Open Access
Add to BibSonomyAbstract
A miniature, simplified and planar plasmonic lens based on the circular array of nano-pinholes for on-axis beaming has been proposed and investigated systematically in the visible spectrum. Focusing properties of the designed plasmonic lens illuminated under circular polarized (CP) light for different radius of circular ring, filled with different dielectrics, with different numbers of pinholes have been investigated and analyzed in detail by finite element method (FEM). Our simulated results demonstrate such a miniature single-turn structure can also generate a totally centrosymmetric focusing spot under the CP illumination. Besides, by properly manipulating the filled dielectric and incident wavelengths, enhanced transmission, elongated depth of focus have also be realized, which can be used to modulate the transmitting fields effectively. Such a miniature and simplified plasmonic focusing lens can open up a vital path toward fiber-end planar photonic devices for biosensing and imaging.
© 2015 Optical Society of America
1. Introduction
Surface plasmon polaritons (SPPs) are generated by the coupling between light and oscillation of electrons at metal/dielectric interfaces. The excitation of SPPs results in a strong local enhancement of the electromagnetic field at the interface [1], and makes it possible to be focused into a strongly confined spot with size beyond the diffraction limit by appropriately designed plasmonic lens structures. Owing to the subwavelength scale feature and field enhancement effects of SPPs, they have attracted a variety of optical applications, such as probes of the scanning near-field optical microscopy [2], high-density optical data storage [3,4 ], analyzing circularly polarized lights [5–9 ], light focusing [10–12 ] and so on.
At optical frequencies, planar focusing devices have been demonstrated by using arrays of nanoslits [13,14 ], nanoholes [15–19 ]. In recent years, more attentions have been paid to the radiation mode of SPPs into free space and its optical applications, such as on-axis light beaming or focusing [20], extraordinary optical transmission [21]. Multiple-turn nano-pinholes based plasmonic nanostructures including circular pinholes structure [15] and elliptical pinholes structures [16,17 ] have been proposed for realizing superfocusing. And Alexander and his associates have also proposed a holey-metal lens structure [18] by controlling the phase front of transmitted light to manipulate the focusing property. All of these investigations have advantages in micron-scale propagation distance with spatial resolution beyond diffraction limit. However, it is difficult to fabricate the multiple-turn tiny holes array with pretty accuracy of the corresponding paprameters. Hence, here, for realizing focusing effect in micron-scaled propagation distance, we propose a plasmonic lens composed of single-turn circularly arranged pinholes array.
In this paper, we have presented a systematic investigation on the single-turn subwavelength structure for plasmonic beaming. Focusing performances of the structures with different parameters under the CP light illumination have been investigated by FEM simulations. In order to grasp the beaming characteristics of the lens, the electric field intensity distributions in the near-field region and far-field region have been analyzed in detail. Besides, the existence of the azimuthal polarization component of the circularly polarized illumination has also been intensively analyzed for confirming its contributions to the focusing performance. The designed miniature and simplified plasmonics lens can effectively focus the CP lights into a totally centrosymmetric subwavelength spot with tunable focal length and elongated depth of focus, which will open up a vital path toward nano-photolithography, biosensor and data storage.
2. Lens structure and simulations
The schematic diagram of the proposed single-turn circularly arranged pinholes structure for plasmonic beaming under CP light is illustrated in Fig. 1 . The 24 nano-pinholes are uniformly arranged along a circular ring. In this design, free space wavelength of λ = 660nm is adopted in the simulation, and the corresponding SPP wavelength is λspp = 629nm when the filling dielectric is air. The nano-pinholes are penetrated through gold thin film with a thickness of 250nm. The left-handed circularly polarized (LCP) light is illuminated from the glass side. Owing to the symmetry of this design, it will have the same transmitted electric intensity distribution for the right-handed circularly polarized (RCP) incident light. As shown in Fig. 1(b), the dimensions of the elliptical hole along the radial direction and azimuthal direction are denoted as a and b respectively, which will be discussed and optimized in the follows. The distance between the center of the structure to the center of pinhole is set as r0.
Fig. 1 Schematic diagram of the single-turn pinholes-based plasmonic lens. The 24 nano-pinholes are uniformly arranged along the circular ring. It is illuminated by circularly polarized light at the wavelength of 660nm. (a)The lateral view, (b) the top view.
CP lights can be disassembled into azimuthal polarization and radial polarization components with a spiral phase front. Here, for analyzing the influence of the existence of the azimuthal polarization component of the CP light to the focusing performance, in our simulations, we arbitrarily select three sets of parameters as: (1) a = 50nm, b = 150nm; (2) a = 150nm, b = 50nm; (3) a = b = 150nm, as shown in Figs. 2(a)-2(c) respectively. The structure consists of single-turn circular ring with the radius of r0 = 2λspp. The different electric field intensity patterns for these three sets of parameters are shown in Figs. 2(d)-2(i). Figures 2(d)-2(f) show electric field intensity distributions at the z = −3400nm plane which lies 150nm above the gold surface.
Fig. 2 The nano-pinholes arrays with different parameters, (a) a = 50nm,b = 150nm; (b) a = 150nm, b = 50nm; (c) a = b = 150nm. Electric field intensity distributions in z = −3400nm plane of the different corresponding nano-pinholes arrays (d)(e)(f), and x = 0 plane (g)(h)(i). The incident wavelength is 660nm and the corresponding wavelength of SPPs is 629nm when the dielectric in the pinholes is air. r0 is set to be 2λspp.
When a = 50nm and b = 150nm as shown in Fig. 2(a), the corresponding transmitting intensity distributions in the xoy plane (z = −3400nm: 150nm above the gold surface) and yoz plane as depicted in Figs. 2(d) and 2(g) respectively, which show that the transmitted intensity distributions are similar to those of the circular slit structure [20], because of the polarization-dependence of elliptical nano-holes [22,23 ]. That is to say, only the radial polarization component of the CP lights which is along minor axis of the elliptical hole, can excite the SPPs that devote to the transmitted lights. Owning to the destructive interference between the two counter-propagating SPPs waves from the corresponding nano-holes in the circular ring, the donut-shaped first-order evanescent Bessel vortex beam can be generated in the transmitted intensity distributions as shown in Figs. 2(d) and 2(g). And it mainly polarized along the z-direction, which can be analytically expressed as [24]:
where kspp is the wavenumber of generated SPP, Jq indicates the first kind qth-order Bessel function, and q is the total topological charge [25].When a = 150nm and b = 50nm as shown in Fig. 2(b), the minor axis of the elliptical hole is along the azimuthal direction. In this structure, the excited SPP is mainly concentrated at the position of pinholes as shown in Fig. 2(e), which can be attributed as the interfering enhancement of the SPPs from the adjacent nano-holes. The reradiation of the generated annular SPPs to the free space, will interfere with each other constructively on the Z axis due to the same phase of the scattering lights, therefore, there is a weak focusing along Z axis as shown in Fig. 2(h).
If both a and b are chosen to be 150nm as shown in Fig. 2(c), the transmitted intensity distributions in the xoy plane and yoz plane have also been demonstrated in Figs. 2(f) and 2(i) respectively. Figure 2(f) shows the xoy plane at the position of z = −3400nm where the focusing hasn’t been generated. An obvious on-axis focusing effect can be observed in Fig. 2(i) under the CP light illumination from the zoy cross profile. In this case, the coupling abilities (to SPPs wave) of the azimuthal polarization component and radial polarization component are nearly comparable owning to the inexistence of polarization-dependence for circular nano-pinholes.
To further illuminate the concrete contributions to the electric field intensity distribution shown in Fig. 2(i) in the metal surface region and focusing region, we have also analyzed the single pinhole under the linearly polarized illumination alone. The phase distribution of longitudinal surface plasmons field with x-linearly polarized illumination is shown in Fig. 3(a) . It can be seen that the generated surface plasmons wave at the opposite edge of the pinhole have a π phase difference, which will lead to the destructive interference of the surface plasmons field along the symmetry axis of the pinholes vertical to the x direction. Figure 3(b) shows the logarithmic electric field distribution at the metal/air surface, which can verify the theory of the destructive interference very well. Hence, if these pinholes are arranged along a circular ring, the azimuthal polarization component of the CP light will bring to the destructive interference at the mental/air surface and converts the SPP energy along the circular ring to the far-field radiations. Figure 3(c) illustrates the diagram of optical transmission through the pinholes under the CP illumination. The SPPs generated at the corresponding sides of the single-turn circularly arranged pinholes array have opposite propagating direction to each other, as well as the directions of surface charge flow. Owning to the spiral phase wavefront of the radial polarization component of the CP illumination, the orientation of the field components in our case is different from that of the radial polarized light [26]. The tangential electric fields Ex of the surface charge flow are in the same direction, and the relationship between the tangential field Ex and the vertical field Ez at the metal/air surface can be expressed as Ez = (jkspp/κmedia)Ex, where kspp is the wavenumber of the SPPs wave and the κmedia is the attenuation factor in the medium according to the Max-well’s equation. Therefore, when the direction of tangential field Ex is opposite to the wave vectors of SPPs, the direction of vertical fields Ez will be along the positive direction of z-axis. On the contrary, the direction of vertical fields Ez will be along the negative direction of z-axis. Hence, the directions of vertical fields Ez for the counter-propagating SPPs are opposite, which leads to a donut-shaped intensity distribution owning to the destructive interference of the vertical electric fields Ez components at the metal surface, as indicated by the red dotted line frame in Fig. 2(i).
Fig. 3 (a) the phase distribution of vertical surface plasmon field with X-linearly polarized illumination .The red dashed arrow denoted the input polarization direction.(b) logarithmic electric field distribution at the metal/air surface with X-linearly polarized illumination.(c) diagram of optical transmission through the pinholes of the entire structure.
The circular pinholes actually can be deemed to metal-insulator-metal (MIM) waveguides and the guided SPPs mode in a MIM waveguide will follow the dispersion as follows [27]:
where d is the diameter of the pinhole. As can be seen from Eq. (2), the propagating constant of β can be tuned by changing the diameter d of pinhole, thus the relative phase for incident light transmitted through the hole can be modulated. As the wavefront engineering using phase shifts obtained from multiple-turn holes with different diameters has been investigated [18], here, for our designed single-turn structures, we fix the diameter of the circular pinholes, and systematically analyze the focusing effect for different radius of the circular ring and different numbers of pinholes. That is to say, the relative phases for CP incident lights transmitting through the hole are fixed. To increase the cutoff frequency, we assume the pinholes are filled with SiO2 whose refractive index is 1.5 in the following work, which is because the cutoff wavelength occurs when the diameter of pinholes is less than λ/2n. The transmitting electric field intensities of the structures with different parameters, along the z-axis and x-axis, have been demonstrated in Fig. 4 respectively.Fig. 4 The transmitting electric field intensities along the z-axis (a) and x-axis (b) for different radii (r0) of circular ring, (c) the comparison for different numbers of pinholes, (d) the full-width at half-maximum (FWHM) along the z-axis direction and x-axis direction. (a)(b)(d) are the results for the filling dielectric of glass.
The focusing characteristics of the single-turn circular ring are shown in Fig. 4. It is observed that the length of focusing increases with the growth of the radius of circular ring as depicted in Fig. 4(a). At the same time, the intensity of focusing will be decreased, which can be explained by the equation [28]:
where I0 is the incident intensity, r0 is the radius of the circular ring, Lsp is the propagation length for the SPP and C is the coupling efficiency of the pinholes. C is a complicated function of the pinhole geometry. When the diameter and numbers of the pinholes are fixed, the excited ability of SPP will not change for a specific incident wavelength for this structure. With the increase of r0, the propagating loss of SPP (from the nano pinhole to the center of the circular ring) will be increased. Meanwhile, with the increase of r0, the gap between two adjacent holes will increase accordingly, which will lead to weaker coupling hybridized plasmon resonance modes and result in the decreased localized field intensity [29–32 ]. From these two effects, hence, the focusing intensity will be decreased accordingly with the increasing r0. We have also tried to compare the influence of the different filling dielectrics (air and glass), which can be attributed to the different cutoff frequency for the different filling dielectrics. The comparisons for different numbers of pinholes are shown in Fig. 4(c), and we can find that with the increasing number of the pinholes, the transmitting intensity will be enhanced accordingly, which can be attributed to the enhanced coupling efficiency of C with the increasing number of the pinholes. Figure 4(c) also indicates that the length of focusing is not related to the filling dielectric and the numbers of pinholes directly. The focusing quality of the structures can be quantified by the depth of focus (DOF) which is defined as the full-width at half-maximum (FWHM) of the intensity profiles along the z-axis direction. With increasing of r0, DOF is also increased as shown in Fig. 4(d).The size of the focusing spot, D, is defined by the values of the FWHM along the x-axis direction, as shown in Fig. 4(d), which is in sub-wavelength scale (D/λ0 is around 0.6). We have also simulated the structural parameter of r0 from 1300nm to 3000nm by a step of 340nm and the simulation results as depicted in Fig. 5 display the same tendency as shown in Figs. 4(a) and 4(b). When the other parameters are fixed, with the increasing r0, the focusing length will increase and the focusing intensity will decrease correspondingly. It can be observed from Fig. 5 when r0 = 3000nm, the focusing intensity can keep as a constant nearly, though it is not very strong, which have great potential applications in imaging and lithography.
Fig. 5 The electric field intensity along the z-axis for the structure with different r0 from 1300nm to 3000nm by a step of 340nm.
The transmitting distributions of the electric field intensity of the designed structures with different r0 (1258nm, 2516nm, 2660nm, 3000nm) at zoy plane have also been demonstrated in Figs. 6(a)-6(d) respectively, from which the obvious variation of focusing characteristics can be observed. Meanwhile, we can find that the designed single-turn structures can be used as the beaming lens. And the simulated results as shown in Figs. 6(a)-6(d) can also further verify that with the increasing r0, the focusing length will increase and the focusing intensity will decrease respectively.
Fig. 6 The electric field intensity distributions at zoy plane for (a)r0 = 1258nm, (b)r0 = 2516nm, (c)r0 = 2660nm, (d)r0 = 3000nm. The diameter of pinhole is set to be a = b = 150nm and the dielectric in holes is set to be glass.
The simulation results for the structure with r0 = 3λspp but different diameters of nano-pinholes are shown in Fig. 7 , where the electric field intensity at zoy plane for the structure with a = b = 200nm is shown in Fig. 7(a), and the intensity profiles along the z-axis direction for the structures with different diameters of the nano-pinholes is shown in Fig. 7(b). Here, we chose r0 = 3λspp because the 24 pinholes with a = b = 200nm will overlap with each other for r0 = 2λspp. For a = b = 100nm case, the focusing effect is relatively weak compared with the others owning to the cutoff wavelength effect. The focusing length will be increasing with the increasing diameters of the pinholes, which can be attributed as that increasing the diameter of nano-pinholes is equivalent to the case of reducing incident wavelength. If the wavelength is smaller than 2nd (n is the refractive index and d is the diameter of the pinholes), there will not exist the cutoff wavelength effect. Therefore, more incident light will transmit through pinholes, finally contributing to the focusing.
Fig. 7 The electric field intensity distributions(a) at x = 0 plane for a = b = 200nm with the radius of circular ring r0 = 3λspp. Corresponding intensity profile comparison (b) for a = b = 100nm, 125nm, 150nm, 175nm and 200nm along the z-axis direction.
3. Conclusion
We have demonstrated the focusing performance of a single-turn circular pinholes structure. Without modulating the phase shift of the pinholes at different circular rings, such miniature, simplified and planar plasmonic structure can generate on-axis beaming effect with micron-scale propagating distance. The influence factors for focusing effect are analyzed in detail. First, the focusing length and the DOF increases with the increment of the radius of circular ring while the focusing intensity is decreased. Second, the focusing spot indicated by the FWHM along the x-axis is around 400nm for different radius of circular ring and the minimum spot size D/λ0 of 0.58 can be obtained when r0 = 2λspp. Finally, we demonstrated that increasing the diameter of the pinholes can increase the focusing length and the focusing intensity, which is equivalent to the case of reducing the incident wavelength. That means, for short wavelength the focusing performance will be better according to the cutoff wavelength effect. Such a single-turn structure has the advantages of possessing large DOF along the propagating direction, micron scale focusing length and relative small focus spot. The designed lens have great potentials toward compact integrated optical applications, such as imaging with a spatial resolution beyond diffraction limit, sensing and data storage.
Acknowledgment
The authors gratefully acknowledge the financial supports for this work from the Fundamental Research Funds for the Central Universities (2015HGCH0010), and the Foundation of Hefei University of Technology of China (HFUT. 407-037026).
References and links
1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
2. T. J. Antosiewicz, P. Wróbel, and T. Szoplik, “Performance of scanning near-field optical microscope probes with single groove and various metal coatings,” Plasmonics 6(1), 11–18 (2011). [CrossRef] [PubMed]
3. H. Ditlbacher, B. Lamprecht, A. Leitner, and F. R. Aussenegg, “Spectrally coded optical data storage by metal nanoparticles,” Opt. Lett. 25(8), 563–565 (2000). [CrossRef] [PubMed]
4. P. Zijlstra, J. W. Chon, and M. Gu, “Five-dimensional optical recording mediated by surface plasmons in gold nanorods,” Nature 459(7245), 410–413 (2009). [CrossRef] [PubMed]
5. S. Yang, W. Chen, R. L. Nelson, and Q. Zhan, “Miniature circular polarization analyzer with spiral plasmonic lens,” Opt. Lett. 34(20), 3047–3049 (2009). [CrossRef] [PubMed]
6. K. A. Bachman, J. J. Peltzer, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Spiral plasmonic nanoantennas as circular polarization transmission filters,” Opt. Express 20(2), 1308–1319 (2012). [CrossRef] [PubMed]
7. W. Chen, R. L. Nelson, and Q. Zhan, “Efficient miniature circular polarization analyzer design using hybrid spiral plasmonic lens,” Opt. Lett. 37(9), 1442–1444 (2012). [CrossRef] [PubMed]
8. R. Li, Z. Guo, W. Wang, J. Zhang, A. Zhang, J. Liu, S. Qu, and J. Gao, “Ultra-thin circular polarization analyzer based on the metal rectangular split-ring resonators,” Opt. Express 22(23), 27968–27975 (2014). [CrossRef] [PubMed]
9. J. Zhang, Z. Guo, R. Li, W. Wang, A. Zhang, J. Liu, S. Qu, and J. Gao, “Circular polarization analyzer based on the combined coaxial Archimedes’ spiral structure,” Plasmonics (posted 24 Mar. 2015, in press).
10. L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012). [CrossRef]
11. J. Li, C. Yang, J. Li, Z. Li, S. Zu, S. Song, H. Zhao, F. Lin, and X. Zhu, “Plasmonic focusing in nanostructures,” Plasmonics 9(4), 879–886 (2014). [CrossRef] [PubMed]
12. W. Wang, Z. Guo, R. Li, J. Zhang, Y. Liu, X. Wang, and S. Qu, “Ultra-thin, planar, broadband, dual-polarity plasmonic metalens,” Photon. Res. 3(3), 68–71 (2015). [CrossRef]
13. J. Dong, J. Liu, B. Hu, J. Xie, and Y. Wang, “Subwavelength light focusing with a single slit lens based on the spatial multiplexing of chirped surface gratings,” Appl. Phys. Lett. 104(1), 011115 (2014). [CrossRef]
14. L. Cheng, P. Cao, Y. Li, W. Kong, X. Zhao, and X. Zhang, “High efficient far-field nanofocusing with tunable focus under radial polarization illumination,” Plasmonics 7(1), 175–184 (2012). [CrossRef]
15. Y. Fu, C. Du, W. Zhou, and L. E. N. Lim, “Nanopinholes-based optical superlens,” Res. Lett. Phys. 2008, 148505 (2008). [CrossRef]
16. Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010). [CrossRef]
17. Y. Zhang, Y. Fu, and X. Zhou, “Investigation of metallic elliptical nano-pinholes structure-based plasmonic lenses: from design to testing,” Insciences J 1, 18–29 (2011). [CrossRef]
18. S. Ishii, V. M. Shalaev, and A. V. Kildishev, “Holey-metal lenses: sieving single modes with proper phases,” Nano Lett. 13(1), 159–163 (2013). [CrossRef] [PubMed]
19. Y. J. Liu, H. Liu, E. S. P. Leong, C. C. Chum, and J. H. Teng, “Fractal holey metal microlenses with significantly suppressed side lobes and high‐order diffractions in focusing,” Adv. Opt. Mater. 2(5), 487–492 (2014). [CrossRef]
20. S. Y. Lee, I. M. Lee, J. Park, C. Y. Hwang, and B. Lee, “Dynamic switching of the chiral beam on the spiral plasmonic bull’s eye structure [Invited],” Appl. Opt. 50(31), G104–G112 (2011). [CrossRef] [PubMed]
21. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
22. M. Pournoury, H. E. Arabi, and K. Oh, “Strong polarization dependence in the optical transmission through a bull’s eye with an elliptical sub-wavelength aperture,” Opt. Express 20(24), 26798–26805 (2012). [CrossRef] [PubMed]
23. M. Pournoury, H. E. Joe, J. H. Park, T. Nazari, Y. M. Sung, B. K. Min, S. Im, D. Kim, and K. Oh, “Polarization-dependent transmission through a bull's eye with an elliptical aperture,” Opt. Commun. 316, 1–4 (2014). [CrossRef]
24. C. D. Ku, W. L. Huang, J. S. Huang, and C. B. Huang, “Deterministic synthesis of optical vortices in tailored plasmonic archimedes spiral,” Photonics J. 5(3), 4800409 (2013). [CrossRef]
25. S. W. Cho, J. Park, S. Y. Lee, H. Kim, and B. Lee, “Coupling of spin and angular momentum of light in plasmonic vortex,” Opt. Express 20(9), 10083–10094 (2012). [PubMed]
26. 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). [CrossRef] [PubMed]
27. R. Gordon and A. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13(6), 1933–1938 (2005). [CrossRef] [PubMed]
28. Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5(9), 1726–1729 (2005). [CrossRef] [PubMed]
29. C. G. Biris and N. C. Panoiu, “Excitation of dark plasmonic cavity modes via nonlinearly induced dipoles: applications to near-infrared plasmonic sensing,” Nanotechnology 22(23), 235502 (2011). [CrossRef] [PubMed]
30. A. Ahmadivand, S. Golmohammadi, M. Karabiyik, and N. Pala, “Fano resonances in complex plasmonic necklaces composed of gold nanodisks clusters for enhanced LSPR sensing,” Sensors Journal, IEEE 15(3), 1588–1594 (2015). [CrossRef]
31. A. Ahmadivand and N. Pala, “Tailoring the negative-refractive-index metamaterials composed of semiconductor–metal–semiconductor gold ring/disk cavity heptamers to support strong Fano resonances in the visible spectrum,” J. Opt. Soc. Am. A 32(2), 204–212 (2015). [CrossRef]
32. A. J. Pasquale, B. M. Reinhard, and L. Dal Negro, “Concentric necklace nanolenses for optical near-field focusing and enhancement,” ACS Nano 6(5), 4341–4348 (2012). [CrossRef] [PubMed]
