Surface plasmon converging and diverging ... - OSA Publishing

Surface plasmon converging and diverging properties modulated by polymer refractive structures on metal films D. G. Zhang1, 3, X.-C.Yuan2*, J. Bu2, G. H. Yuan1, 3, Q. Wang1, J. Lin1, X. J. Zhang1, P. Wang3, H. Ming3, and T. Mei1 1

School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798, Singapore 2 Institute of Modern Optics, Key Laboratory of Optoelectronic Information Science & Technology, Ministry of Education of China, Nankai University, Tianjin 300071, China 3 Departments of Physics, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China * Corresponding author: [email protected]

Abstract: Polymer refractive microstructures are fabricated on metallic thin films and employed to modulate surface plasmons (SPs) propagations in a refractive manner. SP waves converging with different focal lengths and diverging effects are realized by the refractive structures. Authors investigated the modulation effect on SP waves as a function of different thicknesses and different shapes of the polymer micro-structures based on the effective refractive index model, where imaging properties of the SPs are observed experimentally by detecting the leaky radiation intensity of the SPs. 2009 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (240.6690) Surface waves; (120.5060) Phase modulation; (110.0180) Microscopy.

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#108865 - $15.00 USD Received 18 Mar 2009; revised 15 May 2009; accepted 27 May 2009; published 22 Jun 2009

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14. A. Hohenau, J. R. Krenn, A. L. Stepanov, A. Drezet, H. Ditlbacher, B. Steinberger, A. Leitner, and F. R. Aussenegg, "Dielectric optical elements for surface plasmons," Opt. Lett. 30, 893-895 (2005). 15. S. Griesing, A. Englisch, and U. Hartmann, "Fabrication and SNOM characterization of plasmon-optical elements," J. Phy: Conference Series, 364 (2007). 16. S. Griesing, A. Englisch, and U. Hartmann, "Refractive and reflective behavior of polymer prisms used for surface plasmon guidance," Opt. Lett. 33, 575-577 (2008). 17. H.Rather, "Surface Plasmons on Smooth and Rough Surfaces and Gratings," Springer (1988). 18. A. Bouhelier, and G. P. Wiederrecht, "Surface plasmon rainbow jets," Opt. Lett, 30, 884-886 (2005). 19. Rashid. Zia, Mark D.Selker, and Mark L.Brongersma, "Leaky and bound modes of surface plasmon waveguides," Phy. Rev. B , 71, 165431 (2005). 20. Q. Wang, X. Yuan, P. Tan, and D. Zhang, "Phase modulation of surface plasmon polaritonsby surface relief dielectric structures," Opt. Express, 16, 19271-19276 (2008). 21. A. V. Krasavin and A. V. Zayats, "Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides," Phys. Rev. B. 78, 045425 (2008). 22. A. V. Krasavin and A. V. Zayats, "Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides," Appl. Phy. Lett. 90, 211101 (2007).

1. Introduction Surface plasmons (SPs) waves are electromagnetic modes constituted by light fields coupled to collective electron oscillations propagating along the interface between metal film and dielectric substrate [1, 2]. As signal carriers, SPs waves have extensively been considered for nanoscale two-dimensional optical circuits, where many different approaches are proposed to modulate the behaviors of SPs, for example, SPs waveguide composed by metal stripes in a dielectric environment, grooves and ridges on metal surfaces, metal particle array, dielectric stripes fabricated on metallic films [3-7]. Two dimensional optical elements have widely been investigated for mirrors, beam-splitters and interferometers composed by metallic nanoparticles array [8, 9]. For the purpose of imaging and coupling, now there are also some structures (e.g. Parabola-shaped PMMA mirror with a rectangular bi-grating area formed inside [10]; PMMA rings array [11, 12]; Ag film containing holes arranged on a quarter circles [13], cylindrical SiO2 structure on gold film [14] ,et. al ) used to efficiently guide SPs around corners with converging effect on the metallic surface. This converging effect is essential for many applications of SPs enabled lab-on-a-chip photonic circuits. In these papers, the authors only showed that such structure can be used to focus SP but do not show how to shaping SPs through shape of the structures, such as adjusting the focal length or diverging SPs, which are also very important in integrated optics. In this letter, we mainly concentrated on modulation of SPs by dielectric refractive structures to shape SPs wave, as converging with different focal length or diverging, which were not reported in previous papers. PMMA microstructures are fabricated on metallic films by using electron beam lithography (EBL), which work as the refractive structures to modulate the SPs. Since PMMA is a common photo-resist for EBL with high fabrication resolution, the fabrication process is more convenient than SiO2 or other dielectric materials on metal. When compared with metallic structures for modulation of SPs, polymer structures have advantages of lower edge scattering loss, lower absorption loss, and more convenient fabrication process. In this letter, we experimentally demonstrated SP converging and diverging phenomena by PMMA circular disc, semi-circular disc and double-concave shaped islands. SPs waves converging with different focal lengths and SPs diverging are realized experimentally by modulating the phase of SPs through changing the shape of PMMA structures. The SPs wave refraction at the linear boundaries between metal and dielectric/metal boundaries are also investigated. Different PMMA layer thickness (h) showed different refraction effect on SPs waves, which has also been theoretically investigated in Ref [15, 16]. Effective refractive index model based on attenuated total reflection (ATR) curves was used to explain the experimental results.


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2. Theory The SPs wave-vector excited at the metal/air interface is described as k sp ( ω ) = ω / c * ε 0 ε m ( ω ) /( ε 0 + ε m ( ω )) , where εm (ω ) and ε 0 is dielectric constants of metal and air respectively and ω the frequency of incident light. In our experiment, instead of a single interface, we got a thin film constituted by an air/PMMA/gold/glass multilayer, where effective k sp (ω ) depends on the index of all the four media and on thickness of both Au and PMMA. The ATR curves can clearly show the SPs excitation position[14, 17]. In this four-layer system, if the metal film and dielectric are selected, the k sp (ω ) can be modified by changing the thickness of the metallic film or dielectric layer. In our experiment, when the gold and PMMA are selected and the gold film thickness is fixed, thickness of PMMA layer is changed to realize modification of k sp (ω ) and result in the change of effective refractive index of SPs wave. If different shapes of the PMMA relief structures are used, the SPs wave can be shaped into different patterns. Simulated ATR curves with different thickness (0nm, 65nm, 110nm) of the PMMA layer are shown in Fig.1. The wavelength of the incident laser is 780 nm and the thickness of the gold film is about 47nm. Refractive indices of PMMA, glass and gold are 1.5166, 1.525 and 0.16+4.67i respectively. In the ATR curves, the reflection minimum is the SPs excitation position, meaning that the energy of the incident light transfer into the SPs energy at this incident angle (the incident angle θ inside the glass corresponding to the in-plane wave-vector k = k0 n * sin(θ ) , n is the refractive index of the glass, k 0 = 2π / λ0 , is the wave-vector of the incident light in free space). At this minimum position, the in-plane wave-vector of the incident light is equal to that of excited SPs ( k sp = k 0 n * sin(θ sp ) ). The curves show that the wave vector (ksp) of the SPs increased with the PMMA thickness. The effective refractive index of the SPs can be expressed as neff = ksp/k0, As a result, the neff increases with the thickness of PMMA. When SPs wave passing through these dielectric structures, its phase can be differentially changed with respect to the surface propagation on the bare gold film with no PMMA relief. So we can shape SPs wave by changing the shape of the thin dielectric layers.

Fig. 1. Simulated Attenuated Total Reflection (ATR) curves for different PMMA thickness (h)

3. Experiment The fabricated samples are shown in Fig. 2(a), where three microstructures with a diameter of 10 µm are inscribed by EBL on a 110 nm thick PMMA layer. The PMMA is spin coated onto a 47 nm thick gold film and the thickness of the glass substrate is 170 µm. In the experiment, the SPs propagation is observed by the leaky radiation imaging method, which is commonly used in far-field SPs imaging with advantages of quantitative measurements of SPs intensity [18, 19]. The experimental set-up is shown in Fig. 2(b), where #108865 - $15.00 USD Received 18 Mar 2009; revised 15 May 2009; accepted 27 May 2009; published 22 Jun 2009

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a high N.A (1.42, 60X) oil-immersed objective is employed to excite the SPs by a fiber coupled diode laser beam with collimator (wavelength, 780nm, FWHM of the spot size=0.7mm). The leaky radiation of SPs can be collected by the same objective and imaged by a CCD camera. In our set-up, once the beam splitter is fixed, the laser beam from the fiber collimator can be shifted either vertically or horizontally. An advantage of this configuration is that the propagation direction of the excited SPs can be controlled by shifting the laser beam: when the laser beam strikes on different positions in the back plane of the objective, wave vector of the emitting beam from the front plane would be of various directions. Therefore, if the polarization of the laser beam has a component perpendicular to the gold film, and k sp = k 0 n * sin(θ sp ) is satisfied, SPs beam will be excited with various propagation directions in the plane of the metallic film.

Fig. 2. (a) Optical image of PMMA micro-structures and (b) Schematic graph of the experimental set-up

4: Results and discussions The SPs were locally excited beside these three structures and propagating toward them. Due to the different effective refractive index of the SPs on air/Au/glass and air/PMMA/Au/glass interface, the SPs beam would be modulated when passing through these PMMA refractive structures. For different shapes of the PMMA structures, the SPs beam would shaped into different patterns as shown in Fig.3, where the leaky radiation microscope image the launched SPs beams interacting with PMMA disc, semi disc and concave lens. The SPs beams are either focused by the disc and semi disc with different focal lengths or diverged by the concave lens. The focal lengths of the semi disc and disc are about: 25 µm and 20 µm. (The focal length is defined as the distance between the highest point of the structures and the focal point). Similar to geometric optics, it is found that the semi disc has longer focal length than that of full disc for SPs. The PMMA concave lens disk can diverge the SPs beam just like the ordinary concave lens in traditional optics. Experimental results demonstrated that SPs wave can be modulated by the shaped dielectric structures on metallic film. For different dielectric shape, the SPs wave can be shaped into different patterns, such as converging or diverging in this experiment. It should be explained in Fig.3 that there are some fringes along the SPs propagation paths on the images. The fringes are due to the unwanted interference of the coherent laser beam. Although the interference exists, it does not destroy the images of the SPs, and the leaky radiation images can stilly display the SPs beam propagation, focusing and diverging.


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Fig. 3. SPs converging and diverging. Leaky radiation microscope images of SPs beam modulated by polymer disc (a), semi-disc (b) and concave lens (c). The PMMA layer thickness was 110nm, and diameter of the disc was 10µm. The dashed lines represent the position of the micro-structures.

Apart from the shape, the thickness of the dielectric structure can also be used to as a tool to modulate the SPs beams. To verify this point, we investigate the SPs refraction between dielectric/metal regions with different thickness of the dielectric layers. Based on the theoretical discussion above, the effective refractive index of SPs beam can be modulated by changing the thickness of the PMMA thickness. Two samples are fabricated with PMMA thicknesses of 65nm and 100nm on 47nm gold film respectively. The boundaries between Air/Au and Air/PMMA/Au are fabricated by using the EBL technique. According to the ATR curves in Fig.1, the wave-vector for SPs on air/Au, air/65nm PMMA/Au, and air/110nm PMMA/Au were1.0258 k0, 1.1882 k0 and 1.3557 k0 respectively (k0 is the in plane wave vector of incident laser in vacuum). As a theoretical result, the effective refractive index (ratio of ksp (air/PMMA/Au/Glass) and ksp (air/Au/glass)) for 65nm and 110nm PMMA are 1.1583 and 1.3216 respectively. Refraction would happen as SPs passing through the boundary between air/Au/glass and air/PMMA/Au/glass. For different PMMA thickness, the refraction angle will be different due to the different effective refractive index. The leaky radiation image of SPs refraction phenomena is shown in Fig. 4(a), where the thickness of PMMA is 65nm, and the incidence angle was 36o, the refraction angle is 30o. In Fig. 4(b), the PMMA thickness is 110 nm. The incident angle is 42o, and the refraction angle 30o. The effective refractive indexes (ratio of ksp (air/PMMA/Au/Glass) and ksp (air/Au/glass)) calculated based on the experimental results and Snell’s law is 1.1756 and 1.3383 for 65 nm and 110 nm PMMA respectively. The experimental results are quiet in a good agreement with the theoretical result. Experiment result and theoretical results both show that the effective refractive index is enhanced when the PMMA layer becomes thicker. So the phase and propagation angle of the SPs wave can be changed when it passing through different thickness structures. For examples, the focal length of the polymer circle shown in Fig. 2(a) can also be changed by adjust the thickness of the polymer films, or the SPs wave pattern can be shaped when SPs wave passing dielectric structures with different thickness. It should be noted that the tilt of plasmons beams in Fig. 4 from the initial direction was well behind the boundary between the bare Au surface and PMMA covered area (marked by horizontal lines in Fig.4). The reason is that in the leaky radiation microscope, there are some minor departure between the laser beam image and the micro-structure image. The refraction happened in the real boundary. But this departure does not influence the refraction angle and also the diverging and converging properties of SPs.


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Fig. 4. SPs refraction with different PMMA thickness. (a) Thickness was 65nm; (b) thickness was about 110nm. The black lines represent the propagation direction. Refraction angle is 30° in both cases, while incidence angle is 36° and 42° respectively

5. Conclusion In summary, the spatial modification of the SPs waves and the phase velocity (effective refractive index) with polymer refractive structures deposited on top of the metallic film are described in this work. We mainly concentrated on the modulation of SPs wave by means of PMMA refractive structures with different shape and thickness to realize various SPs wave patterns. SPs wave converging with different focal length, and diverging are realized experimentally with PMMA disc, semi-disc, and biconcave lens in this letter. The refraction phenomenon shows that the effective refractive index can be enhanced by increasing thickness of the dielectric layer (below cut-off thickness of waveguide mode in PMMA layer), which is consistent with the theoretical predication and can also be used to modulate the phase of SPs waves. This result is useful for future precise control of SPs wave with dielectric refractive structures on metallic films to realize various SPs patterns or related devices, such as SPs Mach–Zehnder (MZ) interferometer, dielectric Fresnel zone plane on metallic film[20], and so on. Furthermore, the converging or diverging of SPs with polymer structures can be used to couple SPs waves into waveguide fabricated on metallic films or SPs imaging, which has potential applications in the lab-on-a-chip type integrated optical elements [21, 22]. Acknowledgments This work was partially supported by the National Natural Science Foundation of China under Grant No. (60778045), the National Research Foundation of Singapore under Grant No. NRFG-CRP 2007-01 and the Ministry of Science and Technology of China under Grant no. 2009DFA52300 for China-Singapore collaborations. XCY acknowledges the support given by Nankai University (China) and Nanyang Technological University (Singapore). Hai Ming acknowledges the funding support given by the National Natural Science Foundation of China under Grant No.60736037 and the National Key Basic Research Program of China under Grant No. 2006CB302905.


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