1. Introduction

Surface plasmon-polaritons are complex electromagnetic oscillations [1] resulting from coupling between an electromagnetic wave [2] and collective oscillations of surface electron charge density. The optical characteristics of many systems can be significantly enhanced by surface plasmon-polaritons (SPPs) [3]. Such is, e.g., the well-known strong surface enhanced Raman scattering (SERS) [4]. The backscattering of light from random defects at a metal surface also can be enhanced by SPPs [5]. The longitudinal component of such oscillations that does not exist in electromagnetic waves propagating in free space (volume or homogeneous waves) is the reason for strong localization of SPPs near the metal surface. This property ensures very high sensitivity of SPPs propagation [6,7] and scattering to surface defects [8–11].

It is known that with SPPs excitation surface local field intensity increases and the intensity enhancement factor is about 100 (10) for silver (gold) films [12]. This enhancement factor can be revealed by the measurements of total scattered intensity as function of angle of incidence or polarization of incident beam [13]. In such experiments, scattered light is produced by scattering of surface waves from weak interface roughness, including scattering by nanosized defects and particles that may be present near a surface.

On the other hand, SERS originates from enhancement of local electromagnetic field near various surface defects or centers. SERS enhancement factor can be as high as many orders of magnitude.

An interesting issue is that local field enhancement (well known in SERS) is not observed for elastic light scattering. There are few theoretical publications [14–18] dealing with the important enhancement factor in elastic light scattering of surface waves by different defects. In ref [14], the authors have found that for elliptical particles, the cross-section of SPP scattering increased by many orders of magnitude at resonance frequencies determined by the particle shape and size. The authors of [15,16] have calculated that the backscattering of light by dielectric nanosized particles is enhanced by 7-11 orders of magnitude. Very large enhancement of the intensity (over 10⁴) was predicted in [17,18] for fractal surfaces, but we do not know about experimental observation of such an enhancement factor.

The present publication deals with experimental study of the effect weak surface scatterers on the SPPs scattering. We demonstrate that SPPs excitation leads to giant enhancement of the scattered intensity compared to the case when SPPs are not excited.

2. Samples

The SPPs scatterers under investigation were prepared as a diffraction grating (DG). The grooves of the DG structure were rectangular in shape with a period p of 240 μm and the width of the groove a of 14 μm. Such a big structure sizes (as compared to the light wavelength) were chosen to study SPPs scattering by single defects. These periodic structures were fabricated by electron beam lithography in a 20 nm thick transparent PMMA 950K film, n = 1.48. The film was spin-coated on the surface of a 47 nm thick Au film that supports propagation of SPPs. The Au film was evaporated onto a glass prism substrate (n = 1.514).

An atomic force microscopy (AFM) image of a single groove is presented in Fig. 1 . The surface of the transparent film was characterized by an r.m.s. roughness σ _PMMA of 0.28 nm, while the roughness of the Au film σ _Au was about 0.60 nm. The parameters of the structure were chosen to ensure optimal conditions for SPPs excitation in the Kretschmann configuration. For this structure, the dependence of specular reflectivity R on the angle of incidence γ reached the minimal value, so that R(γ _min) < 3%.

 

Fig. 1 (Color online). AFM image of a groove etched in a PMMA film. The upper part of the structure is a transparent PMMA film placed on a gold film substrate.

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3. Optical measurements

In our study, SPPs were excited according to the Kretschmann scheme with a semiconductor laser (Modulated Laser Diode Module type 194-004 Radiospares Components, λ = 670 nm, 3 mW). The polarization ratio I_P/I_S of the laser beam was increased by using a Glan prism: I_P/I_S ≅ 10⁶. The setup described in [19,20] was modified to increase angular resolution of scattering measurements to 0.005°.

The measured scattered light intensity dI was normalized to the incident light intensity I⁰_, and solid angle of photodetector dΩ in order to calculate the Angle Resolved Scatter (ARS) function: $ARS(\theta )=\frac{dI(\theta )}{I^{0}d\Omega }$, where θ is the polar angle taken from the normal to the surface. Positive θ values correspond to the direction of SPPs propagation.

Optical image of the DG zone was obtained with a microscope MBS-10 whose optical axis was tilted by ~60° relative to the normal to the sample surface.

Total Integrated Scatter (TIS) measurements were performed by integrating the main part of the scattered light intensity with a spherical mirror that covers [-20°− + 80°] θ range. The TIS intensity was measured with a Si photodiode.

4. Results and discussion

The optical microscopy image of DG-zone is shown in Fig. 2 . If the incident beam is P polarized, the DG image is well visible (Fig. 2(P)). Contrary, it disappears completely in the case of S polarization as shown in (Fig. 2(S)). Apart from DG image some surface defects, visible in both images.

 

Fig. 2 The optical microscopy image of DG-zone with five grooves. Image label is polarization of the incident beam. The angle of incidence corresponds to optimal conditions of SPPs excitation.

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In Fig. 2(P), only the third groove is sharply focused, the other grooves are out of focus because of important tilting between the image plane and DG surface and limited microscope depth of focus.

The experimentally measured angular distribution of SPPs scattered light for the DG zone and positive θ values is presented in Fig. 3(a,b) . The ARS data are presented here in two forms: as ARS(cosθ) itself – Fig. 3(a) and as its moving Fast Fourier Transform (FFT) spectra, Fig. 3(b). The last one was obtained in the following way. The FFT spectrum was calculated for Δ = 2^k ARS points centered at θ value. For this value, the calculated spectra are presented with false colors coded vertical line of Fig. 3(b). This procedure was repeated for the whole range of θ.

 

Fig. 3 ^P ARS(cos θ) – (a, c) and its moving FFT spectra – (b, d) for the experimentally measured (a,b) and theoretically calculated (c,d) scattering intensities.

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From these data, one can see clearly very strong regular oscillations of scattered intensity for DG zone in the forward (relative to SPPs propagation) direction and for P polarization of the incident beam (^P ARS). Note a very high absolute value of ^P ARS for diffraction structure. The S polarized component of the ^P ARS structure is negligible.

The experimentally measured ^P ARS(cos θ) distribution in Fig. 3(a,b) can be compared with the theoretically calculated data presented in Fig. 3(c). The angular distribution of light intensity I diffracted by N grooves with a period p and width a was calculated using the following relation:

Fig. 3(c) presents the results of calculation for p = 240 μm and a = 14.6 μm and in Fig. 3(d) presents its moving FFT spectra. From the comparison of the data in Fig. 3, one can conclude that angular distribution of the diffracted light is in a good agreement with the theoretical prediction by Eq. (1).

For a sample area without DG (flat zone), the origin of scattering is a native surface and interface roughness. The results of polarization measurements of scattered light for the DG and the flat zones of the sample are presented in Fig. 4 . These data were obtained for the angle of incidence γ _min that corresponds to the conditions of optimal SPPs excitations.

 

Fig. 4 Polarization dependencies of normalized scattered light intensity for diffraction grating zone with P (S) polarizations - DG, P (DG, S) and flat zone with P(S) polarizations - Flat, P (Flat, S), measured outside of the prism.

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A comparison of the ^P ARS(θ) data for the DG zone with the scattering data when incident beam is S polarized ^S ARS(θ) (see Fig. 4) shows a significant decrease of the scattered intensity and complete quenching of diffraction structure in the ^SARS(θ) dependence.

This observation corresponded to the absence of the DG image in Fig. 2(S). A close examination of the ^S ARS(θ) scattering data revealed no noticeable traces of the DG diffraction structure. The FFT analysis of these data neither not showed the presence of diffraction structure frequency components similar to those shown in Fig. 3. Therefore, if a diffraction structure were present, it should be at least 100-1000 times weaker than the noise level of ^S ARS(θ) data. The same result was obtained for volume waves scattering, when a laser beam impinged the DG zone from the air side of prism. In this case, no traces of diffraction were found using the same analysis procedure. These results mean that diffraction intensity of volume and evanescent waves is significantly smaller than the scattering of these waves by native surface and interface roughness. Actually, this result was expected since a DG structure with few groves etched in 20 nm transparent film has a weak diffraction efficiency.

When SPPs are excited, the light diffracted by DG is significantly amplified because of the strong enhancement of local SPPs field in the proximity of the DG grooves. Doubling the non-focused grooves’ image in Fig. 2(p) confirmed that diffracted structure is produced by scattering of SPPs on the edges of rectangular grooves. The edges of these grooves are the areas where SPPs field is significantly enhanced according to ref [17]. Therefore the scattered field is enhanced as well. Despite a big ^P ARS values for DG zone, the TIS(γ) dependence shows that its maximal value is less than 0.15%, which confirms that the DG is a weak scatterer. Using these arguments, the enhancement factor of SPPs scattering by DG can be estimated as ^P ARS /^S ARS ratio of angular oscillation’ amplitude. The value of the enhancement factor evaluated by this ratio is above 5 × 10⁵–5 × 10⁶. To our knowledge, this is the first observation of such an giant enhancement of the elastic SPPs scattering.

We observed similar effects on the DG zones with different numbers of grooves, like those containing three and even a single groove. All of them were characterized by very strong and regular diffraction structure in space distribution of SPPs scattering. At the same time, none of these diffraction patterns were detected in scattering distribution of the evanescent (S polarization of incident beam) and volume waves.

Oscillations of ^P ARS(θ) distribution originate from the SPPs diffraction. This conclusion is proved by observation of diffracted structure in the light reflected into the prism, in the proximity of the reflected beam, as shown in Fig. 5 . A strong peak in this Figure is a remainder of the reflected beam. This peak is surrounded by a diffraction structure. An interesting feature of this distribution is a shift between the reflected beam and the maximum of the diffraction structure. As soon as the angle of incidence is changed, the angle of the reflected beam changes too. At the same time, the angular position of diffracted structure did not change because of the fixed value of the SPPs wave vector.

 

Fig. 5 Angular dependence of light scattered into the prism. The angle of incidence corresponds to the minimum of R(γ) value.

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The enhancement processes discussed above arise from SPPs scattering by artificially made DG grooves. When analyzing the features of Fig. 2(P), one can see extended and point-like areas of strong scattering intensity located not near the DG grooves. The same areas in Fig. 2(S) are dark, so they also can be characterized by high ^P ARS /^S ARS ratio. Such a behavior can be explained if there is similar enhancement of SPPs scattering by the above surface defects not made artificially.

The giant enhancement due to SPP scattering can open new possibilities for significant increase of sensitivity of sensors based on the SPP excitation phenomena.

5. Conclusion

We have observed experimentally giant (more than 10⁵−10⁶) enhancement of elastic SPPs scattering from regular and irregular surface singularities. We believe that the origin of such an enhancement is related to very strong enhancement of electromagnetic field by local surface inhomogeneities. This scattering structure was not registered when surface was exposed to the volume or evanescent electromagnetic waves.