Optical antenna arrays in the visible range - OSA Publishing

Optical antenna arrays in the visible range Daniel R. Matthews and Huw D. Summers School of Physics and Astronomy, Cardiff University, 5 The Parade, Cardiff, CF24 3YB, UK. [email protected]

Kerenza Njoh, Sally Chappell, Rachel Errington and Paul Smith School of Medicine, Cardiff University, Heath Park, Cardiff, CF14 4XN, UK.

Abstract: We report on experimental observations of highly collimated beams of radiation generated when a periodic sub-wavelength grating interacts with surface bound plasmon-polariton modes of a thin gold film. We find that the radiation process can be fully described in terms of interference of emission from a dipole antenna array and modeling the structure in this way enables the far-field radiation pattern to be predicted. The directionality, multiplicity and divergence of the beams can be completely described within this framework. Essential to the process are the surface plasmon excitations: these are the driving mechanism behind the beam formation, phase-coupling radiation from the periodic surface structure and thus imposing a spatial coherence. Detailed fitting of the experimental and modeled data indicates the presence of scattering events involving the interaction of two surface plasmon polariton modes. ©2007 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (050.2770) gratings; (030.1670) coherent optical effects.

References and links 1.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667-669 (1998). 2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal and T. W. Ebbesen, “Beaming light from a sub-wavelength aperture,” Science 297, 820-822 (2002). 3. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163-182 (1944). 4. W. L. Barnes, A. Dereux and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003). 5. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata and R. A. Linke “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology, 13, 429-432 (2002). 6. J. R. Lakowicz, “Radiative decay engineering 5: metal-enhanced fluorescence and plasmon emission,” Analyt. Biochem. 337, 171 (2005). 7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629-3651 (2004). 8. L. Martin-Moreno, F. L. Garcia-Vidal, H. J. Lezec, A. Degiron and T. W. Ebbesen, “Theory of higly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett. 90, 167401-1-167401-4 (2003). 9. D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14, 3503-3511 (2006). 10. A. A. Oliner and A. Hessel, “Guided waves on sinusoidally-modulated reactance surfaces,” IRE Trans. Antennas Propag. AP-7, S202-S208 (1959). 11. A. A. Oliner and D. R. Jackson, “Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 1: basic features,” IEEE Antennas and Propagation Society International Symposium, 2, 1091-1094 (2003). 12. D. R. Jackson, T. Zhao, J. T. Williams and A. A. Oliner, “Leaky surface-plasmon theory for dramatically enhanced transmission through a subwavelength aperture, Part 2: Leaky-wave antenna model,” IEEE Antennas and Propagation Society International Symposium 2, 1095-1098 (2003).

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Received 3 October 2006; revised 11 January 2007; accepted 16 January 2007

19 March 2007 / Vol. 15, No. 6 / OPTICS EXPRESS 3478

13. E. Krestshmann, “Decay of non radiative surface plasmons into light on rough silver films. Comparison of experimental and theoretical results,” Opt. Commun. 6, 185-187 (1972). 14. J. Moreland, A. Adams and P. K. Hansma, “Efficiency of light emission from surface plasmons,” Phys. Rev. B 25, 2297-2300 (1982). 15. L. B. Yu, D. Z. Lin, Y. C. Chen, Y. C. Chang, K. T. Huang, J. W. Liaw, J. T. Yeh, J. T. Yeh, J. M. Liu, C. S. Yeh and C. K. Lee, “Physical origin of directional beaming emitted from a subwavelength slit,” Phys. Rev. B 71, 041405-1-041405-4 (2005). 16. K. G. Sullivan, O. King, C. Sigg and D. G. Hall, “Directional enhanced fluorescence from molecules near a periodic surface,” Appl. Opt. 33, 2447-2454 (1994). 17. H. Raether, Springer Tracts in Modern Physics, Vol. 111: Surface Plasmons on Smooth and Rough Surfaces and on Gratings, (Spinger-Verlag Berlin Heidelberg, 1988). 18. J. D. Kraus and D. A. Fleisch, Electromagnetics with Applications (McGraw-Hill, 1999). 19. E. S. Kwak, J. Henzie, S. H. Chang, S. K. Gray, G. C. Shatz and T. W. Odom, “Surface plasmon standing waves in large-area subwavelength hole arrays,” Nano. Lett. 5, 1963-1967 (2005). 20. E. Hecht, Optics (Addison-Wesley, 2002). 21. M. Born and E. Wolf Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (Pergamon Press, 1965).

1.

Introduction

One of the most striking effects of exciting a surface charge oscillation at the interface of a metal and dielectric is the extraordinary transmission of light through any sub-wavelength aperture in that metal1, 2. Standard diffraction theory suggests that when the aperture size is significantly small compared with the photon wavelength the transmission of energy becomes inhibited3. This process can be enhanced somewhat by the presence of a surface corrugation which allows the incident light to excite surface plasmon (SP) oscillations4, or by forming a closely spaced array of identical apertures. The basic premise is that excitation of surface modes allows light to penetrate the metal over a wide frequency range and with a significant enhancement over the bare aperture case. A number of physical mechanisms have been invoked to describe these enhancement effects. In the first instance enhancement factors of several thousand were reported and were attributed to the large electric field amplitude associated with the SP modes transmitted through the sub-wavelength slit or aperture5. Many near-field optical processes are based on this mechanism of field enhancement: for example it is responsible for the enhancement of molecular fluorescence intensity that can be achieved in the vicinity of an appropriately designed metal surface6. Other descriptions have been put forward which seeks to explain the transmission of light by the excitation of surface evanescent, or diffracted7, modes on the output side of the aperture which can then be made to radiate into free-space by the inclusion of an appropriate periodic structure. Another feature of these experiments is that not only does an enhancement of transmission occur, but rather than diffracting into all directions, the transmitted light takes the form of an extremely well defined beam8, 9. This beam formation has drawn parallels with radio and microwave antenna theory and in fact the authors of references 10-12 have sought to encapsulate the physics of the enhancement and beaming processes in a so-called leaky wave antenna model. The authors view the various effects as an interaction of guided waves with a modulated reactance surface10, a description which is similar to that used in the explanation of beam formation by sub-wavelength slits where the far-field is often described in terms of diffracted, radiating or leaky modes. The similarity between radiation from corrugated metal surfaces and antennas has been noted before: in their original paper on optical beaming1 Lezec et al alluded to a phase coupling mechanism mediated by the SP to explain the pronounced directionality of emission. In addition to light beams generated by sub-wavelength apertures, light emission is to be expected from structures which do not include such apertures. As will be described below, SP polaritons can be made to radiate providing that their momentum can be slowed sufficiently. This can be done with an appropriate grating structure or even by a roughened surface13. It has

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been shown that SP emission efficiency can approach 80% in an attenuated total reflection (ATR) coupled device by including a sinusoidal modulation of the output silver surface14. Although the authors do not comment on the underlying physical processes, or whether beam formation is possible, the experimental conditions required to achieve this efficiency can be estimated using a simple wave vector matching approach; an approach which is routinely cited in the discussion of the beaming of radiation from sub-wavelength structures15. There are also numerous other situations where guided modes can be transformed into radiating modes, one noteworthy example being the enhanced fluorescence achieved by placing the molecular species of interest close to the periodic surface of a metal-clad waveguide. The electric field enhancement achieved by coupling light to surface plasmons has been combined with a grating structure to achieve an increase of intensity of a factor of approximately 103 into a very narrow angular range16. The literature review above is of direct relevance to this work which reports on the formation of out-coupled beams of radiation from periodic metallic corrugations, but without the use of any sub-wavelength apertures: we find that optical transparency of an opaque gold structure can be achieved by using the metal corrugation as a means for radiating surface modes into the far-field. In this paper we explicitly assume that plasmon radiation can be viewed as a form of dipole antenna emission. Specifically we treat a patterned metal surface as an array of radiating point dipoles and apply standard theory of dipole antenna arrays to describe the optical beams emitted from such a surface, and relate this to the more commonly used k-vector descriptions based on the photon and plasmon dispersion relations. Experimentally we show that the metallic surface corrugations included in our samples can emit light at an arbitrary angle into well-defined beams, with very low angular divergence up to distances of several thousand microns from the sample surface. 2.

Grating fabrication

Our experimental arrangement is illustrated in figure 1. A continuous 40 nm thick gold film was thermally evaporated onto a glass substrate (a 1 cm2 piece of 150 µm thick coverglass) and 1-D line grating structures were then fabricated by electron beam lithography on 100x100 µm regions of the gold covered substrate. The gratings consist of 200 nm wide, 30 nm high ridges of gold, defined by a lift-off process, and show up as the dark squares in the microscope image, captured with a x5 objective lens, in Fig. 1(a). This method of manufacture is extremely versatile allowing the number, shape and size of the grating elements, and their spatial location to be easily varied. We excite SPs in the structure by close-coupling a 630 nm emitting laser diode to the edge of the glass substrate as shown schematically in Fig. 1(b).

Grating

Out-coupled light Laser light

(a)

(b)

(c)

Fig. 1. (a) A bright wide-field image captured with a x5 objective lens of four 100x100 µ m gratings. (b) A schematic diagram of SP excitation and beam formation. (c) The gratings structures under laser excitation.

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This configuration is to be distinguished from an ATR experiment by virtue of the fact that precise control of the angle of the incident light is unnecessary and is therefore not included. The refractive index step between the glass substrate and the surrounding air is relatively high, thus forming an optical waveguide with a large acceptance angle. Laser light impinging on its edge experiences total internal reflection at angles beyond ~ 41o to the normal and it is therefore the evanescent field associated with the guided light that results in SP excitation at the metal-air interface. The laser diode used here operates at 630 nm and at this wavelength the resonance angle for SP excitation, using values of the dielectric constant given in reference 17, turns out to be approximately 44o for this particular configuration. The far-field distribution of the laser diode has an elliptical shape, with the major axis parallel to the plane of incidence, and subtends an angle of approximately 22o. Therefore rays propagate in the substrate at angles from 41o up to approximately 63o, covering the range of angles at which it is possible to excite SP polaritons. As the light emitted by the laser traverses the substrate SPs are excited but, as the schematic diagram in Fig. 1(b) shows, in general light cannot be emitted by these SPs since there is no mechanism to decrease their momentum sufficiently. This situation changes when the light reaches the sub-wavelength grating. The corrugation allows the SPs to ‘slow’ and light to emanate strongly from these regions as illustrated in Fig. 1(c) where the gratings show up as bright squares on the mostly dark field. It was evident in our studies that there are regions of the sample where light is unintentionally radiated; the bright spot marked by the red arrow in Fig. 1(c) gives an example of such a region. This effect is a result of blemishes in the metal, scratches or surface roughness, which scatter SP polaritons. This behavior is inevitable since the surface of the sample cannot be kept completely free of debris during the manufacturing process and a certain level of roughness of the metal film is introduced during the thermal evaporation process. The light generated as a result of scattering with these defects is emitted into all directions allowing us to easily distinguish them from the grating structures which emit into well defined beams. 3.

Out-coupled radiation

Here we outline the general optical properties of the grating structures described in section 2. False color intensity maps, reconstructed from microscope images captured with a CCD camera attached to an upright Nikon E600 fluorescence microscope are shown in Fig. 2. Images were captured while the objective lens of the microscope was stepped away from the surface of the sample at increments of 10 µm for (a), (b) and (d) and 50 µm for (c). An intensity-line-scan was obtained for each step and a color map was applied to the intensity scale of each scan. Visualizing the data in this way allows the beaming angles of the outcoupled radiation to be easily extracted to provide a quantitative comparison. Figure 2 shows 450, 550, 750 and 900 nm pitch gratings in (a)-(d) respectively and it is clear that the directionality, and multiplicity, of the beams is controlled by the pitch of the surface corrugation. A near normal beam is generated in the case of the 450 nm grating whereas an increase in the pitch to 900 nm produces three beams, two of which have a relatively pronounced intensity. It is worth noting that with respect to the plane of the images the guided laser emission is traversing the substrate in the direction of increasing line-scan distance. This means that despite the fact that the Poynting vector of the exciting radiation is parallel to the plane of the sample, beams of out-coupled light are produced which propagate in the opposite direction. These “reverse traveling” beams are a striking, and somewhat unexpected, feature of the data. This indicates that the radiation process is in some sense decoupled from the excitation process. These data also serve to highlight another remarkable property of these structures. The beams generated have an extremely low angular divergence in the direction perpendicular to the grating lines (Δθ < 1o), giving the out-coupled light a strongly collimated nature. In fact the data for the 750 nm pitch given in Fig. 2 (c) shows that although the intensity becomes reduced with increasing distance, the divergence is still extremely low at 2000 µm from the sample surface. Laser diodes have notoriously poor beam characteristics #75764 - $15.00 USD

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(an elliptical beam with a divergence of 30o along the major axis and 15o along the minor) and at a distance of a few millimeters from the output facet the beam quality is drastically diminished, therefore this low divergence is not related to the fact that a laser is used for excitation but rather, as will be described in detail below, is due to the nature of the radiation process itself.

(a)

(b)

(c)

(d)

Fig. 2. Re-constructed images of the beams generated by (a) a 450 nm pitch grating, (b) a 550 nm pitch grating, (c) a 750 nm pitch grating and (d) a 900 nm pitch grating. In (a) and (b) it is also possible to make out beams from adjacent gratings in the periphery of the images.

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Fig. 3. A re-constructed image, plotted on a grey-scale of gratings with 10 and 50 lines located at 400 and 600 µm on the linescan distance axis. The solid white lines form a guide for the eye.

Further experiments have shown that this is indeed the case. Figure 3 shows an example of two gratings where the pitch was fixed and the number of lines was varied. In the example on the left of the image the grating contains just 10 lines whereas that on the right has been increased to 50. Since the beam intensity of the grating with just 10 lines falls off rapidly with increasing distance from the surface of the metal, we have encoded the line-scan intensity on a grey-scale in order to provide a greater contrast than could be achieved with the standard color-map. The effect of varying the number of elements is quite clear: the beam divergence is greatly reduced by increasing the number of diffracting elements (the white solid lines form a guide for the eye). An analysis of the divergence angles shows that Δθ ~ 12o (210 mrad) for the grating with 10 lines reducing to ~ 0.5o (9 mrad) for the grating with 50 lines. 4.

Antenna arrays and the role of surface plasmons

The nature of the beam formation described in section 3 suggests to us a similarity with antenna radiation. Although this has been alluded to in a number of publications, we believe the physical mechanisms resulting in optical beam formation can be explicitly captured by standard dipole array theory. In our model we regard each individual grating line as a radiating dipole such that the grating becomes an isotropic antenna array. The physics describing the generation of beams from such antenna arrays is well developed for radio frequencies and this can be viewed as their optical counterpart. The spatial distribution in the far-field of the electric field associated with an isotropic antenna array (or a dipole array viewed end-on) is given by the relation shown in Eq. (1)18:

E=

⎛1⎞ ⎜ ⎟ ⎝n⎠

sin⎛⎜ nψ ⎝

sin⎛⎜ψ ⎝

⎞

2 ⎟⎠

2

⎞ ⎟ ⎠

(1)

Here the electric field is normalized to the number of emitting elements in the array, n. The phase of the array in the far-field is represented by ψ and can be calculated as shown in Eq. (2) where Λ is the spacing of the array elements (the grating pitch); λ is the free-space emission wavelength; θ is the viewing angle in the far-field relative to the surface and δ is the phase difference between individual elements of the array.

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ψ=

2πΛ

λ

cos θ + δ

(2)

It is this δ-factor which links the antenna array theory to the surface plasmons present in the metal film. We assume that the dipole array formed by successive grating lines, is coupled by the SP wave propagating across the surface. The relative phase between dipoles is then determined by the phase of the SP as shown in Eq (3).

δ = 2π

Λ

(3)

λ sp

Polar plots of the normalized electric field generated by Eq. (1)-(3) for antenna arrays with a pitch of 550 nm (blue line), 650 nm (red line) and 750 nm (black line) are given in Fig. 4. It is immediately obvious that this model, despite its simplicity, can re-produce important features of the experimental data: the beam multiplicity and directionality can be controlled by the element spacing, or grating pitch. For a fixed free-space wavelength there is a tendency to produce a greater number of beams as the element spacing is increased. This can be seen in Fig. 4(a) by noting the number of electric field lobes for each of the 550, 650 and 750 nm arrays respectively. Furthermore, if we track the lobe closest to the normal (the 90o line) this component effectively changes direction when the pitch is increased; this kind of directionality, and indeed multiplicity of beams, is a natural consequence of optical interference in the far-field from an array of dipole emitters.

(a)

(b)

Fig. 4. Polar plots of the normalized electric field of 550 (blue line), 650 (red line) and 750 nm (black line) pitch antenna arrays where the number of elements n is (a) 10 and (b) 50.

Another obvious feature of the data is the effect that the number of elements, n, has on the divergence Δθ, of the beam. The beams generated by dipole arrays with the same element spacing as in (a) but with n increased from 10 to 50 are shown in Fig. 4(b). A dramatic reduction in the beam divergence, from a full-width at half-maximum of 10o as shown in (a), to around 0.7o in (b) was observed, and it is also notable that the amplitude of the end-fire beam (θ = 1800) produced for all arrays when n = 5 is diminished by a factor of approximately 100. From a qualitative point of view there is strong agreement between the antenna array model and the experimental data. However, a quantitative match becomes more difficult due to a number of considerations. The first is related to the viewing angle available to the objective lens used when examining the structures described in section 3. The data were obtained using a 20x objective lens with an NA of 0.45, which equates to a collection angle of ±27o. This means that the microscope can view beams on either side of the normal when the #75764 - $15.00 USD

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emission angle is less than 27o. A comparison of the emission angles measured experimentally with the lobe position generated by the model are given in Fig. 5 where the acceptance angle of the measurement is marked by the horizontal, dashed black lines. The solid blue lines, labeled as “1st order” in the legend, are solutions from the model as described above. It is clear that most of the experimental data points (the black squares) match the model extremely closely, there are however, points for the 650, 750 and 900 nm pitch gratings which do not match these first-order solutions. We therefore included solutions of a ‘second-order’ nature (the red curves in the figure) which equate to a phase difference of 2δ in Eq. 2 giving good agreement of experiment and theory for all data points.

Model 2nd order Model 1st order Experimental data

Emission Angle (Degrees)

180

120

60

0 400

600

800

1000

Grating pitch (nm)

Fig 5. Far-field emission angle plotted as a function of grating pitch. The data points represent the experimental data while the solid lines show the fits generated by the antenna array model.

It is clear that multiple beams of varying angle of emission in the far-field are naturally produced by this type of analysis. For a single dipole emitter the electric field pattern inhabits the full 4π radians of space. In the case of multiple dipoles of equal spacing, in certain directions determined by δ there is constructive interference and thus a maximum in the electric field. The the beam formation process in this analysis is illustrated in Fig. 6 which plots the far-field phase, ψ (blue curve), and the beam amplitude (red curve) as a function of the far-field viewing angle θ for a 900 nm pitch array. The phase difference, δ, between the individual elements of the array determined by the element spacing compared to the SP wavelength, controls the far-field angle at which ψ reaches a multiple of 2π. Maxima in the electric field amplitude are produced whenever this condition is met and therefore multiple beams are inevitable.

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π

1.0

6

0.8

es ah p ldei fra F

π

4

0.6

0.4

π

2

0.2

0

ed tuli p m a m eab de isla m ro N

0 0

100

200

300

Viewing angle (degrees)

Fig 6. The far-field phase (blue line) and beam amplitude (red line) plotted as a function of angle. A maximum of the E-field occurs whenever ψ is a multiple of 2π.

The antenna array model is concerned solely with the emitted light and so does not allow us to directly infer details about the excitation process. However re-casting Eq. 2 and 3 in terms of a wave vector, k leads to momentum matching conditions and some degree of physical insight. As noted in the preceding paragraph, peaks in the electric field (i.e. radiation beams) are obtained when ψ is equal to an integer multiple of 2π. Under this condition Eq. 2 and 3 combine to give:

m k g = k0 cos θ + k sp

(4)

where ksp, k0 and kg are the wave-vectors of the SP, the free space photons and the grating respectively. This is the commonly used in-plane momentum matching condition required for photon emission from SP polaritons at a metal-air interface. This is usually assumed a-priori, but here it is a natural outcome of the consideration of far-field interference from an array of dipole emitters. The multiple, first-order beams (blue lines in Fig. 5) produced from the dipole array correspond to solutions of Eq. 4 and are due to multiple reflections of plasmons by the metallic grating. The second-order curves (red lines in Fig. 5) were obtained using a phase factor of 2δ which in k-vector notation corresponds to: m k g = k0 cos θ + 2k sp

(5)

Thus this second-order process corresponds to interactions involving two surface plasmons. This type of process has been seen previously in subwavelength-hole arrays where propagating SP polaritons interfere and generate standing waves between adjacent holes with fringes at half the SP wavelength19. Although antenna theory has been invoked to describe beam formation from sub-wavelength slits the approach taken was to calculate a propagation constant for the surface mode and show that under certain circumstances this surface mode can be converted to a radiating mode. Here we have shown that the standard dipole antenna array theory can be used to predict the far-field radiation pattern from a metallic grating formed by what is essentially an interference process. It should come as no surprise that this is possible: this is precisely the theory used to describe diffraction by apertures in opaque screens20. The diffracting element is first split into a number of coherent oscillators and the far-field diffraction pattern is then constructed from the total field associated with each #75764 - $15.00 USD

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individual oscillator. The far-field is then linked to the spatially coherent field at the aperture by the Werner-Citterke theorem21. The beams emanating from our grating structures result because SP excitations are driving the process and provide stringent momentum matching conditions. This means that regardless of the range of incident angles provided by the laser diode excitation, ultimately it the conditions given in Eq. (4) and (5), which are a natural consequence of our treatment, which will determine the directionality in the far-field of the emitted radiation. 5.

Summary

In this paper we have described a process by which highly collimated beam of light can be generated by coupling light to metallic gratings via the excitation of SP polaritons. We find experimentally that the pitch of the grating can be used to control the directionality and multiplicity of the beams and the angular divergence can be adjusted by the inclusion of varying numbers of grating elements. These results are well described by the standard theory for radiation from a dipole array with the grating elements viewed as point dipole sources which are phase-coupled by a surface plasmon wave. We show that this approach is mathematically consistent with the more commonly used k-vector description of plasmonphoton interactions. A complete match of this theory to the experimental data requires the inclusion of two-plasmon processes. This approach of using antenna theory to describe plasmon-photon interactions provides not only a means of predicting far-field radiation patterns but also gives a physical picture of the radiation process. It is worth noting that the dipole array approach is precisely the theory used when describing diffraction by an aperture of arbitrary shape. Thus the beaming seen from these metallic gratings is a direct consequence of the coherence induced by the SP as it couples radiating sources across the grating i.e. the spatial coherence is determined by the coherence length of SP excitations along the surface of the sample rather than photons.

This research was funded by the RCUK Basic Technology program under the ‘Optical Biochips’ project and by the Wellcome Trust.

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