Abstract

We constructed a metallic grating on a deep-subwavelength scale and tested its plasmonic features in visible frequencies. The deep-subwavelength metallic grating effectively acts as an anisotropic homogeneous uniaxial form-birefringent metal, exhibiting different optical responses for polarizations along different optical axes. Therefore, this form-birefringent metal supports anisotropic surface plasmon polaritons that are characterized by directly imaging the generated plasmonic index ellipsoids in reciprocal space. The observed plasmonic index ellipsoids also show a rainbow effect, where different colors are dispersively distributed in reciprocal space.

© 2011 Optical Society of America

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References

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  1. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003).
  2. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
    [PubMed]
  3. I. Richter, P. C. Sun, F. Xu, and Y. Fainman, “Design consideration of form birefringent microstructures,” Appl. Opt. 34, 2421–2429 (1995).
    [CrossRef] [PubMed]
  4. R. C. Tyan, A. A. Salvekar, H. P. Chou, C. C. Cheng, A. Scherer, F. Xu, P. C. Sun, and Y. Fainman, “Design, fabrication and characterization of form-birefringent multilayer polarizing beam splitter,” J. Opt. Soc. Am. A 14, 1627–1636 (1997).
    [CrossRef]
  5. F. Xu, R. C. Tyan, P. C. Sun, Y. Fainman, C. C. Cheng, and A. Scherer, “Form-birefringent computer generated holograms,” Opt. Lett. 21, 1513–1515 (1996).
    [CrossRef] [PubMed]
  6. U. Levy and Y. Fainman, “Dispersion properties of inhomogeneous nanostructures,” J. Opt. Soc. Am. A 21, 881–889(2004).
    [CrossRef]
  7. U. Levy, C. H. Tsai, L. Pang, and Y. Fainman, “Engineering space-variant inhomogeneous media for polarization control,” Opt. Lett. 29, 1718–1720 (2004).
    [CrossRef] [PubMed]
  8. L. Pang, M. Nezhad, U. Levy, C. H. Tsai, and Y. Fainman, “Form-birefringence structure fabrication in GaAs by use of SU-8 as a dry-etching mask,” Appl. Opt. 44, 2377–2381(2005).
    [CrossRef] [PubMed]
  9. A. G. Zhukov and V. I. Smirnov, “Polarizing properties of wire gratings in the long wave infrared,” J. Appl. Spectrosc. 3, 304–307 (1965).
    [CrossRef]
  10. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
    [CrossRef] [PubMed]
  11. J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
    [CrossRef]
  12. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  13. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  14. L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
    [CrossRef]
  15. L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
    [CrossRef] [PubMed]
  16. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
    [CrossRef]
  17. Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
    [CrossRef] [PubMed]
  18. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
    [CrossRef] [PubMed]

2011 (2)

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

2010 (1)

L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
[CrossRef]

2008 (1)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

2006 (1)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

2005 (2)

2004 (2)

1997 (1)

1996 (1)

1995 (1)

1968 (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

1965 (1)

A. G. Zhukov and V. I. Smirnov, “Polarizing properties of wire gratings in the long wave infrared,” J. Appl. Spectrosc. 3, 304–307 (1965).
[CrossRef]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Bartoli, F. J.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Cheng, C. C.

Chou, H. P.

Cowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Ding, Y. J.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Elser, J.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Fainman, Y.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Feng, L.

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
[CrossRef]

Gan, Q.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Gao, Y.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Levy, U.

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Liu, Z.

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Lomakin, V.

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
[CrossRef]

Mizrahi, A.

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

Narimanov, E. E.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Nezhad, M.

Palik, E. D.

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

Pang, L.

Podolskiy, V. A.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Richter, I.

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salvekar, A. A.

Scherer, A.

Smirnov, V. I.

A. G. Zhukov and V. I. Smirnov, “Polarizing properties of wire gratings in the long wave infrared,” J. Appl. Spectrosc. 3, 304–307 (1965).
[CrossRef]

Stacy, A.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Sun, P. C.

Tsai, C. H.

Tyan, R. C.

Vezenov, D.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Wagner, K.

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Wangberg, R.

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

Xu, F.

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003).

Zamek, S.

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

Zhukov, A. G.

A. G. Zhukov and V. I. Smirnov, “Polarizing properties of wire gratings in the long wave infrared,” J. Appl. Spectrosc. 3, 304–307 (1965).
[CrossRef]

ACS Nano (1)

L. Feng, A. Mizrahi, S. Zamek, Z. Liu, V. Lomakin, and Y. Fainman, “Metamaterials for enhanced polarization conversion in plasmonic excitation,” ACS Nano 5, 5100–5106 (2011).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

J. Elser, R. Wangberg, V. A. Podolskiy, and E. E. Narimanov, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett. 89, 261102 (2006).
[CrossRef]

L. Feng, Z. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96, 041112 (2010).
[CrossRef]

J. Appl. Spectrosc. (1)

A. G. Zhukov and V. I. Smirnov, “Polarizing properties of wire gratings in the long wave infrared,” J. Appl. Spectrosc. 3, 304–307 (1965).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. 21, 1530–1533 (1968).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

Q. Gan, Y. Gao, K. Wagner, D. Vezenov, Y. J. Ding, and F. J. Bartoli, “Experimental verification of the rainbow trapping effect in adiabatic plasmonic gratings,” Proc. Natl. Acad. Sci. USA 108, 5169–5173 (2011).
[CrossRef] [PubMed]

Science (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005).
[CrossRef] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials,” Science 321, 930 (2008).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (3)

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

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 2003).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the designed deep- subwavelength Au grating with the parameters: d = 140 nm , a = 100 nm , and h = 55 nm . (b) SEM micrograph of the fabricated nanostructure using FIB milling.

Fig. 2
Fig. 2

Plasmonic index ellipsoids at the wavelength of 540 nm . (a) Simulated SPP’s index ellipsoid in a representation of reflected power distribution in reciprocal space. (b) Experimental imaging of reflection from the deep- subwavelength Au grating in reciprocal space. The dark elliptical curves indicate the excitation of anisotropic SPP waves and are the corresponding SPP index ellipsoids.

Fig. 3
Fig. 3

Plasmonic index ellipsoids with the polarization state in the y direction as indicated by arrows. (a) Simulated and (b) measured index ellipsoids of SPPs at the wavelength of 540 nm . (c) Simulated and (d) measured index ellipsoids of SPPs at the wavelength of 620 nm .

Fig. 4
Fig. 4

(a) Dispersion relation of SPPs in the y direction on the deep-subwavelength Au grating. Black curve, red curve, and blue dots correspond to the data retrieved from analytical calculations according to Eqs. (1, 2, 3), numerical simulations, and experimental measurements, respectively. For experimental data, the error bar in wavelengths indicates the bandwidth ( 10 nm ) of the bandpass filters used in the experimental measurement. (b) Measured plasmonic index ellipsoid with a y-polarized broad-band incidence covering all the wavelengths in (a).

Equations (3)

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

ε eff = ( ε 0 0 0 ε 0 0 0 ε ) ,
ε = ε m ε 0 ( 1 f ) ε m + f ε 0 , ε = f ε m + ( 1 f ) ε 0 ,
k spp = k 0 ε 0 ε ε 0 + ε ,

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