OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 6845–6850
« Show journal navigation

Split ring aperture for optical magnetic field enhancement by radially polarized beam

Y. Yang, H. T. Dai, and X. W. Sun  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 6845-6850 (2013)
http://dx.doi.org/10.1364/OE.21.006845


View Full Text Article

Acrobat PDF (2079 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Inspired by Babinet’s principle, we proposed a new plasmonic structure for enhancing the optical magnetic field, i.e. split ring aperture, whose complement is the well-known split ring. The split ring aperture exhibits a much better performance under radially polarized excitation than linearly polarized excitation. We attribute the ultra-high intensity enhancement in magnetic field to the symmetric matching between the aperture geometry and the direction of the electric field vector in each direction of radially excitation. The impact of the design parameters on the intensity enhancement and resonant wavelength is also investigated in details.

© 2013 OSA

1. Introduction

Meanwhile, the optical features of all the structures aforementioned is found to be dominated by localized surface plasmon resonance, the collective electron density oscillations found in noble metal nanostructures, which is strongly dependent on the geometry of the structures and the polarization state of the incident light. Linear polarized and circularly polarized field are commonly used to excite the OAs. Recently, radially polarized beams, a subset of cylindrical vector beams, has been proved to be promising sources in several applications, such as super-resolution imaging and plasmonic focusing [13

13. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

].

In this paper, we propose the complementary structure of a split ring, i.e. split ring aperture (SRA, as shown in Fig. 1(a)
Fig. 1 (a) Schematic representation of a split ring aperture and parameter definitions: aperture length, D, gap width, G and strip width, W. (b) The intensity and field profiles of radially polarized beam. The maximum of the field is indicated as the white circle in Fig. 1(b), whose diameter equals to D.
) to achieve optical magnetic field enhancement. The most promising optical feature of SRA, as well as the distinct discrepancy comparing to DA and CBA, is the capability to efficiently couple the radially polarized light into localized surface plasmon that leads to the near-field magnetic field enhancement. Moreover, several interesting optical features in SRAs are observed through the simulation, which show that it is possible to tune the resonance by altering the width of the strips or adding strips.

2. Radially polarized beam and split ring aperture

2.1 Radially polarized beam

As shown in Fig. 1(b), radially polarized beam is the optical field in which the electric field at each point is oriented parallelly to the radial vector from the beam axis and its electric component can be described by the following equation [13

13. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

]:
Er=HG10ex+HG01ey
(1)
where Er denotes the electric field with radially polarization, HG10 and HG10 represent Hermite–Gauss modes. ex and ey are unit vectors in their respective direction. For this radially polarized electric field, the corresponding magnetic field in the transverse plane is aligned in the azimuthal direction and thus forms the complementary field of azimuthally polarized electric field. The Hermite-Gauss mode can be expressed as:
E(x,y,z)=E0Hm(2xw(z))Hn(2yw(z))w0w(z)exp(iφmn(z))exp(ikr22q(z))
(2)
Here Hm(x) denotes the Hermite polynomials. E0 is the constant electric field amplitude, w(z)=w02/[1+(2zkw02)2] is the beam size, w0 is the size at the beam waist (w0 = w(0)), z0=(πw02)/λ is the Rayleigh range, q(z) = z-iz0 is the complex beam parameter, φmn=(m+n+1)tan1(z/z0) is the Gouy phase shift, r is the radial coordinate and k = 2π/λ. Thus, diameter of the circle formed by the maximum of the incident field can be deduced as dmax=2z0/k. For a given dmax, the beam parameters can be decided completely.

2.2 Split ring aperture

As shown in Fig. 1(a), a typical split ring aperture is actually an aperture whose shape is like a split ring, i.e. the complement of a split ring aperture. The geometry of the aperture can be characterized by four parameters: the aperture diameter, D; the strip width, W; the gap width, G and the aperture thickness, T (not labeled in the Fig. 1(a)). T is kept constant at 50nm, which is thinner than the skin depth of gold in near-infrared region. The aperture is standalone and deposited on a glass substrate with a refractive index of 1.5 and surrounded by air.

3. Simulation results

Lumerical FDTD Solutions [14

14. Lumerical FDTD Solution, FDTD Solutions 7.5, http://www.lumerical.com/.

], a commercial electromagnetic software based on the finite-difference time-domain method, is employed to investigate the magnetic response. A time step of Δt = 0.004 fs and a mesh size of Δx = Δy = Δz = 3 nm were used to ensure the stability and precision of the simulation. The perfectly-matched layers (PMLs) are used to minimize non-physical reflections at the simulation space boundaries. The permittivity function of gold used in the simulations is taken from Ref. 15

15. W. M. Haynes and D. R. Lide, Handbook of chemistry and physics (CRC Press, 2003).

and fitted by the Lumerical’s Multi-coefficient Materials in near- and mid- infrared region. The structure will be excited by either a plane wave polarized along x or a radially polarized beam from the substrate side at normal incidence. The incident wave will propagate along z + direction. In the case of the radially polarized illumination, D equals to dmax (refer to the white circle in Fig. 1(b)).

3.1 Field enhancement

In typical structure such as DA, the area of cross section of the central strip is found to be a key geometry parameter for magnetic field enhancing. Thus, the optical behavior of SRA with various strip width is firstly investigated. Here, the magnetic field intensity enhancement for the aperture is defined as the ratio between the magnetic field intensity at one point 10 nm above the strip and the maximum intensity of whole incident magnetic field without the metal layer [10

10. T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011). [CrossRef] [PubMed]

, 11

11. N. Zhou, E. C. Kinzel, and X. Xu, “Complementary bowtie aperture for localizing and enhancing optical magnetic field,” Opt. Lett. 36(15), 2764–2766 (2011). [CrossRef] [PubMed]

]. G and D are kept 50 nm and 300 nm, respectively. The magnetic field intensity enhancement of W = {30, 40, 50} nm are shown in Fig. 2(a)
Fig. 2 (a) Magnetic field intensity enhancement under radially polarized excitation (full curves) and linearly polarized excitation (dotted curves). The resonant wavelengths are 3.15 μm, 3.04 μm and 2.93 μm for w = 30nm, 40nm and 50nm for both radially and linearly polarized excitations. Magnetic field intensity (b and c), volume current density (d) and electric field intensity (e) distributions for SRA under radially polarized excitation at resonance (3.15μm), when D = 300nm, G = 50nm and W = 30nm.
for both the radially and linearly polarized excitation. It is evident that enhancement factor is improved for both the radially and linearly polarized excitation with decreasing W accompanied by red shift of the resonant wavelength (λres). As the strip width decreases from W = 50nm to 30nm, λres shifts from 2.93 μm to 3.15 μm and the enhancement factor increases from 4.00 × 104 to 7.24 × 104 times for radially polarized excitation. For given W, the λres didn’t shift under different polarized excitations due to the invariant resonant conditions. The enhancement factors with radial polarization, however, are improved by two orders than that with the linearly polarization.

As we all know, the surface plasmons can only be excited in noble metal structures by the TM polarized wave. For a SRA, which exhibits rotational symmetry, a radially polarized beam is TM polarized along the entire metal/dielectric interface of SRA and thus allows efficient coupling all incident power to surface plasmon modes. Subsequently, higher field enhancement factor can be achieved with radially polarized wave in circular symmetric SRA.

To illustrate plasmonic resonance, Figs. 2(b), 2(c), 2(d) and 2(e) show the near-field distributions of the magnetic field intensity (xy and xz plane), current density (xy plane), and the electric field intensity (xy plane) generated by a SRA at a wavelength of 3.15 μm for the radial case. The structure parameters used is of D = 300 nm, W = 30 nm and G = 50 nm. The magnetic field intensity distribution is taken at the plane 10 nm above the nanoantenna whereas the current density and electric field distributions are taken in the middle plane of the metal layer.

According to Fig. 2(b), the magnetic hot spot is generated resonantly above the strip with the full width at half maximum (FWHM) size of 67.8 nm (x) × 51.6 nm (y), which is determined by the width of the strip. Figure 2(c) shows that the magnetic field is intensely trapped along strip in the x-z plane. Although the maximum of the two hot spot in Fig. 2(c) is close, the magnetic field in the substrate side is still higher than the air side due to the different refractive index between both sides of SPA and the asymmetric incident. This phenomenon is also observed in Ref. 10

10. T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011). [CrossRef] [PubMed]

. Figure 2(d) clearly shows the current density is concentrated in the same location of the magnetic spot. Actually, a SRA can be seen as a composition of a circular disc and a circular aperture connected by a strip. If excited at resonance, the aperture is polarized and charges accumulated on the edges of the disc will lead to high electric field enhancement along the edges (Fig. 2(e)). Subsequently, the current density will be concentrated in the strip and amplified by the central disc efficiently. Following Ampere’s law, the local concentration of the current intensity will lead to a strong magnetic field intensity enhancement surround the strip. In another point of view, magnetic hot spot can be considered as the result of Babinet’s principle, which states a complementary structure illuminated by a complementary wave field causes a complementary scattering response. As it is well known, the azimuthally polarized electric field could improve the electric hot spot in split ring [18

18. J. Scheuer, “Ultra-high enhancement of the field concentration in Split Ring Resonators by azimuthally polarized excitation,” Opt. Express 19(25), 25454–25464 (2011). [CrossRef] [PubMed]

], the complementary wave of the azimuthally polarized electric field, i.e. azimuthally polarized magnetic field, therefore, can improve the magnetic hot spot in split ring aperture, which denotes as the complementary structure of split ring.

3.2 Structural investigation

In order to further develop the design rules to describe the operation of SRA, the resonant enhancement factor and λres have been plotted versus the aperture length (D) and the gap width (G). As shown in Figs. 3(a)
Fig. 3 The variation of resonant wavelength (indicated as dots with full lines) with D (a) and G (b) for radially polarized illumination. The resonant wavelengths by linearly polarized excitation are almost identical comparing to that by radially polarized excitation. The relationship of magnetic field intensity enhancement (indicated as triangles with dotted lines) with D (a) and G (b) for both the two illumination. G is kept 50 nm in (a) and D is kept 300 nm in (b).
and 3(b), both enhancement and λres increase as increasing the aperture dimension (increasing D) or increasing the disc (decreasing G), which is equivalent to increase the effective length of the aperture. The red shift of λres is understood as the result of the longer antenna length while longer λres leads to higher enhancement, which is ascribed to the decrease of loss in metal with increasing incident wavelength.

Besides altering the structural parameters above, it is also possible to modify the resonance behavior and enhancement factors by introducing additional strips to the structure. Figure 4
Fig. 4 Magnetic spectral response under the radially polarized illumination for one- (in red), two- (in blue) and four-strip (in black) split ring aperture, whose resonant wavelength are 3.15μm, 1.90μm and 1.23μm, respectively
presents the schematics of SRA with one (in red), two (in blue) and four strips (in black), and their respective magnetic response. It is obvious that the more strips a SRA have, the smaller the enhancement and λres will be. For example, the enhancement decrease from 7.24 × 104 to 1.46 × 104 times after adding a strip to the one-strip SRA. A similar condition is also observed in a split ring resonator [18

18. J. Scheuer, “Ultra-high enhancement of the field concentration in Split Ring Resonators by azimuthally polarized excitation,” Opt. Express 19(25), 25454–25464 (2011). [CrossRef] [PubMed]

]. When coming to four-strip case, the enhancement factor decreases to 614 times. Unlike the one-strip SRA, in a multi-strip structure, the current density won’t be concentrated in the one and only strip and the effective length of SRA will be dramatically reduced by the additional strips. Therefore, both λres and the enhancement decrease with increasing the number of the strip. In addition, another factor that contributes to the decrease of the magnetic field intensity enhancement in a multi-strip SRA is the blue shift of λres, which will increase the imaginary part of the dielectric constant and the loss in metal.

4. Conclusion

In conclusion, inspired by Babinet’s principle, we have investigated the operation of split ring apertures in near-infrared region, whose complement is the well-known split ring. Magnetic field intensity enhancement for the apertures is presented. Radially polarized beam can be more efficiently coupled into SPPs modes via the circular symmetric structure and lead to higher enhancing factor of the magnetic field. The resonance can be easily tuned into the near infrared or even visible region by add more strips. We anticipate that the results from this investigation will contribute to both theoretical and experimental investigations into optical antennas for higher magnetic field intensity enhancement.

Acknowledgment

This work was supported by the National Natural Science Foundation of China under Grant No. 61177061, 61177014, 61076015, 61006037, 11204208 and Research Fund for the Doctoral Program of Higher Education of China (New Teacher) under Grant No. 20110032120070 and Tianjin Natural Science foundation (Project Nos. 11JCZDJC21900 and 11JCYDJC25800).

References and links

1.

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon. 1(3), 438–483 (2009). [CrossRef]

2.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011). [CrossRef]

3.

L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett. 10(4), 1229–1233 (2010). [CrossRef] [PubMed]

4.

L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem. 57(1), 303–331 (2006). [CrossRef] [PubMed]

5.

A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett. 6(3), 355–360 (2006). [CrossRef] [PubMed]

6.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

7.

Z. Gao, L. Xu, and Z. Wang, “Broadband plasmonic nanoantenna for magnetic field enhancement,” J. Electromagn. Waves Appl. 25(17-18), 2341–2352 (2011). [CrossRef]

8.

E. Vourc’h, P.-Y. Joubert, and L. Cima, “Analytical and numerical analyses of a current sensor using nonlinear effects in a flexible magnetic transducer,” Prog. Electromagnetics Res. 99, 323–338 (2009). [CrossRef]

9.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313(5786), 502–504 (2006). [CrossRef] [PubMed]

10.

T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett. 11(3), 1009–1013 (2011). [CrossRef] [PubMed]

11.

N. Zhou, E. C. Kinzel, and X. Xu, “Complementary bowtie aperture for localizing and enhancing optical magnetic field,” Opt. Lett. 36(15), 2764–2766 (2011). [CrossRef] [PubMed]

12.

F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. 93(19), 197401 (2004). [CrossRef] [PubMed]

13.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009). [CrossRef]

14.

Lumerical FDTD Solution, FDTD Solutions 7.5, http://www.lumerical.com/.

15.

W. M. Haynes and D. R. Lide, Handbook of chemistry and physics (CRC Press, 2003).

16.

D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single “bowtie” nanoantennas resonant in the visible,” Nano Lett. 4(5), 957–961 (2004). [CrossRef]

17.

L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B 107(30), 7343–7350 (2003). [CrossRef]

18.

J. Scheuer, “Ultra-high enhancement of the field concentration in Split Ring Resonators by azimuthally polarized excitation,” Opt. Express 19(25), 25454–25464 (2011). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optics at Surfaces

History
Original Manuscript: October 31, 2012
Revised Manuscript: December 29, 2012
Manuscript Accepted: March 4, 2013
Published: March 12, 2013

Citation
Y. Yang, H. T. Dai, and X. W. Sun, "Split ring aperture for optical magnetic field enhancement by radially polarized beam," Opt. Express 21, 6845-6850 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-6845


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Adv. Opt. Photon.1(3), 438–483 (2009). [CrossRef]
  2. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics5(2), 83–90 (2011). [CrossRef]
  3. L. Cao, J. S. Park, P. Fan, B. Clemens, and M. L. Brongersma, “Resonant germanium nanoantenna photodetectors,” Nano Lett.10(4), 1229–1233 (2010). [CrossRef] [PubMed]
  4. L. Novotny and S. J. Stranick, “Near-field optical microscopy and spectroscopy with pointed probes,” Annu. Rev. Phys. Chem.57(1), 303–331 (2006). [CrossRef] [PubMed]
  5. A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, and W. E. Moerner, “Toward nanometer-scale optical photolithography: utilizing the near-field of bowtie optical nanoantennas,” Nano Lett.6(3), 355–360 (2006). [CrossRef] [PubMed]
  6. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008). [CrossRef] [PubMed]
  7. Z. Gao, L. Xu, and Z. Wang, “Broadband plasmonic nanoantenna for magnetic field enhancement,” J. Electromagn. Waves Appl.25(17-18), 2341–2352 (2011). [CrossRef]
  8. E. Vourc’h, P.-Y. Joubert, and L. Cima, “Analytical and numerical analyses of a current sensor using nonlinear effects in a flexible magnetic transducer,” Prog. Electromagnetics Res.99, 323–338 (2009). [CrossRef]
  9. M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science313(5786), 502–504 (2006). [CrossRef] [PubMed]
  10. T. Grosjean, M. Mivelle, F. I. Baida, G. W. Burr, and U. C. Fischer, “Diabolo nanoantenna for enhancing and confining the magnetic optical field,” Nano Lett.11(3), 1009–1013 (2011). [CrossRef] [PubMed]
  11. N. Zhou, E. C. Kinzel, and X. Xu, “Complementary bowtie aperture for localizing and enhancing optical magnetic field,” Opt. Lett.36(15), 2764–2766 (2011). [CrossRef] [PubMed]
  12. F. Falcone, T. Lopetegi, M. A. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett.93(19), 197401 (2004). [CrossRef] [PubMed]
  13. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009). [CrossRef]
  14. Lumerical FDTD Solution, FDTD Solutions 7.5, http://www.lumerical.com/ .
  15. W. M. Haynes and D. R. Lide, Handbook of chemistry and physics (CRC Press, 2003).
  16. D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. E. Moerner, “Gap-dependent optical coupling of single “bowtie” nanoantennas resonant in the visible,” Nano Lett.4(5), 957–961 (2004). [CrossRef]
  17. L. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and width,” J. Phys. Chem. B107(30), 7343–7350 (2003). [CrossRef]
  18. J. Scheuer, “Ultra-high enhancement of the field concentration in Split Ring Resonators by azimuthally polarized excitation,” Opt. Express19(25), 25454–25464 (2011). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited