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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11523–11535
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Quantitative plasmonic measurements using embedded phase stepping confocal interferometry

Bei Zhang, Suejit Pechprasarn, and Michael G. Somekh  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11523-11535 (2013)
http://dx.doi.org/10.1364/OE.21.011523


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Abstract

In previous publications [Opt. Express 20, 7388 (2012), Opt. Express 20, 28039 (2012)] we showed how a confocal configuration can form an surface plasmon microscope involving interference between a path involving the generation of surface plasmons and one involving a directly reflected beam. The relative phase of these contributions changes with axial scan position allowing the phase velocity of the surface plasmon to be measured. In this paper we extend the interferometer concept to produce an ‘embedded’ phase shifting interferometer, where we can control the phase between the reference and surface plasmon beams with a spatial light modulator. We demonstrate that this approach facilitates extraction of the amplitude and phase of the surface plasmon to measure of the phase velocity and the attenuation of the surface plasmons with greatly improved signal to noise compared to previous measurement approaches. We also show that reliable results are obtained over smaller axial scan ranges giving potentially superior lateral resolution.

© 2013 OSA

1. Introduction

The hardware configuration used in this paper is the same as that used in [2

2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

], however, we use the versatility afforded by the configuration to perform some new phase stepping measurements. We show that the system forms a phase stepping interferometer between the paths P1 and P2 of Fig. 1(a). Data extraction from the system allows the amplitude and phase corresponding to the SP excitation to be extracted directly. This allows both the real and imaginary parts of the SP k-vector to be extracted which can, of course, be equated to the phase velocity and attenuation of the SPs.

The idea is presented in Fig. 1(a) which shows a defocused sample where the SPs are excited at a specific incident angle. Reciprocity dictates that the excitation and reradiation efficiency of surface waves is similar, so that energy will reradiate continuously along the propagation path of the SPs; indeed it is this uncertainty in the path of the detected radiation that limits the spatial resolution of most plasmonic imaging systems. Examining Fig. 1(a) we see that the presence of the confocal pinhole ensures that only light appearing to come from the focus returns to the pinhole. The presence of the confocal pinhole thus defines the allowable propagation paths (P2 of Fig. 1(a)) of the detected SPs thus ensuring that the resolution is determined by the footprint of the optical beam rather than their propagation length [6

6. M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “Optical V(z) for high-resolution 2pi surface plasmon microscopy,” Opt. Lett. 25(11), 823–825 (2000). [CrossRef] [PubMed]

]. When the sample is moved away from the focus towards the objective there are two major contributions to the signal detected at the confocal pinhole. The first is light close to normal incidence that will return to the pinhole and the second is the SP path discussed above. As the sample defocus, z, is incremented by a distance, Δz, assuming a well beved pupil function, the phase between the normal incident beam and the SP beam changes:
Δϕref=4πnλΔzΔϕplas=4πnλcosθpΔz
(1)
where the subscripts ‘ref’ and ‘plas’ denote the phase shifts associated with the normal incidence and the plasmon beams, n is the refractive index of the couplant, essentially, the coupling oil, θp denotes the incident angle for excitation of SPs, and λ is the wavelength of the illuminating radiation in vacuum. The phase shift of the SP can be calculated from the incident wavevector of the excitation beam, which is2πncosθpλor by considering the ray paths which include both the phase shift due to defocus and the phase accumulated by the SP as it propagates along the surface. The relative phase between the reference and the SP contributions at the pinhole thus varies with changing defocus Δz as:
Δϕ=4πnλ(1cosθp)Δz
(2)
so that the relative phase changes by with a period given by:
Δzp=λ2n(1cosθp)
(3)
This phase shift corresponds to one cycle of oscillation observed on the so-called V(z) curve, so the period of the oscillation can be used to determine θp from which the real part of the wave number of the SPs (=2πnsinθp/λ) or phase velocity c/(nsinθp) can be determined.

Two simulated V(z) curves are presented in Fig. 2
Fig. 2 Simulated V(z) curves of uncoated (red) and sample coated with 10nm of indium tin oxide (blue) showing different periods of oscillations
which show the difference in periods between a bare gold layer compared to a thin indium tin oxide (ITO) (c.10 nm) coated gold. The V(z) curve is the output signal as a function of defocus, z. This is a complex quantity involving the integral of the detected field contributions [1

1. B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express 20(7), 7388–7397 (2012). [CrossRef] [PubMed]

] although in many cases the intensity signal, |V(z)|2 is measured. The |V(z)|2 curve can be obtained by mechanical scanning of the sample in the axial direction [1

1. B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express 20(7), 7388–7397 (2012). [CrossRef] [PubMed]

] or by imposing the same phase shifts electronically in the back focal plane using a spatial light modulator (SLM) [2

2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

]. The average period of each |V(z)| curve can be used to determine the plasmonic angle using Eq. (3). Although this equation is not exact and relies on a well apodized pupil function [9

9. L. Berguiga, S. Zhang, F. Argoul, and J. Elezgaray, “High-resolution surface-plasmon imaging in air and in water: V(z) curve and operating conditions,” Opt. Lett. 32(5), 509–511 (2007). [CrossRef] [PubMed]

], it, nevertheless, gives an excellent measure of the change in plasmonic angle when an analyte is deposited. Here, we will show how modifications to the |V(z)| curve using phase stepping and pupil function engineering can be used to determine the properties of SPs in a convenient and effective manner. We modulate the phase of the reference while keeping the phase of the SPs fixed. This provides a quicker, more robust and more accurate method to extract the SP properties. A detailed simulation analysis is presented to compare the two methods in section 3.

2. Experimental setup

The experimental system has been described in [2

2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

]. Essentially the system is a mechanical scanned confocal microscope with a phase SLM (BNS 512512 phase SLM) inserted in the back focal plane to control the interference signal detected at the pinhole. The pinhole was formed by projecting the 1000 times magnified focal spot onto the CCD array. The pinhole size can thus be selected by selecting the appropriate pixels from the array. The light source was a 632.8nm He-Ne laser (10mW) and 1.45 NA oil immersion objective (Zeiss) was used to excite SPs. Further details are given in [2

2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

].

3. Beam profile modulation in the back focal plane

The SLM shown in Fig. 1(b) is used to control the profile of the beam in the back focal plane. This is necessary to ensure that the reference beam gives a good approximation to the phase variation depicted by Eq. (3), if the beam is not apodized at the edges of the objective aperture there is a considerable amount of signal induced by the edge which effects the phase of the reference beam and, in turn, the accuracy with which θp can be recovered. The red curve in Fig. 3
Fig. 3 (a) Pupil function distribution (red curve) and calculated reflection coefficient for p-incident polarization on an uncoated sample (blue curve); the vertical cyan lines represent the range of angles over which the phase stepping of the reference beam was imposed. (b) is the back focal plane (BFP) image by setting the adjacent pixels in antiphase on a phase-only SLM and (c) is the same with no modulation of the mid-frequencies.
shows a typical pupil function imposed on the back focal plane, where the angles around normal incidence and θp are allowed to pass through the lens. In principle the angles in the mid-range of the pupil can be allowed to pass but since they only contribute background it is better to block them. Note that since we only employ a phase only SLM blocking the light that passes is accomplished by setting adjacent pixels in antiphase [2

2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

]. Experimental images of back focal plane (BFP) are shown in Fig. 3. Figure 3(b) is modulated by using the phase SLM in antiphase for the mid frequencies and in Fig. 3(c) the mid frequencies are allowed to pass. The phase cancellation also allows the sharp edge of the clear aperture to be smoothed.

If we now assume that confocal system forms a two beam interferometer between the reference beam and the beam involving excitation and reradiation of SPs, we can use the phase shifting ability of the SLM to form a phase stepping interferometer between sample and reference. The experimental measurements and simulations will allow us to evaluate the effectiveness of this assumption and also to see the values of defocus where the assumption is valid.

Taking four phase shifts as the vector diagrams shown in Fig. 4
Fig. 4 Effect of phase stepping on relative phase of reference and plasmon beams, green line is the reference signal R, cyan line is the SP phasor, red line is the resultant signal V.
, we form the standard interferometric expressions thus:
In(z)=|R(z)|2+|S(z)|2+2|R(z)||S(z)|cos(φ(z)+αn)
(4)
where In(z)is the |V(z)|2 curve subject to different relative phase shifts imposed by the spatial light modulator, αn=(n1)π2and n = 1, 2, 3, 4; R and S represent the reference and signal (surface plasmon) beams respectively, and φ represents the relative phase between the reference and signal beams. These signals can then be readily processed to extract φ; the phase stepping also allows one to extract |R|2+|S|2as well as |R||S|, since the reference beam can be independently measured by blocking excitation of SPs the value of S can also be obtained uniquely. The distribution of the patterns we used for the phase-stepping procedure is shown in Fig. 3(a). In a conventional interferometer arrangement, the phase of the resultant (red) is extracted rather than the plasmonic phase (cyan) which is accessible in our embedded interferometer.

4. Phase stepping to obtain the plasmon angle, θp

We now combine the phase stepping approach with V(z) and obtain the relative phase between reference and signal beams as a function of defocus, z. The sample was scanned axially through each defocus position, z, and at each defocus position 4 phase steps were performed. The four |V(z)| curves on bare gold obtained by shifting the phase of the reference in increments of 90 degrees are shown in Fig. 5
Fig. 5 V(z) curves variations of bare gold obtained by shifting the phase of the reference in increments of 90 degrees. From lower to upper figures we have: zero phase shift (red), 90 degree phase shift (blue), 180 degree phase shift (black) and 270 degree phase shift (cyan). Successive curves are shifted by 0.1 units for clarity.
. From lower to upper figures we have: zero phase shift (red), 90 degree phase shift (blue), 180 degree phase shift (black) and 270 degree phase shift (cyan).

Then the four |V(z)| curves are used to obtain the relative phase between reference and signal at each defocus, φ(z). The relation between the φ(z) and the plasmonic angle is expressed as:
φ(z)=2kz(1cos(θp))+β
(5)
θp is a phase constant accounting for the offset phase between sample and reference. The slope of the unwrapped phase is thus:
sslope=2k(1cos(θp))
(6)
By measuring the slope of the fitted line, we can therefore calculate the plasmonic angle θp.

We introduced the phase stepping measurement above and assert that this method is more accurate and robust in calculating the plasmonic angle θp compared to other methods compared to direct measurement of the ripple period or Fourier transform measurement. In order to validate this we carried out a set of Monte Carlo simulations to assess the performance of these three measurement methods. The definitions of the three methods are as follows: 1) Direct measurement of the ripple period; the ripple period Δz was calculated by averaging the first few ripples as shown in Fig. 7(a)
Fig. 7 (a) shows the method of measuring the ripple period measurement (b) shows 3rd order polynomial fit (black) to locate a minimum position for ripple period measurement; (c) shows regions on φ(z) and corresponding ripple positions.
and then the plasmonic angle θp can be calculated using Eq. (3). The minimum positions of the ripples are determined by 3rd order polynomial curve fitted to 25 data points (over a range of 200 nm) around the minimum as shown in Fig. 7(b). 2) For the Fourier Transform measurement, the average ripple period Δz was determined from Fourier transform of the windowed pattern of ripples. Details of the phase stepping measurement have been described above.

In order to compare the three methods fairly we used four times as many measurements for the direct measurement and the Fourier method as the phase stepping measurement requires four different measurements.

Now let us consider the case where there is noise. We will consider a shot noise source. The noise levels were calculated on the basis that the maximum signal in the V(z) curve contained obtained without phase shifting. The SNR is presented in dB and each value corresponds to a fixed number of photons. For N incident photons the optical SNR is N, so the electrical signal to noise is N, so that 60dB corresponds to 106 measured photons. Values below the peak value are scaled appropriately, so have proportionately worse SNR values. The V(z) curves were sampled at intervals of 8 nm, The optical signal to noise ratio is defined as:

SNRopticalsignal=(SNRelectricalsignal)2=μ2σ2
(7)

where μ is the mean value and σ2 is the variance, the ratio thus gives the signal to noise ratio. Monte Carlo simulations were carried out over 106 cases. Standard derivation (S.D. in degrees) between the mean plasmonic angle (noiseless case) and the plasmonic angle recovered from the three methods (noisy cases) were determined in order to compare performance of each method as shown in Figs. 8(a)
Fig. 8 (a) Mean standard deviation in degrees versus SNR level in dB for single ripple measurements and half ripple measurement for phase stepping. Solid black is for 1 ripple phase stepping measurement, dashed black for 1 ripple period measurement, dotted black for 1 ripple FFT measurement and solid blue for half ripple phase stepping measurement. (b) Mean standard deviation in degrees versus SNR level in dB for first three ripple measurements. Solid black curve is for 3 ripples phase stepping measurement, dashed black curve is for 3 ripples period measurement, dotted black for 3 ripples FFT measurement.
and 8(b). It may, of course, be argued that in many situations the noise is not shot noise limited, nevertheless, the relative performance between the different methods is retained provided each method is subject to a similar noise models. Our general conclusions are therefore valid for other independent noise processes.

We now apply the Monte Carlo method to evaluate the signal to noise of our experimental measurement. The experimental results of Fig. 6 shows straight line fits to ϕ(z) obtained from the experimental curves of Fig. 5. We estimated the noise in the ϕ(z) curves for different noise levels in V(z) curves. We then selected those curves that gave the same variance of the deviation from the straight line as obtained in the experimental measurements presented in Fig. 6. We then used the Monte Carlo simulation with similar noise levels and sampling intervals to estimate the expected variations in ϕ(z) and the corresponding errors in the measurement of film thickness. Probability distributions of the variation in the measured thickness values were obtained by running the Monte Carlo simulation 50,000 times. These probability distributions are shown in Fig. 9
Fig. 9 Probability density function (pdf) of variation from expected value for ½ ripple period phase stepping measurement (blue), 1 ripple period phase stepping measurement (green), 2 ripple periods phase stepping measurement (red) and 3 ripple periods phase stepping measurement (cyan). These results were simulated with the noise level corresponding to the experimental results shown in Fig. 6. The ½, 1, 2 and 3 ripples are equivalent to 375 nm, 750 nm, 1,500 nm and 2,250 nm in z defocus distance respectively.
for different ranges of measurement defocus. The first thing to notice is that the phase stepping approach recovers film thicknesses with well-defined values even when the underlying measurements are relatively noisy. As expected when we extend the range over which the measurement is made the uncertainty decreases. This is presented in Table 1

Table 1. Standard deviation (S.D.) of the measurement error for the defocus ranges presented in Fig. 9

table-icon
View This Table
which shows the standard deviation of the measurement error for the defocus ranges presented in Fig. 9. There is a considerable reduction in measurement uncertainty with increasing defocus range; this improvement arises partly from the better signal to noise expected when more data points are included and also from the fact that a larger measurement range gives superior performance when measuring the gradient of a line. Doubling the measurement range reduces the variance by a factor of greater than 6 which is considerably better than the value of 2 expected from considerations of signal to noise alone.

5. Measurement of SP propagation length

In Fig. 10(a), the green curve shows the measurements obtained by the direct method and the red curve shows the measurements obtained by the indirect method. The calculated attenuation is shown by the fitted curve. Figure 10(b) shows the comparison of the attenuation values between the 29nm and 46nm gold layer. The results demonstrate clearly that the 29nm gold layer provides higher attenuation than the 46nm case. Figure 10(c) shows values of attenuation obtained for different thicknesses of gold (which affects the attenuation strongly) by using the direct and indirect methods. The simulation results are shown on the black curve. We can see, as may be expected, that the direct method shows a smaller variance around the fitted values, nevertheless, both measurements show a similar trend. The standard deviations from the third order fits are smaller for the direct method (1.09 microns) compared to the indirect method (1.63 microns) as shown in Fig. 10(c). This suggests that better measurement precision is obtained with the direct method, provided the fitted curve can be taken as a reasonable reference point. The measurement of attenuation of SP can therefore be obtained using pupil function engineering.

It is clear that the error in the attenuation measurement is far greater compared to the measurement of the real part of the wave number. Indeed similar observations were made in the measurement of velocity and attenuation of surface acoustic waves using the V(z) method in the scanning acoustic microscope, where relative accuracy of around 1 part in 103 was obtained for the measurement of velocity but ‘a few’ per cent for attenuation [10

10. J. Kushibiki and N. Chubachi, “Material characterization by line-focus-beam acoustic microscope,” Trans. Sonics Ultrason. 32(2), 189–212 (1985). [CrossRef]

].

6. Conclusions

Acknowledgments

The authors gratefully acknowledge the financial support of the Engineering and Physical Sciences Research Council (EPSRC) for a platform grant, ‘Strategies for Biological Imaging’, the UK and China Scholarship Council (CSC) for Bei Zhang’s Scholarship. We thank Dr. Darren Albutt for his help in the sample thickness measurement.

Reference and links

1.

B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express 20(7), 7388–7397 (2012). [CrossRef] [PubMed]

2.

B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express 20(27), 28039–28048 (2012). [CrossRef] [PubMed]

3.

E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Zeitschrift Fur Naturforschung Part a-Astrophysik Physik Und Physikalische Chemie A , 23(12), 2135 (1968).

4.

H. Kano, S. Mizuguchi, and S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B 15(4), 1381–1386 (1998). [CrossRef]

5.

M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “High-resolution scanning surface-plasmon microscopy,” Appl. Opt. 39(34), 6279–6287 (2000). [CrossRef] [PubMed]

6.

M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “Optical V(z) for high-resolution 2pi surface plasmon microscopy,” Opt. Lett. 25(11), 823–825 (2000). [CrossRef] [PubMed]

7.

S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: resolution, sensitivity and crosstalk,” J. Microsc. 246(3), 287–297 (2012). [CrossRef] [PubMed]

8.

F. Argoul, T. Roland, A. Fahys, L. Berguiga, and J. Elezgaray, “Uncovering phase maps from surface plasmon resonance images: Towards a sub-wavelength resolution,” C. R. Phys. 8(8), 800–814 (2012). [CrossRef]

9.

L. Berguiga, S. Zhang, F. Argoul, and J. Elezgaray, “High-resolution surface-plasmon imaging in air and in water: V(z) curve and operating conditions,” Opt. Lett. 32(5), 509–511 (2007). [CrossRef] [PubMed]

10.

J. Kushibiki and N. Chubachi, “Material characterization by line-focus-beam acoustic microscope,” Trans. Sonics Ultrason. 32(2), 189–212 (1985). [CrossRef]

OCIS Codes
(060.4080) Fiber optics and optical communications : Modulation
(110.0110) Imaging systems : Imaging systems
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(180.0180) Microscopy : Microscopy

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: February 22, 2013
Revised Manuscript: April 10, 2013
Manuscript Accepted: April 14, 2013
Published: May 3, 2013

Virtual Issues
Vol. 8, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Bei Zhang, Suejit Pechprasarn, and Michael G. Somekh, "Quantitative plasmonic measurements using embedded phase stepping confocal interferometry," Opt. Express 21, 11523-11535 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11523


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References

  1. B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express20(7), 7388–7397 (2012). [CrossRef] [PubMed]
  2. B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express20(27), 28039–28048 (2012). [CrossRef] [PubMed]
  3. E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Zeitschrift Fur Naturforschung Part a-Astrophysik Physik Und Physikalische Chemie A, 23(12), 2135 (1968).
  4. H. Kano, S. Mizuguchi, and S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B15(4), 1381–1386 (1998). [CrossRef]
  5. M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “High-resolution scanning surface-plasmon microscopy,” Appl. Opt.39(34), 6279–6287 (2000). [CrossRef] [PubMed]
  6. M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “Optical V(z) for high-resolution 2pi surface plasmon microscopy,” Opt. Lett.25(11), 823–825 (2000). [CrossRef] [PubMed]
  7. S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: resolution, sensitivity and crosstalk,” J. Microsc.246(3), 287–297 (2012). [CrossRef] [PubMed]
  8. F. Argoul, T. Roland, A. Fahys, L. Berguiga, and J. Elezgaray, “Uncovering phase maps from surface plasmon resonance images: Towards a sub-wavelength resolution,” C. R. Phys.8(8), 800–814 (2012). [CrossRef]
  9. L. Berguiga, S. Zhang, F. Argoul, and J. Elezgaray, “High-resolution surface-plasmon imaging in air and in water: V(z) curve and operating conditions,” Opt. Lett.32(5), 509–511 (2007). [CrossRef] [PubMed]
  10. J. Kushibiki and N. Chubachi, “Material characterization by line-focus-beam acoustic microscope,” Trans. Sonics Ultrason.32(2), 189–212 (1985). [CrossRef]

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