Abstract

We suggest a plasmonic nanodevice for performing the second-order spatial derivative of light fields. The device consists of five gold nanorods arranged to evanescently couple to each other so that emit cross-polarized output proportional to the second-order differentiation of the incident wave. A theoretical model based on the electrostatic eigenmode analysis is derived and numerical simulations using the finite-difference time-domain methods are provided as supporting evidence. It is shown in both the analytic and numerical methods that the proposed plasmonic circuit performs second-order differentiation of the phase of the incident light field in transmission mode with a subwavelength planar resolution. The resolution of 0.29 λ−1 is numerically demonstrated for a 20 nm thick circuit at the wavelength of 700 nm. The suggested plasmonic device has potential application in miniaturized systems for all-optical computation.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
  5. Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2017 (7)

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

T. Davis and D. Gómez, “Colloquium: An algebraic model of localized surface plasmons and their interactions,” Rev. Mod. Phys. 89, 011003 (2017).
[Crossref]

Y. Fang, Y. Lou, and Z. Ruan, “On-grating graphene surface plasmons enabling spatial differentiation in the terahertz region,” Opt. Lett. 42, 3840–3843 (2017).
[Crossref] [PubMed]

W. Wu, W. Jiang, J. Yang, S. Gong, and Y. Ma, “Multilayered analog optical differentiating device: performance analysis on structural parameters,” Opt. Lett. 42, 5270–5273 (2017).
[Crossref] [PubMed]

2016 (3)

Y. Hwang and T. J. Davis, “Optical metasurfaces for subwavelength difference operations,” Appl. Phys. Lett. 109, 181101 (2016).
[Crossref]

A. Youssefi, F. Zangeneh-Nejad, S. Abdollahramezani, and A. Khavasi, “Analog computing by brewster effect,” Opt. Lett. 41, 3467–3470 (2016).
[Crossref] [PubMed]

T. J. Davis, D. E. Gómez, and A. Roberts, “Plasmonic circuits for manipulating optical information,” Nanophotonics 6, 543–559 (2016).
[Crossref]

2015 (3)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).
[Crossref]

S. AbdollahRamezani, K. Arik, A. Khavasi, and Z. Kavehvash, “Analog computing using graphene-based metalines,” Opt. Lett. 40, 5239–5242 (2015).
[Crossref] [PubMed]

2014 (4)

2012 (1)

U. Hohenester and A. Trügler, “Mnpbem–a matlab toolbox for the simulation of plasmonic nanoparticles,” Comp. Phys. Commun. 183, 370–381 (2012).
[Crossref]

2011 (1)

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

2010 (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010).
[Crossref]

2009 (2)

T. Davis, K. Vernon, and D. Gómez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[Crossref]

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

2008 (1)

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

2006 (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

2002 (1)

F. G. De Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[Crossref]

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[Crossref]

Abdollahramezani, S.

Alù, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Arik, K.

Bach, U.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Bezus, E. A.

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

Bykov, D. A.

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Chao, W.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Coenen, T.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Davis, T.

T. Davis and D. Gómez, “Colloquium: An algebraic model of localized surface plasmons and their interactions,” Rev. Mod. Phys. 89, 011003 (2017).
[Crossref]

T. Davis, K. Vernon, and D. Gómez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[Crossref]

Davis, T. J.

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Y. Hwang and T. J. Davis, “Optical metasurfaces for subwavelength difference operations,” Appl. Phys. Lett. 109, 181101 (2016).
[Crossref]

T. J. Davis, D. E. Gómez, and A. Roberts, “Plasmonic circuits for manipulating optical information,” Nanophotonics 6, 543–559 (2016).
[Crossref]

F. Eftekhari, D. E. Gómez, and T. J. Davis, “Measuring subwavelength phase differences with a plasmonic circuit–an example of nanoscale optical signal processing,” Opt. Lett. 39, 2994–2997 (2014).
[Crossref] [PubMed]

De Abajo, F. G.

F. G. De Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[Crossref]

Doskolovich, L. L.

Ee, H.-S.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Eftekhari, F.

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Etheridge, J.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Fan, S.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Fang, Y.

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[Crossref]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010).
[Crossref]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Genov, D.

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Gómez, D.

T. Davis and D. Gómez, “Colloquium: An algebraic model of localized surface plasmons and their interactions,” Rev. Mod. Phys. 89, 011003 (2017).
[Crossref]

T. Davis, K. Vernon, and D. Gómez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[Crossref]

Gómez, D. E.

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

T. J. Davis, D. E. Gómez, and A. Roberts, “Plasmonic circuits for manipulating optical information,” Nanophotonics 6, 543–559 (2016).
[Crossref]

F. Eftekhari, D. E. Gómez, and T. J. Davis, “Measuring subwavelength phase differences with a plasmonic circuit–an example of nanoscale optical signal processing,” Opt. Lett. 39, 2994–2997 (2014).
[Crossref] [PubMed]

Gong, S.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

Hane, K.

Hohenester, U.

U. Hohenester and A. Trügler, “Mnpbem–a matlab toolbox for the simulation of plasmonic nanoparticles,” Comp. Phys. Commun. 183, 370–381 (2012).
[Crossref]

Hokari, R.

Hopkins, B.

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Howie, A.

F. G. De Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[Crossref]

Hwang, Y.

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

Y. Hwang and T. J. Davis, “Optical metasurfaces for subwavelength difference operations,” Appl. Phys. Lett. 109, 181101 (2016).
[Crossref]

Jalali, B.

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).
[Crossref]

Jiang, W.

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Kanamori, Y.

Kang, J.-H.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Kastel, J.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Kavehvash, Z.

Khavasi, A.

Kim, K.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010).
[Crossref]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Lee, Y.-H.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Lin, J.

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Liu, A. C.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Liu, M.

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Lloyd, J. A.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Lou, Y.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Y. Fang, Y. Lou, and Z. Ruan, “On-grating graphene surface plasmons enabling spatial differentiation in the terahertz region,” Opt. Lett. 42, 3840–3843 (2017).
[Crossref] [PubMed]

Ma, Y.

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010).
[Crossref]

Mitchell, A.

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Monticone, F.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Ng, S. H.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

Nielsen, M. G.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

Park, H.-G.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Pors, A.

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

Qiu, M.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Roberts, A.

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

T. J. Davis, D. E. Gómez, and A. Roberts, “Plasmonic circuits for manipulating optical information,” Nanophotonics 6, 543–559 (2016).
[Crossref]

Ruan, Z.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Y. Fang, Y. Lou, and Z. Ruan, “On-grating graphene surface plasmons enabling spatial differentiation in the terahertz region,” Opt. Lett. 42, 3840–3843 (2017).
[Crossref] [PubMed]

Seo, M.-K.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Soifer, V. A.

Solli, D. R.

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).
[Crossref]

Trügler, A.

U. Hohenester and A. Trügler, “Mnpbem–a matlab toolbox for the simulation of plasmonic nanoparticles,” Comp. Phys. Commun. 183, 370–381 (2012).
[Crossref]

Vernon, K.

T. Davis, K. Vernon, and D. Gómez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[Crossref]

Wang, D.

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Wang, Y.

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Wu, W.

Yang, J.

Ye, H.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Yoon, T.-Y.

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Youssefi, A.

Yuan, X.-C.

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Zangeneh-Nejad, F.

Zhang, S.

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Zhang, X.

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Zhou, Y.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Zhu, T.

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

Zhu, Y.

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

ACS Nano (1)

J. A. Lloyd, S. H. Ng, A. C. Liu, Y. Zhu, W. Chao, T. Coenen, J. Etheridge, D. E. Gómez, and U. Bach, “Plasmonic nanolenses: Electrostatic self-assembly of hierarchical nanoparticle trimers and their response to optical and electron beam stimuli,” ACS Nano 11, 1604–1612 (2017).
[Crossref] [PubMed]

ACS Photonics (1)

D. E. Gómez, Y. Hwang, J. Lin, T. J. Davis, and A. Roberts, “Plasmonic edge states: An electrostatic eigenmode description,” ACS Photonics 4, 1607–1614 (2017).
[Crossref]

Appl. Phys. Lett. (1)

Y. Hwang and T. J. Davis, “Optical metasurfaces for subwavelength difference operations,” Appl. Phys. Lett. 109, 181101 (2016).
[Crossref]

Comp. Phys. Commun. (1)

U. Hohenester and A. Trügler, “Mnpbem–a matlab toolbox for the simulation of plasmonic nanoparticles,” Comp. Phys. Commun. 183, 370–381 (2012).
[Crossref]

J. Appl. Phys. (1)

T. Davis, K. Vernon, and D. Gómez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[Crossref]

Laser Photonics Rev. (1)

Y. Hwang, B. Hopkins, D. Wang, A. Mitchell, T. J. Davis, J. Lin, and X.-C. Yuan, “Optical chirality from dark-field illumination of planar plasmonic nanostructures,” Laser Photonics Rev. 11, 1700216 (2017).
[Crossref]

Nano Lett. (1)

A. Pors, M. G. Nielsen, and S. I. Bozhevolnyi, “Analog computing using reflective plasmonic metasurfaces,” Nano Lett. 15, 791–797 (2015).
[Crossref]

Nanophotonics (1)

T. J. Davis, D. E. Gómez, and A. Roberts, “Plasmonic circuits for manipulating optical information,” Nanophotonics 6, 543–559 (2016).
[Crossref]

Nat. Commun. (2)

T. Zhu, Y. Zhou, Y. Lou, H. Ye, M. Qiu, Z. Ruan, and S. Fan, “Plasmonic computing of spatial differentiation,” Nat. Commun. 8, 15391 (2017).
[Crossref]

J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2, 582 (2011).
[Crossref] [PubMed]

Nat. Mater. (1)

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the drude damping limit,” Nat. Mater. 8, 758–762 (2009).
[Crossref] [PubMed]

Nat. Photonics (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
[Crossref]

D. R. Solli and B. Jalali, “Analog optical computing,” Nat. Photonics 9, 704–706 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961).
[Crossref]

Phys. Rev. B (2)

F. G. De Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[Crossref]

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Phys. Rev. Lett. (1)

S. Zhang, D. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. 101, 47401 (2008).
[Crossref]

Rev. Mod. Phys. (2)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257 (2010).
[Crossref]

T. Davis and D. Gómez, “Colloquium: An algebraic model of localized surface plasmons and their interactions,” Rev. Mod. Phys. 89, 011003 (2017).
[Crossref]

Science (2)

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) The plasmonic circuit that outputs the second derivative of the wavefield across its inputs. The three nanorods (1, 2 and 3) aligned along the y-axis are input nanorods while the other two rods (4 and 5) aligned along the x-axis are the output nanorods. The input wavefield is linearly polarized to y-direction whereas the output is polarized to x-direction. (b) A diagram illustrates the position vectors of the rods, observer, and the displacement.
Fig. 2
Fig. 2 The spectra of the scattering cross-section σS depending on the polarization of the incident wave and the profiles of the surface charge density ρ of the corresponding modes. The circuit is composed of five identical gold nanorods whose physical dimension is 90 × 40 × 30 nm3. The second and the fourth modes are not shown in the spectra since they are dark modes.
Fig. 3
Fig. 3 Scattered intensities of the plasmonic circuits of first and second derivatives as functions of incidence angle θ of a plane wave polarized along the input nanorods. The calculation is performed in the electrostatic regime using the boundary element method. The inset indicates the oblique incidence on the second derivative circuit.
Fig. 4
Fig. 4 FDTD simulation results for a large (90 × 40 × 30 nm3) and a small (50 × 20 × 20 nm3) circuits for second-order differentiation. (a) Calculated scattered intensities (points) as functions of the phase difference ϕ overlaid with the fit curves (lines). (b) The induced Ex-field profiles at the indicated ϕ. The scale bar is 100 nm.

Equations (6)

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( a ˜ 1 a ˜ 2 a ˜ 3 a ˜ 4 a ˜ 5 ) = ( 1 0 0 f G 0 0 1 0 f G f G 0 0 1 0 f G f G f G 0 1 0 0 f G f G 0 1 ) 1 ( a 1 a 2 a 3 a 4 a 5 )
a ˜ 4 = f G ( a 1 a 2 ) + f 3 G 3 ( a 2 + a 3 2 a 1 ) ( 1 f 2 G 2 ) ( 1 3 f 2 G 2 ) a ˜ 5 = f G ( a 3 a 2 ) + f 3 G 3 ( a 1 + a 2 2 a 3 ) ( 1 f 2 G 2 ) ( 1 3 f 2 G 2 ) .
ψ e i k s r 0 = f G ( a 1 2 a 2 + a 3 ) cos ( k s d / 2 ) 1 3 f 2 G 2 + i f G ( a 1 + a 3 ) sin ( k s d / 2 ) 1 f 2 G 2 .
ψ e i k s r 0 = A 2 p G ( E 1 2 E 2 + E 3 ) cos ( k s d / 2 ) ( ω ω ˜ r ) 2 3 A 2 G 2 + i A 2 p G ( E 1 E 3 ) sin ( k s d / 2 ) ( ω ω ˜ r ) 2 A 2 G 2 ,
ψ e i k s r 0 = 4 A 2 p G E 0 sin 2 ( ϕ / 4 ) cos ( k s d / 2 ) ( ω ω ˜ r ) 2 3 A 2 G 2 + 2 A 2 p G E 0 sin ( ϕ / 2 ) sin ( k s d / 2 ) ( ω ω ˜ r ) 2 A 2 G 2 ,
I ( ϕ ) = I 0 sin 4 ( ϕ / 4 ) .

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