## Abstract

Surface Plasmon Polaritons (SPPs) are excited at the interface between a thin gold film and air *via* the illumination of nanoslits etched into the film. The coupling efficiency to the two propagation directions away from the slits is determined by leakage radiation microscopy, when the angle of incidence of the pump beam is changed from 0° to 20°. We find that preferential coupling of SPPs into one direction can be achieved for non-normal incidence in the case of single slits and slit pairs. The proportion of SPP excited into one direction can be in excess of 90%. We further provide a simple model of the process, and directly compare the performances of the two approaches.

© 2012 Optical Society of America

## 1. Introduction

Using Surface Plasmon Polaritons (SPPs), confined electromagnetic waves at metal/dielectric interfaces, to transfer information, has the potential to bridge the gap between microelectronics and photonics, provided their intrinsically lossy character can be mitigated [1]. Indeed, as SPPs can transport optical signals on waveguides of truly nanoscale dimensions [2], they would allow for the use of the bandwidth and speed provided by optical systems, but on nanometric scales so far accessible only to semiconductor electronics [3]. In a context of information transfer and processing, it is important to design means to convert optical signals into SPPs to link long distance transfers, using standard low loss photonic devices, with miniaturised functions that would benefit from the use of SPPs. Such a converter should be compact and able to excite SPPs in a specific direction, towards the region of information processing.

SPPs have an in-plane momentum *k*_{SPP} larger than the momentum of free space propagating light, which means that converting light into SPPs requires the use of methods providing extra in-plane momentum to the photons. Many methods have been used to achieve this goal, but the ones relevant for nanoscale integration all use corrugations in the metal film sustaining the SPPs. Periodic arrangements of holes for instance allow for the excitation of SPPs and directionality of the excitation can be achieved when the pump beam impinges on the grating at oblique incidence [4–6]. Preferential SPP launch can be obtained under illumination at normal incidence of a grating provided the symmetry of the grating is broken [7–9]. A very efficient asymmetric grating coupler using concepts similar to the Yagi Uda antenna has been demonstrated recently [10]. Unfortunately, efficient gratings have a footprint of many wavelengths on the metal film: more compact approaches are desirable.

Schemes based on the use of one or two slits in the metal film are much more compact. A variety of such schemes have been proposed and studied theoretically [11, 12]. When a single slit is used to excite SPPs, the excitation efficiency depends on the width of the slit compared to the SPP wavelength [11–13], and directionality of the SPP excitation is possible for excitations at oblique incidence [14]. Similarly to the gratings, breaking the symmetry of a single slit can lead to a directional coupling of SPPs at normal incidence [15,16]. Furthermore, adding a Bragg reflector next to the slit allows for a directional coupling at normal illumination, but of course has the same drawback as for a grating: the footprint of the whole system represents many wavelengths [17]. Systems using two parallel nanoslits have been discussed as well and lead to directionality of SPP excitation at oblique incidence [18]. Filling each slit with dielectrics of different refractive index is expected to allow for directionality with excitation at normal incidence, although this has not been demonstrated experimentally so far [19, 20]. More schemes for directional coupling under normal incidence have been discussed theoretically [21–23].

To date, there is a lack of experimental demonstrations of all the schemes proposed. One report has shown that the SPP excitation efficiency of a single nanoslit depends on its width [24]. Another one demonstrated directional launch of SPP for one slit with illumination at 75° [25]. Both of these studies are performed using Scanning Near-field Optical Microscopy (SNOM), which is expensive, complex to implement, and SNOM images are long to acquire. The role of SPPs in the optical transmission of a pair of slits has been observed in the far-field, for slits separated by many wavelengths [26]. Eventually, the directional coupling of SPP under oblique incidence *via* a pair of nanoslits has been observed using gratings to out-couple the SPPs generated at the nanoslits – which allows for observations in a narrow wavelength range only [18].

In this article, we use leakage radiation microscopy (LRM) [27–31] to study comprehensively how light is coupled to SPPs *via* the use of arrangements of slits. LRM is extremely flexible and allows for a fast exploration of the full parameter space of the problem. In contrast to SNOM, it is cheap to implement, simple to operate and measurements are fast. Moreover, no out-coupling gratings are required to observe the SPPs: thanks to this LRM allows for the use of any wavelength without modification of the setup or sample. We show that single and double slits under oblique illumination allow for directional coupling of SPP, probing for the first time the whole parameter space of interest: angles up to 20°, slit widths/distances in the range 150 to 950 nm (*λ*_{0}/4 to 1.5*λ*_{0}, with *λ*_{0} = 633 nm). The experimental findings are well described by a simple model accounting for the diffraction of the incoming beam by the slits. Eventually, our approach allows for a direct comparison between the performances of single and double slit-based devices.

## 2. Leakage radiation microscopy

To conduct our studies, we use the fact that on a thin metal film (a few tens of nanometer thick) deposited on a glass substrate, the SPPs bound to the metal/air interface ”leak” on the glass side [29], i.e. they are coupled back to a propagating light field on the glass side. This emission occurs at an angle larger than the total internal reflection angle of a glass/air interface. Therefore, collecting the leakage radiation requires the use of an oil immersion objective. Figure 1(a) presents the schematic of the leakage radiation microscope. Its design is similar to the one described in Ref. [28]. The beam from a polarised HeNe laser is focused on the sample by a 20×, NA 0.4 microscope objective (O_{1}). A polariser and half waveplate are inserted in the beam path before the objective, to align the polarisation of the beam perpendicularly to the slits (cf. Fig 1(c)). The width of the beam is much smaller than the pupil of the objective. This allows to change the angle of incidence of the beam onto the sample by translating the laser perpendicularly to the optical axis, keeping it parallel to it, as shown on Fig. 1(a) and 1(c). The spot size at the sample level is about 10 *μ*m in diameter. The light then goes through a 100×, NA 1.49, oil immersion microscope objective (O_{2}), which allows for the collection of light leaking from the SPPs excited at the gold/air interface. The lens L_{1} projects the back focal plane of O_{2} (which is contained inside O_{2}) onto the lens L_{2}. Placing masks in front of L_{2} could allow for a physical filtering in the Fourier space of the image from the sample’s surface (we do not use this in the present study). The lens L_{3} then images on a CCD camera either the surface of the sample, in position A, or the back focal plane of O_{2}, in position B.

The samples are produced by thermal evaporation of a 3 nm thick germanium layer on Corning glass coverslips, followed by the evaporation of a 36 nm gold layer. The germanium serves as sticking layer for the gold, and its influence on the optical properties of the system are negligible. Slits of 20 *μ*m length are then produced by Focused Ion Beam milling (Helios Nanolab 50 DualBeam). Figure 1(b) presents SEM micrographs of some of the slits used in this article.

The measurements of the SPP intensity are done in Fourier space, projected on the detector by an appropriate arrangement of the lenses in the leakage microscope. Figure 2 presents a typical measurement in the Fourier plane: in the example presented, the laser is focused on a slit pair separated by 350 nm. In the Fourier plane, one can observe three elements: a disc of intense light, where the detector is saturated, a broad bright line, and two spots of light symmetrically positioned compared to the center of the image (Fig. 2(a) and 2(b)). The saturated spot corresponds to the pump light directly transmitted through the sample, which is partly transparent. The position of the spot indicates the angle of incidence. The broad line is the light diffracted by the slit. Its alignment is perpendicular to the slits. The twin spots placed symmetrically from the center of the image are due to the light leaking from the SPPs. The intensity of the left- and right-propagating plasmons are measured thanks to profiles taken along the Fourier images, as shown in Fig. 2(c).

## 3. Theoretical model

The experimental results are compared to a simple analytical model to describe the efficiency of coupling of the incident light into SPPs. The underlying principle is that the pump light is diffracted by the slits, and the angular spectrum of the diffracted light can be calculated by a Fourier Transform of the field at the slit’s position. We assume that the intensity of the SPPs excited is proportional to the intensity of the component of this angular spectrum matching the SPPs’ wavevector [13, 14].

The slits are represented by the rectangular function
$\text{rect}(\frac{x-{x}_{0}}{w})$, with *x*_{0} the position of the center of the slit considered and *w* its width. By definition:

The pump beam is a plane wave of wavelength *λ*_{0} impinging on the sample at an angle *θ*. The field is polarized perpendicular to the slits, as illustrated on Fig. 1(c). The component of the electric field along the samples’ surface at the surface of the glass substrate in the absence of the slits is
$E\left(x\right)=\text{exp}(i2\pi x\frac{sin\hspace{0.17em}\theta}{{\lambda}_{0}})$. When the slits are considered, we make the approximation, derived from the scalar diffraction theory of Fourier optics, that the metal film prevents the radiation from reaching the substrate, whereas it is not perturbed at the position of the slits. Once this assumption is made, at the sample surface and in the presence of the slits the component of the field along the sample surface becomes:

*x*

_{1}and

*x*

_{2}the positions of slit 1 and 2,

*w*

_{1}and

*w*

_{2}their widths, as depicted in Fig. 1(c). In the following, to simplify the expression we will take

*x*

_{1}=0.

The angular spectrum of *E*(*x*) at the slits position is obtained *via* a Fourier transform of the field *Ẽ*(*α*), where *α* is the coordinate of the angular spectrum corresponding to the *x* coordinate in real space. Using the properties of scaling, shifting in space and frequency domain of the Fourier transforms, it can be shown that:

To estimate the SPP generation efficiency, we then calculate the intensity of the angular spectrum for *α* = *α*_{SPP}, where *α*_{SPP} is derived from the dispersion relation of the leaky SPPs mode in our system. This dispersion relation is derived as described in Ref. [29], and the values of the dielectric function for gold *ε*_{Au}(*λ*) are taken from Ref. [32]. With a thickness of gold of 36 nm, *λ*_{0}=633 nm and (*ε*_{Au}(633 nm) = −11.43 + 1.19i), we find an effective index of n_{SPP} = 1.048. Right-propagating SPPs and left-propagating SPPs are given by *I*_{right} = |*Ẽ*(*α*_{SPP})|^{2} and *I*_{left} = |*Ẽ*(–*α*_{SPP})|^{2}, respectively.

From this expression, we can derive the maximum coupling efficiency for single slit width *w* = *w*_{Max}. They happen to correspond to the conditions for distance between slits giving the weakest coupling in a double slit system, *x*_{2} = *d*_{Min}:

*m*an integer. Similarly, on can derive the width for minimal coupling for individual slits

*w*

_{Min}and distance for optimal coupling in slit pairs

*d*

_{Max}

*n*an integer. Further in the text, the extremal coupling conditions towards one direction will be indicated with the direction in superscript. For instance, the widths giving maximal coupling towards left-propagating SPPs in single slits will be denoted by ${w}_{\text{Max}}^{\text{Left}}$.

The directionality *D* of the SPP generation is then defined as:

*D*reflects the proportion, from the total energy coupled into SPPs, of energy coupled into left propagating SPPs. Hence, it does not reflect the coupling efficiency. A value of 1 (resp. 0) indicates that only left-propagating (resp. right-propagating) SPPs are excited, and 0.5 corresponds to a symmetric excitation. The plots presented further use Eq. (4) and (7) to calculate the SPP generation efficiency and directionality.

As will be seen further, this model gives a qualitative description of the phenomenon, and is useful to identify simply the regions of high coupling efficiency as well as high directionality. We direct the reader to Ref. [11–13, 33–35] for more in-depth descriptions of the interplay between the scattering of slits and the generation of SPPs.

## 4. Single slits

Let us first turn our attention to the case of a single slits used to excite SPPs. In the experiment, slits of increasing widths have been milled into the gold film, by steps of 50 nm (100 nm, 150 nm,..., 950 nm). The experimental plots are generated by making a linear extrapolation of the values between measured values. Fig. 3(a) presents the intensity measured for the left propagating SPPs, normalised to the highest intensity, alongside with the results of Eq. (4) in Fig. 3(b). The agreement between experiment and the simple model is remarkable.

The directionality of SPP generation by single slits is presented in Fig. 3(c) and 3(d). As can be seen on these figures, regions showing directionality in excess of 90% can be found: more than 90% of the generated SPPs are launched preferentially in one direction. For the case presented here, such high directionality are obtained with slits of widths between 450 and 550 nm, and angles close to 20°.

Optimal directionality/excitation efficiency of SPP occur at the intersection of the curves of maximum coupling efficiency into one direction *w*_{Max} and the curves of minimum coupling efficiency into the other direction *w*_{Min} obtained thanks to Eq. (5) and (6). In Fig. 3(b) and 3(d), we highlight
${w}_{\text{Max}}^{\text{Left}}$ in solid black lines and the
${w}_{\text{Min}}^{\text{Right}}$ in solid green lines. From these considerations, it appears that there is a general trade-off to be found between angle of incidence and width of slits for optimal operation. To operate at small angles, one has to use wide slits (for instance in this case: operation for 10° is optimal for a slit width of 750 nm). Conversely, the optimal point with narrowest slit (455 nm width here) occurs at an angle of operation of −20.7°. A more complete picture of
${w}_{\text{Max}}^{\text{Left}}$ and
${w}_{\text{Min}}^{\text{Right}}$ can be found in Fig. 5(a).

## 5. Double slits

We now consider the case of parallel sub-wavelength slit pairs. The slits milled by FIB are 90 nm wide, and the distance between slits is varied between 150 nm and 700 nm by steps of 50 nm. Again here the experimental plots are generated by using a linear extrapolation between the values actually measured. Figure 4 presents the excitation efficiency of left propagating SPPs, as well as directionality, depending on slit distance and angle of incidence. Similarly to Fig. 3, the agreement between experiment and model is good, although the measurements here are slightly more noisy. The slits milled here have a width approaching the resolution limit of the fabrication method employed, which could explain the increased noise compared to the single slits. Indeed the quality of the milling varies more from one slit to the next when we operate close to the limits of the instrument, which can lead to variations in the optical transmission of the slits, and thus variations along the horizontal axis in Fig. 4(a). The directionality is not affected by this as it is a ratio of intensities, thus insensitive to variations in absolute coupling to SPPs. Indeed, Fig. 4(c) does not show the sharp variations visible in Fig. 4(a). The directionality depends little on the slit width (data not shown, but can be calculated using Eq. (4) and (7)), which means that the key parameter is the distance between the slits.

The specific situation shown in Fig. 2(c) (slit distance 350 nm, *θ* = −18° and 0°) can be analyzed further in light of these considerations. The large directionality observed exists due to the fact that the coupling efficiency towards the left direction changes little between *θ* = −18° and 0° (from 0.08 to 0.06 normalized units, Fig. 4(b)), whereas the coupling efficiency to right propagating SPP increases from 0.06 to 0.44.

To better compare the performances of single and double slits, we now introduce a Figure Of Merit (FOM). We define the FOM for left propagating SPPs as the product of the directionality *D*, rescaled between −1 and 1, and the left-propagating SPP intensity *I*_{left} (from the theoretical model). In this definition a majority of right-propagating SPPs are represented by a negative FOM:

*and*the directionality is large. Optimal performances for directional coupling of SPPs are obtained for the highest FOMs.

The base 10 logarithm of the FOM is plotted on Fig. 5. The purple regions represent regions where right-propagating SPPs are preferentially excited, or extremely inefficient coupling to a majority of left propagating SPPs. Figure 5 highlights the fact that high directionality combined with high SPP excitation occurs on different regions for single and double slits. These plots can be used to determine what system is best to achieve a specific goal. For instance, one can be interested to have a directional coupler with the smallest footprint possible. The footprint of a slit pair is the distance between slits, plus the width of one individual slit (in the case presented here, 90 nm). With these considerations, the point of optimal coupling for smallest device occurs for a footprint of ≈ 455 nm for single slits, and ≈ 545 nm for double slits (cf. Fig. 5, points *A* and *B*) – a single slit will always provide smaller footprint. Moreover, if one can sacrifice some coupling efficiency, single slits allow to work at smaller angles, as shown by the region lying between point *A* and the line *θ* = 0.

## 6. Conclusions

In this study, we directly compare the directionality of SPP launch by single and double slits on a thin metal film. The measurements, using leakage radiation microscopy, allow for a rapid probing of the parameter space of this problem: slit width, distance, and angle of incidence of the pump beam. Moreover, the wavelength of illumination can be changed without modifications to the sample. The experimental findings are well described by a model using the angular spectrum of the light diffracted by the slits to estimate the SPP generation efficiency. Single as well as double slits allow for directional SPP excitation provided that the illumination is at oblique incidence. There is a general trade-off between size of the devices and the angle of incidence required for optimal coupling. Overall, single slits allow for better performances than double slits and have a smaller footprint. The approach developed here should allow for extensive studies of most of the other schemes proposed for unidirectional SPP coupling, and performs better than the ones used in all previous reports.

## Acknowledgments

The authors gratefully acknowledge fruitful advices from Aurélien Drezet while building the leakage radiation microscope, and Markus Schmidt for the calculation of the effective index of the SPPs in our system. S.A.M. and Y.S. acknowledge support by the UK Engineering and Physical Sciences Research Council. Y.S., G.D. and D.Y.L. acknowledge funding from the Leverhulme Trust.

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