Abstract

An ensemble of interacting metal nanostructures supporting localized surface plasmon resonances can be described as a plasmonic circuit. We show that such circuits can perform all-optical linear mathematical operations on multiple input signals, a mechanism we describe as nanoscale optical signal processing. An example plasmonic circuit that mixes together two optical signals at the subwavelength scale and outputs a measure of their phase difference is demonstrated experimentally. It is also shown that the difference circuits function as meta-atoms in a metamaterial that has potential for position-dependent signal processing of an incident light wave.

© 2014 Optical Society of America

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  2. D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
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  9. J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
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  10. H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
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  11. N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
    [CrossRef]
  12. Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
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  18. A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
    [CrossRef]

2014

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

2013

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

2012

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

2010

T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010).
[CrossRef]

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

2009

F. Nunes and J. Weiner, IEEE Trans. Nanotechnol. 8, 298 (2009).
[CrossRef]

T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009).
[CrossRef]

2008

A. Alù and N. Engheta, Nat. Photonics 2, 307 (2008).
[CrossRef]

A. Alù, M. Young, and N. Engheta, Phys. Rev. B 77, 144107 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef]

2007

N. Engheta, Science 317, 1698 (2007).
[CrossRef]

2006

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

2005

N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005).
[CrossRef]

Alù, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

A. Alù and N. Engheta, Nat. Photonics 2, 307 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef]

A. Alù, M. Young, and N. Engheta, Phys. Rev. B 77, 144107 (2008).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005).
[CrossRef]

Bozhevolnyi, S.

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Caglayan, H.

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Davis, T.

T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Davis, T. J.

T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009).
[CrossRef]

T. J. Davis, in Plasmons: Theory and Applications, K. N. Helsey, ed. (Nova Science Publishers, 2011), pp. 111–141.

Edwards, B.

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

A. Alù, M. Young, and N. Engheta, Phys. Rev. B 77, 144107 (2008).
[CrossRef]

A. Alù and N. Engheta, Nat. Photonics 2, 307 (2008).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef]

N. Engheta, Science 317, 1698 (2007).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005).
[CrossRef]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Gómez, D.

T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Gómez, D. E.

T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009).
[CrossRef]

Gramotnev, D.

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

Greffet, J.

J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Halas, N.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Hong, S.

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

Kagan, C.

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

Laroche, M.

J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Liu, N.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Liu, X.

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

Lu, H.

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

Mao, D.

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

Marquier, F.

J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Monticone, F.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Nordlander, P.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Nunes, F.

F. Nunes and J. Weiner, IEEE Trans. Nanotechnol. 8, 298 (2009).
[CrossRef]

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005).
[CrossRef]

Silva, A.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Sun, Y.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

Vernon, K.

T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Vernon, K. C.

T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009).
[CrossRef]

Wang, G.

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

Wang, Y.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Weiner, J.

F. Nunes and J. Weiner, IEEE Trans. Nanotechnol. 8, 298 (2009).
[CrossRef]

Wen, F.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

Young, M.

A. Alù, M. Young, and N. Engheta, Phys. Rev. B 77, 144107 (2008).
[CrossRef]

Zhao, Y.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

IEEE Trans. Nanotechnol.

F. Nunes and J. Weiner, IEEE Trans. Nanotechnol. 8, 298 (2009).
[CrossRef]

J. Appl. Phys.

T. Davis, K. Vernon, and D. Gómez, J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Nano Lett.

N. Liu, F. Wen, Y. Zhao, Y. Wang, P. Nordlander, N. Halas, and A. Alù, Nano Lett. 13, 142 (2013).
[CrossRef]

T. J. Davis, D. E. Gómez, and K. C. Vernon, Nano Lett. 10, 2618 (2010).
[CrossRef]

Nanotechnology

H. Lu, X. Liu, G. Wang, and D. Mao, Nanotechnology 23, 444003 (2012).
[CrossRef]

Nat. Mater.

Y. Sun, B. Edwards, A. Alù, and N. Engheta, Nat. Mater. 11, 208 (2012).
[CrossRef]

Nat. Photonics

D. Gramotnev and S. Bozhevolnyi, Nat. Photonics 4, 83 (2010).
[CrossRef]

A. Alù and N. Engheta, Nat. Photonics 2, 307 (2008).
[CrossRef]

Phys. Rev. B

A. Alù, M. Young, and N. Engheta, Phys. Rev. B 77, 144107 (2008).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gómez, Phys. Rev. B 79, 155423 (2009).
[CrossRef]

Phys. Rev. Lett.

H. Caglayan, S. Hong, B. Edwards, C. Kagan, and N. Engheta, Phys. Rev. Lett. 111, 073904 (2013).
[CrossRef]

A. Alù and N. Engheta, Phys. Rev. Lett. 101, 043901 (2008).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 95504 (2005).
[CrossRef]

J. Greffet, M. Laroche, and F. Marquier, Phys. Rev. Lett. 105, 117701 (2010).
[CrossRef]

Science

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

N. Engheta, Science 317, 1698 (2007).
[CrossRef]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, Science 343, 160 (2014).
[CrossRef]

Other

T. J. Davis, in Plasmons: Theory and Applications, K. N. Helsey, ed. (Nova Science Publishers, 2011), pp. 111–141.

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Figures (4)

Fig. 1.
Fig. 1.

Two examples of nano-plasmonic circuits based on evanescent coupling between LSPs that show the circuit diagrams and their representations as metal nanorods. In the circuit diagrams, the solid lines represent the paths by which optical signals are transmitted to and from the circuits and the rectangles represent metal nanorods supporting LSPs. The “+” and “” signs indicate the relative charge distributions of the LSPs: (a) adder circuit and (b) difference circuit.

Fig. 2.
Fig. 2.

Experimental configuration for testing the plasmonic difference circuits. (a) Scanning electron microscopy (SEM) image of one circuit during its fabrication that shows the resist pattern on a gold film after EBL exposure and development, just prior to etching, (b) configuration of optical components used in the experiment. The arrows show the orientations of the polarizers, which were chosen so the incident light only excited the circuit inputs and the microscope lens only collected light scattered in multiple directions from the output, and (c) phase difference ϕ across the inputs depends on the tilt θ of the incident light beam.

Fig. 3.
Fig. 3.

Results of experiments on the plasmonic difference circuit. (a) Microscope image showing light scattered from a circuit and the four alignment nanorods (see text for details), which were arranged in a “+” pattern (inset is not to scale), (b) scattering intensity obtained with the substrate correctly aligned and with normal incident light (zero phase difference), (c) with light incident at θ=30° the circuit appears as a bright spot at the center of the image, (d) scattering spectrum from the plasmonic circuit, (e) intensity as a function of the phase difference between the two inputs (dots are experimental data, the solid curve is theory). The light source was a narrow band LED with a peak response at 785 nm and a FWHM of 40 nm. The phase was calculated from the angle of incidence with Δ=180nm and λ=780nm. Also shown is the null-response of the circuit (ψ=90°) (square points). The dashed line is the expected response in the null orientation, and (f) similar results as per (e) but using white light from a quartz–halogen globe passed through a 550 nm long-pass filter.

Fig. 4.
Fig. 4.

(a) Metamaterial of plasmonic difference circuits imaged with unpolarized light and (b) response to optical phase differences using white light. Circular points are experimental results for ψ=0° and rectangular points are for the null direction ψ=90°.

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