Plasmonics (2012) 7:377–381 DOI 10.1007/s11468-011-9318-0

Far-Field Focusing of Spiral Plasmonic

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 Introduction effect in the far field for a spiral plasmonic lens with a concentric annular groove by using finite-difference time Surface plasmon polaritons (SPPs) have subwavelength domain simulation. The simulation result demonstrates that scale feature and field enhancement effects [1], making a left-hand spiral plasmonic lens can concentrate an incident them very attractive in a variety of applications such as right-hand circular polarization into a focal spot at the high-density optical data storage [2, 3], probes of the scan- exit surface. And this spot can be focused into far field due ning near-field optical [4], light focusing [5], to constructive interference of the scattered light by the and plasmonic devices [6–8]. Because of the short effective annular groove. The focal length and the focal depth can , surface plasmon waves can be focused into a be adjusted by changing the groove radius and number of highly confined spot with a size beyond the diffraction limit. grooves within a certain range. These properties make it Zhang et al. demonstrated experimentally an annular plas- possible to probe the signal of spiral plasmonic lens in far monic lens with a subwavelength annular slit milled into a field by using conventional optical devices. 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/ Keywords Surface plasmon . Spiral structure . Far-field dielectric boundary of the exit surface. focus . Superfocusing . FDTD 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 J. Miao : Y. Wang : C. Guo : Y. Tian : J. Zhang : Q. Liu (*) National Center for Nanoscience and Technology, excited from all directions and can be homogeneous focused No. 11, Beiyitiao, by constructive interference when using radially polarized Beijing 100190, China incident light. However, it has a shortcoming that the center e-mail: [email protected] of radially polarized light must be exactly aligned to the J. Miao : Z. Zhou plasmonic lens center. To overcome the disadvantage men- Academy for Advanced Interdisciplinary Studies, tioned above, a spiral plasmonic lens with nanostructure has Peking University, been developed [12–14]. In our previous work, a left (right)- Beijing 100871, China hand spiral plasmonic lens has been illustrated to be able to H. Misawa concentrate an incident right (left)-hand circular polarization Research Institute for Electronic Science, Hokkaido University, light into a focal spot at the exit surface, and the electric field Sapporo 0010021, Japan intensity at the exit surface center could be modulated by altering the turns, the size and the width of the spiral slot [15]. J. Miao : Y. Wang : C. Guo : Y. Tian : J. Zhang Graduate School of the Chinese Academy of Sciences, It is obvious that the surface plasmon wave decays expo- Beijing 100190, China nentially with the distance away from the structure surface and 378 Plasmonics (2012) 7:377–381

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 possi- Scheme and Principle bilities for practical applications in the far field. Structures formed by linear slits and grooves can be used as another type Figure 1a shows a typical left-hand spiral plasmonic lens, of focusing devices and nanoscale focusing in the far field can which is formed by a spiral slit milled into a silver film. A be realized by controlling the diffraction of the electro- right-hand circularly polarized plane wave is incident along magnetic field in periodic grooves irradiated by SPPs [16– the positive z direction. Surface plasmons excited at the 18], which establishes the foundation of far-field nanoscale spiral slot will propagate along the exit facet and interfere focusing effect using spiral plasmonic lens. with each other constructively. The Bessel-like electric field In this paper, we propose a simple structure that is just distribution is generated near the exit surface, just as the constructed by a spiral metallic slit and a concentric groove. simulated electric field intensity distribution shown in By converging the propagating waves scattered from the Fig. 1b. The intensity of this Bessel-like electric field rea- SPPs at the groove, this structure can actualize the nanoscale ches its maximum at the exit surface center and an obvious focusing in the far field. Moreover, its focal length can be focal spot is formed in the near field. As demonstrated in adjusted flexibly just by changing the radius of the single early works, the subwavelength metallic groove can scatter groove.

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, Fig. 2 Schematic diagram of the structure proposed under the illumi- respectively. The inset depicts the |E|2 distributions on the optical axis nation of right-hand circular polarization plane wave along the positive for the structures with no groove, r201.06 μm and r200.90 μm, z direction respectively Plasmonics (2012) 7:377–381 379

Fig. 4 a |E|2 distribution in the x–z plane for a left-hand spiral plasmonic lens with groove ra- dius r200.90 μm under right- hand 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 groove is used to scatter SPPs to propagating waves into free according to a certain angular spectrum distribution. Utiliz- space. The propagating waves scattered by different positions ing this feature, a subwavelength concentric annular groove of the groove interfere constructively on the optical axis is added in the spiral plasmonic lens as shown in Fig. 1c and because they are in-phase, thus a bright focal spot in the far the corresponding electric field intensity distribution shown field can be generated. 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 de- Simulation Result and Discussion scribed in Fig. 2. The structure consists of a spiral slit penetrated through a silver thin film with a thickness of To investigate the influence of the parameters of this struc-

300 nm, and the slit width w1 is chosen to be 100 nm, which ture on the focusing properties, three-dimensional finite- is smaller than half wavelength of the incident light. In the difference time domain (FDTD) simulations are carried out cylindrical coordinates, the spiral structure can be described [19]. The dispersive data are based on the experimental data as given by Palik [20]. In this design, free space wavelength λ 0660 nm is adopted, corresponding to the surface plas- f 0 rðfÞ¼r þ l ; f p; ð Þ mon wavelength λSP0641 nm, and the relative permittivity 1 p sp for 0 2 1 2 of the silver material used in the FDTD is εm0−17.7+1.18 j. The parameters of the structure shown in Fig. 2 are set as the where, r1 is a constant and λsp is the wavelength of the following: the inner radius of the spiral slit r102,700 nm, surface plasmon. And a concentric circular groove within the inner radius of annular groove is r2, the annular groove the spiral slit in the exit metallic layer is added so as to focus width w 0100 nm, the thickness of annular groove is h. light to the far field. A right-hand circularly polarized plane 2 The simulation result demonstrates that the focal length is wave is incidentally along the positive z direction as shown mainly determined by the groove position. In this simula- in Fig. 2. The incident wave is generated by using the tion, the groove depth h is fixed to be 50 nm and the groove superposition of two linearly polarized plane waves (trans- radius r2 is changed from 500 to 2,000 nm. The intensity verse magnetic and transverse electric) with a phase difference ! distributions on the optical axis with different values of r2 π E ¼ p1ffiffi !e þ ie! of /2, which can be expressed as 2 x y .The are shown in Fig. 3. When there is no groove in this structure, spiral slit is used to excite SPPs propagating along the surface intensity distribution of the surface electric field is Bessel-like when it is irradiated by the incident light, and the circular 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 circu- lar polarization light; b with one groove (r200.90 μm) under left- hand circular polarization light 380 Plasmonics (2012) 7:377–381 intensity values will appear when the groove radius r2 is equal length is about 1.2 μm and what is more interesting is that it to 0.58, 0.90, 1.22, 1.54, and 1.86 μm, respectively. If a has a quite high focal depth about 1.52 μm. This result implies groove is set at these places (nodes), respectively, an intensity that we can adjust the focal depth by controlling the number peak (focal spot) would appear on the optical axis several and radius of the grooves, which is quite useful in optical away from the silver film surface, and the focal detection and imaging. As contrast, we also investigate the length increases monotonically with the increase of the groove far-field focusing properties of the left-hand circular polariza- radius. According to [21], the scattering angle range and the tion incident light illuminating the left-hand spiral plasmonic energy of scattering light of each groove (at nodes) are nearly lens. In this circumstance, the transmitted light focuses into a the same. As the groove radius increases, the intensity of focal ring with a dark center spot [12]. And when a groove is spot diminishes but interference region along z direction introduced, the spot can also be focused into far field keeping increases. So the focal depth also increases. When the location the same spot shape as shown in Fig. 5b. And it should be of the groove is moved, the focusing phenomenon still exists. indicated that the focusing properties in this case is quite However, the focus intensity will become weaker. The shorter similar to that using right-hand circular polarization incident the distance between the groove and the nodes is, the better the light. focusing effect will be. If the groove radius is increased by

λSP/4 (160 nm) to the locations where the intensity is maxi- mum value, for example, the groove radius r2 increases from Summary 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 The nanoscale-focusing effect has been realized in the far field intensity along the optical axis is shown in the inset in by a spiral plasmonic lens with a concentric annular groove. Fig. 3, indicating that the groove cannot scatter the SPPs into The spiral slit is used to excite the SPPs, and the electric field radiation light and focusing in the far field cannot be actualized on the outer plane of the silver thin film is proportional to zero- when the annular groove is set in these places. order Bessel function. The concentric groove is introduced to Figure 4a shows the intensity distribution of |E|2 in the convert the SPPs wave to propagating waves in free space. The x–z plane with groove radius r200.90 μm. From this figure, simulation results demonstrate that a left-hand spiral plasmonic we can see that the scattered light by the groove with curved lens can concentrate an incident right-hand circular polariza- wavefront in the diffraction zone gradually converged to- tion light into a focal spot at the exit surface. And this spot can ward the geometrical center from all directions while the be focused in the far field due to constructive interference of intensity in the center of the structure was enhanced gradu- the scattered light by the annular groove, and the FWHM of the ally along the propagation direction. Consequently, a bright focal spot can always be kept less than a half wavelength of the circular focal spot emerged, and the full width at half max- incident light. More interestingly, the focal length and the focal imum (FWHM) of the focus is only 0.44λ0, which is smaller depth can be adjusted by changing the groove radius, the than half of the incident light wavelength (λ0). Subsequent- number of grooves in a certain range. These properties make ly, the intensity in the center of the focal spot gradually it possible to probe the signal of spiral plasmonic lens in far faded away along the propagation direction. Furthermore, field by using conventional optical devices. we study the influences of groove depth on the focusing efficiency. The groove radius r2 is set to be 900 nm; while Acknowledgment We gratefully acknowledge the support to this the sliver layer thickness H varies from 300 to 800 nm. The work by NSFC (10974037), NBRPC (2010CB934102), Project of simulations are carried out with the groove depth h changed International S&T Cooperation (2010DFA51970), and Eu-FP7 (no. 247644). 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 References important is that when the groove radius r2 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 scat- 1. Knoll W (1998) Interfaces and thin films as seen by bound elec- tering efficiency will be different when the groove depth h is tromagnetic waves. Annu Rev Phys Chem 49:569–638 changed. By using this feature, we can regulate the intensity 2. Zijlstra P, Chon JWM, Gu M (2009) Five-dimensional optical recording mediated by surface plasmons in gold nanorods. Nature of the focal spot within a certain range. 459:410–413 As discussed above, the focal length increases monotoni- 3. Ditlbacher H, Krenn JR, Lamprecht B, Leitner A, Aussenegg FR cally with the increase of the groove radius, so what will (2000) Spectrally coded optical data storage by metal nanopar- – happen if several grooves were used at the same time. ticles. Opt Lett 25(8):563 565 4. Antosiewicz TJ, Wróbel P, Szoplik T (2011) Performance of scan- Figure 5a shows the focusing effect when five grooves radius ning near-field optical microscope probes with single groove and r200.58, 0.90, 1.22, 1.54, and 1.86 μm, respectively. The focal various metal coatings. Plasmonics 6:11–18 Plasmonics (2012) 7:377–381 381

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