In the field of nanophotonics, tuning the focus of near-field signals has been a great issue due to the demands on near-field imaging for, e.g., biomedical sensors and plasmonic tweezers. Using subwavelength structures for active control of plasmonic systems would be highly desirable. Here, we propose a plasmonic meta-slit, a simple but powerful structure that can switch the direction and length of its focus by changing optical polarization. It is composed of single or double arrays of nanoslit segments with a specific tilted angle distribution for a strong and flexible polarization dependency. Three representative examples of meta-slits for polarization-sensitive focusing, directional switching, and asymmetric focusing are theoretically and experimentally demonstrated. We expect that the proposed scheme can be applied not only to plasmonic switches and tunable lenses, but also as a design method for shaping near-field signals.
© 2015 Optical Society of America
Controlling a light focus with optical components such as tunable lenses [1,2], spatial light modulators [3,4], and holograms  has been of great interest in the field of optics. Tuning the characteristics of a light focus such as the position of the focal point, the focal length, and the depth of focus without changing the alignment of the optical system has great potential for designing microscopes and optical tweezing systems [6 –8].
Typically, light focusing and imaging can be achieved by altering the wavefront of the incident source. In conventional optics, this control of the wavefront can be achieved with a medium—by introducing spatially different optical path lengths. Although this method is sufficient for bulk optics, it is not appropriate in plasmonics because of the large size of the optical devices required to induce a sufficient difference in optical path lengths and the resulting high losses .
On the other hand, the rapid progress in recent plasmonics has uncovered an alternate solution for achieving light focusing and beam shaping without the need to use bulk materials. Such a solution, which is frequently referred to as metasurface, is composed of patterned arrays of metallic scatterers [10 –12]. Individual scatterers can be demonstrated in various ways such as apertures on a metal film , subwavelength-scale antenna structures [14,15], and periodic arrays of grooves [16,17]. The key function of the metasurface (or an individual scatterer or unit cell) is to introduce arbitrary changes in amplitude or abrupt phase differences in light that is transmitted through it .
However, to the best of our knowledge, these metasurfaces are largely used for generating far-field focusing and imaging of light, i.e., in free space far above the metal film [19,20]. In other words, only the radiated fields from individual scatterers are considered without much attention being paid to the surface fields. Although some studies have demonstrated complicate shaping of surface plasmon polariton (SPP) patterns such as Airy beams [21,22] and plasmonic vortices , tuning of the resulting patterns is quite difficult because, in these studies, the physical locations of slits were simply shifted so as to create a phase difference. Very recently, various polarization-controlled plasmonic directional launching methods were reported [24 –27], but techniques for tuning the location of plasmonic focus were still limited. Only a small lateral shift of plasmonic focus via spin-orbital interactions in a semicircular slit or plasmonic vortex lenses has been reported . Controlling and tuning the characteristic of near-field focus with metasurfaces has great potential since these techniques can be applied to make polarization-multiplexed near-field images or surface plasmon holography.
Here, we propose a plasmonic meta-slit structure that is applicable for use in various areas, including near-field focusing such as focal length tuning, directional switching, and asymmetric focusing. The terminology of “meta-slit” is adopted since the proposed structure is composed of arrays of subwavelength-scale nanoslit segments. It is distinguished from conventional metasurfaces because metasurfaces use two-dimensional patterns as an effective thin layer for shaping images that are far above that surface, whereas our structure focuses on the shaping of SPPs or near-fields, going sideways from the straight-lined pattern, which seems like an artificial slit pattern for generating various near-field distributions. The three types of representative meta-slit structures discussed in this paper are shown in Fig. 1. A single-lined meta-slit in which the tilted angle of the nanoslit segments has a parabolic distribution is used for bidirectional polarization-sensitive focusing [Fig. 1(a)], whereas double-lined meta-slits, in which nanoslit segments are positioned according to the radius of a Fresnel zone plate (FZP), can be used for directional switching [Fig. 1(c)] and asymmetric focusing controlled by the incident polarization state [Fig. 1(e)].
2. CHARACTERISTICS OF SPP LAUNCHED FROM A NANOSLIT ARRAY
Throughout this paper, a meta-slit is assumed to be composed of single- or double-lined arrays of subwavelength-scale rectangular nanoslits fabricated on a metal film. Since the overall SPP generation by the meta-slit structure can be expressed by the interference between that of each nanoslit, let us start with an SPP generation from a single nanoslit. It is known that an infinitely long nanoslit can launch SPPs only for the polarization state in which the electric-field component is perpendicular to the slit direction . For the case of a rectangular-shaped nanoslit with a high aspect ratio, the amount of SPP generation is significantly dependent on the orientation of the incident polarization . In Fig. 2(a), the angular distribution of the propagating SPPs from a nanoslit with a cross section of is shown. The nanoslit launches strong SPPs only for polarization that is perpendicular to the slit, while the amount of SPP excitation is significantly diminished (by a factor of about 300) in the case of polarization that is parallel to the slit.
Due to these large differences in the amount of launched SPPs, it is possible to model each nanoslit segment as a dipole source that lies on the metal surface directing normal to the longer axis of the nanoslit. Such an approximation is often considered for analyzing radiated far fields  or surface fields that are far away from the nanoslit . By superposing light fields generated from each dipole source, it is possible to investigate the mechanism of the proposed meta-slit geometry. Thus, the electric-field component of the scattered light due to the nanoslit array can be expressed as 1(c)], respectively. Basically, the location is discretely separated along the direction with a period of and has a fixed value in the direction. The functions and represent free-space and surface Green dyadic tensors for the three-dimensional Helmholtz equation, respectively. The former indicates the radiated field from the dipole source without reflection on the metal surface, whereas the latter includes reflected as well as surface fields due to the metal surface. The phase term represents the relative phase differences between dipole sources. It is expressed as , (); for circularly polarized lights where the plus and minus signs correspond to the cases of left- and right-handed circular polarizations (LCP and RCP), respectively. More details on Eq. (1) can be found in Supplement 1 (Part A) with details of numerical calculation methods.
Our initial interest is to show that SPPs generated by the nanoslit array with a constant tilted angle (i.e., for all ) do not diffract and, thus, form a type of surface beam. In Fig. 2(b), the normalized overlap integral between the light-field distribution generated by an array of dipole sources with and that from a simple bare slit calculated by the finite element method (FEM) simulation is plotted. Here, the total length of the dipole source array and the -directional length of the bare slit have the same value of . The direction of the major beam generated by the tilted array of nanoslit segments is perpendicular to the slit orientation when their arranging period is much longer than the effective wavelength of the SPP () as shown in the lower-side insets of Fig. 2(b). Due to the interference of each source, multiple beams are produced when is large, and the number of beams is gradually reduced as becomes shorter. Finally, the direction of the beam finally follows that of the bare slit when the period is much smaller than , as shown in the upper-side inset of Fig. 2(b). A dramatic transition occurs near , which is related to the diffraction limit of the light. Such a phenomenon is observed not only for the tilted angle of but also for arbitrary tilted angles.
Although the spatial distribution of a light field launched from the nanoslit array is no more different from that of the single bare slit when is shorter than , its absolute amplitude and phase profiles can be tuned by the tilted angle () of the nanoslit segment when circular polarized light is adopted. In Figs. 2(c) and 2(d), changes in the relative amplitude and phase of the SPP wave generated from the nanoslit array are plotted for various tilted angles . was set to 400 nm, and the results are those at 50 μm away from the center of the nanoslit segment. The results show that the phase of the quasi-plane SPP wave launched from the tilted-nanoslit array changes linearly with , and a phase difference of as much as can be obtained. The amplitude of the SPP wave is also dependent on . It becomes the highest for and approaches zero for . Unfortunately, the amplitude and phase of the launched SPP wave are correlated with each other and the range of phase variance is restricted to . Hence, it may restrict the shaping of arbitrary SPP fields. However, the strong polarization dependency of the tilted nanoslits enables various types of tunable surface plasmon focusing, as will be discussed in the following sections.
3. DEMONSTRATION OF META-SLITS FOR CONTROLLING NEAR-FIELD FOCUS
A. Single-Lined Meta-Slit for Polarization-Sensitive Focusing
We show that the amplitude and phase of SPPs launched from a meta-slit can be tuned by adjusting the tilted angle of each nanoslit segment (). Below, we consider a single-lined meta-slit structure whose nanoslit segments have different tiled angles, especially when they have a slowly varying distribution along the direction as shown in Fig. 1(a). A complex field generated from such a meta-slit can be expressed as a function of the tilted angle profile,2(c) and 2(d). Since is subwavelength scale, it can be assumed that is continuous. In order to create a plasmonic focus with a focal length of , it is necessary to find a specific tilted angle distribution that satisfies a conventional lens transfer function with a focal length of , i.e., a parabolic function along the direction. The reason for choosing a lens transfer function with focal length of for designing a plasmonic focus with a focal length of will be explained below.
As we noted in the previous section, the range of phase variance induced by the artificial rotation of a nanoslit segment is restricted to . If we set for the nanoslit segment located at the center of the meta-slit and , and then rotate the other nanoslits following a parabolic profile of [see Fig. 1(a)], it is possible to implement a transfer function with a focal length of . However, the effect of , which can be approximated as , also needs to be considered. By writing and (plus sign for LCP), where is a unit step function, we finally have3) is composed of two terms, one containing a focusing wave with a focal length of (upper sign for LCP) and a quasi-plane wave. Since the case of indicates a virtual focus, it may be possible to obtain divergent waves from the meta-slit. In Fig. 3(a), field distributions calculated by the dipole modeling method are shown for LCP and RCP light incidences. Here, we set the focal length as , where the detailed tilted angle of each nanoslit segment can be found in the Supplement 1 (Part D). For the case of LCP, it is possible to discern constant wavefronts and a virtual focus of . Therefore, the meta-slit cannot make a focus with the LCP incident light as shown in the upper-side image of Fig. 3(a).
On the other hand, for the case of the incidence of RCP light, constant wavefronts and a real focus at are possible. Hence, a plasmonic focus is formed near the designed focal length as shown in the lower-side image of Fig. 3(a). The extracted focal length in the numerical calculation results was 13.5 μm, which is slightly shorter than the designed value but within a reasonable range of error. The mismatch between the designed and measured focal lengths originates from the finite length of the meta-slit.
For the fabrication of the meta-slit, an e-beam evaporator (MUHAN, MHS-1800) was used for the deposition of a 200 nm Ag film on a Si wafer. A focused ion beam machine (FIB) (FEI, Quanta 200 3D) was then used for the patterning of each slit segment. The acceleration voltage and exposing current for patterning were set at 30 kV and 10 pA, respectively. To reduce the surface roughness of the Ag film, a substrate was attached by a transparent adhesion solution and the Ag layer was lifted off. Experimental results of the proposed structure are shown in Fig. 3(b). A 980 nm laser source illuminated the back side of the sample and the transmitted side of the sample was scanned using a tip-based near-field scanning microscope (NSOM) attached to an atomic force microscope (AFM). The near field was coupled to a cantilever type metal-coated (Cr/Au) NSOM tip with a diameter of 250 nm, and the power of the signal was measured by an avalanche photo diode (Agilent 81634B). The feedback mode in the NSOM system was the noncontact mode, in which the tip was tapping over the sample. We scanned a region of divided into pixels (the maximum limit of our piezo system) with a duration time of 30 ms for each pixel. Measured intensity distributions are shown in Fig. 3(b) for the cases of RCP and LCP polarization. The experimental images are quite similar to the numerical results (even the node lines and weak caustic patterns are observed in NSOM images). We can find clearly different intensity profiles depending on the optical handedness and detect a near-field focus only in the case of the RCP light incidence. In Fig. 3(c), intensity profiles of LCP (dotted) and RCP (solid) cases along focal plane are shown, which verifies that a plasmonic focus was formed in the RCP case. The full width at half-maximum (FWHM) for numerical and experimental foci was nearly the same (about 1.43 μm). These results show that we can implement a clear on/off switching of the plasmonic focus by changing the polarization state of the incident light. The plots along the axis of focus can be found in Supplement 1 (Part C).
Figure 3(d) shows the variance of the focal length of some meta-slits with different when the incident wavelength is changed. Since the characteristics of phase delay caused by the orientation of the nanoslit [shown in Fig. 2(d)] are not sensitive to the incident wavelength for subwavelength size of nanoslit, the focal length of the meta-slit is strictly governed by the tilted angle distribution . Hence, regardless of the designed focal length, the product value of maintains for the broadband region, but the exact focal length is decreased for longer wavelengths due to the fixed phase delay along the meta-slit.
B. Directional Switching of SPP Focus with Double-Lined Fresnel Zone Meta-Slit
We demonstrated in the above that a single-lined meta-slit can be used for polarization-sensitive plasmonic focus without any shift in slit location. Below, we consider a more complex situation, a double-lined Fresnel zone (DFZ) meta-slit shown in Fig. 4(a), which will be shown to have directional surface-wave switching characteristics. Although the DFZ structure has regions with and without nanoslit pairs, let us first consider two lines of a nanoslit array having tilted angles of and , respectively, as shown in the inset of Fig. 4(a). We will fix the observing plane as the left side of the meta-slit. As was demonstrated in the previous section, quasi-plane SPP waves are launched from two nanoslit lines [denoted as line A and B in Fig. 4(a)], and interfere at the observing plane. When an LCP light illuminates the meta-slit, the phase of the quasi-plane wave launched from line A [; solid black arrow in Fig. 4(b)] leads relative to that from line B [; solid blue arrow in Fig. 4(b)] if the phase delay due to the physical separation between the two nanoslit lines is ignored. On the other hand, lags relative to when an RCP light is used [see the dotted blue arrow in Fig. 4(b)]. However, the phase delay due to the separation between the two lines must be taken into account. Here, we assume that the phase delays caused by the multiple reflections between two lines of the nanoslit array are negligible. The SPP wave at the observation plane with RCP light incidence is then perfectly canceled out if the distance between two lines is given by4) is satisfied, the total phase of the wave from line B [; dotted red arrow of Fig. 4(b)] becomes opposite to that of the wave from line A (). However, such cancelation is not observed in the LCP case [see the solid red arrow of Fig. 4(b)] since the initial phase difference between and is different from that of the RCP case. Although we considered observation planes at the left side of the meta-slit, a similar argument can be formulated for the observation planes at the right side as if the optical handedness were reversed, due to the -directional symmetry of the structure. Thus, when Eq. (4) is satisfied, SPP launching toward the left side is reduced to a minimum while that toward the right side is reinforced. Since SPP launching toward the right side can be maximized only when (this can also be verified from a Huygens-like viewpoint ), the extinction ratio, defined as the ratio of the intensity of the right-side SPP to that of the left-side SPP, can be maximized under these conditions (See Supplement 1 Part B).
Let us return to the main structure of this section, a DFZ meta-slit, as shown in Fig. 4(a). Even though the tilted angle is changed for the double-lined meta-slit structure, the phase of quasi-plane SPP wave superposed from each line is not changed since the excited phase from each line has mirror symmetry.
Hence, a type of discrete amplitude modulation along the direction can be applied to form a plasmonic focus rather than the phase modulation introduced in the previous section. This can be easily achieved by distributing the nanoslit segments of two arrays following the profile of the radius of the well-known FZP, which can be written as
In Fig. 4(c), we show the numerical results for a DFZ meta-slit with a 20 μm focal length. To introduce a sufficient number of Fresnel zone radii, the total length of the meta-slit is adjusted to . From these results, it can be clearly seen that a bright plasmonic focus was generated only at a single side of the meta-slit. Weak SPP fields following the typical caustics patterns of the lens can be seen at the other side of the meta-slit, due to the finite extinction ratio of the meta-slit structure. The extinction ratio, at the left- and right-side foci, was about 6.53. Although the result of the extinction ratio may seem much lower than some other unidirectional launching schemes [26,35], we would like to comment that these works demonstrated unidirectional launching of SPPs only for plane surface waves, not a finely tuned focus. When we do not use the Fresnel lens geometry but a simple periodic array of tilted nanoslits, output signals becomes a plane surface wave but the extinction ratio can also reach the order of 100, which is sufficiently comparable with the previous results [See Fig. S1(a) of Supplement 1 Part B]. The degradation of extinction ratio comes from too short intervals between adjacent Fresnel radii. This can also be observed from Fig. 4(c); the SPP focus at the unwanted direction is merged from the ends of meta-slits, not from the center region.
Experimental results measured with NSOM are shown in Fig. 4(d). Similar to the numerical results, SPPs were generated only for one selected direction and converged at a specific focal point at a distance of 20 μm from the meta-slit. The FWHM of this focused spot was about 1.6 μm, which was somewhat wider than the numerical result of . This degradation in quality appears to rise from limitations associated with the fabrication conditions such as imperfect FIB milling, or from the approximation of nanoslit segments as ideal dipole sources in the numerical simulation. The graphical plots along the axis of focus and along the focal plane can be found in the Supplement 1 (Part C).
In addition to near-field scan, we also performed far-field measurements using grating couplers, which are shown in the inset of Fig. 4(d). Output grating couplers were located at a distance of 20 μm from the center of the DFZ meta-slit, and the scattered SPP fields were measured using a CCD camera. The results of these measurements are shown in the inset of Fig. 4(d). Only a small part of the output coupler was bright at one side of the output gratings, thus successfully demonstrating the directional switching of SPPs.
From now, we would like to briefly comment on the wavelength dependency and coupling efficiency of the proposed DFZ meta-slit structure. Similar to the case of a single-lined meta-slit, the focal length of the DFZ decreases when the incident wavelength is increased. The reason for such wavelength dependency naturally comes from the fixed geometry of the Fresnel radius, governed by Eq. (5). In addition, the bandwidth of the extinction ratio is restricted because the perfect destructive interference condition [Eq. (4)] is significantly related to . The bandwidth of the extinction ratio for the DFZ structure (designed for ) is obtained as 70 nm. Since the dipole modeling is not appropriate to calculate the coupling efficiency, we implement an additional full electromagnetic simulation with the FDTD method. The maximum field intensity of the focus normalized by that of incident field is obtained as 6.5%. See Supplement 1 Part D for details.
C. Asymmetric Focusing with a Hybrid Fresnel Zone Meta-Slit
The DFZ meta-slits in the previous section could form a plasmonic focus at either the left or the right side of the slit depending on the handedness of the incident light, but the left- and right-side focal lengths were the same. For further application of the proposed meta-slit, it would be desirable for them to simultaneously generate left- and right-side foci, with different focal lengths. To achieve this, we propose the use of a hybrid Fresnel zone meta-slit that has such asymmetric foci.
The key idea is to simultaneously use different types of nanosilt-segment pairs. To create different focal lengths for left- and right-side foci, at least three types of nanoslit-segment pairs that can perform left-side-only, right-side-only, and bidirectional launchings of SPPs are needed. As we have seen in the previous section, a nanoslit pair with opposite tilted angles has switchable unidirectional launching characteristics, and its extinction ratio can be maximized when the tilted angles are . This structure can thus be selected for the right- (Type 1) and left-side-only (Type 2) launching of SPPs. For the bidirectional excitation of SPPs, we choose a similar one, a nanoslit pair with (Type 3), which has some benefits compared to a single array of nanoslits in that the amplitude of the excited SPPs can be adjusted by controlling the distance between the two arrays. These three types of nanoslit pairs [shown in Fig. 5(a)] form the hybrid DFZ meta-slit. By appropriately arranging these nanoslit pairs and designing the focal lengths of the meta-slits differently ( and ) as shown in Fig. 5(b), it is possible to implement asymmetric foci.
Due to the switchable launching characteristics of Type 1 and Type 2 meta-slits via incident polarization, the positions of asymmetric foci of the hybrid DFZ meta-slit can be also switched by changing the optical handedness.
The numerical results obtained by the dipole modeling method for the cases of RCP and LCP cases are shown in Fig. 5(c). As predicted, two asymmetric focal spots with the desired focal lengths are clearly observed, and their FWHM sizes were not degraded compared to those of the DFZ meta-slit demonstrated in the previous section (see Supplement 1 Part C). In Fig. 5(d), we also show experimental results obtained by NSOM. Due to the limit in the maximum scanning range of the NSOM, only the right-side part of the hybrid DFZ meta-slit changing the optical handedness is compared. From the figure, we can see that the measured results coincide very well with the numerical results and theoretical predictions. We also observe a clear difference in the focal lengths of right- and left-side foci, thus confirming that their positions can be switched by changing the handedness of the incident light. As in the case of the DFZ meta-slit, the FWHM sizes of the experimental foci were degraded for similar reasons, i.e., imperfect fabrication conditions and numerical errors involved in the ideal dipole modeling. See Supplement 1 for more details (Part C).
In conclusion, we theoretically and experimentally demonstrate a one-dimensional plasmonic metasurface, which we refer to as a meta-slit. It is composed of single or double arrays of tilted nanoslit segments, the tiled angles and positions of which have specific well-designed distributions. Contrary to the case of far-field focusing via so-called metasurfaces, the function of the meta-slit is to focus SPPs or surface fields on a desired focal point having various tunable features such as polarization-switchability, directional switching, and asymmetric focal characteristics. Although, in this report, we demonstrate only the formation and tuning of single near-field foci, the working principle of the meta-slit can be used for more complex purposes such as multiple focusing, arbitrary beam shaping, or plasmonic vortex generation. Unlike the case of a bare slit, the potential of the meta-slit is based on the flexible design ability of excited amplitude and phase as a function of a change in optical handedness. Such characteristics can enable us to design a route for the spatial modulation of excited SPPs without the need for an additional optical controller such as spatial light modulators but, rather, by a simple change in optical polarization. Although the ranges of amplitude and phase variations were restricted in our method, it is likely that the variation range can be expanded to an arbitrary complex value by appropriately designing the slit geometry, which might be solved in future studies. We expect that the proposed method of designing a meta-slit can be applied to plasmonic switches, tunable plasmonic lenses, and further arbitrary shaping of optical near fields.
National Research Foundation of Korea
See Supplement 1 for supporting content.
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