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 ; 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). The distance between the central point and the exit surface is 350 nm 238 Plasmonics (2011) 6:235–239 once they propagate to the edge of the internal circle intensity at the focal point shows an increase with the slit (black dotted line), although the phases are different when width. This is mainly because that the slit width could they were excited at the spiral slot initially. Such patterns strongly affect the transmissivity of the incident light. It of the phase are same as that of SAPL illuminated by the should be noted that the size of the focal spot is mainly radially polarized incident light. More importantly, due to related to the wavelength of the incident light, therefore it the isotropy of the circular polarization, the SPL avoids can be kept nearly constant when we adjust the turns, the the difficulty of having to align the center of the incident width, and r0 of the spiral slot. radially polarized beam to be coincident with the center of As discussed above, the intensity of the focal spot can be the SAPL, thereby providing a more practical plasmonic flexibly controlled by varying the turns, r0 and the slit lens array. width of the spiral slot while the FWHM remains nearly constant for a given wavelength of the incident light. Hence, an array of the SPL with different parameters could Numerical Analysis and Discussion be applied as an attenuator of light intensity or/and a nano- scale beam splitter, as shown in Fig. 4. Figure 2a shows the intensity distribution of |E|2 in the x–y As a contrast, we also investigate the effect of the left- plane at the longitudinal distance z=350 nm from the out hand circular (LHC) polarization incident light illuminating plane of the silver thin film. From this figure, we can see the left-hand SPL. Unlike the RHC polarization focusing that the left-hand SPL focuses a RHC polarization into a into a central peak spot, the LHC polarization focus into a spot with a central peak. The electric field at the point of ring with a dark center spot as shown in Fig. 5. This (R, ϕ) on the outer plane of the silver thin film is property will be quite useful in detecting polarization proportional to zero-order Bessel function J0(krR), as characters of light for a nano-scale area. showninFig.2a. The cross section of the field intensity pattern is shown in the Fig. 2c.Thefullwidthathalf maximum (FWHM) of the focal spot is about 240 nm Summary

(∼0.33λ0), lower than the diffraction limit. And the non- spreading effect of zero-order evanescent Bessel beam In conclusion, the left-hand SPL with multiple-turn Archi- favors a beam focus in high quality. From Fig. 2b and d, medes’ spiral slot under the illumination of a RHC we can also see that the FWHM of the focal beam nearly polarization can focus the light into a small bright spot at keeps a constant along the z axis, indicating the focus spot the center of the lens with a high focal depth, and can also with a high focus depth. focus the LHC polarization light into a dark spot at the Furthermore, we investigate the influence of the struc- center. Unlike SAPL with a radial polarization, the SPL ture parameters of the spiral slot to the performance of the does not require alignment of the radiation to the center of left-hand spiral plasmonic lens under RHC illumination, the structure. Therefore, our method supplies a much more such as the size, the number of turns, and the width of the effective and convenient way for the practical use of spiral slot, as shown in the Fig. 3. It is obvious that the plasmonic lenses in optical probing and plasmonic lens relative electric field intensity can be controlled by adjusting arrays. More interestingly, we found that the electric field the turns of the spiral slot. We can see from Fig. 3a that the intensity at the center of the exit surface could be intensity becomes stronger and stronger with the increase of modulated by altering the turns, the size and the width of the turns of the spiral slot from one to five. And the intensity the spiral slot, while nearly keeping the FWHM in a will begin to reach a plateau when the number of turns is constant, which have many potential applications for five. Moreover, the increasing rate will decrease quickly with intensity actuating, focusing beams, nano-scale beam the further increase of the turns because of the limitation of splitters, and other applications. the propagation length of the SPPs. Since more energy can be coupled to the focal spot with Acknowledgments We gratefully acknowledge the support to this the increase of r , the intensity of the focal spot increases work by NSFC (10974037), NBRPC (2010CB934102) and Program 0 of International S&T Cooperation (2010DFA51970). by expanding the turning radius, r0, as show in Fig. 3b. The slit width of the spiral structure is also a key parameter to manipulate the focusing intensity. The results of simula- References tions for the electric field intensity for varying the slit width from 0.1 to 0.3 μm by a step of 0.05 μm relative to that 1. Knoll W (1998) Interfaces and thin films as seen by bound with a slit width of 250 nm at the center point (z=350 nm) – μ electromagnetic waves. Annu Rev Phys Chem 49:569 638 are shown in Fig. 3a. Here, we use only one turn (r0=4 m) 2. Dahlin A, Zach M, Rindzevicius T, Kall M, Sutherland DS, Hook of the spiral structures to simplify the analysis. The F (2005) Localized surface plasmon resonance sensing of lipid- Plasmonics (2011) 6:235–239 239

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