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Highly efficient plasmonic nanofocusing is proposed and demonstrated in a T-shape micro-slit surrounded by multi-slits. The nanofocusing phenomenon is achieved based on the multimode interference in the micro-slit, the constructive interference in the T-shape slit, and also the multiple-beam interference of the light radiated from the multi-slits and the transmitted light from the T-shape micro-slit. Because of the large illumination areas of the incident light on the wide slit aperture in the proposed structure, a large amount of light can pass through the wide slit. This leads to a highly efficient nanofocusing. Meanwhile, the wide slit means easy fabrication. In the experiment, the focusing phenomenon in the proposed structure was successfully demonstrated with a scanning near-field optical microscopy (SNOM) technology.
©2012 Optical Society of America
1. Introduction
Surface Plasmon polaritons (SPPs) are electromagnetic waves propagating along dielectric-metal interfaces [1–4] and can be confined by metallic nanostructures beyond the diffraction limit. So they are widely used in designing nano-focusing structures, which have great application potentials in nano-scale beam shaping, integrated optics, data storage, and near-field imaging [5–8]. To realize such potentials, ultra-small apertures, such as subwavelength holes or slits [5–9], are usually utilized to realize nano-focusing based on the subwavelength field confinement of SPPs by the ultra-small metallic structures [9] and the extraordinary optical transmission (EOT) effect [10]. For example, the slit-grating structures, consisting of a single nanoslit surrounded by multi-grooves [4–9,11–13] or dielectric strips [14, 15], can realize nano-focusing based on the constructive interference of the scattered light from the grooves (or strips) and the directly transmitted light from the nanoslit at the focusing spot. However, the focusing efficiencies of these structures are quite low because the focusing light mainly comes from the single nanoslit (very small illuminated areas). Using multi-nanoslits [16,17], the nanofocusing with increased efficiency were predicted theoretically due to the relatively large illuminated areas of the incident light on the multi-nanoslit apertures. For these nanofocusing structures, the multi-slits with different depths [16] or widths [17] were designed to retard the phases to realize the constructive interference of the transmitted light from different nanoslits. However, the different slit depths or widths in these multi-nanoslit structures mean increased difficulty of sample fabrication. Based on the Talbot effect, periodic nanostructures were usually used to realize nanofocusing [18–20]. But this effect in a single structure due to the multimode interference has not been utilized to realize light focusing experimentally. Moreover, all of the previous nanofocusing devices are made of various nanostructures, and their focusing efficiencies are not very high.
In the paper, we experimentally demonstrated a nano-focusing structure with high focusing efficiencies and easy fabrication by using a T-shape micro-slit surrounded by multi-slits of the same depth and width. The highly efficient nanofocusing phenomenon was caused by three factors. First, the light focusing with high efficiencies in a micro-slit is obtained due to the multimode interference [21] in the wide slit, which is used for the first time to achieve light focusing. The high focusing efficiency results from a large illumination area of the incident light on the wide slit aperture. This can lead to a great amount of light directly passing through the wide slit. Second, adding two grooves in immediate contacting with the wide slit to form a T-shape micro-slit, the focusing efficiency is further improved due to constructive interference. Third, by designing multi-slits on both sides of the T-shape micro-slit, nanofocusing with a subwavelength spot size is realized owing to the multiple-beam interference of the light radiated from the multi-slits and the transmitted light from the T-shape micro-slit at the focusing spot position. Experimentally, the efficient focusing effect in the proposed structure was successfully demonstrated with a scanning near-field optical microscopy (SNOM) system. It is found that these results agree well with the simulation results.
2. Principle and simulation
2.1 Micro-slit for efficient light focusing based on multimode interference
The investigated micro-slit (width of w) on a metal film with the thickness of t is schematically shown in Fig. 1(a) , a 300-nm-thick gold film with a micro-slit placed on a SiO2 substrate. The wide single-slit is used for the first time to achieve light focusing. It is well known that the micro-slit in the optical-thick metal film can support multi-order modes when p-polarized light (magnetic vector parallel to the slit, TM mode) illuminates the micro-slit from the back side [22]. In order to investigate this complex phenomenon in the wide slit, the field distributions of the transmitted light were calculated using the Finite Element Method (FEM) of Comsol Multiphysics. In the simulations, the wavelength of the incident p-polarized light is assumed to λ = 633 nm, and the corresponding permittivity of the gold and substrate are εAu = −11.815 + 1.239i [23] and εSiO2 = 1.452, respectively. Figure 1(b)–1(d) display the calculated intensity distributions of the transmitted light from the micro-slit for three typical widths of w = 1200 nm, w = 1800 nm, and w = 2400 nm. From these figures, it is obviously observed that energy concentration emerges. As we know, for a planar structure supporting a large number of modes, due to the cross interference between different modes, self-imaging occurs at periodic intervals, once or multiple times along the direction of light propagation [21,24]. Thus, the energy concentration in Fig. 1(b)–1(d) is due to the multimode interference in the wide slit [21, 24], which can support multi-order modes [22]. For example, the focusing intensity is about I = 1.2 and the focusing spot size (full-width at half-maximum, FWHM) is about FWHM = 720 nm for the slit width of w = 1200 nm, as shown in Fig. 1(b). Here, the focusing intensity is normalized according to that of the incident light. Moreover, it is noted that the focusing intensities (I) and focal lengths (f) increase with the slit width [21,24], as shown in Fig. 1(b)–1(d). The increased focusing intensities result from the increased illumination areas of the incident light on the wide slit aperture.
Fig. 1 (a) Geometry of a micro-slit under illumination of p-polarized light. Intensity distribution calculated by FEM for three typical slit widths of (b) w = 1200 nm, (c) w = 1800 nm, and (d) w = 2400 nm, respectively.
Simulations also show that the micro-slit with an infinite thickness nearly exhibits the same energy concentration as that in Fig. 1(b) and 1(c) in the propagation direction. This strongly demonstrates that the light focusing in the micro-slit result from the multimode interference. Comparing with the slit with an infinite thickness, the micro-slit with the finite thickness is more easily fabricated in the experiment.
2.2 T-shape micro-slit to improve focusing performance
The focusing performance can be improved by adding two grooves (with depths of d and widths of wgroove) in immediate contacting with the micro-slit, which constructs a T-shape micro-slit, as schematically shown in Fig. 2(a) . When p-polarized light illuminates the structure from the back side, a part of light can pass through the micro-slit directly, and the other can generate SPPs propagating along the bottom of the groove. The generated SPPs can be reflected and scattered by the two walls of the grooves, and then interfere with the directly passing light at the focusing spot. This interference can affects the focusing spot, and it is easy to obtain that the phase difference between the scattered SPPs by the groove walls and the directly passing light is determined by
where, kSPP is the wave vector of SPPs; L(wgroove) = wgroove + [(w/2 + wgroove)2 + f2]1/2-f is the optical path difference between these two interference parts; f is the focal length; and φ is the phase shift caused by the SPP generations and the SPP reflections off the groove walls. According to Eq. (1), constructive (or destructive) interference in the structure should occur when Φ is equal to even (or odd) multiples of π. At constructive interference, the transmittance of the T-shape micro-slit is enhanced, so the focusing light intensity increases accordingly. When the groove width is much greater than the focal length, the optical path difference between these two interference parts is equal to L(wgroove)≈2wgroove + w/2. Thus, the period referring to wgroove is equal to half of the SPP wavelength in this case (wgroove/f>>1).Fig. 2 (a) Schematic and geometric parameters of the T-shape micro-slit. (b) Dependences of the focusing intensities on the slit widths. (c) Intensity distribution in the T-shape micro-slit for w = 1200 nm and wgroove = 150 nm.
To explore the improvement of the focusing performance in the T-shape micro-slit, the dependence of the focusing intensity on the groove widths in the investigated structure for micro-slit width of 1200 nm and groove depth of 150 nm were calculated, and the results are shown in Fig. 2(b). In the calculations, it is found that the focal length is less than 1000 nm and changes slightly when varying “wgroove”. Thus, the normalized intensity shown in Fig. 2(b) is taken at the focusing position that changes accordingly. From Fig. 2(b), it is observed that the focal intensity efficiencies display an oscillation behavior. The period of the oscillation curve is a little greater than λspp/2 = 300 nm when the groove width is small (wgroove<1000 nm); while the period approaches a constant of λspp/2 = 300 nm when the groove width becomes large (wgroove>2000 nm). This well coincides with the analysis based on Eq. (1). Moreover, it is observed that Fig. 2(b) shows a decay of the focused intensity oscillation. This is due to the propagation loss of SPPs (propagation length of only about 10 μm) on the groove bottom. Particularly, the focusing intensity reaches about 1.8 at wgroove = 150 nm for the constructive interference in the T-shape micro-slit. This focusing intensity is about 1.5 times that (I = 1.2) in the micro-slit without adding the grooves [Fig. 1(b)]. The corresponding field distribution of the T-shape micro-slit is shown in Fig. 2(c). Comparing with Fig. 1(b), higher focusing intensity (increased by 50%) is observed. Moreover, the focusing spot becomes tighter, and the spot size of FWHM = 490 nm decreases to 1/1.47 times that (FWHM = 720 nm) in Fig. 1(b). This nearly consists with the increase of the focusing intensity. Thus, the improvement of the focusing performance in the T-shape micro-slit is due to the constructive interference.
2.3 T-shape micro-slit surrounded by multi-slits for efficient nanofocusing
To realize the focusing with subwavelength spatial resolutions, the T-shape micro-slit (micro-slit width of w = 1200 nm and groove depth of d = 150 nm) was designed to be surrounded by multi-slits with the same slit width of wm, as shown in Fig. 3(a) . The groove width is chosen to be wgroove = 150 nm in consideration of the propagation loss of SPPs owing to the ohmic loss of Au and the fabrication roughness by FIB. For the multi-slits, the SPPs are excited in the slits and then scattered into radiation lights. It is easy to obtain that the phase difference between the light radiated from the s-th surrounding slit and the light transmitted from the T-shape micro-slit at the focusing spot position is about
where, xs is the center position of the s-th slit, and k0 = 2π/λ is the vacuum wave vector of the incident light. According to Eq. (2), the constructive interference should occur when ψ is equal to 2mπ (m = 1,2,3…). In this case, the focusing intensity in the structure can be further improved and the spot size can reach the subwavelength scales due to the multiple-beam interference.Fig. 3 (a) Schematic diagram of the T-shape micro-slit surrounded by multi-slits. (b) Field intensity distribution and (c) cross section of the normalized intensity along the x-axis direction at the spot position of z = 1600 nm.
For simplicity, we assume s = m, so it can be easily got that the center position of the s-th slit is determined by xs = ± (2mf/λ + m2)1/2λ. In the simulations, the focal length and the number of the multi-slits are set to be f = 460 nm and mmax = 10, respectively. The width of the multi-slits is assumed to wm = 150 nm, which is also easily fabricated by focused ion beams (FIB) in the experiment [25,26]. It is should be pointed out that the choice of the width of the multi-slits wm = 150 is arbitrary. Other widths (wm = 100~300 nm) are also OK providing that the multi-slits can be easily fabricated. Simulations show that the focusing (such as intensity and spot size) can be influenced when the number of the multi-slits is very small. When the number becomes large (> = 10), the focusing will nearly not be influenced. The calculated field distribution of the proposed structure is shown in Fig. 3(b). It is clearly observed that a tight focusing spot appears above the exit of the T-shape slit of z = 1600 nm, where the top surface of the Au film is set to be at z = 1000 nm in the simulation model. The cross section of the focus spot along the x-axis direction is given in Fig. 3(c), indicating a high focusing intensity of about I = 5.7 and a spot size of only about FWHM = 248 nm (<λ/2). The focusing intensity in the proposed structure is more than 10 times that in the slit-grating structures [4–15] and 5-slits with different depths [16], and it is even better than that in the 65-slits with different widths [17], which is difficult to be fabricated in the experiment. Therefore, based on the multimode interference in the micro-slit, the constructive interference in the T-shape slit, and the multiple-beam interference of the light radiated from the multi-slits and the transmitted light from the T-shape micro-slit, the nano-focusing with high efficiency and subwavelength spot size is successfully realized in the T-shape micro-slit surrounded by multi-slits with the same slit widths and depths.
3. Experiment and results
To further test our proposal experimentally, the T-shape micro-slit surrounded by multi-slits was fabricated using FIB in an about 300-nm-thick gold film. The inset in Fig. 4(a) shows the detailed scanning electron microscopy (SEM) image of the nanofocusing structure. In the middle of the image is the micro-slit with a width of about w = 1150 nm and a length of about 10 μm. Both sides of the micro-slit are flanked by a shallow groove to form the T-shape micro-slit. The left and right parts of the T-shape micro-slit are the designed multi-slits (10 slits) with the same slit width (wm). Herein, the center position of the m-th slit is determined by xs = ± (2mf/λ + m2)1/2λ inferred from Eq. (2). The measured geometrical parameters of the nanofocusing structure are as follows: the groove width and depth are about wgroove = 150 nm and d = 150 nm, respectively; and the multi-slit widths are about wm = 150 nm.
Fig. 4 (a) Schematic of the experimental process in the T-shape micro-slit surrounded by multi-slits. Inset shows the detailed SEM image of the fabricated sample. (b) Topographic image of the fabricated sample by SNOM. Field distributions of the transmitted light on the planes (parallel to metal surface) (c) far from and (d) near the focusing spot position by SNOM.
In the experiment, the structure was normally illuminated from the back side by a p-polarized laser beam with the wavelength of 632.8 nm (He-Ne laser) with a radius of about 100 μm, as shown in Fig. 4(a). To measure the field distribution near the focusing spot position on such an ultra-small structure, we utilized a scanning near-field optical microscopy (SNOM) system (NT-MDT Spectra, Russian). The field distributions of the transmitted light above the metal surface was collected in the near field around the focusing spot planes (parallel to metal surface) using a gold-coated fiber tip (chemically etched) with the aperture diameter of about 200 nm, as shown in Fig. 4(a). In the measurement, the topographic signals and the optical signals could be obtained simultaneously. Figure 4(b) displays a topographic image of the fabricated sample, which matches very well with the SEM image in the inset in Fig. 4(a). The measured field distributions at different planes (parallel to metal surface) along the z-axis direction are shown in Fig. 4(c) and Fig. 4 (d). Far from the focusing spot position (close to the metal surface), the transmitted light is weakly concentrated with a low intensity, as shown in Fig. 4(c). Approaching the focusing spot position, an obvious focusing phenomenon emerges. As a result, the spot size of the transmitted light becomes small and the focusing intensity increases, as shown in Fig. 4(d).
To detailedly observe the focusing effect by the proposed structure, the above measured field distribution along the x-axis direction are presented by the black lines in Fig. 5(a) and Fig. 5(b). It is clearly observed that the transmitted light is weakly confined (spot size of about 2000 nm) at the plane far away from the focusing spot position [Fig. 5(a)] and becomes well focused (spot size of about 600 nm) at the plane near the focusing spot position. Here, the focusing spot size is greater than the simulation results. This is mainly due to that it is a little difficult to exactly put the scanning fiber tip on the focusing plane, as well as that the fiber tip has an aperture size of 200 nm. Last, we made a comparison of the measured results with the simulations using the FEM method, and the simulation results (after the convolution of the finite probe size [7]) for z = 1300 nm and z = 1400 nm are displayed by the red lines in Fig. 5(a) and Fig. 5(b), respectively. It is found that the experiment results agree well with the simulation results. This also reveals that the measured planes is not exactly the focusing plane of z = 1600 nm.
Fig. 5 Experimental and simulation results of the field distributions for the cross section along the x-axis direction for different positions of (a) z = 1300 nm and (b) z = 1400 nm.
4. Conclusion
In summary, we proposed and experimentally demonstrated a highly efficient nanofocusing structure, which consist of a T-shape micro-slit surrounded by multi-slits with the same widths and depths. Simulations found that the transmitted light can be focused by a micro-slit because of the multimode interference. Due to the large illumination areas of the incident light on the wide slit aperture, a great amount of light can pass through the wide slit, resulting in a high focusing efficiency. Adding grooves in immediate contacting with the wide slit to form a T-shape micro-slit, the focusing performance (intensity and spot size) was further improved because of constructive interference. At last, by designing multi-slits on both sides of the T-shape micro-slit, nanofocusing with higher efficiency and spot size of only 248 nm was achieved owing to the multiple-beam interference of the light radiated from the multi-slits and the transmitted light from the T-shape micro-slit at the focusing spot position. Experimentally, the efficient focusing in the proposed structure with large illuminated areas was demonstrated with the SNOM system, which agreed well with the simulation results. The T-shape micro-slit surrounded by multi-slits for highly efficient nanofocusing has great significance for the application such as nano-scale beam shaping, integrated optics, data storage, and near-field imaging.
Acknowledgments
This work was supported by the National Basic Research Program of China (Grant Nos. 2010CB923200 and 2009CB930504) and the National Natural Science Foundation of China (Grant Nos. 10804004, 10821062, and 90921008).
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