1. Introduction

Surface plasmons (SPs) are electromagnetic waves that propagate along the interface between a metal with negative real permittivity and a dielectric. Their utility lies in their ability to confine light into regions considerably smaller than the optical wavelength, moreover, the propagation properties are highly sensitive to the ambient dielectric; for this reason, these waves are widely used as sensors. Although SPs are extremely sensitive to the changes in the local ambient conditions, they propagate for a considerable distance along the metal/dielectric interface, this means that it is difficult to have dense arrays of sensors since there is considerable crosstalk between adjacent elements [1,2]. In previous publications [3,4] we have shown how a modified confocal system operating with the sample slightly above the optical focus acts as a means of controlling the propagation length of the SPs. This is explained with reference to Fig. 1 where we can see that a wave is excited at point ‘a’ and reradiates light continuously as it propagates, however, only the light that appears to come from the focus, emerging at point ‘b’ returns to the confocal pinhole (the reverse path ‘b’ to ‘a’ is clearly also detected). The detected light from the interferometer thus follows path B. In a non-confocal system light that reradiates from all points is detected, so the interaction region between the sample and SPs is not well defined. The other light path that appears to originate from the focus and thus passes through the pinhole corresponds to light incident close to normal incidence (path A of Fig. 1). This leads to another significant advantage of the confocal microscope arrangement as these two beam paths form two arms of a highly compact interferometer. As discussed in [1] the limit of sensitivity in terms of refractive index units is comparable to prism based SP systems but the smaller area of interrogation means that the number of molecules in the probe region is reduced by two orders of magnitude or better.

 

Fig. 1 (a) Simplified schematic diagram of the confocal plasmon microscope, (b) Detailed schematic diagram. The confocal microscope is illuminated with 633nm HeNe Laser (Melles Griot, linearly polarized version) and then magnified by two lenses. It is reflected by a beamsplitter to the spatial light modulator. The spatial light modulator (Holoeye, LETO Phase Only) is aligned on a plane conjugate to the BFP plane of the objective lens (Nikon, CFI Apo TIRF 60x). After phase modulation, the beam is projected on the back focal plane of the objective lens and focused by the objective lens. After reflection, the image is viewed onto the CMOS camera (C1) with 2250x magnification and the back focal plane is projected onto the CMOS camera (C2).

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We have further improved the utility of this method by inserting a spatial light modulator (SLM) in the back focal plane [3,5]. This can be used to impose a phase curvature on the illuminating beam to replicate the effect of defocus [3], z. For a well-designed pupil function, as the sample is defocused the relative phase, ϕ, between the reference beam A and the beam producing the SP (beam B) changes as:

In order to evaluate the phase of the SP at defocus, z, we use the SLM to impose a phase shift on beam A relative to B so the phase of the SP can be recovered using a standard phase shifting algorithm. This requires 3 or 4 phase shifts per measurement point. In the present implementation of our system the need to switch the phase at each defocus limits the speed of data acquisition, since it takes approximately 500ms to switch the SLM from one state to another. In the present paper we examine how the interferometer may be implemented with a single shot measurement. The pupil function corresponding to this situation is depicted in Figs. 2(a) and 2(b).

 

Fig. 2 (a) Radial intensity distribution imposed on the SLM in the back focal plane, the vortex region extends to nsinθ = 0.66 (b) Phase distribution imposed on the pupil function (c) Experimental distribution of in the back focal plane in the presence of surface plasmon excitation (camera C2 of Fig. 1(b)). (d) Light distribution in the image plane, (camera C1 in Fig. 1(d)) showing data processing method at 4 symmetrical points.

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2. Vortex reference beam interferometry

The idea of vortex beams is of considerable interest in optics. To form a vortex beam, the back focal plane is illuminated with a spiral phase distribution whose phase varies between 0 and 2$\pi$ [6]. At the focus of the objective this forms a beam with zero intensity on the optical axis, so the intensity distribution is a toroidal shape. Spiral phase filters have been used in phase contrast microscopy to extract sample phase [7] and removal of phase ambiguity allowing elevations and depressions to be distinguished [8].

As mentioned in the introduction the interference occurs between the reference beam incident for low angles of incidence originating from close to the center of the back focal plane and the beam generating SPs. In order to accomplish single shot operation, we therefore impose an azimuthally varying phase distribution at low angles of incidence, not over the whole of the back focal plane, and for the angles corresponding to SP excitation we use a radially symmetric pupil function. This is shown in Fig. 2(a) which shows the intensity weighting of the pupil function with radial position, where reduced intensity is generated by phase cancellation betwen adjacent pixels on the SLM by imposing a relative π phase shift; this is discussed in more detail in [3]. Figure 2(b) shows the phase profile imposed on the SLM, where can see the azimuthal phase variation is applied to low incident angles. The reference beam projected onto the sample surface due to the azimuthal phase distribution is toroidal, which is imaged onto the camera C1 of Fig. 1(b), the intensity distribution is shown in Fig. 2(d). While the reference beam is toroidal in intensity as shown in Fig. 2(d), the phase varies azimuthally from 0 to 2$\pi$ in a similar fashion to the generating function in the back focal plane.

The output intensity I on the image plane as a function of azimuthal angle, $\alpha$can be represented as:

3. Experimental procedure

The SLM was used to impose the phase distribution of Fig. 2(b), the phase varied with azimuthal angle up to a radius in the back focal plane corresponding to nsinθ = 0.66. This intensity distribution varied with radial position as shown in Fig. 2(a). From Fig. 2(a), we gently apodize the two excitation regions so that there are no sharp edges to the pupil function leading to spurious oscillations in the output response. The light returning to the back focal plane for linear incident polarization is shown in Fig. 2(c), which shows the effect of the pupil function and also the intensity dip due to SP excitation where there is a substantial TM polarization component. Moreover, reducing the light from angles that do not contribute to useful signal allows one to use the dynamic range of the detector more efficiently [4].

The input polarization onto the sample can be radial, linear or circular. We have performed experiments with both linear and radial polarization. Radial polarization has the advantage that the phase varies uniformly with azimuthal angle and the whole of the ring may be used, however, the optics for linear polarization is more straightforward and the necessary processing will be best explained with reference to this case.

Figure 2(d) shows the experimentally obtained distribution in the detector plane. To recover the phase of the SP we used 4 phase steps to extract the phase. The signal from 4 symmetrical regions shown schematically in the right hand image of Fig. 2(d) was used for the 4 phase steps. The diameter of each region corresponded to 40 nm on the sample and each detection region was centered 47 nm from the central position. Although, the signal level is relatively low in this position the intensity distribution is much more uniform close to the center thus allowing one to apply the reconstruction algorithm without generating significant artefacts.

In addition to extracting the signal close to the center it is necessary to ensure that the regions from which the signal is extracted are correctly placed. In order to do this the relative positions and size of the detection regions were fixed and the center position was varied until the associated phase shifts were the closest value to the expected symmetry, that is the phase shifts associated with the detection points should be ϕ_0, π-ϕ₀, π + ϕ₀ and 2π−ϕ₀ respectively. Although the phase does not vary precisely linearly with azimuthal angle there must still be mirror symmetry about the central line in the back focal plane parallel to the polarization direction. The phase at each point was measured by defocusing the sample through a range of defocus values, the so-called V(z) curve, windowing the distribution, Fourier transforming and extracting the phase. This process is depicted in Fig. 3.

 

Fig. 3 (a) A Schematic V(z) obtained at a particular axial position in the image plane (b) FFT of windowed V(z) and (c) Extraction of phase for use in reconstruction algorithm, repeat at different detection position on the back focal plane.

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Defocus of the SP signal was effected by introducing phase curvature on the distribution in the back focal plane as described in [3]. There is one key difference to the procedure discussed there, in that paper we applied the defocus function over the whole of the back focal plane to replicate the effect of a real physical defocus. The phase curvature that applied to the higher incident angles is required to change the surface plasmon propagation length. On the other hand, defocusing the reference beam is not so desirable as its magnitude decreases with defocus, for this reason we apply phase curvature to the part corresponding to SP region (B) of Fig. 2(a) and keep the phase in the radial direction constant in the radial direction in the region of the vortex (A of Fig. 2(a)). This idea is discussed in more detail in a future publication.

4. Results

In order to validate the measurements, we used a test sample with layers of different thicknesses of Indium Tin Oxide (ITO) sputtered onto the gold layer. This sample was similar to the one used in [9]. We performed measurements on the coated gold layers using a surface profiler (model: P10 from KLA Tencor) to measure the ITO thickness, shown in Table 1, and an ellipsometer (model: M-2000 from J.A. Woollam Co) to measure the refractive index of the ITO. The ellipsometer measurements were obtained by directly illuminating the ITO. SP measurements were, of course, obtained imaging through the gold.

Table 1. Comparison of measurements from vortex, phase-step measurement and back focal plane measurements. Average thickness of the ITO layers is measured with the surface profiler. An independent measure of refractive index of ITO was measured with the ellipsometer.

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Measurements were obtained using the vortex illuminated SP microscope to obtain values of ϕ(z). The 4 phase steps were obtained from regions 1, 2, 3, 4 of Fig. 2(d), these 4 positions correspond to different phase step values. If the polarization is radial then we expect the phase to vary linearly with azimuthal polarization, for linear polarization the varying contributions of the p- and s- reflected polarized components mean that the phase variation is not exactly monotonic. This combined with small aberration and the finite size of the detection region meant that the phases corresponding to each reference region were not separated by exactly 90 degrees and thus needed to be measured. The values were obtained from the V(z) processing described in the section above and these values were inserted into a generalized phase stepping algorithm [10] to extract the value of ϕ(z) which are shown in Fig. 4. The precise position where the phase step values were extracted is described in section 3, so the best match to the expected symmetry is achieved. The gradient of these curves allowed θ_p to be obtained for the different thicknesses of ITO as shown in Table 1. These values were converted to thickness values of ITO from the measured value of refractive index (1.98) obtained using ellipsometry and from the refractive index of gold (0.19609 + 3.2558i) at 633nm from Rakic [11].

 

Fig. 4 Unwrapped phase of SP relative to the reference beam as a function of defocus for 4 different thicknesses of ITO extracted using the vortex reference beam.

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To validate the performance of our approach we compared our results with the following two methods (i) Determination of the position of the dip in the back focal plane. This could be performed using data such as that shown in Fig. 2(c), however if a rotating diffuser is placed conjugate with the back focal plane to remove the spatial coherence a far cleaner image is obtained. It should be mentioned in this case the light is distributed over the whole field of the microscope objective rather than a tight focus. A typical pattern from the back focal plane is shown in Fig. 5(a). The cross sectional patterns, for different thicknesses of indium tin oxide (ITO) deposited on the gold are shown in Fig. 5(b), these can be used to determine θ_p, although the precision of the method is inferior to the defocus approach and the results are even poorer if a well-defined single point is measured as the back focal plane must now be illuminated with a spatially coherent source. (ii) The phase stepping SP confocal method where 4 phase steps are used to extract the value of θ_p. The pupil function used for these measurements is shown in Fig. 6(a). The back focal plane distribution is shown Fig. 6(b). The distribution in the image plane Fig. 6(c) has a peak value in the center as expected. The values of ϕ(z) versus defocus were plotted for the vortex interferometer and processed in the same way.

 

Fig. 5 (a) Experimental back focal plane distribution using a rotating diffuser (b) cross sections of back focal plane for different thicknesses of ITO.

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Fig. 6 Pupil function and back focal plane distributions. (a) Radial distribution intensity distribution imposed on the back focal plane phase-step pupil (b) BFP with pupil function and (c) focal image

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Table 1 shows the values of ITO thickness recovered by the different methods. All the values are standardized to bare gold and the additional thickness is determined by matching the changes in SP k-vector to the film thickness using the measured parameters and the Fresnel equations for layered structures. From Table 1 we see that the single shot vortex method recovers values in excellent agreement with the phase step methods, which, in turn, agree well with the profiler measurements. Since the profiler measures from the ITO side of the sample the exact measurement position may differ slightly from the SP measurements. As expected the measurements from the back focal plane deviate somewhat from the other methods, since determination of the dip position cannot be made with so much precision.

5. Conclusion

We have extended the idea of using a modified confocal microscope as an interferometer for SP measurement with a locally generated reference beam, so that it may be used in single shot mode removing the need to perform phase stepping. This utilizes vortex illumination as the reference which covers the full range of phases required to recover the phase of the SP contribution. The method has been demonstrated as a rapid way to extract properties of the SP, and should be particularly valuable for microscope multipoint imaging of localized binding reactions where the reduction in the number of patterns imposed on the SLM will greatly enhance measurement speed. The measurement method discussed can, of course, be used for characterizing general surface waves including waveguide modes. To adapt for these applications the SLM would need to be modified to cover a more limited range of azimuthal angles, this will be reported subsequently. Moreover, the single beam interferometer with spatial heterodyning introduced by the vortex reference beam may be expected to have applications in such diverse fields as particle tracking within the diffraction limited focus of the microscope and in non-contacting surface profilometry.