Wireless energy transfer, including interference enhancement

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 and 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,
• and wherein for a desired range of the distances D, the resonance angular frequencies for the resonator structures increase transmission efficiency T by accounting for radiative interference, wherein the increase is relative to a transmission efficiency T calculated without accounting for the radiative interference.

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,
• wherein the energy transfer is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, with a coupling factor k, 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, and is radiative in the far field, with an associated radiation quality factor Q1,rad≧Q1, 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 and is radiative in the far field, with an associated radiation quality factor Q2,rad≧Q2,
• wherein an absolute value of a difference of said angular frequencies ω1 and ω2 is smaller than broader of said resonant widths Γ1 and Γ2, and a strong-coupling factor being defined as U=k√{square root over (Q1Q2)},
• wherein the apparatus is configured to employ interference between said radiative far fields of the resonant fields of the first and second resonator, with an interference factor Vrad, to reduce a total amount of radiation from the apparatus compared to an amount of radiation from the apparatus in the absence of interference, a strong-interference factor being defined as V=Vrad√{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}.

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,
• wherein the energy transfer is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, with a coupling factor k, 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, and is radiative in the far field, with an associated radiation quality factor Q1,rad≧Q1, 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, and is radiative in the far field, with an associated radiation quality factor Q2,rad≧Q2,
• wherein an absolute value of a difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1 and Γ2, and an average resonant angular frequency is defined as ωo=√{square root over (ω1ω2)}, corresponding to an average resonant wavelength λo=2πc/ωo, where c is the speed of light in free space, and a strong-coupling factor is defined as U=k√{square root over (Q1Q2)},
• wherein the apparatus is configured to employ interference between said radiative far fields of the resonant fields of the first and second resonator, with an interference factor Vrad, to increase efficiency of energy transfer for the apparatus compared to efficiency for the apparatus in the absence of interference, the strong-interference factor being defined as V=Vrad√{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}.

A method for wireless energy transfer, the method comprising:

• providing a first resonator structure configured for energy transfer with a second resonator structure over a distance D,
• wherein the energy transfer is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, with a coupling factor k, 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, and is radiative in the far field, with an associated radiation quality factor Q1,rad≧Q1, 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, and is radiative in the far field, with an associated radiation quality factor Q2,rad≧Q2,
• wherein an absolute value of a difference of said angular frequencies ω1 and ω2 is smaller than broader of said resonant widths Γ1 and Γ2, and the strong-coupling factor is defined as U=k√{square root over (Q1Q2)}, and
• employing interference between said radiative far fields of the resonant fields of the first and second resonator, with an interference factor Vrad, to reduce a total amount of radiation from the first and second resonator compared to an amount of radiation from the first and second resonator in the absence of interference, a strong-interference factor being defined as V=Vrad√{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}.

A method for wireless energy transfer, the method comprising:

• providing a first resonator structure configured for energy transfer with a second resonator structure over a distance D,
• wherein the energy transfer is mediated by evanescent-tail coupling of a resonant field of the first resonator structure and a resonant field of the second resonator structure, with a coupling factor k, 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, and is radiative in the far field, with an associated radiation quality factor Q1,rad≧Q1, 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, and is radiative in the far field, with an associated radiation quality factor Q2,rad≧Q2,
• wherein an absolute value of the difference of said angular frequencies ω1 and ω2 is smaller than the broader of said resonant widths Γ1 and Γ2 , and an average resonant angular frequency is defined as ωo=√{square root over (ω1ω2)}, corresponding to an average resonant wavelength λo=2πc/ωo, where c is the speed of light in free space, and the strong-coupling factor is defined as U=k√{square root over (Q1Q2)}, and
• employing interference between said radiative far fields of the resonant fields of the first and second resonator, with an interference factor Vrad, to increase efficiency of energy transfer between the first and second resonator compared to efficiency of energy transfer between the first and second resonator in the absence of interference, a strong-interference factor being defined as V=Vrad√{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}{square root over ((Q1/Q1,rad)(Q2/Q2,rad))}.