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Controlling the propagation of surface plasmons along a metal-dielectric interface is a key feature for the development of surface plasmon based circuits. We have designed various two-dimensional refractive dielectric optical elements for surface plasmons (SP) and characterized their capacity to route SP, using near- or far-field techniques. We first present basic devices analogous to usual optical components and the associated challenges for SP optics. We then use a metamaterial approach to locally vary the refractive index and fabricate gradient index structures for SP circuitry.
©2010 Optical Society of America
1. Introduction
The challenge to make highly integrated photonic circuits using surface plasmons (SP) [1] lies in the development of various tools to launch, control and process the SP in the circuit. Previous experiments have shown that high quality SP beams can be launched by micro-gratings [2–4] while other studies have investigated the coupling efficiency of light to surface plasmons generated by other types of sources like slits, ridges, holes or chains of particles [5–10]. The next logical step is then to guide and route SP beams by specifically designed two-dimensional devices. For instance, SP can be confined in waveguides made of metal or dielectric stripes, or even V-shaped grooves [11–15]. The present work focuses on the guiding of SP along extended metal films. Photonic band-gap structures [16], diffractive components such as Bragg mirrors [17–19] and refractive elements [20,21] have already been reported for this purpose. Here we extend the study of refractive optical components made of a dielectric material. We start by characterizing two dimensional continuous dielectric structures on gold films and by analyzing the related issues. Playing on metamaterial concepts to induce a local change of the refractive index, for a given thickness of dielectric, we then elaborate new structures made of discretized dots, thus opening a new way to build optical elements for SP circuitry.
2. Basic optical components and issues
We first prepared basic dielectric components such as a plane parallel slab and a prism, analogous to classical optical devices and characterized it in the far-field using the source-probe design studied in ref [2].We chose to use polymethylmethacrylate (PMMA) to realize our optical elements as it has several advantages. When exposed to an electron beam with high voltage, it cross-links and becomes a negative resist. Moreover it can be further doped with molecules or quantum dots to enable active optical elements [22–25]. The polymer layer was prepared by spin-coating PMMA layers on top of gold films of different thicknesses deposited by electron beam evaporation. Indeed according to the optical technique used to characterize the dielectric element, we prepared either 160nm gold films on top of thick glass substrates (1mm thick, for far and near field measurements) or 50nm gold films on top of thin glass slides (0.17mm thick, for leakage radiation microscopy). The refractive micro-optical components were fabricated by electron beam lithography (EBL), while a focused ion beam (FIB) was used to mill plasmonic structures in the gold film to enable the local coupling or decoupling of light to SP [2,3].
As shown in Fig. 1 , the source structure supplies the SP beam when illuminated by a laser beam. The probe is an array similar to the source, but it is not illuminated by the excitation laser and its role is to enable the back-conversion of SP to freely propagating light as seen in the far-field. We can observe the refraction of the SP beam by both the slab and the prism, as proven by the decoupling of SP into light at a position that is shifted as compared to the propagation direction of the incident SP beam. By measuring the beam deviation, an experimental index contrast of 1.5 ± 0.02 can be deduced from the Snell-Descartes law. Note that in the case of SP with wavevector kSP, the effective index nSP is defined as the ratio kSP/k0 where k0 is the wavevector of light in vacuum. In the case of a flat interface between a dielectric and a metal of respective permittivities εdielectric and εmetal the refractive index is nSP = (εdielectricεmetal/(εdielectric+εmetal))1/2 [26]. The experimental index contrast is in good agreement with the calculated value nSP,PMMA-gold/nSP,Air-gold = 1.53/1.02 = 1.50 considering the gold dielectric function [27] and the fact that 200 nm of PMMA covers most of SP evanescent field which has a decay length of ca. 110 nm (at 800 nm) normal to the surface.
Fig. 1 Top: scanning electron microscope (SEM) images (tilted at 52°) of the source-probe setup with the dielectric element inbetween: (a) is a plane-parallel PMMA slab (side 10µm, length 30µm, angle 45°) and (b) is a prism (side 30µm, equilateral triangle). Both of them are 200nm thick. Bottom: corresponding far-field optical images (c) for the slab and (d) for the prism. The source array is made of 11x11 holes with periodicity p = 760nm and diameter d = 250nm. It was illuminated from below by a focused laser diode (785nm, spot size 10µm) at normal incidence in order to couple to the ( ± 1,0) modes [2,3]. Observations were made with a 40X objective on a Nikon TE200 microscope coupled to a Princeton Instruments CCD camera. The scale bars in all images correspond to 10 µm.
An important issue that is often neglected is the decoupling of the SP as it enters the dielectric element as can be best seen in the far-field images such as Fig. 1 (c) and (d). This is due to the strong impedance mismatch at the interface of the element [1]. This is a serious concern in the context of photonic circuits, since it results in losses and structures need to be developed that overcome this problem. We will see later in the paper a possible solution.
After this proof of principle, near-field optical (NFO) measurements were also carried out to allow more detailed observations. The experimental setup we used is described in details in ref [11]. It enables the illumination of the sample from below with a Ti-Sapphire laser beam, focused with an angle of ± 8° and a spot diameter of 10µm. The near-field probe usually scans the surface at a height around 100nm: a second sample had thus to be fabricated with a smaller thickness of PMMA (60nm) in order to avoid touching the optical element with the scanning probe. Illumination was done at 800nm, 47° incidence, in order to excite the (−2,0) mode of the source hole array [4].
We first tested a plane-parallel slab (Fig. 2(a) ) and the observed deviation is weaker than before (Fig. 1) due to a smaller index contrast nSP,PMMA-gold/nSP,Air-gold as the PMMA layer is much thinner. In this latter case, an effective index has to be calculated, taking into account that the SP amplitude also extends into the air with lower refractive index compared to the dielectric. We used the differential method [28,29] to calculate its value for 60nm of PMMA on top of a gold film and obtained 1.15. It is totally consistent with the experimental value 1.15 ± 0.01 deduced from the deviation measured in the plane parallel slab (6° ± 0.5°). The second device is a biconvex lens having a radius of curvature R = 5µm and an optical pathlength e = 5µm (Fig. 2(b)).
Fig. 2 Top: SEM images (tilted at 52°) of the source and dielectric elements: (a) is a plane parallel slab (width 15µm, length 20µm, tilt angle 40°) and (b) is a biconvex lens (radius 5µm, optical pathlength 5µm). Both of them are 60nm thick and the SP source is the same than on Fig. 1. Bottom: Corresponding NFO images centered on the exit of the dielectric elements, for the slab (c) and for the lens (d) (source arrays are out of frame on the left). The scale bars in all images correspond to 5µm.
With these values, one can estimate the focal from the classical lens formula [30]:
This expression leads to f = 15.6 ± 1µm with n = 1.15 ± 0.01: once again it is in very good agreement with the focal point distance measured directly on the near-field image (Fig. 2.(d)). We also checked that it is possible to vary the focal length by playing on the radius of the lens (not shown here).
We have observed that the shape of SP beam and its dimensions compared to the optical element can lead to misinterpretation of the data. For instance, the source array involved here delivers a SP beam which presents a variable width: close to the source array, the SP beam presents two transverse maxima that further merge into a single transverse, narrower peak [4]. This phenomenon could be confused with the refractive effect of a converging lens. To check this, we made a comparison between the optical effect of the previous lens in Fig. 3(b) with that of a non-focusing device (Fig. 3(c)), i.e. a plane-parallel rectangular slab at normal incidence), and the beam shape in the absence of any dielectric element (Fig. 3(a)). In Fig. 3(e) are plotted the transverse cuts of the SP beam, taken at the same distance (35µm) from the SP source, in the three configurations. The result leaves no doubt about the focusing effect of the biconvex lens.
Fig. 3 NFO measurements of the SP beam intensity in the case (a) of a freely propagating beam, (b) traveling through a lens (radius 5µm, optical pathlength 5 µm), (c) traveling through a non focusing rectangular device (length 20µm, optical pathlength 10µm) and (d) traveling through a non focusing square device (10x10µm2). The source array (same than in Fig. 1 and 2) is out of frame, on the left and the SP beam is propagating from the left to the right. (e) Beam profiles along cross-cuts represented with white dashed line on (a),(b),(c),(d) for the comparison between: (A) no device, (B) the focusing device, (C) the non-focusing rectangle, and (D) the non-focusing square. The scale bars in all images correspond to 5µm.
In addition, edge effects can happen when the structure dimensions are close to the transverse width of the beam. In such case part of the beam is deflected and scattered by the edges of the structure acting as reflectors or beam splitters. When it overlaps with the normally transmitted beam, it gives rise to an interference pattern that can be misinterpreted as focusing, as can be observed on the experiment presented on Fig. 3.(d) and (e). It is therefore essential in studying such refractive structures to ensure that they are much larger than the SP beam.
3. Properties of refractive metamaterial structures
Controlling the effective index of an optical element by its thickness is not ideal because it would be very difficult to implement different thicknesses in a given circuit or a single chip. A much more elegant solution would be to create optical elements where the effective index is controlled by subwavelength structuring of the dielectric material, in other words using metamaterial concepts [31]. For this purpose we explored the properties of optical elements made of discreet dots of polymer. To behave as a homogeneous effective medium, the features size must be much smaller than the SP wavelength λSP. This condition has already been shown valid in the case of arrays of metal nanoparticles for modifying the refractive index of a metal film [32]. We have explored a range of filling factor corresponding to periodicities from 185 nm to 360 nm, which are indeed smaller than λSP/2. The resolution of the cross-linked PMMA, when used as a negative resist, is about 50nm [33], which is enough to fabricate such small structural features. This can be achieved experimentally by playing on the parameters of the spin coating and the EBL. Calculations based once again on the differential method [28,29] show that the effective index of the metamaterial can be finely tuned by varying the filling factor (FF) of the dots for a given thickness of PMMA (Fig. 4 ).
Fig. 4 SP effective index variation as a function of the PMMA dots filling factor. Calculations have been done by the differential method, considering dots of PMMA (height h), deposited on a gold film: black curve for h = 65nm; red curve for h = 105nm; green curve for h = 120nm.
We first fabricated a rectangular plane parallel slab, this time filled with discrete dots of PMMA (Fig. 5(a) ), and used leakage radiation microscopy (LRM) to characterize it. LRM allows obtaining precise and useful near-field information in the direct space, as well as in the reciprocal space by imaging the Fourier plane [for a description of the analysis procedure, see ref. 8]. As shown in Fig. 5, this metamaterial approach works well in changing the effective index and the experimental data compare well to the predicted effective index (see Fig. 4). Nevertheless the FF range was limited by the fact that we used PMMA as negative resist. It could easily be extended using it as a positive resist (where the resolution goes down to 20nm [33]) or alternatively with higher index dielectric materials for the dots.
Fig. 5 (a) SEM image of a slab (15x30µm2) made of discreet PMMA dots and a slit SP launcher (width 250nm, length 20µm). Inset shows a detail of the polymer dots constituting the effective index medium (diameter 90nm, height 106nm, image tilted at 52°). The continuous scale bar corresponds to 10 µm, the dashed one to 1 µm. (b) Dependence of the effective refractive index of the discreet structure on the PMMA filling factor obtained from the LRM images in the Fourier space like the one shown in the inset. Absolute values of kSP can be extracted from radial cross-sections on these images. Note that a slit was used as SP launcher because of its more convenient properties for Fourier space analysis.
4. Gradient index optics
Results obtained with discretized optical elements (such as in Fig. 5) led us naturally to consider the possibility of generating more complex refractive elements. For instance, the density of polymer dots can be gradually changed and as a consequence the refractive index varies within the element. This is known as a gradient index (GRIN) medium [34]. Such media make the light bend and can be exploited to produce plane-parallel lenses and GRIN fibers among others.
The structure is here again a plane parallel slab made of discreet dots of PMMA (Fig. 6(a) ) but this time the filling factor is kept constant along one dimension of the structure, and decreased along the other, leading to an index variation through the width of the slab (Fig. 6(b)). We used again a slit source because it allowed us to compare the propagation direction of the SP beam traveling through the GRIN structure on one side with the freely propagating SP beam on the other (Fig. 6(c) and (d)).
Fig. 6 (a) SEM image of the GRIN slab (15x20µm2) and the slit launcher (width 250nm, length 20µm) (the scale bar correspond to 5µm). The red spot shows the position of the laser on the slit, and the arrows the propagation direction of SP. Inset shows a detail of the discreet polymer dots constituting the GRIN medium (diameter and height 60nm). (b) Plot of the effective index variation along the width of the slab. (c) Direct space and Fourier space LRM images of the SP beams propagating away from the slit source. (d) Angular distribution of the SP resonance intensity measured on the left side of the Fourier plane (kx<0, GRIN slab side, blue curve) and on the right side (kx>0, “empty” side, orange curve)
A deviation of the SP beam propagating through the GRIN medium can be observed in the direct space: the SP propagation is bent with the center of curvature pointing towards the high index region, in a similar way to mirage effects (Fig. 6(c)). In the Fourier space, the beam steering operated by the GRIN medium is also observed, as one can see when comparing the beams propagating on either side of the slit (Fig. 6(c)). The deviation of the SP beam, slightly higher than 8°, is most clearly seen with the cross-sections shown in Fig. 6(d). For a plain continuous slab having a refractive index of 1.13 (value of nSP at the position where the SP beam enters the slab), one obtains according to Snell-Descartes law a deviation of 6°. The additional SP beam deflection of 2° is thus due to the presence of the index gradient. Such results are a proof of principle that GRIN structures can be used to control SP beams. Larger deviations can be achieved with either greater dot thicknesses or densities. The GRIN structures thus provide greater beam control than homogeneous optical elements.
Finally, we apply this GRIN approach to make a lens: we fabricated squares with PMMA dots having an increased filling factor from the horizontal edges to the center, to create a zone of higher index along the propagation axis of the SP beam. We tested different gradients and one example is shown on Fig. 7 . As can be seen, the beam is progressively focused as it travels inside the lens as one would expect (Fig. 7(c)). Note that here the focal spot is inside the GRIN lens and so in practice a lens with a shorter pathlength is sufficient for the index contrast used. The cuts of Fig. 7(d) show that, at the focal spot position, the initial SP beam width is decreased by a factor of 2.3, a value comparable to what we obtained with the plain continuous biconvex lens of section 2.
Fig. 7 (a) Effective index variation into the GRIN lens (dimensions 10x10µm2) shown in (b). (b) SEM image of a GRIN lens made of polymer rods (diameter 65nm, height 120nm) colored in red for clarity. (c) LRM image of SP launched by an 11x11 holes array (p = 760nm, d = 250nm) and going through the GRIN lens structure (λ = 785nm). The GRIN lens position is marked by the red square. The scale bars in both images correspond to 10 µm. (d) Beam profiles along cross-cuts represented with white dashed line on (c) at positions A,B,C and D.
We also applied the metamaterial approach to structure the edge of plain continuous slabs, to soften the impedance mismatch at the entrance of a dielectric element reported in section 2 which leads to unwanted decoupling of SP into freely propagating light. One can see in the inset of Fig. 8 an example of the edge of such a slab. We used again a source-dielectric element arrangement and characterized it in the far-field. On Fig. 8, a cut of the intensity along the propagation direction of the SP beam going through a continuous thick slab is compared to a cut of the same SP beam going through a slab having its edges discretized with a gradient of dots over a 2µm length. We observe that losses are indeed reduced by a factor of about 3 at the entrance of this modified slab (red curve), compared to the continuous slab case (black curve), thus confirming another potential application for the GRIN structures.
Fig. 8 Comparison of the cut along the SP beam propagation direction through a continuous PMMA slab (10x30µm2, 120nm thick) and a PMMA slab of the same dimensions and thickness but having its edge discretized on 2µm length in a gradient of PMMA dots. The intensity has been recorded in the far-field. Inset: SEM image of the modified edge. The dashed scale bar corresponds to 1µm.
5. Conclusion
We have seen different methods to tune the optical properties of SP-based refractive optics and the associated challenges. In the most classical way, one can play on the in-plane geometry of the optics whereas in the direction normal to the interface now, it is possible to play on the thickness of the optics in order to achieve a precise index contrast. Experimentally speaking, it is thus possible to modify the optical properties (focal length, steering angle) of these dielectric refractive elements. Alternatively, we have shown that a metamaterial approach can be used to modify locally the effective index within a structure by changing the dielectric medium filling factor. The GRIN structures that we demonstrate are distinct from plasmonic crystals or Bragg mirrors as their feature size is much smaller than the wavelength. They can be considered as homogeneous materials and interacts with SP in a refractive way. This experimental demonstration of a GRIN structure and of its potential applications to SP routing is a first step toward the fabrication of promising structures that could be tailored to particular needs of surface plasmons optics and circuits.
Acknowledgments
The authors acknowledge support from the ERC (Grant 227557). B. Stein acknowledges the support of the Studienstiftung des deutschen Volkes and the Stiftung der Deutschen Wirtschaft (sdw).
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