Plasmonic Lens with Multiple-Turn Spiral Nano-Structures

Transcription

1 Plasmonics (2011) 6: DOI /s 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 properties of a plasmonic lens with multiple-turn spiral nano-structures, and analyze its field enhancement effect based on the phase matching theory and 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 with a high focal depth. The intensity of the focal spot could be controlled by altering the number of turns, the radius and the width of the spiral slot. And the focal spot is smaller and has a higher intensity compared to the incident linearly polarized light. This design can also eliminate the requirement of centering the incident beam to the plasmonic lens, making it possible to be used in plasmonic lens array, optical data storage, detection, and other applications. Keywords Plasmonic lens. Archimedes spiral slot. Superfocusing. FDTD J. Miao : Y. Wang : C. Guo : Y. Tian : S. Guo : Q. Liu (*) National Center for Nanoscience and Technology, No. 11, Beiyitiao, Beijing , China liuq@nanoctr.cn J. Miao : Z. Zhou State Key Laboratory on Advanced Optical Communication Systems and Networks, Peking University, Beijing , China J. Miao : Y. Wang : C. Guo : Y. Tian Graduate School of the Chinese Academy of Sciences, Beijing , China Introduction Surface plasmon polaritons (SPPs) are surface electromagnetic waves bound to a metal/dielectric interface with subwavelength scale features and field enhancement effects [1], making them very attractive for a variety of applications such as sensor [2, 3], microscopy [4, 5], light focusing [6], and plasmonic devices [7 9]. Surface plasmon waves can be focused into a highly confined spot with a size beyond the diffraction limit, because of the short effective wavelength. Taking advantage of this property, Zhang et al. proposed a plasmonic lens with metallic nano-structures, which can confine the electromagnetic energy to a small region and focus the energy at a desired location. A single annular structure plasmonic lens (SAPL) with a subwavelength slit milled into a metal layer is in common use [10]. 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. However, SPPs can only be excited by transverse magnetic polarized light and their phase difference on the two ragged edges of a spiral slit is π [11]. This results in a low coupling efficiency and a separation of the focal spot into two parts around the focal center, limiting application of the SAPL. Recently, the much smaller and finer focal spots have been achieved by using radially polarized incident light instead of linearly polarized incident light [12 17]. The reason for the improvement is that surface plasmons are excited from all directions and then homogeneous focus through constructive interference. And due to the angular selection of the SPPs, the plasmonic focus generated in

2 236 Plasmonics (2011) 6: this way is an evanescent non-spreading Bessel beam [12]. However, it is impossible to build the SAPL array in this case, because the center of radially polarized light must be exactly aligned to the center of the SAPL. Therefore, further study should be carried out to realize the practical application of plasmonic lenses by improving the structure of the lens and adopting more suitable incident light. Interactions between chiral metallic structures and circularly polarized light have been reported recent years [18 22]. A plasmonic vortex induced by Archimedes spiral grooves was investigated, where the spiral grooves serve as gratings to excite the surface plasmon [19]. It hasbeenalsodemonstratedthataspiralplasmoniclens can be used as a miniature circular polarization analyzer, because it can focus the left- and right-hand circular polarizations into spatially separated plasmonic fields [20, 21]. In addition, complex polarization response and symmetry-breaking features have been studied in the spiral structures [22]. Scheme and Structure Layout In this work, we study a simpler, more practical design of a plasmonic lens with a multiple-turn spiral slot structure. In our design of the spiral plasmonic lens (SPL), a thin metallic film-based spiral structure is used to manipulate the required phase modulation for superfocusing. The focusing properties for clockwise and anticlockwise circular polarizations, as well as the relations among the focus intensity, the size, the width, and the turns of the spiral slot, are studied systematically in the SPL. We consider the left-hand multiple-turn Archimedes spiral slot structure as a plasmonic lens for subwavelength focusing, as shown in Fig. 1a. The structure consists of multiple turns penetrated through a silver thin film with a thickness of 300 nm, the slit width w is chosen to be 250 nm, the structure can be described as r n ðþ¼r f n0 þ f 2p l sp; for 0 f 2p; n ¼ 1; 2; 3 ; ð1þ where r n0 is a constant of the nth turn, r n (φ) is the distance from the point (r n, φ) on the inner side of nth spiral slot to the center of the structure in the polar coordinate, and the pitch of spiral slot is equal to the wavelength of the surface plasmon. A right-hand circularly (RHC) polarized plane wave is incident along the negative z-direction as shown in Fig. 1b. 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 e! x þ ie! y. Surface plasmons excited at the spiral slot will propagate along the exit facet and interfere with each other constructively. Method and Parameters The electromagnetic field intensity for the SPL is analyzed by the three-dimensional finite-difference time-domain (FDTD) approach with an absorption boundary condition. The dispersive data are based on the experimental data given by Palik [23]. In this design, free space wavelength λ 0 =660 nm is adopted, and the relative permittivity of the silver material used in the FDTD is ε m = j. The effective refractive index of the surface plasmon at the interface between the Ag layer and air is n sp =1.03, corresponding to the surface plasmon wavelength λ SP = 641 nm. The surface plasmons excited at all azimuthal 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 illumination 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 polarization. The red, yellow, green, and blue arrows correspond to the out-of-plane electric field E z with relative phases of 3π/2, π, π/2, and 0, respectively

3 Plasmonics (2011) 6: 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 section of E 2 at the focal plane, 350 nm away from the exit surface (in the z-direction). d Spot size versus z Fig. 4 Array of left-hand SPL (the white parts) with four different r 0 (2λ SP,3λ SP,4λ SP,5λ SP ) 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(k sp ) r], where sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k sp ¼ 2p " 0 m þ " d l " 0 m " : ð2þ d Here, ε d and " 0 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 L p =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. 3 Simulated E 2 at the central point versus a the slit width (one turn, the outmost r 0 =4 μm) and the turns of the spiral nano-structures (slit width w=250 nm, maximal r 0 =4 μm), b r 0 (one turn, slit width w=250 nm). The distance between the central point and the exit surface is 350 nm Fig. 5 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 LHC illumination

4 238 Plasmonics (2011) 6: once they propagate to the edge of the internal circle (black dotted line), although the phases are different when they were excited at the spiral slot initially. Such patterns of the phase are same as that of SAPL illuminated by the radially polarized incident light. More importantly, due to the isotropy of the circular polarization, the SPL avoids the difficulty of having to align the center of the incident radially polarized beam to be coincident with the center of the SAPL, thereby providing a more practical plasmonic lens array. Numerical Analysis and Discussion Figure 2a shows the intensity distribution of E 2 in the x y plane at the longitudinal distance z=350 nm from the out plane of the silver thin film. From this figure, we can see that the left-hand SPL focuses a RHC polarization into a spot with a central peak. The electric field at the point of (R, ϕ) on the outer plane of the silver thin film is proportional to zero-order Bessel function J 0 (k r R), as 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 ( 0.33λ 0 ), lower than the diffraction limit. And the nonspreading effect of zero-order evanescent Bessel beam favors a beam focus in high quality. From Fig. 2b and d, we can also see that the FWHM of the focal beam nearly keeps a constant along the z axis, indicating the focus spot with a high focus depth. Furthermore, we investigate the influence of the structure parameters of the spiral slot to the performance of the left-hand spiral plasmonic lens under RHC illumination, such as the size, the number of turns, and the width of the spiral slot, as shown in the Fig. 3. It is obvious that the relative electric field intensity can be controlled by adjusting the turns of the spiral slot. We can see from Fig. 3a that the intensity becomes stronger and stronger with the increase of the turns of the spiral slot from one to five. And the intensity will begin to reach a plateau when the number of turns is five. Moreover, the increasing rate will decrease quickly with the further increase of the turns because of the limitation of the propagation length of the SPPs. Since more energy can be coupled to the focal spot with the increase of r 0, the intensity of the focal spot increases by expanding the turning radius, r 0, 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 simulations 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 with a slit width of 250 nm at the center point (z=350 nm) are shown in Fig. 3a. Here, we use only one turn (r 0 =4 μm) 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. It should be noted that the size of the focal spot is mainly related to the wavelength of the incident light, therefore it can be kept nearly constant when we adjust the turns, the width, and r 0 of the spiral slot. As discussed above, the intensity of the focal spot can be flexibly controlled by varying the turns, r 0 and the slit 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 be applied as an attenuator of light intensity or/and a nanoscale beam splitter, as shown in Fig. 4. As a contrast, we also investigate the effect of the lefthand circular (LHC) polarization incident light illuminating the left-hand SPL. Unlike the RHC polarization focusing into a central peak spot, the LHC polarization focus into a ring with a dark center spot as shown in Fig. 5. This property will be quite useful in detecting polarization characters of light for a nano-scale area. Summary In conclusion, the left-hand SPL with multiple-turn Archimedes spiral slot under the illumination of a RHC polarization can focus the light into a small bright spot at the center of the lens with a high focal depth, and can also focus the LHC polarization light into a dark spot at the center. Unlike SAPL with a radial polarization, the SPL does not require alignment of the radiation to the center of the structure. Therefore, our method supplies a much more effective and convenient way for the practical use of plasmonic lenses in optical probing and plasmonic lens arrays. More interestingly, we found that the electric field intensity at the center of the exit surface could be modulated by altering the turns, the size and the width of the spiral slot, while nearly keeping the FWHM in a constant, which have many potential applications for intensity actuating, focusing beams, nano-scale beam splitters, and other applications. Acknowledgments We gratefully acknowledge the support to this work by NSFC ( ), NBRPC (2010CB934102) and Program of International S&T Cooperation (2010DFA51970). References 1. Knoll W (1998) Interfaces and thin films as seen by bound electromagnetic waves. Annu Rev Phys Chem 49: Dahlin A, Zach M, Rindzevicius T, Kall M, Sutherland DS, Hook F (2005) Localized surface plasmon resonance sensing of lipid-

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