to the first or second resonator structure with a coupling rate Γsupply drives the resonator structure, to which it is coupled, at a frequency f and supplies power Ptotal, wherein the absolute value of the difference of the angular frequencies ω=2π f and ω1 is smaller than the resonant width Γ1, and the absolute value of the difference of the angular frequencies ω=2π f and ω2 is smaller than the resonant width Γ2. 53. The apparatus of claim 52, wherein, if the power supply is coupled to the first resonator, the quantity [(Γsupply/Γ1)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than about 2, and if the power supply is coupled to the second resonator, the quantity [(Γsupply/Γ2)2−1]/(κ/√{square root over (Γ1Γ2)})2 is at least larger than 0.5 and smaller than about 2. 54. The apparatus of claim 52, further comprising the power supply. 55. The apparatus of claim 52, wherein, during the energy exchange, power Prad is radiated and the radiation loss ηrad=Prad/Ptotal is less that 10%. 56. The apparatus of claim 52, wherein, during the energy exchange, power Prad is radiated and the radiation loss ηrad=Prad/Ptotal is less that 1%. 57. The apparatus of claim 38, wherein the resonant fields are electromagnetic. 58. The apparatus of claim 57, wherein f is at least larger than 100 kHz and smaller than 500 MHz. 59. The apparatus of claim 57, wherein f is at least larger than 1 MHz and smaller than 50 MHz. 60. The apparatus of claim 57, wherein f is within one of the frequency bands specially assigned for industrial, scientific and, medical (ISM) equipment. 61. The apparatus of claim 57, wherein the resonant fields are primarily magnetic at a distance Dp from the center of the closest resonant object, whose characteristic size is LR, and the ratio of the average electric field energy density to the average magnetic field energy density is smaller than about 0.1 for Dp/LR less than 3. 62. The apparatus of claim 57, wherein the resonant fields are primarily magnetic at a distance Dp from the center of the closest resonant object, whose characteristic size is LR, and the ratio of the average electric field energy density to the average magnetic field energy density is smaller than about 0.01 for Dp/LR less than 3. 63. The apparatus of claim 57, wherein at least one of the first and second resonator structures comprises a capacitively loaded loop or coil of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon. 64. The apparatus of claim 63, wherein the resonator structure receiving energy from the other resonator structure comprises a capacitively loaded loop of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said loop is less than 10 cm and the width of said conducting wire or Litz wire or ribbon is less than 1 cm. 65. The apparatus of claim 63, wherein the resonator structure receiving energy from the other resonator structure comprises a capacitively loaded loop of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said loop is less than 30 cm and the width of said conducting wire or Litz wire or ribbon is less than 5 cm. 66. The apparatus of claim 57, wherein at least one of the first and second resonator structures comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon. 67. The apparatus of claim 66, wherein the resonator structure receiving energy from the other resonator structure comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said rod is less than 10 cm and the width of said conducting wire or Litz wire or ribbon is less than 1 cm. 68. The apparatus of claim 66, wherein the resonator structure receiving energy from the other resonator structure comprises an inductively loaded rod of at least one of a conducting wire, a conducting Litz wire, and a conducting ribbon, wherein the characteristic size of said rod is less than 30 cm and the width of said conducting wire or Litz wire or ribbon is less than 5 cm. 69. The apparatus of claim 38, further comprising a feedback mechanism for maintaining the resonant frequency of one or more of the resonant objects. 70. The apparatus of claim 69, wherein the feedback mechanism comprises an oscillator with a fixed frequency and is configured to adjust the resonant frequency of the one or more resonant objects to be about equal to the fixed frequency. 71. The apparatus of claim 69, where the feedback mechanism is configured to monitor an efficiency of the energy transfer, and adjust the resonant frequency of the one or more resonant objects to maximize the efficiency. 72. A method for wireless energy transfer, the method comprising: providing a first resonator structure and transferring energy with a second resonator structure, over a distance D larger than a characteristic size L1 of said first resonator structure or larger than a characteristic size L2 of said second resonator structure, wherein the energy transfer has a rate κ and is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, wherein said resonant field of the first resonator structure has a resonance angular frequency ω1, a resonance frequency-width Γ1, and a resonance quality factor Q1=ω1/2Γ1 at least larger than 100, and said resonant field of the second resonator structure has a resonance angular frequency ω2, a resonance frequency-width Γ2, and a resonance quality factor Q2=ω2/2Γ2 at least larger than 100, wherein the absolute value of the difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1 and Γ2. 73. A method for wireless energy transfer, the method comprising: providing a first resonator structure and transferring energy with a second resonator structure, over a distance D larger than a characteristic thickness T1 of said first resonator structure or larger than a characteristic size L2 of said second resonator structure, wherein the energy transfer has a rate κ and is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, wherein said resonant field of the first resonator structure has a resonance angular frequency ω1, a resonance frequency-width Γ1, and a resonance quality factor Q1=ω1/2Γ1 at least larger than 100, and said resonant field of the second resonator structure has a resonance angular frequency ω2, a resonance frequency-width Γ2 , and a resonance quality factor Q2=ω2/2Γ2 at least larger than 100, wherein the absolute value of the difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1 and Γ2. 74. The apparatus of claim 1, further comprising: a third resonator structure configured to transfer energy non-radiatively with one or more of the first and second resonator structures, wherein the non-radiative energy transfer between the third resonator structure and the one or more of the first and second resonator structures is mediated by a coupling of the resonant field evanescent tail of the one or more of the first and second resonator structures and a resonant field evanescent tail of the third resonator structure. 75. The apparatus of claim 74, wherein the third resonator structure is configured to wirelessly receive energy from one of the first and second resonator structures and wirelessly transfer energy to the other one of the first and second resonator structures to cause the energy transfer between the first and second resonator structures. 76. The apparatus of claim 38, further comprising: a third resonator structure configured to transfer energy non-radiatively with one or more of the first and second resonator structures, wherein the non-radiative energy transfer between the third resonator structure and the one or more of the first and second resonator structures is mediated by a coupling of the resonant field evanescent tail of the one or more of the first and second resonator structures and a resonant field evanescent tail of the third resonator structure. 77. The apparatus of claim 76, wherein the third resonator structure is configured to wirelessly receive energy from one of the first and second resonator structures and wirelessly transfer energy to the other one of the first and second resonator structures to cause the energy transfer between the first and second resonator structures. 78. The method of claim 72, wherein the energy transfer between the first and second resonator structures involves a third resonator structure that wirelessly receives energy from one of the first and second resonator structures and wirelessly transfers energy to the other one of the first and second resonator structures. 79. The method of claim 73, wherein the energy transfer between the first and second resonator structures involves a third resonator structure that wirelessly receives energy from one of the first and second resonator structures and wirelessly transfers energy to the other one of the first and second resonator structures.