Abstract

An optical electrode design is presented that theoretically allows 100% optical transmission through an interdigitated metallic electrode at 50% metal areal coverage. This is achieved by redirection of light incident on embedded metal electrode lines to an angle beyond that required for total internal reflection. Full-field electromagnetic simulations using realistic material parameters demonstrate 84% frequency-averaged transmission for unpolarized illumination across the entire visible spectral range using a silver interdigitated electrode at 50% areal coverage. The redirection is achieved through specular reflection, making it nonresonant and arbitrarily broadband, provided the electrode width exceeds the optical wavelength. These findings could significantly improve the performance of photovoltaic devices and optical detectors that require high-conductivity top contacts.

© 2014 Optical Society of America

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References

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  1. C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
    [CrossRef]
  2. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
    [CrossRef]
  3. S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).
  4. A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
    [CrossRef]
  5. C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).
  6. K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).
  7. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  8. E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1985).

2012 (2)

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

2011 (2)

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

2007 (1)

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef]

2001 (1)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Akozbek, N.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

Alu, A.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Argyropoulos, C.

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

Barve, A.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Bloemer, M. J.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Brueck, S. R. J.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

D’Aguanno, G.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Garcia-Vidal, F. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Genet, C.

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef]

Ghosh, G.

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

Jang, W. Y.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Krishna, S.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Ku, Z. Y.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Le, K. Q.

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

Lee, S. J.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Lezec, H. J.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Martin-Moreno, L.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Mattiucci, N.

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Montoya, J.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Noh, S. K.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Palik, E. D.

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

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Pendry, J. B.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

Reisinger, A.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Sundaram, M.

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

J. Appl. Phys. (1)

K. Q. Le, C. Argyropoulos, N. Mattiucci, G. D’Aguanno, M. J. Bloemer, and A. Alu, J. Appl. Phys. 112, 094317 (2012).

Nat. Commun. (1)

S. J. Lee, Z. Y. Ku, A. Barve, J. Montoya, W. Y. Jang, S. R. J. Brueck, M. Sundaram, A. Reisinger, S. Krishna, and S. K. Noh, Nat. Commun. 2, 286 (2011).

Nature (1)

C. Genet and T. W. Ebbesen, Nature 445, 39 (2007).
[CrossRef]

Phys. Rev. B (2)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, Phys. Rev. B 85, 024304 (2012).

Phys. Rev. Lett. (2)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef]

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Other (1)

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Cassegrain telescope design. (b) Cross section of an interdigitated electrode showing incident light (blue arrows) and reflection loss (green arrows). (c) Embedded electrode structure using a Cassegrain-like light gathering approach, showing collection of light incident on the electrodes as well as surface reflection loss by the secondary mirror. (d) Catoptric electrode consisting of sculpted electrode lines covered with an index-matching layer and an antireflection coating.

Fig. 2.
Fig. 2.

(a) Cross section of a catoptric electrode with 50% metal areal coverage and a surface tilt of 15° showing complete transmission of all light incident on the metal electrode area. (b) Minimum electrode surface tilt to achieve total internal reflection (green line) and optimum scaled cover layer thickness D/P necessary for 100% transmission at a surface tilt equal to the minimum tilt (solid blue line) and at a surface tilt 20% (dashed line) and 40% (dotted line) above the minimum surface tilt.

Fig. 3.
Fig. 3.

(a) Electric field distribution under normal incidence TE illumination and (b) magnetic field distribution under TM illumination at λ=417nm of an interdigitated silver electrode on a substrate with refractive index n=2, embedded in an index-matched layer covered with an 88 nm thick antireflection coating (n=1.41) for a surface tilt of 20°, an electrode period of 2 μm, and a cover layer thickness of 368 nm. (c) Simulated TE transmission and (d) TM transmission (blue lines), reflection (green lines), and absorption (red lines) of the electrode. (e) Transmission of unpolarized light (blue line) and degree of polarization (gray line).

Fig. 4.
Fig. 4.

Simulated light transmission through an aluminum catoptric electrode structure optimized for high transmission at ultraviolet wavelengths, showing (a) the electric field distribution under normal incidence TE illumination and (b) the magnetic field distribution under TM illumination at λ=250nm of an interdigitated rectangular aluminum electrode with a cross section of 75nm×25nm, a periodicity of 150 nm, a cover layer thickness of 30 nm, and an antireflection coating with index n=1.41 and thickness 44 nm. (c) Simulated TE transmission and (d) TM transmission (blue lines), reflection (green lines), and absorption (red lines) of the electrode. (e) Transmission of unpolarized light (blue line) and degree of polarization (gray line). (f) Electric field distribution under normal incidence TE illumination at λ=210nm, and (g) magnetic field distribution under TM illumination at λ=330nm.

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