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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28450–28455
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Experimental demonstration of a wave plate utilizing localized plasmonic resonances in nanoapertures

Jasper J. Cadusch, Timothy D. James, and Ann Roberts  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28450-28455 (2013)
http://dx.doi.org/10.1364/OE.21.028450


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Abstract

Here we demonstrate the fabrication and characterization of a plasmonic wave plate. The device uses detuned, orthogonal nanometric apertures that support localized surface plasmon resonances on their interior walls. A device was fabricated in a thin silver film using focused ion beam milling and standard polarization tomography used to determine its Mueller matrix. We demonstrate a device that can convert linearly polarized light to light with an overall degree of polarization of 88% and a degree of circular polarization of 86% at a particular wavelength of 702 nm.

© 2013 Optical Society of America

1. Introduction

2. Analytic model and numerical calculations

A schematic of the device under consideration is shown in Fig. 1(a).
Fig. 1 (a). Schematic diagram of the unit cell of a plasmonic quarter-wave plate. The geometric parameters are film thickness, T = 40 nm, slot width, W = 40 nm, unit cell periodicity P = 300 nm and Lx, Ly, the slot lengths, are varied. A 2 nm Ge adhesion layer is also shown in green. (b) Transmission spectra for an array of 120 nm by 140 nm cross apertures, with a period of 300nm in a 40 nm Ag film calculated using the FEM for three polarization angles; 0° (blue line) 45° (black) and 90° (red). At a wavelength of 700 nm the intensity transmission is independent of the angle of linear polarization; this is the operating wavelength of the QWP.
An infinite square array (period, P) of cross-shaped apertures of arm lengths, L, and widths, W are located in a silver film of thickness, T. The intensity transmission, calculated using the Finite Element Method (FEM), implemented in COMSOL Multiphysics 4.3a [14

14. COMSOL Multiphysics,” www.comsol.com.

] is shown in Fig. 1(b). The transmission, normalized to that in the absence of metal, is shown as a function of wavelength for a device with a square array of symmetric apertures with a fixed arm-width of 40 nm and variable arm-length in a Ag film of thickness 40 nm is shown in Fig. 1(b). The period of the array is 300 nm and the refractive index of the substrate is taken to be 1.52. Optical constants of bulk Ag were taken from Johnson and Christie [15

15. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. A clear resonance is seen in Fig. 2(a), where transmission of 700 nm light through the array as a function of antenna length is shown.
Fig. 2 (a). Computed transmission, Tλ(L), of 700 nm light through a rectangular aperture in a 40 nm Ag film on a SiO2 substrate as a function of aperture length, L. The full-width half-maximum, Δλ, is 28 nm and is indicated by the dashed lines. (b) An SEM image of the fabricated plasmonic QWP. The cross apertures were milled using a focused ion beam. Each element is 300 nm from its neighbor.
This resonance is associated with the excitation of surface charges on the inner walls of the aperture leading it to behave as an electric dipole [16

16. J.-H. Choe, J.-H. Kang, D.-S. Kim, and Q. H. Park, “Slot antenna as a bound charge oscillator,” Opt. Express 20(6), 6521–6526 (2012). [CrossRef] [PubMed]

]. If a design wavelength of λ is selected and a Lorentzian dipole behavior assumed, the amplitude transmission, tλ, is given by:
tλ(l)=ai(LL0λ)+Δλ2,
(1)
where L is the length at resonance and Δλ the loss term (full-width at half maximum) at λ and a is a parameter depending on the amplitude transmission on resonance. This gives a power transmission,
Tλ(L)=|a|2(LL0λ)2+Δλ2/4,
(2)
and the phase of the transmitted field is
Φλ=arctan(2(LL0λ)Δλ).
(3)
If the lengths of the cross arms in the x and y directions are equally detuned by δ, so that L=L0λ±δ, then the transmission should be independent of the state of linear polarization and there is a retardation, Γλ, between light polarized in the x and y directions, given by
Γλ=ΦyΦx=2arctan(2δΔλ),
(4)
assuming the x-direction is positively detuned and the y-direction is negatively detuned. Hence, if we desire a specific retardation, we require a detuning given by:
δ=Δλ2tan(Γλ2).
(5)
In the case of a quarter-wave plate, the retardation due to each arm is ± π/4 and the appropriate detuning is:
δ=Δλ2.
(6)
If we select a design wavelength of 700 nm, the Lorentzian profiles have a resonant length, L of 117 nm and width, Δλ, of 28 nm. This suggests that a detuning, δ, of ± 14 nm will produce a quarter-wave plate, operational at 700 nm.

3. Fabrication

An aperture array was fabricated in 40 nm thick layers of Ag deposited using an Intlvac Nanochrome II electron beam deposition system onto a glass microscope slide on a 2 nm adhesion layer of Ge. The aperture array was defined using Focused Ion Beam (FIB) milling with a FEI Helios NanoLab 600 Dual Beam system using 30 keV Ga ions. An array with a periodicity of 300 nm and total dimension 160 µm × 160 µm was produced. Typical writing time is of the order of 110 minutes. The beam current used was 28 pA and the dwell time was set to 3.8 ms. A single serpentine scan of the beam was employed over the target area. A scanning electron microscope (SEM) image of the device is shown in Fig. 2(b). From the SEM, it is apparent that the modeled square profile cross-apertures are significantly rounded and the fabricated crosses have vertical arm-length (132.5 ± 7) nm and horizontal arm-length (145 ± 6) nm.

4. Device characterization

The device was characterized in a bench-top polarimetry system shown in Fig. 3(a).
Fig. 3 (a). A schematic diagram of the bench top polarimetry set up. The incident beam passes through a collimator, a linear polarizer (LP) and an achromatic quarter wave-plate (QWP) and is then focused onto the array with an objective lens (OL). The analyzer consists of the same optical elements, in reverse order. (b) The principle axis of the array forms an angle, αwith the x-axis. The angle of polarization,θ,is measured from thex-axis. (c) The measured intensity of linearly polarized light transmitted through the plasmonic QWP for 0° (blue line) 45° (black line) and 90° (red line) angle of polarization. At a wavelength of 702 nm the transmission is polarization independent.
Light from a multi-mode fiber-coupled tungsten-halogen bulb (Ocean Optics HL-2000-FHSA) was collimated and focused onto samples using a 0.4 NA Olympus Plan N microscope objective. The state of polarization of the input field was controlled using a linear polarizer (Thorlabs LPVIS050-MP) and a broad-spectrum quarter-wave plate (Thorlabs AQWP05M-600). The light transmitted through the device was analyzed with an identical linear polarizer and a quarter-wave plate. Figure 3(c) shows the measured transmitted intensity spectra.

The polarization independent point is at a wavelength of 702 nm, in excellent agreement with the design wavelength of 700 nm. The model, however, underestimates fabrication errors and the loss assumed when using the optical properties of bulk Ag [15

15. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

]. This has led to a reduction in the relative amplitude of the transmission of light polarized at 0°, which can be seen by comparing Figs. 1(b) and 3(c). Full polarization tomography (FPT) was then performed on the fabricated array. The maximum likelihood estimation method was used to calculate a Mueller matrix for the plasmonic QWP [17

17. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, “Maximum-likelihood estimation of Mueller matrices,” Opt. Lett. 31(6), 817–819 (2006). [CrossRef] [PubMed]

]. A set of 42 polarization measurements were performed, to measure the intensity of light, polarized at 0°, 45°, 90°, 135° with respect to the x-axis, left- and right-hand circular polarization states, transmitted in those same polarization states (36 measurements for all combinations of the 6 initial states and the 6 final states as well as 6 normalization measurements performed without the analyzer). The measured Mueller matrix is shown in (7) and resembles the Mueller matrix of a classical depolarizing QWP [18

18. M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light (CUP Archive, 1999).

],
=[0.900.0680.0780.0180.0680.780.140.240.0760.0850.0770.720.00.260.690.037].
(7)
Unlike the standard linear reconstruction algorithms typically used for FPT [19

19. P.-C. Chen, Y.-L. Lo, T.-C. Yu, J.-F. Lin, and T.-T. Yang, “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Opt. Express 17(18), 15860–15884 (2009). [CrossRef] [PubMed]

], the Hermitian matrix associated with, found using the maximum likelihood estimation method is guaranteed to be positive semi-definite and is, thus, physical [17

17. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, “Maximum-likelihood estimation of Mueller matrices,” Opt. Lett. 31(6), 817–819 (2006). [CrossRef] [PubMed]

, 20

20. D. G. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” JOSA A 11(8), 2305–2319 (1994). [CrossRef]

]. In order to test the veracity of our Mueller matrix we use it to compute the resulting Stokes’ vector when the plasmonic array is illuminated with linearly polarized light at −45° to the x-axis.
S45°=[0.900.0680.0780.0180.0680.780.140.240.0760.0850.0770.720.00.260.690.037]  [1010]= [0.820.0670.00120.69],
(8)
which after normalization becomes
Sout=[1.00.080.000.84].
(9)
The large value for S3 indicates that the array is an approximation to a plasmonic quarter-wave plate, turning linearly polarised light into near-circularly polarised light.

It is possible to extract several optical properties of the sample from the Mueller matrix in (7). For instance, the phase retardance can be calculated, in this case it is 87.1°, which is very close to the desired phase retardance, Γλ=90,for a QWP [18

18. M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light (CUP Archive, 1999).

, 19

19. P.-C. Chen, Y.-L. Lo, T.-C. Yu, J.-F. Lin, and T.-T. Yang, “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Opt. Express 17(18), 15860–15884 (2009). [CrossRef] [PubMed]

]. The diattenuation, D, the differential transmission of orthogonal polarization states (which has a value between 0 and 1), can also be derived from the Mueller matrix. For this structure D = 0.084, which indicates a negligible dependence on polarization angle for the transmitted intensities at the operating wavelength [19

19. P.-C. Chen, Y.-L. Lo, T.-C. Yu, J.-F. Lin, and T.-T. Yang, “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Opt. Express 17(18), 15860–15884 (2009). [CrossRef] [PubMed]

].

Importantly, the principle axis of this plasmonic quarter-wave plate can also be extracted. The principle axis in fact lies 9.8° clockwise from the x-axis. It is expected that the principle axis of the plasmonic quarter-wave plate is coincident with the long arm of the crosses in the array. Hence, the horizontal arms of the crosses in the array are not parallel to the horizontal measurement axis as intended, but, in fact, form an angle of 9.8° with the horizontal measurement axis. The Mueller matrix, however, is robust to issues such as this. Rotating the sample by α is equivalent to performing a unitary basis transformation on.The Mueller matrix for the rotated sample, '(α) is given by [21

21. J. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt. 43(2), 283–292 (2004). [CrossRef] [PubMed]

],
'(α)=[10000cosαsinα00sinαcosα00001][10000cosαsinα00sinαcosα00001].
(10)
The Stokes’ vector of a transmitted beam that was linearly polarized at - to the principle axis of the fabricated plasmonic quarter-wave plate can then be calculated,
'(9.8°)S45°=[0.900.090.050.020.090.820.120.010.050.160.090.760.000.000.730.04][1010]=[0.850.130.040.73],
(11)
which upon normalization gives the output Stokes’ vector,
S'out=[1.000.160.040.86].
(12)
The degree of polarization is 0.88 and the degree of circular polarization of the transmitted beam is 0.86, ideally this would be 1, however due to imperfections in the fabrication process this was not realized.

5. Conclusion

We have demonstrated a simple Lorentzian model can be used to design an ultrathin plasmonic quarter-wave plate operational at optical wavelengths. One such design was fabricated in a 40 nm thin Ag film using focused ion beam lithography and full polarization tomography measurements were performed on this device. This research could be useful in future telecommunications technologies, new imaging systems and for biosensing applications.

Acknowledgments

This research was supported under the Australian Research Council's Discovery Projects funding scheme (project number DP110100221). This work was performed in part at the Melbourne Centre for Nanofabrication.

References and links

1.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008). [CrossRef] [PubMed]

2.

A. Pors, M. G. Nielsen, G. Della Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett. 36(9), 1626–1628 (2011). [CrossRef] [PubMed]

3.

J. Yang and J. Zhang, “Subwavelength quarter-waveplate composed of L-shaped metal nanoparticles,” Plasmonics 6(2), 251–254 (2011). [CrossRef]

4.

M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A. 109(31), 12364–12368 (2012). [CrossRef]

5.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012). [CrossRef] [PubMed]

6.

F. Wang, A. Chakrabarty, F. Minkowski, K. Sun, and Q.-H. Wei, “Polarization conversion with elliptical patch nanoantennas,” Appl. Phys. Lett. 101(2), 023101 (2012). [CrossRef]

7.

P. G. Thompson, C. G. Biris, E. J. Osley, O. Gaathon, R. M. Osgood, N. C. Panoiu, and P. A. Warburton, “Polarization-induced tunability of localized surface plasmon resonances in arrays of sub-wavelength cruciform apertures,” Opt. Express 19(25), 25035–25047 (2011). [CrossRef] [PubMed]

8.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]

9.

P. F. Chimento, N. V. Kuzmin, J. Bosman, P. F. Alkemade, G. W’t Hooft, and E. R. Eliel, “A subwavelength slit as a quarter-wave retarder,” Opt. Express 19(24), 24219–24227 (2011). [CrossRef] [PubMed]

10.

E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett. 36(13), 2498–2500 (2011). [CrossRef] [PubMed]

11.

A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett. 37(11), 1820–1822 (2012). [CrossRef] [PubMed]

12.

H. Cheng, S. Chen, P. Yu, J. Li, L. Deng, and J. Tian, “Mid-infrared Tunable optical polarization converter composed of asymmetric graphene nanocrosses,” Opt. Lett. 38(9), 1567–1569 (2013). [CrossRef] [PubMed]

13.

L. Lin and A. Roberts, “Light transmission through nanostructured metallic films: coupling between surface waves and localized resonances,” Opt. Express 19(3), 2626–2633 (2011). [CrossRef] [PubMed]

14.

COMSOL Multiphysics,” www.comsol.com.

15.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

16.

J.-H. Choe, J.-H. Kang, D.-S. Kim, and Q. H. Park, “Slot antenna as a bound charge oscillator,” Opt. Express 20(6), 6521–6526 (2012). [CrossRef] [PubMed]

17.

A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, “Maximum-likelihood estimation of Mueller matrices,” Opt. Lett. 31(6), 817–819 (2006). [CrossRef] [PubMed]

18.

M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light (CUP Archive, 1999).

19.

P.-C. Chen, Y.-L. Lo, T.-C. Yu, J.-F. Lin, and T.-T. Yang, “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Opt. Express 17(18), 15860–15884 (2009). [CrossRef] [PubMed]

20.

D. G. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” JOSA A 11(8), 2305–2319 (1994). [CrossRef]

21.

J. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt. 43(2), 283–292 (2004). [CrossRef] [PubMed]

OCIS Codes
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Plasmonics

History
Original Manuscript: August 7, 2013
Revised Manuscript: October 30, 2013
Manuscript Accepted: November 4, 2013
Published: November 12, 2013

Citation
Jasper J. Cadusch, Timothy D. James, and Ann Roberts, "Experimental demonstration of a wave plate utilizing localized plasmonic resonances in nanoapertures," Opt. Express 21, 28450-28455 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28450


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References

  1. A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett.101(4), 043902 (2008). [CrossRef] [PubMed]
  2. A. Pors, M. G. Nielsen, G. Della Valle, M. Willatzen, O. Albrektsen, and S. I. Bozhevolnyi, “Plasmonic metamaterial wave retarders in reflection by orthogonally oriented detuned electrical dipoles,” Opt. Lett.36(9), 1626–1628 (2011). [CrossRef] [PubMed]
  3. J. Yang and J. Zhang, “Subwavelength quarter-waveplate composed of L-shaped metal nanoparticles,” Plasmonics6(2), 251–254 (2011). [CrossRef]
  4. M. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U.S.A.109(31), 12364–12368 (2012). [CrossRef]
  5. N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett.12(12), 6328–6333 (2012). [CrossRef] [PubMed]
  6. F. Wang, A. Chakrabarty, F. Minkowski, K. Sun, and Q.-H. Wei, “Polarization conversion with elliptical patch nanoantennas,” Appl. Phys. Lett.101(2), 023101 (2012). [CrossRef]
  7. P. G. Thompson, C. G. Biris, E. J. Osley, O. Gaathon, R. M. Osgood, N. C. Panoiu, and P. A. Warburton, “Polarization-induced tunability of localized surface plasmon resonances in arrays of sub-wavelength cruciform apertures,” Opt. Express19(25), 25035–25047 (2011). [CrossRef] [PubMed]
  8. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett.92(3), 037401 (2004). [CrossRef] [PubMed]
  9. P. F. Chimento, N. V. Kuzmin, J. Bosman, P. F. Alkemade, G. W’t Hooft, and E. R. Eliel, “A subwavelength slit as a quarter-wave retarder,” Opt. Express19(24), 24219–24227 (2011). [CrossRef] [PubMed]
  10. E. H. Khoo, E. P. Li, and K. B. Crozier, “Plasmonic wave plate based on subwavelength nanoslits,” Opt. Lett.36(13), 2498–2500 (2011). [CrossRef] [PubMed]
  11. A. Roberts and L. Lin, “Plasmonic quarter-wave plate,” Opt. Lett.37(11), 1820–1822 (2012). [CrossRef] [PubMed]
  12. H. Cheng, S. Chen, P. Yu, J. Li, L. Deng, and J. Tian, “Mid-infrared Tunable optical polarization converter composed of asymmetric graphene nanocrosses,” Opt. Lett.38(9), 1567–1569 (2013). [CrossRef] [PubMed]
  13. L. Lin and A. Roberts, “Light transmission through nanostructured metallic films: coupling between surface waves and localized resonances,” Opt. Express19(3), 2626–2633 (2011). [CrossRef] [PubMed]
  14. COMSOL Multiphysics,” www.comsol.com .
  15. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972). [CrossRef]
  16. J.-H. Choe, J.-H. Kang, D.-S. Kim, and Q. H. Park, “Slot antenna as a bound charge oscillator,” Opt. Express20(6), 6521–6526 (2012). [CrossRef] [PubMed]
  17. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, “Maximum-likelihood estimation of Mueller matrices,” Opt. Lett.31(6), 817–819 (2006). [CrossRef] [PubMed]
  18. M. Born and E. Wolf, Principles of Optics: Electromagnetic theory of propagation, interference and diffraction of light (CUP Archive, 1999).
  19. P.-C. Chen, Y.-L. Lo, T.-C. Yu, J.-F. Lin, and T.-T. Yang, “Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Opt. Express17(18), 15860–15884 (2009). [CrossRef] [PubMed]
  20. D. G. Anderson and R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” JOSA A11(8), 2305–2319 (1994). [CrossRef]
  21. J. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt.43(2), 283–292 (2004). [CrossRef] [PubMed]

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