Plasmonic focusing in spiral nanostructures under linearly polarized illumination Jie Li,1 Chaojie Yang,1 Huabo Zhao,1 Feng Lin,1 and Xing Zhu1,2,* 1
School of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China 2 National Center for Nanoscience and Technology, Beijing 100190, China *[email protected]
Abstract: We have investigated the focusing properties of nanostructured plasmonic spiral lens by using linearly polarized illumination, and analysed its field enhancement effect based on the phase matching theory and finitedifference time-domain simulation. We demonstrate that under linearly polarized illumination, spiral plasmonic lens shows focusing property regardless its polarization directions, and the focal spot is about 250nm when the incident wavelength is 671nm. The intensity of the focal spot could also be controlled by altering the radius, the number of turns and the width of the nanostructured spiral slot which are confirmed by finitedifference time-domain simulation. © 2014 The Optical Society OCIS codes: (240.6680) Surface plasmons; (260.5430) Polarization; (170.5810) Scanning microscopy.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824– 830 (2003). Z. Y. Fang, C. F. Lin, R. M. Ma, S. Huang, and X. Zhu, “Planar Plasmonic Focusing and Optical Transport Using CdS Nanoribbon,” ACS Nano 4(1), 75–82 (2010). W. T. Song, Z. Y. Fang, S. Huang, F. Lin, and X. Zhu, “Near-field nanofocusing through a combination of plasmonic Bragg reflector and converging lens,” Opt. Express 18(14), 14762–14767 (2010). B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010). T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5(7), 475–479 (2009). D. F. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005). Z. Y. Fang, L. R. Fan, C. F. Lin, D. Zhang, A. J. Meixner, and X. Zhu, “Plasmonic Coupling of Bow Tie Antennas with Ag Nanowire,” Nano Lett. 11(4), 1676–1680 (2011). X. Y. Lang, L. H. Qian, P. F. Guan, J. Zi, and M. W. Chen, “Localized surface plasmon resonance of nanoporous gold,” Appl. Phys. Lett. 98, 093701 (2011). D. C. Kennedy, L. L. Tay, R. K. Lyn, Y. Rouleau, J. Hulse, and J. P. Pezacki, “Nanoscale Aggregation of Cellular beta2-Adrenergic Receptors Measured by Plasmonic Interactions of Functionalized Nanoparticles,” ACS Nano 3(8), 2329–2339 (2009). Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear Optical Properties of Core-Shell Nanocavities for Enhanced Second-Harmonic Generation,” Phys. Rev. Lett. 104(20), 207402 (2010). F. M. Huang, D. Wilding, J. D. Speed, A. E. Russell, P. N. Bartlett, and J. J. Baumberg, “Dressing Plasmons in Particle-in-Cavity Architectures,” Nano Lett. 11(3), 1221–1226 (2011). L. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). A. B. Evlyukhin, S. I. Bozhevolnyi, A. L. Stepanov, R. Kiyan, C. Reinhardt, S. Passinger, and B. N. Chichkov, “Focusing and directing of surface plasmon polaritons by curved chains of nanoparticles,” Opt. Express 15(25), 16667–16680 (2007). H. Kim and B. Lee, “Diffractive slit patterns for focusing surface plasmon polaritons,” Opt. Express 16(12), 8969–8980 (2008).
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16686
16. Z. Y. Fang, Q. A. Peng, W. T. Song, F. H. Hao, J. Wang, P. Nordlander, and X. Zhu, “Plasmonic Focusing in Symmetry Broken Nanocorrals,” Nano Lett. 11(2), 893–897 (2011). 17. Q. W. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31(11), 1726–1728 (2006). 18. W. B. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. W. Zhan, “Experimental Confirmation of Miniature Spiral Plasmonic Lens as a Circular Polarization Analyzer,” Nano Lett. 10(6), 2075–2079 (2010). 19. S. Y. Yang, W. B. Chen, R. L. Nelson, and Q. W. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009). 20. W. B. Chen, R. L. Nelson, and Q. W. Zhan, “Efficient miniature circular polarization analyzer design using hybrid spiral plasmonic lens,” Opt. Lett. 37(9), 1442–1444 (2012). 21. A. Bouhelier, F. Ignatovich, A. Bruyant, C. Huang, G. Colas des Francs, J.-C. Weeber, A. Dereux, G. P. Wiederrecht, and L. Novotny, “Surface plasmon interference excited by tightly focused laser beams,” Opt. Lett. 32(17), 2535–2537 (2007). 22. G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9(5), 2139–2143 (2009). 23. W. Song, Z. Fang, S. Huang, F. Lin, and X. Zhu, “Near-field nanofocusing through a combination of plasmonic Bragg reflector and converging lens,” Opt. Express 18(14), 14762–14767 (2010). 24. A. Taflove and K. R. Umashankar, “The Finite-Difference Time-Domain Method for Numerical Modeling of Electromagnetic-Wave Interactions,” Electromagnetics 10(1-2), 105–126 (1990). 25. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985). 26. J. Miao, Y. Wang, C. Guo, Y. Tian, S. Guo, Q. Liu, and Z. Zhou, “Plasmonic lens with multiple-turn spiral nano-structures,” Plasmonics 6(2), 235–239 (2011).
1. Introduction Surface plasmon polaritons (SPPs) are collective electromagnetic excitations that propagate at the interface between dielectric and metallic layers, evanescently confined in the direction perpendicular to the interface [1]. SPP waves have a shorter wavelength and stronger field enhancement than light, making them favorable for many applications such as plasmon focusing [2–4], subwavelength waveguiding [5–8], molecules detection [9], surface Raman scattering enhancement [10–12], etc. As one of the important part in this field, SPPs focusing has been intensively in the recent years since it can manipulate light in spatially confined regions much smaller than the Opt.ical diffraction limit, resulting in a substantial enhancement of the electric field intensity [1, 4]. It works with the interference of SPPs propagating from the nanoscale plasmonic structures to produce subwavelength focusing spot. Some previous works have both numerically and experimentally demonstrated plasmonic focusing techniques using arrays of nanometric holes [13], chains of nanoparticles [14] and other diffractive slit patterns [15, 16]. In all above cases linearly polarized light with certain polarization angle have been employed. Alternatively, plamonic focusing can be achieved on annular nanoslit with radially polarized light source [17]. But the efficient focusing is only achieved when the center of the incident beam is perfectly aligned with the center of the lens in the order of a few micrometers, which is difficult in experiment. Q. Zhan et al. have investigated the spiral plasmonic lens for the SPP focusing under circular polarized light [18–20]. They demonstrated a spiral plasmonic lens can focus circular polarization light with a given handedness while simultaneously defocus the circular polarization of the opposite chirality. Based on their work, instead of circular polarized light, we try to use linearly polarized light to excite spiral nanostructures to realize surface plasmon focusing. Our method may be simpler for saving the trouble of acquisition of certain kind of circular polarized light. 2. Model analysis and experiment results We first studied a simpler schematic model of a plasmonic lens with one turn spiral slot structure, which is illustrated in Fig. 1. A right-handed single Archimedes’ spiral slot was etched into a thin metal film (such as Au) deposited on glass substrate (SiO2). In the cylindrical coordinates, the right-handed spiral structure can be described as,
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16687
r = r0 +
d ϕ 2π
(1)
where r0 is a constant and d equals the surface plasmon polariton wavelength λspp. The illumination is along the z direction, which comes out of the plane. When we use linearly polarized light, SPPs are originating from every two opposite points along the circumference
Fig. 1. Schematic diagram of a right-handed single-turn Archimedes’ spiral and the parameters used in analysis. The illumination is along the z direction, which comes out of the plane.
of annular slot and propagating towards the center. Because of uniform distribution of the linearly polarized light, SPP waves excited by the every two opposite points with their Ez pointing in the opposed z direction. That is the reason why an axially symmetric annular slot cannot focus SPPs by using linearly polarized light. But in the case of spiral structure as is showed in Fig. 1, we can see that for every two opposite points, such as A and C or B and D, r2 - r0 = r3- r1 = 0.5λSPP when d = λspp. A relative phase shift of π for SPPs launched from every two opposite points when the radius mismatch is 0.5λSPP, which results in a constructive interference at the corral center. So we can infer that whatever the linear polarization direction of the light used, the radius mismatch of the every two opposite points is always 0.5λSPP, and the relative phase shift π for SPPs propagation can result in a constructive interference at the center. In this consideration, we designed a spiral structure to confirm our idea. A 200nm thick gold film was deposited onto a glass substrate by e-beam evaporation. A right-handed Archimede’s spiral slots with three turns were fabricated by a Focused Ion Beam (FIB) on the gold film as shown in Fig. 2(a). The use of multi-turns is to enhance the focusing effect. The sample was illuminated from the bottom by a linearly polarized laser beam with the wavelength of 671nm. The SPP wavelength λspp was calculated to be 640 nm. During the fabrication, the spiral parameters in Eq. (1) were set to be r0 = 2λspp and d = λspp. The slot width of the spiral lens was chosen to be 200 nm. The two-dimensional intensity distribution of SPPs was measured by a SNOM (Nanonics SNOM-100). The probe of the SNOM is an Al-coated, tapered cantilever Opt.ical fiber, with an apex diameter of 100nm. The collection of SPP light is acquired by an Avalanche Photo Diode system.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16688
Fig. 2. SEM images of three-turn Archimedes’ spiral in gold film fabricated with FIB milling with each turn spiral d equal to (a) 640nm (λspp) and (b) 1280nm (2λspp) respectively. The thickness of the gold film is 200nm and the width of the slot is 200nm.
Under linearly polarized light, SPPs are excited at the slot edge of the spiral lens and propagate along the air/gold interface. The surface plasmon intensity distribution is directly imaged by a SNOM as is showed in Fig. 3(a). The average full-width at half-maximum (FWHM) of the focal spots is about 250nm (Fig. 3(b)). Moreover, because of the spirality of the structure, we can infer that whatever the linear polarization direction of the light used, a constructive interference will always appear at the center (Figs. 3(c), 3(d)).
Fig. 3. (a, c, d) SNOM images at the air/gold interface with spiral plasmonic lens of Fig. 2(a) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles. (b) Cross sections through the center of the plasmonic lens along the polarized direction according to (a).
For comparison purposes, we design another structure as is shown in Fig. 2(b). In this structure, we change the spiral parameter d to 2λspp. In this case, the radius mismatch is r2 - r0 #209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16689
= r3- r1 = λspp and the SPP interference pattern can be turned to the destructive one, resulting in a doughnut spot with a dark center (Fig. 4).
Fig. 4. (a, b) SNOM images at the air/gold interface with spiral plasmonic lens of Fig. 2(b) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles.
Basically, the coupling efficiency of longitudinal component |Ez|2 is much lower than the transversal components |Er|2 for a probe with such small aperture size [21], and the scatteringSNOM is more suitable for the z-component detection. However, in our opinion, the zcomponent is not as small as not-detectable for the following two main reasons. First, we can get that the ratio |Ez|2/ |Er|2 is more than 30 in the FDTD simulation, meaning that despite of the weak coupling of |Ez|2 to the probe, the measured intensity is still expected to correspond mostly to |Ez|2. The similar results and explanations can also be found in other works [22, 23]. Second, the enhanced coupling of |Ez|2 can be achieved by imperfections in the probe, such as the sharp perturbations or nonsymmetrical probe. Although the product label on our probe says that the aperture size is 100nm, it may well be much larger than that after being used for a long time in our lab. As reported in the literature [22], even using two probes with the same nominal parameters, there are also large variance in coupling efficiency of |Er|2 and |Ez|2 component to the probe. Besides, we used tapping mode in the SNOM detection. The probe with a high-frequency vibration near the sample surface will disturb near field and enhance the coupling efficiency of |Ez|2 component. In this case, the metallic coating is acting similar as the probe of scattering-SNOM, which can help us to increase the coupling efficiency of zcomponent. 3. FDTD simulations and discussions To verify the focusing condition, we use finite-difference time-domain (FDTD) method [24] for the theoretical simulations. The simulated dispersive data are based on the experimental data given by Palik [25]. In our design, free space wavelength λ0 = 671nm is adOpt.ed, and the relative permittivity of the Au used in FDTD is εm = −12.3 + 1.13j. The effective refractive index of the surface plasmon at the interface between the Au layer and air is nspp = 1.05, corresponding to the surface plasmon wavelength λspp = 640nm. The propagation length of the surface plasmon in this case is Lspp = 12.6nm. Figure 5 show the FDTD simulations of |Ez|2 distribution with the structural parameters of Fig. 2(a). We can see that under different polarization directions of linearly polarized light, there are always focal spots at the center. For more detailed analysis of the focal spot, as is shown in Fig. 5(b), the FWHM of the focal spot is around 200nm, which is much smaller than half of the surface plasmon wavelength.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16690
Fig. 5. (a, c, d) FDTD simulation of |Ez|2 distribution with spiral plasmonic lens of Fig. 2(a) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles. (b) Cross sections through the center of the plasmonic lens along the polarized direction according to (a).
Furthermore, we investigate the influence of the structure parameters of the spiral slot to the performance of the right-handed spiral plasmonic lens under linearly polarized illumination, such as the size, the number of turns, and the width of the spiral slot. We do the simulations when the focusing condition of the spiral slot is satisfied (d = λspp = 640nm). In this simulation, we use only one turn of the spiral structures to simplify the analysis. Since more energy can be coupled to the focal spot with the increase of r0, the intensity of the focal spot increases by expanding the turning radius, r0, as show in Fig. 6(a). But when the r0 is larger than 10μm, the intensity starts to decrease. That is due to the limitation of the propagation length of the SPPs. The relative electric field intensity can also be controlled by adjusting the number of turns of the spiral slot. As shown in Fig. 6(b), the intensity becomes stronger and stronger with the increase of the turns of the spiral slot from 1 to 3. And the intensity will reach a plateau when the number of turns is 4. Moreover, the increasing rate decreases quickly with the further increase of the turns. But when n = 4, the largest radius of the spiral shot is about 4μm which is smaller than the propagation length of SPPs,so we consider this kind of decrease is mainly attributed to the destructive interference of SPPs excited from different number of turns. The slit width of the spiral structure is also a key parameter to manipulate the focusing intensity. The results of simulations for the electric field intensity for varying the slit width from 100 to 400nm by a step of 50nm are shown in Fig. 6(c). Here, we also use only one turn (r0 = 1280nm) of the spiral structures to simplify the analysis. The intensity at the focal point shows an increase with the slit width. This is mainly because that the slit width could strongly affect the transmissivity of the incident light. But when the slit width is larger than 300nm, the increasing rate will decrease quickly with the further increase of the width. This is
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16691
because the slit width is larger than half wavelength of the incident light and most of the incident light can transmit the slit directly without excite SPPs.
Fig. 6. Simulated |Ez|2 at the central point versus: (a) r0 (one turn, slit width w = 200 nm) (b) the turns of the spiral nano-structures (slit width w = 200 nm, minimal r0 = 1280nm), and (c) the slit width (one turn, r0 = 1280nm).
As it shown above, the field enhancement is decided by the parameters of the structure. Based on the relative Opt.imal parameter, we do the FDTD simulation of 4 turns spiral lens with initial radium of 4μm and slot width of 300nm. The result is shown in Fig. 7. The enhancement factor is more than 11 under linearly polarized light (Fig. 7(a)). When we use circular polarized light, the enhancement factor is more than 18 (Fig. 7(b)), which is close to the result in previous work [26].
Fig. 7. FDTD simulation of |Ez|2 distribution with spiral plasmonic lens under (a) linearly polarized and (b) circular polarized illumination.
It’s true that using linearly polarized light instead of circular polarized light did not have a bigger enhancement factor because of its asymmetry, but there is not a very big difference. And its focusing spot also have a small size as the same as that under circular polarized illumination. On the other hand, spiral plasmonic lens can only focus circular polarization light with a given handedness while simultaneously defocus the circular polarization of the opposite chirality, so it’s suitable for circular polarization analyzer. But for the purpose of SPP focusing, acquisition certain kind of circular polarized light will need extra lens group and some kind of polarization detection equipment in the whole experimental system. It’s not suitable for the future high-integrated Opt.ical devices in which SPP focusing may be just an internal part of the system. Besides, comparing to other focusing structure using linearly polarized light [16], it is more convenient that we can realize the focusing without concerning
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16692
the polarization angle of the linearly polarized light. So we think our method will gain much more superiority in practical application than others. 4. Conclusion In conclusion, we experimentally demonstrated that spiral plasmonic lens can focus SPP by using linearly polarized illumination regardless its polarization directions and the average FWHM of the focal spot is about 250nm. The focusing condition depends mainly on the relationship between the structure parameters and the wavelength of SPP. This method simplified the process for acquisition of circular polarized light and does not need to concern about the polarization directions of the linearly polarized light. Therefore, our method supplies a more effective and convenient way for the practical use of plasmonic lenses. More interestingly, by using FDTD simulation, we found that the electric field intensity at the center of the exit surface can be modulated by altering the size, the turns and the width of the spiral slot, which have many potential applications for intensity actuating, focusing beams, nano-scale beam splitters, and other applications. Acknowledgments The work is supported by the National Science Foundation of China (Grant nos. 61176120, 61378059, 11374023), National Basic Research Program of China (973 Program) Grant no. 2012CB933004 and Beijing Natural Science Foundation (L140007). National Undergraduate Innovational Experimentation Program and NFFTBS Grant no. J1030310, J1103205.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16693
School of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China 2 National Center for Nanoscience and Technology, Beijing 100190, China *[email protected]
Abstract: We have investigated the focusing properties of nanostructured plasmonic spiral lens by using linearly polarized illumination, and analysed its field enhancement effect based on the phase matching theory and finitedifference time-domain simulation. We demonstrate that under linearly polarized illumination, spiral plasmonic lens shows focusing property regardless its polarization directions, and the focal spot is about 250nm when the incident wavelength is 671nm. The intensity of the focal spot could also be controlled by altering the radius, the number of turns and the width of the nanostructured spiral slot which are confirmed by finitedifference time-domain simulation. © 2014 The Optical Society OCIS codes: (240.6680) Surface plasmons; (260.5430) Polarization; (170.5810) Scanning microscopy.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824– 830 (2003). Z. Y. Fang, C. F. Lin, R. M. Ma, S. Huang, and X. Zhu, “Planar Plasmonic Focusing and Optical Transport Using CdS Nanoribbon,” ACS Nano 4(1), 75–82 (2010). W. T. Song, Z. Y. Fang, S. Huang, F. Lin, and X. Zhu, “Near-field nanofocusing through a combination of plasmonic Bragg reflector and converging lens,” Opt. Express 18(14), 14762–14767 (2010). B. Lee, S. Kim, H. Kim, and Y. Lim, “The use of plasmonics in light beaming and focusing,” Prog. Quantum Electron. 34(2), 47–87 (2010). T. Holmgaard, J. Gosciniak, and S. I. Bozhevolnyi, “Long-range dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 18(22), 23009–23015 (2010). A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. D. Snapp, A. V. Akimov, M. H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5(7), 475–479 (2009). D. F. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30(10), 1186–1188 (2005). Z. Y. Fang, L. R. Fan, C. F. Lin, D. Zhang, A. J. Meixner, and X. Zhu, “Plasmonic Coupling of Bow Tie Antennas with Ag Nanowire,” Nano Lett. 11(4), 1676–1680 (2011). X. Y. Lang, L. H. Qian, P. F. Guan, J. Zi, and M. W. Chen, “Localized surface plasmon resonance of nanoporous gold,” Appl. Phys. Lett. 98, 093701 (2011). D. C. Kennedy, L. L. Tay, R. K. Lyn, Y. Rouleau, J. Hulse, and J. P. Pezacki, “Nanoscale Aggregation of Cellular beta2-Adrenergic Receptors Measured by Plasmonic Interactions of Functionalized Nanoparticles,” ACS Nano 3(8), 2329–2339 (2009). Y. Pu, R. Grange, C. L. Hsieh, and D. Psaltis, “Nonlinear Optical Properties of Core-Shell Nanocavities for Enhanced Second-Harmonic Generation,” Phys. Rev. Lett. 104(20), 207402 (2010). F. M. Huang, D. Wilding, J. D. Speed, A. E. Russell, P. N. Bartlett, and J. J. Baumberg, “Dressing Plasmons in Particle-in-Cavity Architectures,” Nano Lett. 11(3), 1221–1226 (2011). L. L. Yin, V. K. Vlasko-Vlasov, J. Pearson, J. M. Hiller, J. Hua, U. Welp, D. E. Brown, and C. W. Kimball, “Subwavelength focusing and guiding of surface plasmons,” Nano Lett. 5(7), 1399–1402 (2005). A. B. Evlyukhin, S. I. Bozhevolnyi, A. L. Stepanov, R. Kiyan, C. Reinhardt, S. Passinger, and B. N. Chichkov, “Focusing and directing of surface plasmon polaritons by curved chains of nanoparticles,” Opt. Express 15(25), 16667–16680 (2007). H. Kim and B. Lee, “Diffractive slit patterns for focusing surface plasmon polaritons,” Opt. Express 16(12), 8969–8980 (2008).
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16686
16. Z. Y. Fang, Q. A. Peng, W. T. Song, F. H. Hao, J. Wang, P. Nordlander, and X. Zhu, “Plasmonic Focusing in Symmetry Broken Nanocorrals,” Nano Lett. 11(2), 893–897 (2011). 17. Q. W. Zhan, “Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam,” Opt. Lett. 31(11), 1726–1728 (2006). 18. W. B. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. W. Zhan, “Experimental Confirmation of Miniature Spiral Plasmonic Lens as a Circular Polarization Analyzer,” Nano Lett. 10(6), 2075–2079 (2010). 19. S. Y. Yang, W. B. Chen, R. L. Nelson, and Q. W. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009). 20. W. B. Chen, R. L. Nelson, and Q. W. Zhan, “Efficient miniature circular polarization analyzer design using hybrid spiral plasmonic lens,” Opt. Lett. 37(9), 1442–1444 (2012). 21. A. Bouhelier, F. Ignatovich, A. Bruyant, C. Huang, G. Colas des Francs, J.-C. Weeber, A. Dereux, G. P. Wiederrecht, and L. Novotny, “Surface plasmon interference excited by tightly focused laser beams,” Opt. Lett. 32(17), 2535–2537 (2007). 22. G. M. Lerman, A. Yanai, and U. Levy, “Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized light,” Nano Lett. 9(5), 2139–2143 (2009). 23. W. Song, Z. Fang, S. Huang, F. Lin, and X. Zhu, “Near-field nanofocusing through a combination of plasmonic Bragg reflector and converging lens,” Opt. Express 18(14), 14762–14767 (2010). 24. A. Taflove and K. R. Umashankar, “The Finite-Difference Time-Domain Method for Numerical Modeling of Electromagnetic-Wave Interactions,” Electromagnetics 10(1-2), 105–126 (1990). 25. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985). 26. J. Miao, Y. Wang, C. Guo, Y. Tian, S. Guo, Q. Liu, and Z. Zhou, “Plasmonic lens with multiple-turn spiral nano-structures,” Plasmonics 6(2), 235–239 (2011).
1. Introduction Surface plasmon polaritons (SPPs) are collective electromagnetic excitations that propagate at the interface between dielectric and metallic layers, evanescently confined in the direction perpendicular to the interface [1]. SPP waves have a shorter wavelength and stronger field enhancement than light, making them favorable for many applications such as plasmon focusing [2–4], subwavelength waveguiding [5–8], molecules detection [9], surface Raman scattering enhancement [10–12], etc. As one of the important part in this field, SPPs focusing has been intensively in the recent years since it can manipulate light in spatially confined regions much smaller than the Opt.ical diffraction limit, resulting in a substantial enhancement of the electric field intensity [1, 4]. It works with the interference of SPPs propagating from the nanoscale plasmonic structures to produce subwavelength focusing spot. Some previous works have both numerically and experimentally demonstrated plasmonic focusing techniques using arrays of nanometric holes [13], chains of nanoparticles [14] and other diffractive slit patterns [15, 16]. In all above cases linearly polarized light with certain polarization angle have been employed. Alternatively, plamonic focusing can be achieved on annular nanoslit with radially polarized light source [17]. But the efficient focusing is only achieved when the center of the incident beam is perfectly aligned with the center of the lens in the order of a few micrometers, which is difficult in experiment. Q. Zhan et al. have investigated the spiral plasmonic lens for the SPP focusing under circular polarized light [18–20]. They demonstrated a spiral plasmonic lens can focus circular polarization light with a given handedness while simultaneously defocus the circular polarization of the opposite chirality. Based on their work, instead of circular polarized light, we try to use linearly polarized light to excite spiral nanostructures to realize surface plasmon focusing. Our method may be simpler for saving the trouble of acquisition of certain kind of circular polarized light. 2. Model analysis and experiment results We first studied a simpler schematic model of a plasmonic lens with one turn spiral slot structure, which is illustrated in Fig. 1. A right-handed single Archimedes’ spiral slot was etched into a thin metal film (such as Au) deposited on glass substrate (SiO2). In the cylindrical coordinates, the right-handed spiral structure can be described as,
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16687
r = r0 +
d ϕ 2π
(1)
where r0 is a constant and d equals the surface plasmon polariton wavelength λspp. The illumination is along the z direction, which comes out of the plane. When we use linearly polarized light, SPPs are originating from every two opposite points along the circumference
Fig. 1. Schematic diagram of a right-handed single-turn Archimedes’ spiral and the parameters used in analysis. The illumination is along the z direction, which comes out of the plane.
of annular slot and propagating towards the center. Because of uniform distribution of the linearly polarized light, SPP waves excited by the every two opposite points with their Ez pointing in the opposed z direction. That is the reason why an axially symmetric annular slot cannot focus SPPs by using linearly polarized light. But in the case of spiral structure as is showed in Fig. 1, we can see that for every two opposite points, such as A and C or B and D, r2 - r0 = r3- r1 = 0.5λSPP when d = λspp. A relative phase shift of π for SPPs launched from every two opposite points when the radius mismatch is 0.5λSPP, which results in a constructive interference at the corral center. So we can infer that whatever the linear polarization direction of the light used, the radius mismatch of the every two opposite points is always 0.5λSPP, and the relative phase shift π for SPPs propagation can result in a constructive interference at the center. In this consideration, we designed a spiral structure to confirm our idea. A 200nm thick gold film was deposited onto a glass substrate by e-beam evaporation. A right-handed Archimede’s spiral slots with three turns were fabricated by a Focused Ion Beam (FIB) on the gold film as shown in Fig. 2(a). The use of multi-turns is to enhance the focusing effect. The sample was illuminated from the bottom by a linearly polarized laser beam with the wavelength of 671nm. The SPP wavelength λspp was calculated to be 640 nm. During the fabrication, the spiral parameters in Eq. (1) were set to be r0 = 2λspp and d = λspp. The slot width of the spiral lens was chosen to be 200 nm. The two-dimensional intensity distribution of SPPs was measured by a SNOM (Nanonics SNOM-100). The probe of the SNOM is an Al-coated, tapered cantilever Opt.ical fiber, with an apex diameter of 100nm. The collection of SPP light is acquired by an Avalanche Photo Diode system.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16688
Fig. 2. SEM images of three-turn Archimedes’ spiral in gold film fabricated with FIB milling with each turn spiral d equal to (a) 640nm (λspp) and (b) 1280nm (2λspp) respectively. The thickness of the gold film is 200nm and the width of the slot is 200nm.
Under linearly polarized light, SPPs are excited at the slot edge of the spiral lens and propagate along the air/gold interface. The surface plasmon intensity distribution is directly imaged by a SNOM as is showed in Fig. 3(a). The average full-width at half-maximum (FWHM) of the focal spots is about 250nm (Fig. 3(b)). Moreover, because of the spirality of the structure, we can infer that whatever the linear polarization direction of the light used, a constructive interference will always appear at the center (Figs. 3(c), 3(d)).
Fig. 3. (a, c, d) SNOM images at the air/gold interface with spiral plasmonic lens of Fig. 2(a) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles. (b) Cross sections through the center of the plasmonic lens along the polarized direction according to (a).
For comparison purposes, we design another structure as is shown in Fig. 2(b). In this structure, we change the spiral parameter d to 2λspp. In this case, the radius mismatch is r2 - r0 #209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16689
= r3- r1 = λspp and the SPP interference pattern can be turned to the destructive one, resulting in a doughnut spot with a dark center (Fig. 4).
Fig. 4. (a, b) SNOM images at the air/gold interface with spiral plasmonic lens of Fig. 2(b) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles.
Basically, the coupling efficiency of longitudinal component |Ez|2 is much lower than the transversal components |Er|2 for a probe with such small aperture size [21], and the scatteringSNOM is more suitable for the z-component detection. However, in our opinion, the zcomponent is not as small as not-detectable for the following two main reasons. First, we can get that the ratio |Ez|2/ |Er|2 is more than 30 in the FDTD simulation, meaning that despite of the weak coupling of |Ez|2 to the probe, the measured intensity is still expected to correspond mostly to |Ez|2. The similar results and explanations can also be found in other works [22, 23]. Second, the enhanced coupling of |Ez|2 can be achieved by imperfections in the probe, such as the sharp perturbations or nonsymmetrical probe. Although the product label on our probe says that the aperture size is 100nm, it may well be much larger than that after being used for a long time in our lab. As reported in the literature [22], even using two probes with the same nominal parameters, there are also large variance in coupling efficiency of |Er|2 and |Ez|2 component to the probe. Besides, we used tapping mode in the SNOM detection. The probe with a high-frequency vibration near the sample surface will disturb near field and enhance the coupling efficiency of |Ez|2 component. In this case, the metallic coating is acting similar as the probe of scattering-SNOM, which can help us to increase the coupling efficiency of zcomponent. 3. FDTD simulations and discussions To verify the focusing condition, we use finite-difference time-domain (FDTD) method [24] for the theoretical simulations. The simulated dispersive data are based on the experimental data given by Palik [25]. In our design, free space wavelength λ0 = 671nm is adOpt.ed, and the relative permittivity of the Au used in FDTD is εm = −12.3 + 1.13j. The effective refractive index of the surface plasmon at the interface between the Au layer and air is nspp = 1.05, corresponding to the surface plasmon wavelength λspp = 640nm. The propagation length of the surface plasmon in this case is Lspp = 12.6nm. Figure 5 show the FDTD simulations of |Ez|2 distribution with the structural parameters of Fig. 2(a). We can see that under different polarization directions of linearly polarized light, there are always focal spots at the center. For more detailed analysis of the focal spot, as is shown in Fig. 5(b), the FWHM of the focal spot is around 200nm, which is much smaller than half of the surface plasmon wavelength.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16690
Fig. 5. (a, c, d) FDTD simulation of |Ez|2 distribution with spiral plasmonic lens of Fig. 2(a) under linearly polarized illumination. The white arrows indicate the incident illumination with different electric field component angles. (b) Cross sections through the center of the plasmonic lens along the polarized direction according to (a).
Furthermore, we investigate the influence of the structure parameters of the spiral slot to the performance of the right-handed spiral plasmonic lens under linearly polarized illumination, such as the size, the number of turns, and the width of the spiral slot. We do the simulations when the focusing condition of the spiral slot is satisfied (d = λspp = 640nm). In this simulation, we use only one turn of the spiral structures to simplify the analysis. Since more energy can be coupled to the focal spot with the increase of r0, the intensity of the focal spot increases by expanding the turning radius, r0, as show in Fig. 6(a). But when the r0 is larger than 10μm, the intensity starts to decrease. That is due to the limitation of the propagation length of the SPPs. The relative electric field intensity can also be controlled by adjusting the number of turns of the spiral slot. As shown in Fig. 6(b), the intensity becomes stronger and stronger with the increase of the turns of the spiral slot from 1 to 3. And the intensity will reach a plateau when the number of turns is 4. Moreover, the increasing rate decreases quickly with the further increase of the turns. But when n = 4, the largest radius of the spiral shot is about 4μm which is smaller than the propagation length of SPPs,so we consider this kind of decrease is mainly attributed to the destructive interference of SPPs excited from different number of turns. The slit width of the spiral structure is also a key parameter to manipulate the focusing intensity. The results of simulations for the electric field intensity for varying the slit width from 100 to 400nm by a step of 50nm are shown in Fig. 6(c). Here, we also use only one turn (r0 = 1280nm) of the spiral structures to simplify the analysis. The intensity at the focal point shows an increase with the slit width. This is mainly because that the slit width could strongly affect the transmissivity of the incident light. But when the slit width is larger than 300nm, the increasing rate will decrease quickly with the further increase of the width. This is
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16691
because the slit width is larger than half wavelength of the incident light and most of the incident light can transmit the slit directly without excite SPPs.
Fig. 6. Simulated |Ez|2 at the central point versus: (a) r0 (one turn, slit width w = 200 nm) (b) the turns of the spiral nano-structures (slit width w = 200 nm, minimal r0 = 1280nm), and (c) the slit width (one turn, r0 = 1280nm).
As it shown above, the field enhancement is decided by the parameters of the structure. Based on the relative Opt.imal parameter, we do the FDTD simulation of 4 turns spiral lens with initial radium of 4μm and slot width of 300nm. The result is shown in Fig. 7. The enhancement factor is more than 11 under linearly polarized light (Fig. 7(a)). When we use circular polarized light, the enhancement factor is more than 18 (Fig. 7(b)), which is close to the result in previous work [26].
Fig. 7. FDTD simulation of |Ez|2 distribution with spiral plasmonic lens under (a) linearly polarized and (b) circular polarized illumination.
It’s true that using linearly polarized light instead of circular polarized light did not have a bigger enhancement factor because of its asymmetry, but there is not a very big difference. And its focusing spot also have a small size as the same as that under circular polarized illumination. On the other hand, spiral plasmonic lens can only focus circular polarization light with a given handedness while simultaneously defocus the circular polarization of the opposite chirality, so it’s suitable for circular polarization analyzer. But for the purpose of SPP focusing, acquisition certain kind of circular polarized light will need extra lens group and some kind of polarization detection equipment in the whole experimental system. It’s not suitable for the future high-integrated Opt.ical devices in which SPP focusing may be just an internal part of the system. Besides, comparing to other focusing structure using linearly polarized light [16], it is more convenient that we can realize the focusing without concerning
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16692
the polarization angle of the linearly polarized light. So we think our method will gain much more superiority in practical application than others. 4. Conclusion In conclusion, we experimentally demonstrated that spiral plasmonic lens can focus SPP by using linearly polarized illumination regardless its polarization directions and the average FWHM of the focal spot is about 250nm. The focusing condition depends mainly on the relationship between the structure parameters and the wavelength of SPP. This method simplified the process for acquisition of circular polarized light and does not need to concern about the polarization directions of the linearly polarized light. Therefore, our method supplies a more effective and convenient way for the practical use of plasmonic lenses. More interestingly, by using FDTD simulation, we found that the electric field intensity at the center of the exit surface can be modulated by altering the size, the turns and the width of the spiral slot, which have many potential applications for intensity actuating, focusing beams, nano-scale beam splitters, and other applications. Acknowledgments The work is supported by the National Science Foundation of China (Grant nos. 61176120, 61378059, 11374023), National Basic Research Program of China (973 Program) Grant no. 2012CB933004 and Beijing Natural Science Foundation (L140007). National Undergraduate Innovational Experimentation Program and NFFTBS Grant no. J1030310, J1103205.
#209287 - $15.00 USD (C) 2014 OSA
Received 31 Mar 2014; revised 30 May 2014; accepted 16 Jun 2014; published 30 Jun 2014 14 July 2014 | Vol. 22, No. 14 | DOI:10.1364/OE.22.016686 | OPTICS EXPRESS 16693
