Abstract

We present a methodology based on quantum mechanics for assigning quantum conductivity when an ac field is applied across a variable gap between two plasmonic nanoparticles with an insulator sandwiched between them. The quantum tunneling effect is portrayed by a set of quantum conductivity coefficients describing the linear ac conductivity responding at the frequency of the applied field, and nonlinear coefficients that modulate the field amplitude at the fundamental frequency and its harmonics. The quantum conductivity, determined with no fit parameters, has both frequency and gap dependence that can be applied to determine the nonlinear quantum effects of strong applied electromagnetic fields, even when the system is composed of dissimilar metal nanostructures. Our methodology compares well to results on quantum tunneling effects reported in the literature, and is simple to extend to a number of systems with different metals and different insulators between them.

© 2014 Optical Society of America

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2013 (4)

2012 (9)

S. Grover and G. Moddel, “Engineering the current–voltage characteristics of metal–insulator–metal diodes using double-insulator tunnel barriers,” Solid-State Electron. 67, 94–99 (2012).
[CrossRef]

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D 45, 433001 (2012).
[CrossRef]

N. C. Nyquist, P. Nagpal, K. M. McPeak, D. J. Norris, and S.-H. Oh, “Engineering metallic nanostructures for plasmonics and nanophotonics,” Rep. Prog. Phys. 75, 036501 (2012).
[CrossRef]

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012).

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[CrossRef]

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

2011 (2)

N. J. Halas, L. Surbhi, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

S. Grover and G. Moddel, “Applicability of metal/insulator/metal (MIM) diodes to solar rectennas,” IEEE J. Photovolt. 1, 78–83 (2011).
[CrossRef]

2010 (7)

M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, “Solar spectrum rectification using nano-antennas and tunneling diodes,” Proc. SPIE 7605, 76050E (2010).
[CrossRef]

S. Bhansali, S. Krishnan, E. Stefanakos, and D. Y. Goswami, “Tunneling junction based rectenna—a key to ultrahigh efficiency solar/thermal energy conversion,” AIP Conf. Proc. 1313, 79–83 (2010).

S. Grover, O. Dmitriyeva, M. J. Estes, and G. Moddel, “Traveling-wave metal/insulator/metal diodes for improved infrared bandwidth and efficiency of antenna coupled rectifiers,” IEEE Trans. Nanotechnol. 9, 716–722 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

R. Alvarez-Puebla, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Light concentration at the nanometer scale,” J. Phys. Chem. Lett. 1, 2428–2434 (2010).
[CrossRef]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
[CrossRef]

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4, 5269–5276 (2010).
[CrossRef]

2009 (3)

2008 (2)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

2007 (2)

M. L. Brongersma, R. Zia, and J. A. Schuller, “Plasmonics—the missing link between nanoelectronics and microphotonics,” J. Appl. Phys. A 89, 221–223 (2007).
[CrossRef]

P. C. Hobbs, R. B. Laibowitz, F. R. Libsch, N. C. LaBianca, and P. P. Chiniwalla, “Efficient waveguide-integrated tunnel junction detectors at 1.6 μm,” Opt. Express 15, 16376–16389 (2007).
[CrossRef]

2004 (2)

M. R. Abdel-Rahman, F. J. Gonzalez, G. Zummo, C. F. Middleton, and G. D. Boreman, “Antenna-coupled MOM diodes for dual-band detection in MMW and LWIR,” Proc. SPIE 5410, 238 (2004).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

2003 (1)

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003).

2002 (1)

J. Robertson, “Band offsets of high dielectric constant gate oxides on silicon,” J. Non-Cryst. Solids 303, 94–100 (2002).
[CrossRef]

1998 (1)

C. Fumeaux, W. Herrmann, F. K. Kneubühl, and H. Rothuizen, “Nanometer thin-film Ni–NiO–Ni diodes for detection and mixing of 30 THz radiation,” Infrared Phys. Technol. 39, 123–183 (1998).
[CrossRef]

1985 (1)

J. R. Tucker and M. J. Feldman, “Quantum detection at millimeter wavelengths,” Rev. Mod. Phys. 57, 1055–1113 (1985).
[CrossRef]

1979 (1)

J. R. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[CrossRef]

1978 (2)

J. R. Tucker and M. F. Millea, “Photon detection in nonlinear tunneling devices,” Appl. Phys. Lett. 33, 611–613 (1978).
[CrossRef]

A. Sanchez, C. F. Davis, K. C. Liu, and A. Javan, “The MOM tunneling diode: Theoretical estimate of its performance at microwave and infrared frequencies,” J. Appl. Phys. 49, 5270–5277 (1978).
[CrossRef]

1972 (1)

M. Nagae, “Response time of metal-insulator-metal tunnel junctions,” Jpn. J. Appl. Phys. 11, 1611–1621 (1972).
[CrossRef]

1971 (1)

R. J. Whitefield and J. J. Brady, “New value for work function of sodium and the observation of surface-plasmon effects,” Phys. Rev. Lett. 26, 380–383 (1971). Erratum: Phys. Rev. Lett. 26, 1005 (1971).
[CrossRef]

1968 (1)

L. O. Hocker, D. R. Sokoloff, V. Daneu, and A. Javan, “Frequency mixing in the infrared and far-infrared using a metal-to-metal point contact diode,” Appl. Phys. 12, 401–402 (1968).

1964 (1)

W. Tantraporn, “Electron current through metal-insulator-metal sandwiches,” Solid-State Electron. 7, 81–91 (1964).
[CrossRef]

1963 (3)

J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
[CrossRef]

J. G. Simmons, “Electric tunnel effect between dissimilar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 2581–2590 (1963).
[CrossRef]

P. K. Tien and J. P. Gordon, “Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films,” Phys. Rev. 129, 647–651 (1963).
[CrossRef]

Abdel-Rahman, M. R.

M. R. Abdel-Rahman, F. J. Gonzalez, G. Zummo, C. F. Middleton, and G. D. Boreman, “Antenna-coupled MOM diodes for dual-band detection in MMW and LWIR,” Proc. SPIE 5410, 238 (2004).
[CrossRef]

Aizpurua, J.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum effects and nonlocality in strongly coupled plasmonic nanowire dimers,” Opt. Express 21, 27306–27325 (2013).
[CrossRef]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012).

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[CrossRef]

Aközbek, N.

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Alù, A.

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Alvarez-Puebla, R.

R. Alvarez-Puebla, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Light concentration at the nanometer scale,” J. Phys. Chem. Lett. 1, 2428–2434 (2010).
[CrossRef]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Aubry, A.

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
[CrossRef]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003).

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design (Wiley, 2005).

Bhansali, S.

S. Bhansali, S. Krishnan, E. Stefanakos, and D. Y. Goswami, “Tunneling junction based rectenna—a key to ultrahigh efficiency solar/thermal energy conversion,” AIP Conf. Proc. 1313, 79–83 (2010).

Bharadwaj, P.

Biagioni, P.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

Bianco, G. V.

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Bloemer, M.

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Boreman, G. D.

M. R. Abdel-Rahman, F. J. Gonzalez, G. Zummo, C. F. Middleton, and G. D. Boreman, “Antenna-coupled MOM diodes for dual-band detection in MMW and LWIR,” Proc. SPIE 5410, 238 (2004).
[CrossRef]

Borisov, A. G.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum effects and nonlocality in strongly coupled plasmonic nanowire dimers,” Opt. Express 21, 27306–27325 (2013).
[CrossRef]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012).

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[CrossRef]

Boscolo, S.

Bozhevolnyi, S. I.

Z. Han and S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

Brady, J. J.

R. J. Whitefield and J. J. Brady, “New value for work function of sodium and the observation of surface-plasmon effects,” Phys. Rev. Lett. 26, 380–383 (1971). Erratum: Phys. Rev. Lett. 26, 1005 (1971).
[CrossRef]

Brongersma, M. L.

M. L. Brongersma, R. Zia, and J. A. Schuller, “Plasmonics—the missing link between nanoelectronics and microphotonics,” J. Appl. Phys. A 89, 221–223 (2007).
[CrossRef]

Bruno, G.

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Capobianco, A.-D.

Chang, W.-S.

N. J. Halas, L. Surbhi, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

Chilkoti, A.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Chiniwalla, P. P.

Choi, K.

M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, “Solar spectrum rectification using nano-antennas and tunneling diodes,” Proc. SPIE 7605, 76050E (2010).
[CrossRef]

Chryssis, A. N.

M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, “Solar spectrum rectification using nano-antennas and tunneling diodes,” Proc. SPIE 7605, 76050E (2010).
[CrossRef]

Ciraci, C.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

D’Aguanno, G.

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[CrossRef]

Sokoloff, D. R.

L. O. Hocker, D. R. Sokoloff, V. Daneu, and A. Javan, “Frequency mixing in the infrared and far-infrared using a metal-to-metal point contact diode,” Appl. Phys. 12, 401–402 (1968).

Someda, C. G.

Stefanakos, E.

S. Bhansali, S. Krishnan, E. Stefanakos, and D. Y. Goswami, “Tunneling junction based rectenna—a key to ultrahigh efficiency solar/thermal energy conversion,” AIP Conf. Proc. 1313, 79–83 (2010).

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Stomeo, T.

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Surbhi, L.

N. J. Halas, L. Surbhi, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

Tantraporn, W.

W. Tantraporn, “Electron current through metal-insulator-metal sandwiches,” Solid-State Electron. 7, 81–91 (1964).
[CrossRef]

Teperik, T. V.

Tien, P. K.

P. K. Tien and J. P. Gordon, “Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films,” Phys. Rev. 129, 647–651 (1963).
[CrossRef]

Trimm, R.

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Tucker, J. R.

J. R. Tucker and M. J. Feldman, “Quantum detection at millimeter wavelengths,” Rev. Mod. Phys. 57, 1055–1113 (1985).
[CrossRef]

J. R. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[CrossRef]

J. R. Tucker and M. F. Millea, “Photon detection in nonlinear tunneling devices,” Appl. Phys. Lett. 33, 611–613 (1978).
[CrossRef]

Urzhumov, Y.

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Van Duyne, R. P.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Vincenti, M.

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Vincenti, M. A.

M. Scalora, M. A. Vincenti, D. de Ceglia, M. Grande, and J. W. Haus, “Spontaneous and stimulated Raman scattering near metal nanostructures in the ultrafast, high-intensity regime,” J. Opt. Soc. Am. B 30, 2634–2639 (2013).
[CrossRef]

J. W. Haus, L. Li, N. Katte, C. Deng, M. Scalora, D. de Ceglia, and M. A. Vincenti, “Nanowire metal-insulator-metal plasmonic devices,” Proc. SPIE 8883, 888303 (2013).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Whitefield, R. J.

R. J. Whitefield and J. J. Brady, “New value for work function of sodium and the observation of surface-plasmon effects,” Phys. Rev. Lett. 26, 380–383 (1971). Erratum: Phys. Rev. Lett. 26, 1005 (1971).
[CrossRef]

Yesilkoy, F.

M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, “Solar spectrum rectification using nano-antennas and tunneling diodes,” Proc. SPIE 7605, 76050E (2010).
[CrossRef]

Zhao, J.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

Zia, R.

M. L. Brongersma, R. Zia, and J. A. Schuller, “Plasmonics—the missing link between nanoelectronics and microphotonics,” J. Appl. Phys. A 89, 221–223 (2007).
[CrossRef]

Zuloaga, J.

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4, 5269–5276 (2010).
[CrossRef]

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef]

Zummo, G.

M. R. Abdel-Rahman, F. J. Gonzalez, G. Zummo, C. F. Middleton, and G. D. Boreman, “Antenna-coupled MOM diodes for dual-band detection in MMW and LWIR,” Proc. SPIE 5410, 238 (2004).
[CrossRef]

ACS Nano (1)

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum plasmonics: optical properties and tunability of metallic nanorods,” ACS Nano 4, 5269–5276 (2010).
[CrossRef]

Adv. Opt. Photon. (1)

AIP Conf. Proc. (1)

S. Bhansali, S. Krishnan, E. Stefanakos, and D. Y. Goswami, “Tunneling junction based rectenna—a key to ultrahigh efficiency solar/thermal energy conversion,” AIP Conf. Proc. 1313, 79–83 (2010).

Appl. Phys. (1)

L. O. Hocker, D. R. Sokoloff, V. Daneu, and A. Javan, “Frequency mixing in the infrared and far-infrared using a metal-to-metal point contact diode,” Appl. Phys. 12, 401–402 (1968).

Appl. Phys. Lett. (2)

J. R. Tucker and M. F. Millea, “Photon detection in nonlinear tunneling devices,” Appl. Phys. Lett. 33, 611–613 (1978).
[CrossRef]

M. Grande, G. V. Bianco, M. A. Vincenti, T. Stomeo, D. de Ceglia, M. De Vittorio, V. Petruzzelli, M. Scalora, G. Bruno, and A. D’Orazio, “Experimental surface-enhanced Raman scattering response of two-dimensional finite arrays of gold nanopatches,” Appl. Phys. Lett. 101, 111606 (2012).
[CrossRef]

Chem. Rev. (1)

N. J. Halas, L. Surbhi, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled nanostructures,” Chem. Rev. 111, 3913–3961 (2011).
[CrossRef]

IEEE J. Photovolt. (1)

S. Grover and G. Moddel, “Applicability of metal/insulator/metal (MIM) diodes to solar rectennas,” IEEE J. Photovolt. 1, 78–83 (2011).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. R. Tucker, “Quantum limited detection in tunnel junction mixers,” IEEE J. Quantum Electron. QE-15, 1234–1258 (1979).
[CrossRef]

IEEE Trans. Nanotechnol. (1)

S. Grover, O. Dmitriyeva, M. J. Estes, and G. Moddel, “Traveling-wave metal/insulator/metal diodes for improved infrared bandwidth and efficiency of antenna coupled rectifiers,” IEEE Trans. Nanotechnol. 9, 716–722 (2010).
[CrossRef]

Infrared Phys. Technol. (1)

C. Fumeaux, W. Herrmann, F. K. Kneubühl, and H. Rothuizen, “Nanometer thin-film Ni–NiO–Ni diodes for detection and mixing of 30 THz radiation,” Infrared Phys. Technol. 39, 123–183 (1998).
[CrossRef]

J. Appl. Phys. (3)

A. Sanchez, C. F. Davis, K. C. Liu, and A. Javan, “The MOM tunneling diode: Theoretical estimate of its performance at microwave and infrared frequencies,” J. Appl. Phys. 49, 5270–5277 (1978).
[CrossRef]

J. G. Simmons, “Generalized formula for the electric tunnel effect between similar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 1793–1803 (1963).
[CrossRef]

J. G. Simmons, “Electric tunnel effect between dissimilar electrodes separated by a thin insulating film,” J. Appl. Phys. 34, 2581–2590 (1963).
[CrossRef]

J. Appl. Phys. A (1)

M. L. Brongersma, R. Zia, and J. A. Schuller, “Plasmonics—the missing link between nanoelectronics and microphotonics,” J. Appl. Phys. A 89, 221–223 (2007).
[CrossRef]

J. Non-Cryst. Solids (1)

J. Robertson, “Band offsets of high dielectric constant gate oxides on silicon,” J. Non-Cryst. Solids 303, 94–100 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. Lett. (1)

R. Alvarez-Puebla, L. M. Liz-Marzan, and F. J. Garcia de Abajo, “Light concentration at the nanometer scale,” J. Phys. Chem. Lett. 1, 2428–2434 (2010).
[CrossRef]

J. Phys. D (1)

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D 45, 433001 (2012).
[CrossRef]

Jpn. J. Appl. Phys. (1)

M. Nagae, “Response time of metal-insulator-metal tunnel junctions,” Jpn. J. Appl. Phys. 11, 1611–1621 (1972).
[CrossRef]

Nano Lett. (3)

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339 (2012).

J. Zuloaga, E. Prodan, and P. Nordlander, “Quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9, 887–891 (2009).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4, 899–903 (2004).
[CrossRef]

Nat. Commun. (1)

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[CrossRef]

Nat. Mater. (2)

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7, 442–453 (2008).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Nature (1)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453, 757–760 (2008).
[CrossRef]

Opt. Commun. (1)

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, “Optical properties of two interacting gold nanoparticles,” Opt. Commun. 220, 137–141 (2003).

Opt. Express (3)

Phys. Rev. (1)

P. K. Tien and J. P. Gordon, “Multiphoton process observed in the interaction of microwave fields with the tunneling between superconductor films,” Phys. Rev. 129, 647–651 (1963).
[CrossRef]

Phys. Rev. B (1)

N. Aközbek, N. Mattiucci, D. de Ceglia, R. Trimm, A. Alù, G. D’Aguanno, M. Vincenti, M. Scalora, and M. Bloemer, “Experimental demonstration of plasmonic Brewster angle extraordinary transmission through extreme subwavelength slit arrays in the microwave,” Phys. Rev. B 85, 205430 (2012).
[CrossRef]

Phys. Rev. Lett. (2)

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Interaction between plasmonic nanoparticles revisited with transformation optics,” Phys. Rev. Lett. 105, 233901 (2010).
[CrossRef]

R. J. Whitefield and J. J. Brady, “New value for work function of sodium and the observation of surface-plasmon effects,” Phys. Rev. Lett. 26, 380–383 (1971). Erratum: Phys. Rev. Lett. 26, 1005 (1971).
[CrossRef]

Proc. SPIE (3)

M. Dagenais, K. Choi, F. Yesilkoy, A. N. Chryssis, and M. C. Peckerar, “Solar spectrum rectification using nano-antennas and tunneling diodes,” Proc. SPIE 7605, 76050E (2010).
[CrossRef]

J. W. Haus, L. Li, N. Katte, C. Deng, M. Scalora, D. de Ceglia, and M. A. Vincenti, “Nanowire metal-insulator-metal plasmonic devices,” Proc. SPIE 8883, 888303 (2013).
[CrossRef]

M. R. Abdel-Rahman, F. J. Gonzalez, G. Zummo, C. F. Middleton, and G. D. Boreman, “Antenna-coupled MOM diodes for dual-band detection in MMW and LWIR,” Proc. SPIE 5410, 238 (2004).
[CrossRef]

Rep. Prog. Phys. (3)

N. C. Nyquist, P. Nagpal, K. M. McPeak, D. J. Norris, and S.-H. Oh, “Engineering metallic nanostructures for plasmonics and nanophotonics,” Rep. Prog. Phys. 75, 036501 (2012).
[CrossRef]

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys. 75, 024402 (2012).
[CrossRef]

Z. Han and S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76, 016402 (2013).
[CrossRef]

Rev. Mod. Phys. (1)

J. R. Tucker and M. J. Feldman, “Quantum detection at millimeter wavelengths,” Rev. Mod. Phys. 57, 1055–1113 (1985).
[CrossRef]

Science (1)

C. Ciraci, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernandez-Dominguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337, 1072–1074 (2012).
[CrossRef]

Solid-State Electron. (2)

S. Grover and G. Moddel, “Engineering the current–voltage characteristics of metal–insulator–metal diodes using double-insulator tunnel barriers,” Solid-State Electron. 67, 94–99 (2012).
[CrossRef]

W. Tantraporn, “Electron current through metal-insulator-metal sandwiches,” Solid-State Electron. 7, 81–91 (1964).
[CrossRef]

Other (4)

H. Kroemer, Quantum Mechanics, 3rd ed. (Prentice-Hall, 1994).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988), Vol. 111.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

C. A. Balanis, Antenna Theory: Analysis and Design (Wiley, 2005).

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Figures (12)

Fig. 1.
Fig. 1.

Illustration of the potential barrier in the MIM structure. In equilibrium, the Fermi energy is the same in both metals. The application of an external voltage depresses the Fermi energy in one metal from its equilibrium value.

Fig. 2.
Fig. 2.

Illustration of two potential functions. The potential labeled with the dashed (brown) curve includes the image potential [37,38]. The potential plotted with the solid line (blue) is the form without the image charge for comparison.

Fig. 3.
Fig. 3.

Maps of the logarithm (base 10) of the tunneling unilluminated current versus applied voltage and gap thickness for three cases: (a) Au/vacuum/Au, (b) Au/SiO2/Au, and (c) Au/TiO2/Au (Right). The minimum gap is 0.2 nm.

Fig. 4.
Fig. 4.

Maps of the logarithm (base 10) of the linear ac conductivity σω(1) versus applied voltage and gap thickness for three cases: (a) Au/vacuum/Au, (b) Au/SiO2/Au, and (c) Au/TiO2/Au. The units of the linear conductivity are S/m.

Fig. 5.
Fig. 5.

Maps of the logarithm (base 10) of the nonlinear TPA conductivity σω(3) versus applied voltage and gap thickness for three cases: (a) Au/vacuum/Au, (b) Au/SiO2/Au, and (c) Au/TiO2/Au. The units of the nonlinear conductivity are Sm/V2.

Fig. 6.
Fig. 6.

Maps of the logarithm (base 10) of the third-harmonic conductivity σ3ω versus applied voltage and gap thickness for three cases: (a) Au/vacuum/Au, (b) Au/SiO2/Au, and (c) Au/TiO2/Au. The units of the nonlinear conductivity are Sm/V2.

Fig. 7.
Fig. 7.

Field enhancement map for gold 3D cylinder dimers with a vacuum gap: (a) Cylindrical, center-fed nanoantenna geometry, (b) classical electromagnetic model, and (c) QCT applied to the vacuum gap.

Fig. 8.
Fig. 8.

Enhanced field maps for gold 2D dimer cylinders embedded in vacuum. The cylinder radii are 10 nm. (a) Illustration of a simple method for assigning linear and nonlinear conductivities in the gap region. The quantum conductivity values are assigned along a straight line connecting the cylinders, and the length of the line is set to the corresponding gap parameter. The current is viewed as flowing along the lines, connecting the two particles so that thicker arrows show greater current flow that tapers off at the edges due to the lower conductivity. (b) Map of the field enhancement using the classical approach. (c) Field enhancement map using QCT. The minimum gap separation is 0.2 nm.

Fig. 9.
Fig. 9.

Enhanced field maps for gold 2D dimer cylinders embedded in silica. (a) Field enhancement using classical approach. (b) Field enhancement using QCT. The cylinder radii are 10 nm.

Fig. 10.
Fig. 10.

Enhanced field maps for gold 2D dimer cylinders embedded in TiO2. (a) Field enhancement using classical approach. (b) Field enhancement using QCT. The cylinder radii are 10 nm.

Fig. 11.
Fig. 11.

Maps of the logarithm (base 10) of several physical quantities for a Na–Vacuum–Na dimer. (a) Tunneling current. (b) Linear ac conductivity. (c) Nonlinear TPA conductivity. (d) Nonlinear THG conductivity.

Fig. 12.
Fig. 12.

Enhanced field maps for sodium dimer cylinders using the quantum conductivity model. (a) Field enhancement using the linear ac quantum conductivity term. The red arrow in the inset shows the electric field polarization of the input plane wave. (b) Field enhancement adding the nonlinear conductivity term σω(3). The applied field irradiance is 1GW/cm2.

Tables (2)

Tables Icon

Table 1. Selected Material Property Values for Metals and Insulators [40]

Tables Icon

Table 2. Summary of Field Enhancement Maxima (FEmax) Data Extracted from the Maps in the Selected Figures

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

Eψ=22m2ψ+V(x,y,z)ψ.
V(x,y,z)=Vmaterial(x,y,z)+Vimage(x,y,z).
φ=WΦ.
Vimage(x,y,z)=e24πKε0[12z+n=1(nd(nd)2z21nd)]1.15ln2e2d8πKε0z(dz),
Jdc(eV¯d)=4πemh30dEzT(Ez)Ez(f(E)f(E+eV¯d))dE,
f(E)=1e(EEF)/kBT+1,
ψ(t)=eiV(t)dt/ψ0(t),
U(t)=eiV(t)dt/,
U(t)=U0UP=eieV¯dt/(V¯ωV¯ω*)/2ωe(V¯ωeiωtV¯ω*eiωt)/2ω.
J(t)=Im{dωdωW(ω)W(ω)ei(ωω)tj(ω+eV¯d)},
Jdc(ω+eV¯d)=Im{j(ω+eV¯d)}.
Up(t)=dωW(ω)eiωt,
W(ω)=n=Jn(α)einϕδ(ωnω).
V¯ω=Eωd,
J(t)=m=0(Jmω2eimωt+c.c.)=Re{dωdωW(ω)W(ω)ei(ωω)tJdc(ω+eV¯d)}.
Jrect=n=Jn2(α)Jdc(nω+eV¯d),
Jmω=n=Jn(α)[Jn+m(α)+Jnm(α)]eimϕJdc(nω+eV¯d).
Jrect=J02(α)Jdc(eV¯d)+J12(α)(Jdc(ω+eV¯d)+Jdc(ω+eV¯d))(1α22)Jdc(eV¯d)+α24(Jdc(ω+eV¯d)+Jdc(ω+eV¯d)).
Jω={J1(α)(J2(α)+J0(α))(Jdc(ω+eV¯d)Jdc(ω+eV¯d))+J1(α)J2(α)(Jdc(2ω+eV¯d)Jdc(2ω+eV¯d))}eiφ{α2(1α28)(1+O(α)4)(Jdc(ω+eV¯d)Jdc(ω+eV¯d))+α2(α24)(Jdc(2ω+eV¯d)Jdc(2ω+eV¯d))}eiφαeiφ2(Jdc(ω+eV¯d)Jdc(ω+eV¯d))+αeiφ2(α28)(2Jdc(2ω+eV¯d)2Jdc(2ω+eV¯d)Jdc(ω+eV¯d)+Jdc(ω+eV¯d)).
J2ω={2J0(α)J2(α)Jdc(eV¯d)+J1(α)(J3(α)J1(α))(Jdc(ω+eV¯d)+Jdc(ω+eV¯d))+J2(α)(J4(α)+J0(α))(Jdc(2ω+eV¯d)+Jdc(2ω+eV¯d))}ei2φ{α24Jdc(eV¯d)α24(Jdc(ω+eV¯d)+Jdc(ω+eV¯d))+α28(Jdc(2ω+eV¯d)+Jdc(2ω+eV¯d))}ei2φ
J3ω={J1(α)(J4(α)+J2(α))(Jdc(ω+eV¯d)Jdc(ω+eV¯d))+J2(α)(J5(α)J1(α))(Jdc(2ω+eV¯d)Jdc(2ω+eV¯d))+J3(α)(J6(α)+J0(α))(Jdc(3ω+eV¯d)Jdc(3ω+eV¯d))}ei3φ{α2α28(Jdc(ω+eV¯d)Jdc(ω+eV¯d))α28α2(Jdc(2ω+eV¯d)Jdc(2ω+eV¯d))+α348(Jdc(3ω+eV¯d)Jdc(3ω+eV¯d))}ei3φ.
Jrect=Jdc(eV¯d)+σ0(2)|Eω|2,Jω=σω(1)Eω+σω(3)|Eω|2Eω,J2ω=σ2ωEω2,J3ω=σ3ωEω3.
σ0(2)=(ed2ω)2(Jdc(ω+eV¯d)+Jdc(ω+eV¯d)2Jdc(eV¯d)),σω(1)=(ed2ω)(Jdc(ω+eV¯d)Jdc(ω+eV¯d)),σω(3)=12(ed2ω)3(2Jdc(2ω+eV¯d)2Jdc(2ω+eV¯d)Jdc(ω+eV¯d)+Jdc(ω+eV¯d)),σ2ω=(ed2ω)2(Jdc(eV¯d)(Jdc(ω+eV¯d)+Jdc(ω+eV¯d))+12(Jdc(2ω+eV¯d)+Jdc(2ω+eV¯d)),σ3ω=12(ed2ω)3((Jdc(ω+eV¯d)Jdc(ω+eV¯d))(Jdc(2ω+eV¯d)Jdc(2ω+eV¯d))+13(Jdc(3ω+eV¯d)Jdc(3ω+eV¯d))).
××Ek02ε¯¯·E=0,
Leff=1I0L/2L/2I(z)dz,

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