Plasmonics (2011) 6:235–239 DOI 10.1007/s11468-010-9193-0 Plasmonic Lens with Multiple-Turn Spiral Nano-Structures Junjie Miao & Yongsheng Wang & Chuanfei Guo & Ye Tian & Shengming Guo & Qian Liu & Zhiping Zhou Received: 17 August 2010 /Accepted: 27 December 2010 /Published online: 18 January 2011 # Springer Science+Business Media, LLC 2011 Abstract In this paper, we investigate the focusing Introduction properties of a plasmonic lens with multiple-turn spiral nano-structures, and analyze its field enhancement effect Surface plasmon polaritons (SPPs) are surface electro- based on the phase matching theory and finite-difference magnetic waves bound to a metal/dielectric interface time-domain simulation. The simulation result demon- with subwavelength scale features and field enhance- strates that a left-hand spiral plasmonic lens can concen- ment effects [1], making them very attractive for a trate an incident right-hand circular polarization light into variety of applications such as sensor [2, 3], microscopy a focal spot with a high focal depth. The intensity of the [4, 5], light focusing [6], and plasmonic devices [7–9]. focal spot could be controlled by altering the number of Surface plasmon waves can be focused into a highly turns, the radius and the width of the spiral slot. And the confined spot with a size beyond the diffraction limit, focal spot is smaller and has a higher intensity compared because of the short effective wavelength. Taking to the incident linearly polarized light. This design can advantage of this property, Zhang et al. proposed a also eliminate the requirement of centering the incident plasmonic lens with metallic nano-structures, which can beam to the plasmonic lens, making it possible to be used confine the electromagnetic energy to a small region and in plasmonic lens array, optical data storage, detection, focus the energy at a desired location. A single annular and other applications. structure plasmonic lens (SAPL) with a subwavelength slit milled into a metal layer is in common use [10]. Keywords Plasmonic lens . Archimedes’ spiral slot . When the incident linearly polarized light reaches the slit, Superfocusing . FDTD the wave couples into SPPs which propagate through the slit and then form a focal spot at the metal/dielectric boundary. However, SPPs can only be excited by transverse magnetic polarized light and their phase : : : : : * J. Miao Y. Wang C. Guo Y. Tian S. Guo Q. Liu ( ) difference on the two ragged edges of a spiral slit is π National Center for Nanoscience and Technology, No. 11, Beiyitiao, [11]. This results in a low coupling efficiency and a Beijing 100190, China separation of the focal spot into two parts around the e-mail: [email protected] focal center, limiting application of the SAPL. Recently, the much smaller and finer focal spots have J. Miao : Z. Zhou State Key Laboratory on Advanced Optical Communication been achieved by using radially polarized incident light Systems and Networks, Peking University, instead of linearly polarized incident light [12–17]. The Beijing 100871, China reason for the improvement is that surface plasmons are excited from all directions and then homogeneous focus J. Miao : Y. Wang : C. Guo : Y. Tian Graduate School of the Chinese Academy of Sciences, through constructive interference. And due to the angular Beijing 100190, China selection of the SPPs, the plasmonic focus generated in 236 Plasmonics (2011) 6:235–239 this way is an evanescent non-spreading Bessel beam multiple turns penetrated through a silver thin film with a [12]. However, it is impossible to build the SAPL array thickness of 300 nm, the slit width w is chosen to be in this case, because the center of radially polarized light 250 nm, the structure can be described as must be exactly aligned to the center of the SAPL. Therefore, further study should be carried out to realize f the practical application of plasmonic lenses by improv- r ðÞ¼f r þ l ; for 0 f 2p; n ¼ 1; 2; 3 ÁÁÁ; ð1Þ n n0 2p sp ing the structure of the lens and adopting more suitable incident light. Interactions between chiral metallic structures and where rn0 is a constant of the nth turn, rn(φ) is the distance circularly polarized light have been reported recent years from the point (rn, φ) on the inner side of nth spiral slot to [18–22]. A plasmonic vortex induced by Archimedes’ spiral the center of the structure in the polar coordinate, and the grooves was investigated, where the spiral grooves pitch of spiral slot is equal to the wavelength of the serve as gratings to excite the surface plasmon [19]. It surface plasmon. A right-hand circularly (RHC) polar- hasbeenalsodemonstratedthataspiralplasmoniclens ized plane wave is incident along the negative can be used as a miniature circular polarization analyzer, z-direction as shown in Fig. 1b. The incident wave is because it can focus the left- and right-hand circular generated by using the superposition of two linearly polarizations into spatially separated plasmonic fields polarized plane waves (transverse magnetic and trans- [20, 21]. In addition, complex polarization response and verse electric) with a phase difference of π/2, which can ! ! ! symmetry-breaking features have been studied in the be expressed as E ¼ e x þ iey. Surface plasmons excit- spiral structures [22]. ed at the spiral slot will propagate along the exit facet and interfere with each other constructively. Scheme and Structure Layout Method and Parameters In this work, we study a simpler, more practical design of a plasmonic lens with a multiple-turn spiral slot The electromagnetic field intensity for the SPL is analyzed structure. In our design of the spiral plasmonic lens by the three-dimensional finite-difference time-domain (SPL), a thin metallic film-based spiral structure is used (FDTD) approach with an absorption boundary condition. to manipulate the required phase modulation for super- The dispersive data are based on the experimental data focusing. The focusing properties for clockwise and anti- given by Palik [23]. In this design, free space wavelength clockwise circular polarizations, as well as the relations λ0=660 nm is adopted, and the relative permittivity of the among the focus intensity, the size, the width, and the silver material used in the FDTD is εm=–17.7+1.18j. The turns of the spiral slot, are studied systematically in the effective refractive index of the surface plasmon at the SPL. interface between the Ag layer and air is nsp=1.03, We consider the left-hand multiple-turn Archimedes’ corresponding to the surface plasmon wavelength λSP= spiral slot structure as a plasmonic lens for subwavelength 641 nm. The surface plasmons excited at all azimuthal focusing, as shown in Fig. 1a. The structure consists of directions propagate along the air-silver interface toward Fig. 1 a Schematic diagram of the left-hand multiple-turn Archimedes’ spiral slot. b The left-hand SPL under the illumi- nation of right-hand circular polarization plane wave along the negtive z-direction. c Schematic diagram of the relative phase of the SP waves excited by the SPL under the right-handed circular polariza- tion. The red, yellow, green, and blue arrows correspond to the out-of-plane electric field Ez with relative phases of 3π/2, π, π/2, and 0, respectively Plasmonics (2011) 6:235–239 237 Fig. 2 a Simulated |E|2 distribution in the x–y plane at the longitudinal distance z=350 nm from the out-of-plane for a left-hand SPL under RHC illumination. b |E|2 distribution in x–z plane. c Cross 2 section of |E| at the focal plane, 350 nm away from the exit surface Fig. 4 Array of left-hand SPL (the white parts) with four different r0 (in the z-direction). d Spot size versus z (2λSP,3λSP,4λSP,5λSP) under the incident RHC polarization light, simulated |E|2 distribution in the x–y plane at the longitudinal distance z=350 nm from the out-of-plane, for the case of one spiral turn and a spiral slot width of 100 nm the center of the plasmonic lens with a propagation loss of exp[−Im(ksp)·r], where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p "0 þ " ¼ 2 m d : ð Þ ksp l "0 " 2 m d ε "0 Here, d and m are the relative permittivity of medium (air) and the real part of the relative permittivity of the silver film, respectively. The propagation length of the surface plasmon in this case is Lp=25.7 μm. Of course we can use other noble metals such as gold or aluminum instead of silver so long as they can excite surface plasmons and the surface plasmons have a large propagation length. If we choose other material of metals or use an incident light with different wavelength, we should pay special attention that the pitch of spiral slot must be equal to the corresponding wavelength of the surface plasmon in order to match phase. The relative phase of the surface plasmon waves in the exit plane of the SPL under the RHC polarization is illustrated in the Fig. 1c. In the exit plane of the silver thin film, the surface plasmon waves will keep the same phase Fig. 5 Simulated |E|2 distribu- tion in the x–y plane at the longitudinal distance z=350 nm from the out-of-plane for a left-hand SPL under LHC Fig. 3 Simulated |E|2 at the central point versus a the slit width illumination (one turn, the outmost r0=4 μm) and the turns of the spiral nano-structures (slit width w=250 nm, maximal r0=4 μm), b r0 (one turn, slit width w=250 nm).