Abstract

We numerically investigate the influence of roughness in layer thicknesses on the properties of hyperbolic metamaterials (HMMs). We show that random spatial variation of dielectric and metal layer thicknesses, similar to what occurs during actual structure fabrication, leads to dramatic absorption increase compared to an ideal, smooth-layer HMM; the absorption increases more strongly when roughness is induced throughout the HMM rather than in its surface layer only. Hence, we have found that moderate surface roughness does not deteriorate the HMM functionality, at least in absorption-related applications, thus eliminating the challenge of ultrasmooth metal layer fabrication. More severe roughness can also prove useful in the design of inexpensive HMM-based broadband absorbers.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (4)

2012 (4)

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B 86(20), 205130 (2012).
[CrossRef]

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

2008 (2)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Z. Jacob and E. E. Narimanov, “Optical hyperspace for plasmons: Dyakonov states in metamaterials,” Appl. Phys. Lett. 93(22), 221109 (2008).
[CrossRef]

2006 (1)

1985 (1)

Alekseyev, L. V.

Alexander, R. W.

Barnakov, Y. A.

Bell, R. J.

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[CrossRef]

Campione, S.

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B 86(20), 205130 (2012).
[CrossRef]

Capolino, F.

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B 86(20), 205130 (2012).
[CrossRef]

Cortes, C. L.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

Cui, Y.

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

Ding, F.

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

Ge, X.

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

Gu, L.

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Guclu, C.

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B 86(20), 205130 (2012).
[CrossRef]

Guo, Y.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

He, S.

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[CrossRef]

Jacob, Z.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

Z. Jacob and E. E. Narimanov, “Optical hyperspace for plasmons: Dyakonov states in metamaterials,” Appl. Phys. Lett. 93(22), 221109 (2008).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

Jin, Y.

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

Kidwai, O.

Kitur, J. K.

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Kivshar, Y.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[CrossRef]

M. Noginov, M. Lapine, V. Podolskiy, and Y. Kivshar, “Focus issue: hyperbolic metamaterials,” Opt. Express 21(12), 14895–14897 (2013).
[CrossRef] [PubMed]

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Lapine, M.

Li, H.

Long, L. L.

Mock, J. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Narimanov, E.

Narimanov, E. E.

E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express 21(12), 14956–14961 (2013).
[CrossRef] [PubMed]

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Z. Jacob and E. E. Narimanov, “Optical hyperspace for plasmons: Dyakonov states in metamaterials,” Appl. Phys. Lett. 93(22), 221109 (2008).
[CrossRef]

Newman, W.

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

Noginov, M.

Noginov, M. A.

E. E. Narimanov, H. Li, Y. A. Barnakov, T. U. Tumkur, and M. A. Noginov, “Reduced reflection from roughened hyperbolic metamaterial,” Opt. Express 21(12), 14956–14961 (2013).
[CrossRef] [PubMed]

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Ordal, M. A.

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Poddubny, A.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[CrossRef]

Podolskiy, V.

Querry, M. R.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Sipe, J. E.

Smith, D. R.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Tumkur, T. U.

Tumkur, U.

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Zhukovsky, S. V.

Adv. Optoelectron. (1)

Y. Guo, W. Newman, C. L. Cortes, and Z. Jacob, “Applications of Hyperbolic Metamaterial Substrates,” Adv. Optoelectron. 2012, 452502 (2012).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

F. Ding, Y. Cui, X. Ge, Y. Jin, and S. He, “Ultra-broadband microwave metamaterial absorber,” Appl. Phys. Lett. 100(10), 103506 (2012).
[CrossRef]

U. Tumkur, L. Gu, J. K. Kitur, E. E. Narimanov, and M. A. Noginov, “Control of absorption with hyperbolic metamaterials,” Appl. Phys. Lett. 100(16), 161103 (2012).
[CrossRef]

Z. Jacob and E. E. Narimanov, “Optical hyperspace for plasmons: Dyakonov states in metamaterials,” Appl. Phys. Lett. 93(22), 221109 (2008).
[CrossRef]

Nat. Photonics (1)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[CrossRef]

Opt. Express (4)

Phys. Rev. B (1)

C. Guclu, S. Campione, and F. Capolino, “Hyperbolic metamaterial as super absorber for scattered fields generated at its surface,” Phys. Rev. B 86(20), 205130 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Other (3)

C. S. T. Microwave Studio and H. Computer Simulation Technology Gmb, http://cst.com .

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

W. W. Salisbury, “Absorbent body for electromagnetic waves,” Patent US2599944 A, 1952.

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Figures (6)

Fig. 1
Fig. 1

(a) An isofrequency contour of the HMM is hyperbolic. The inset shows an example of HMM – a layered metal-dielectric structure. (b) A schematic view of “superabsorption” effect. High-k waves scattered from an inhomogeneity on an HMM surface can couple to high-k HMM bulk plasmons.

Fig. 2
Fig. 2

(a) Schematic of supercell division into 5 × 5 cells. (b) Cross-section of the structure showing accumulation of roughness from right to left. (c) Examples of structures made of 5 metal and dielectric layers with average thickness T0 = 10 nm and randomness parameter δ = 0%, 25% and 100%.

Fig. 3
Fig. 3

Absorbance of the random HMM with period a = 10 nm with no randomness (“smooth”, black), δ = 10% (red), 25% (green), 50% (blue) and 90% (yellow) for the incidence from the flat (a) and rough (b) sides. Shaded areas correspond to the standard deviation from the mean absorbance.

Fig. 4
Fig. 4

Random HMM absorbance tends to regular HMM (“smooth”, black line) with increasing the cell size a from 10 nm (red) to 30 nm (green) to 100 nm (blue), for δ = 10% (a) and δ = 50% (b). Wave incidence is from the rough side.

Fig. 5
Fig. 5

Absorbance of the 5 random layers HMM (R5, red) is larger than that of the HMM consisting of the same 1 terminal rough layer and 4 ordinary smooth layers (R1O4, blue) and regular HMM (“smooth”, black). The inset shows absorbance spectrum of the random outermost layer (R1) only. The peaks (highlighted with orange ovals) correspond to localized plasmonic resonances. Randomness is δ = 10% (a) and 50% (b).

Fig. 6
Fig. 6

The random HMM is very complex in a general case and various physical mechanisms can contribute to light absorption: reflection cancellation due to tapered air-HMM transition, localized plasmonic resonances and coupling to the high-k waves in the HMM.

Equations (1)

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k x 2 + k y 2 ε z k z 2 | ε x , y | = k 0 2 ,

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