Far-Field Focusing of Spiral Plasmonic Lens

Transcription

1 Plasmonics (2012) 7: DOI /s Far-Field Focusing of Spiral Plasmonic Lens Junjie Miao & Yongsheng Wang & Chuanfei Guo & Ye Tian & Jianming Zhang & Qian Liu & Zhiping Zhou & Hiroaki Misawa Received: 23 September 2011 / Accepted: 28 November 2011 / Published online: 8 December 2011 # Springer Science+Business Media, LLC 2011 Abstract In this paper, we study the nanoscale-focusing effect in the far field for a spiral plasmonic lens with a concentric annular groove by using finite-difference time domain simulation. The simulation result demonstrates that a left-hand spiral plasmonic lens can concentrate an incident right-hand circular polarization light into a focal spot at the exit surface. And this spot can be focused into far field due to constructive interference of the scattered light by the annular groove. The focal length and the focal depth can be adjusted by changing the groove radius and number of grooves within a certain range. These properties make it possible to probe the signal of spiral plasmonic lens in far field by using conventional optical devices. Keywords Surface plasmon. Spiral structure. Far-field focus. Superfocusing. FDTD J. Miao : Y. Wang : C. Guo : Y. Tian : J. Zhang : Q. Liu (*) National Center for Nanoscience and Technology, No. 11, Beiyitiao, Beijing , China liuq@nanoctr.cn J. Miao : Z. Zhou Academy for Advanced Interdisciplinary Studies, Peking University, Beijing , China H. Misawa Research Institute for Electronic Science, Hokkaido University, Sapporo , Japan J. Miao : Y. Wang : C. Guo : Y. Tian : J. Zhang Graduate School of the Chinese Academy of Sciences, Beijing , China Introduction Surface plasmon polaritons (SPPs) have subwavelength scale feature and field enhancement effects [1], making them very attractive in a variety of applications such as high-density optical data storage [2, 3], probes of the scanning near-field optical microscopy [4], light focusing [5], and plasmonic devices [6 8]. Because of the short effective wavelength, surface plasmon waves can be focused into a highly confined spot with a size beyond the diffraction limit. Zhang et al. demonstrated experimentally an annular plasmonic lens with a subwavelength annular slit milled into a metal layer [9]. When the incident linearly polarized light reaches the slit, the wave couples into SPPs which propagate through the slit and then form a focal spot at the metal/ dielectric boundary of the exit surface. Recently, the much smaller and finer focal spots have been achieved by using radially polarized incident light instead of linearly polarized incident light [10, 11]. The reason for the improvement is that surface plasmons are excited from all directions and can be homogeneous focused by constructive interference when using radially polarized incident light. However, it has a shortcoming that the center of radially polarized light must be exactly aligned to the plasmonic lens center. To overcome the disadvantage mentioned above, a spiral plasmonic lens with nanostructure has been developed [12 14]. In our previous work, a left (right)- hand spiral plasmonic lens has been illustrated to be able to concentrate an incident right (left)-hand circular polarization light into a focal spot at the exit surface, and the electric field intensity at the exit surface center could be modulated by altering the turns, the size and the width of the spiral slot [15]. It is obvious that the surface plasmon wave decays exponentially with the distance away from the structure surface and

2 378 Plasmonics (2012) 7: Fig. 1 a Schematic diagram of a left-hand spiral plasmonic lens under right-hand circularly polarized illumination; b E 2 distribution for spiral plasmonic lens; c schematic diagram of a left-hand spiral plasmonic lens with a concentric groove under right-hand circularly polarized illumination; d E 2 distribution for the structure c the focus is restricted in the near field, which limits its possibilities for practical applications in the far field. Structures formed by linear slits and grooves can be used as another type of focusing devices and nanoscale focusing in the far field can be realized by controlling the diffraction of the electromagnetic field in periodic grooves irradiated by SPPs [16 18], which establishes the foundation of far-field nanoscale focusing effect using spiral plasmonic lens. In this paper, we propose a simple structure that is just constructed by a spiral metallic slit and a concentric groove. By converging the propagating waves scattered from the SPPs at the groove, this structure can actualize the nanoscale focusing in the far field. Moreover, its focal length can be adjusted flexibly just by changing the radius of the single groove. Scheme and Principle Figure 1a shows a typical left-hand spiral plasmonic lens, which is formed by a spiral slit milled into a silver film. A right-hand circularly polarized plane wave is incident along the positive z direction. Surface plasmons excited at the spiral slot will propagate along the exit facet and interfere with each other constructively. The Bessel-like electric field distribution is generated near the exit surface, just as the simulated electric field intensity distribution shown in Fig. 1b. The intensity of this Bessel-like electric field reaches its maximum at the exit surface center and an obvious focal spot is formed in the near field. As demonstrated in early works, the subwavelength metallic groove can scatter Fig. 2 Schematic diagram of the structure proposed under the illumination of right-hand circular polarization plane wave along the positive z direction Fig. 3 E 2 distributions on the optical axis for the left-hand spiral plasmonic lens with groove radius is 0.58, 0.90, 1.22, 1.54, 1.86 μm, respectively. The inset depicts the E 2 distributions on the optical axis for the structures with no groove, r μm and r μm, respectively

3 Plasmonics (2012) 7: Fig. 4 a E 2 distribution in the x z plane for a left-hand spiral plasmonic lens with groove radius r μm under righthand circular polarization light. The insert is the cross-section of E 2 at focal spot in x y plane. b E 2 variation of the focus spot versus the groove depth h the SPPs into propagating waves in free space effectively according to a certain angular spectrum distribution. Utilizing this feature, a subwavelength concentric annular groove is added in the spiral plasmonic lens as shown in Fig. 1c and the corresponding electric field intensity distribution shown in Fig. 1d. We consider the left-hand Archimedes spiral slot structure with a concentric groove as a plasmonic lens for far-field focusing, and the dimensional conditions are described in Fig. 2. The structure consists of a spiral slit penetrated through a silver thin film with a thickness of 300 nm, and the slit width w 1 is chosen to be 100 nm, which is smaller than half wavelength of the incident light. In the cylindrical coordinates, the spiral structure can be described as rðfþ ¼r 1 þ f 2p l sp; for 0 f 2p; ð1þ where, r 1 is a constant and λ sp is the wavelength of the surface plasmon. And a concentric circular groove within the spiral slit in the exit metallic layer is added so as to focus light to the far field. A right-hand circularly polarized plane wave is incidentally along the positive z direction as shown in Fig. 2. The incident wave is generated by using the superposition of two linearly polarized plane waves (transverse magnetic and transverse electric) with a phase difference of π/2, which can be expressed as! E ¼ p 1 ffiffi! 2 e x þ ie! y.the spiral slit is used to excite SPPs propagating along the surface when it is irradiated by the incident light, and the circular groove is used to scatter SPPs to propagating waves into free space. The propagating waves scattered by different positions of the groove interfere constructively on the optical axis because they are in-phase, thus a bright focal spot in the far field can be generated. Simulation Result and Discussion To investigate the influence of the parameters of this structure on the focusing properties, three-dimensional finitedifference time domain (FDTD) simulations are carried out [19]. The dispersive data are based on the experimental data given by Palik [20]. In this design, free space wavelength λ nm is adopted, corresponding to the surface plasmon wavelength λ SP 0641 nm, and the relative permittivity of the silver material used in the FDTD is ε m j. The parameters of the structure shown in Fig. 2 are set as the following: the inner radius of the spiral slit r 1 02,700 nm, the inner radius of annular groove is r 2, the annular groove width w nm, the thickness of annular groove is h. The simulation result demonstrates that the focal length is mainly determined by the groove position. In this simulation, the groove depth h is fixed to be 50 nm and the groove radius r 2 is changed from 500 to 2,000 nm. The intensity distributions on the optical axis with different values of r 2 are shown in Fig. 3. When there is no groove in this structure, intensity distribution of the surface electric field is Bessel-like standing waves as shown in Fig. 1b and a series of minimal Fig. 5 E 2 distribution in the x z plane for the left-hand spiral plasmonic lens a with five grooves under right-hand circular polarization light; b with one groove (r μm) under lefthand circular polarization light

4 380 Plasmonics (2012) 7: intensity values will appear when the groove radius r 2 is equal to 0.58, 0.90, 1.22, 1.54, and 1.86 μm, respectively. If a groove is set at these places (nodes), respectively, an intensity peak (focal spot) would appear on the optical axis several wavelengths away from the silver film surface, and the focal length increases monotonically with the increase of the groove radius. According to [21], the scattering angle range and the energy of scattering light of each groove (at nodes) are nearly the same. As the groove radius increases, the intensity of focal spot diminishes but interference region along z direction increases. So the focal depth also increases. When the location of the groove is moved, the focusing phenomenon still exists. However, the focus intensity will become weaker. The shorter the distance between the groove and the nodes is, the better the focusing effect will be. If the groove radius is increased by λ SP /4 (160 nm) to the locations where the intensity is maximum value, for example, the groove radius r 2 increases from 0.9 to 1.06 μm, no peak appears in the curves and it is similar to the case when there is no groove. The corresponding intensity along the optical axis is shown in the inset in Fig. 3, indicating that the groove cannot scatter the SPPs into radiation light and focusing in the far field cannot be actualized when the annular groove is set in these places. Figure 4a shows the intensity distribution of E 2 in the x z plane with groove radius r μm. From this figure, we can see that the scattered light by the groove with curved wavefront in the diffraction zone gradually converged toward the geometrical center from all directions while the intensity in the center of the structure was enhanced gradually along the propagation direction. Consequently, a bright circular focal spot emerged, and the full width at half maximum (FWHM) of the focus is only 0.44λ 0, which is smaller than half of the incident light wavelength (λ 0 ). Subsequently, the intensity in the center of the focal spot gradually faded away along the propagation direction. Furthermore, we study the influences of groove depth on the focusing efficiency. The groove radius r 2 is set to be 900 nm; while the sliver layer thickness H varies from 300 to 800 nm. The simulations are carried out with the groove depth h changed from 0 to 600 nm with a step of 10 nm. Figure 4b indicates that the intensity E 2 varies periodically with the groove depth and the variation period is about 220 nm. What is important is that when the groove radius r 2 is changed, the FWHM of the focal spot can always be kept less than a half wavelength of the incident light. This means that the scattering efficiency will be different when the groove depth h is changed. By using this feature, we can regulate the intensity of the focal spot within a certain range. As discussed above, the focal length increases monotonically with the increase of the groove radius, so what will happen if several grooves were used at the same time. Figure 5a shows the focusing effect when five grooves radius r , 0.90, 1.22, 1.54, and 1.86 μm, respectively. The focal length is about 1.2 μm and what is more interesting is that it has a quite high focal depth about 1.52 μm. This result implies that we can adjust the focal depth by controlling the number and radius of the grooves, which is quite useful in optical detection and imaging. As contrast, we also investigate the far-field focusing properties of the left-hand circular polarization incident light illuminating the left-hand spiral plasmonic lens. In this circumstance, the transmitted light focuses into a ring with a dark center spot [12]. And when a groove is introduced, the spot can also be focused into far field keeping the same spot shape as shown in Fig. 5b. And it should be indicated that the focusing properties in this case is quite similar to that using right-hand circular polarization incident light. Summary The nanoscale-focusing effect has been realized in the far field by a spiral plasmonic lens with a concentric annular groove. The spiral slit is used to excite the SPPs, and the electric field on the outer plane of the silver thin film is proportional to zeroorder Bessel function. The concentric groove is introduced to convert the SPPs wave to propagating waves in free space. The simulation results demonstrate that a left-hand spiral plasmonic lens can concentrate an incident right-hand circular polarization light into a focal spot at the exit surface. And this spot can be focused in the far field due to constructive interference of the scattered light by the annular groove, and the FWHM of the focal spot can always be kept less than a half wavelength of the incident light. More interestingly, the focal length and the focal depth can be adjusted by changing the groove radius, the number of grooves in a certain range. These properties make it possible to probe the signal of spiral plasmonic lens in far field by using conventional optical devices. Acknowledgment We gratefully acknowledge the support to this work by NSFC ( ), NBRPC (2010CB934102), Project of International S&T Cooperation (2010DFA51970), and Eu-FP7 (no ). References 1. Knoll W (1998) Interfaces and thin films as seen by bound electromagnetic waves. Annu Rev Phys Chem 49: Zijlstra P, Chon JWM, Gu M (2009) Five-dimensional optical recording mediated by surface plasmons in gold nanorods. Nature 459: Ditlbacher H, Krenn JR, Lamprecht B, Leitner A, Aussenegg FR (2000) Spectrally coded optical data storage by metal nanoparticles. Opt Lett 25(8): Antosiewicz TJ, Wróbel P, Szoplik T (2011) Performance of scanning near-field optical microscope probes with single groove and various metal coatings. Plasmonics 6:11 18

5 Plasmonics (2012) 7: Barnes WL, Dereux A, Ebbesen TW (2003) Surface plasmon subwavelength optics. Nature (London) 424: Hutter E, Fendler JH (2004) Exploitation of localized surface plasmon resonance. Adv Mater 16: Lerman GM, Yanai A, Ben-Yosef N, Levy U (2010) Demonstration of an elliptical plasmonic lens illuminated with radially-like polarized field. Opt Express 18(10): Baron CA, Elezzabi AY (2009) Active plasmonic devices via electron spin. Opt Express 17(9): Liu ZW, Steele JM, Srituravanich W, Pikus Y, Sun C, Zhang X (2005) Focusing surface plasmons with a plasmonic lens. Nano Lett 5 (9): Lerman G, Yanai A, Levy U (2009) Demonstration of nanofocusing by the use of plasmonic lens illuminated with radially polarized Light. Nano Lett 9: Zhan Q (2006) Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam. Opt Lett 31: Gorodetski Y, Niv A, Kleiner V, Hasman E (2008) Observation of the spin-based plasmonic effect in nanoscale structures. Phys Rev Lett 101: Yang S, Chen W, Nelson RL, Zhan Q (2009) Miniature circular polarization analyzer with spiral plasmonic lens. Opt Lett 34: Chen W, Abeysinghe DC, Nelson RL, Zhan Q (2010) Experimental confirmation of miniature spiral plasmonic lens as a circular polarization analyzer. Nano Lett 10(6): Miao J, Wang Y, Guo C, Tian Y, Guo S, Liu Q, Zhou Z (2011) Plasmonic lens with multiple-turn spiral nano-structures. Plasmonics 6: Wang T, Wang X, Kuang C, Hao X, Liu X (2010) Experimental verification of the far-field subwavelength focusing with multiple concentric nanorings. Appl Phys Lett 97: Fu Y, Zhou X (2010) Topical review: plasmonic lenses. Plasmonics 5(3): Wang J, Zhou W (2010) Experimental investigation of focusing of gold planar plasmonic lenses. Plasmonics 5: FDTD Solutions. Lumerical Solutions Inc, Palik ED (1985) Handbook of optical constants of solids. Academic, New York 21. Nikitin A, Lopez-Tejeira F, Martin-Moreno L (2007) Scattering of surface plasmon polaritons by one-dimensional inhomogeneities. Phys Rev B 75(3):35129