## Quantitative plasmonic measurements using embedded phase stepping confocal interferometry |

Optics Express, Vol. 21, Issue 9, pp. 11523-11535 (2013)

http://dx.doi.org/10.1364/OE.21.011523

Acrobat PDF (1491 KB)

### 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

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]

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

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]

*V(z)*response which is proportional to the field amplitude detected as a function of defocus,

*z*. In all previous publications, however, we have used only the amplitude of the confocal or interference signal, although this has considerable advantage compared to the output from a non-confocal system, extraction of the SP phase confers even greater benefits. This measurement can be effected using the spatial light modulator which allows us to configure the confocal instrument as a phase stepping interferometer. Argoul

*et al.*[8

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]

*V(z)*signal), which is the measure obtained when a reference beam is applied to the whole returning field. There is therefore a major distinction between an interference system where the reference beam interferes with all the returning signal and the ‘embedded’ interferometer where the plasmonic and nonplasmonic contributions are interfered with each other. We will elaborate on this point in more detail below. We demonstrate that compared to an amplitude only measurement phase measurement gives much better performance in terms of immunity to noise and lateral resolution.

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]

*k-*vector to be extracted which can, of course, be equated to the phase velocity and attenuation of the SPs.

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]

*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: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,

*θ*denotes the incident angle for excitation of SPs, and

_{p}*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 is

*Δz*as:so that the relative phase changes by

*2π*with a period given by:This

*2π*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

*θ*from which the real part of the wave number of the SPs (

_{p}*V(z)*curves are presented in Fig. 2 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]

*|**V(z)*

*|**is measured. The*

^{2}

*|**V(z)*

*|**curve can be obtained by mechanical scanning of the sample in the axial direction [1*

^{2}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]

*|**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]

*|**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

**20**(27), 28039–28048 (2012). [CrossRef] [PubMed]

**20**(27), 28039–28048 (2012). [CrossRef] [PubMed]

## 3. Beam profile modulation in the back focal plane

*θ*can be recovered. The red curve in Fig. 3 shows a typical pupil function imposed on the back focal plane, where the angles around normal incidence and

_{p}*θ*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

_{p}**20**(27), 28039–28048 (2012). [CrossRef] [PubMed]

*|**V(z)*

*|**curve subject to different relative phase shifts imposed by the spatial light modulator,*

^{2}*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

## 4. Phase stepping to obtain the plasmon angle, *θ*_{p}

_{p}

*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. 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).**

*|*

*|**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:

*θ*is a phase constant accounting for the offset phase between sample and reference. The slope of the unwrapped phase is thus:By measuring the slope of the fitted line, we can therefore calculate the plasmonic angle

_{p}*θ*.

_{p}*φ(z)*for a bare gold layer and a layer with an additional deposited layer of indium tin oxide (ITO). We can see that for positive defocus, that is the sample and objective are separated by more than the focal length (see Fig. 1) there is little systematic difference between the response for the two layers. For negative defocus close to the focal position the change

*φ(z)*curve shows an irregular form, which is clearly not linear. This arises principally because the reference beam cannot be regarded as being a simple linear function as assumed in Eq. (3). Aberration in the lens and possibly the finite number of pixels in the SLM means that the defocus value before the slope is linear is somewhat increased. At larger defocus the unwrapped phase shows a linear form which relates to the value of

*θ*. The values of

_{p}*θ*obtained for the bare layer and coated layers are 43.48 deg. and 46.39 deg. respectively, which correspond to a thickness of 13.4 nm of ITO assuming a refractive index of 1.858. We also measured the thickness value of the ITO with a commercial ellispometer (alpha-SE J. A. Woollam (Inc)) and obtained a value of 11

_{p}*nm*± 2.3

*nm*. The strength of our method for measuring the value of

*θ*arises from several factors (i) the region of defocus where accurate measurements can be obtained is readily observed from the linearity of

_{p}*φ(z)*where the periods of

*V(z)*are stable, (ii) the method uses all the data points in the measurement range thus optimizing the signal to noise ratio and (iii) while clearly the signal to noise ratio improves as the defocus range increases a reliable measurement can be obtained over a very small region of defocus corresponding to less than

*Δz*of Eq. (3). Such a measurement range is not practical if one measures the amplitude only the

_{p}*V(z)*curve without phase stepping. In the next section we compare by simulation the immunity to measurement noise of different processing methods. It demonstrates clearly that the present method is very stable and robust compared to methods used without phase stepping. We reiterate that

*φ(z)*refers to the phase of the SPs rather than the

*V(z)*. In the next section we consider the noise performance of different processing strategies and also show how even the relatively noisy measurements in Fig. 5 lead to well defined measurements of film thickness.

*θ*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

_{p}*Δz*was calculated by averaging the first few ripples as shown in Fig. 7(a) and then the plasmonic angle

*θ*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

_{p}*Δz*was determined from Fourier transform of the windowed pattern of ripples. Details of the phase stepping measurement have been described above.

*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 that 60dB corresponds to 10

^{6}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:

*μ*is the mean value and

*σ*is the variance, the ratio thus gives the signal to noise ratio. Monte Carlo simulations were carried out over 10

^{2}^{6}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) 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.

*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 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 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

*V(z)*measurement where only those angles close to

*θ*are allowed to pass through the system; in other words the reference beam shown in Fig. 3a is blocked. If the phase is not required, there is no need for a reference beam. The detected

_{p}*z.*These curves are then fitted to an exponential function

*Aexp*(-

*Bz*) which allows the attenuation to be obtained. Then the SP propagation length

*l*is obtained from the recovered value of

_{p}*B*using calculated

*V(z)*method in the scanning acoustic microscope, where relative accuracy of around 1 part in 10

^{3}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

## Reference and links

1. | B. Zhang, S. Pechprasarn, J. Zhang, and M. G. Somekh, “Confocal surface plasmon microscopy with pupil function engineering,” Opt. Express |

2. | B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express |

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 , |

4. | H. Kano, S. Mizuguchi, and S. Kawata, “Excitation of surface-plasmon polaritons by a focused laser beam,” J. Opt. Soc. Am. B |

5. | M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “High-resolution scanning surface-plasmon microscopy,” Appl. Opt. |

6. | M. G. Somekh, S. G. Liu, T. S. Velinov, and C. W. See, “Optical |

7. | S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: resolution, sensitivity and crosstalk,” J. Microsc. |

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. |

9. | L. Berguiga, S. Zhang, F. Argoul, and J. Elezgaray, “High-resolution surface-plasmon imaging in air and in water: |

10. | J. Kushibiki and N. Chubachi, “Material characterization by line-focus-beam acoustic microscope,” Trans. Sonics Ultrason. |

**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

Sort: Year | Journal | Reset

### References

- 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]
- B. Zhang, S. Pechprasarn, and M. G. Somekh, “Surface plasmon microscopic sensing with beam profile modulation,” Opt. Express20(27), 28039–28048 (2012). [CrossRef] [PubMed]
- 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).
- 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]
- 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]
- 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]
- S. Pechprasarn and M. G. Somekh, “Surface plasmon microscopy: resolution, sensitivity and crosstalk,” J. Microsc.246(3), 287–297 (2012). [CrossRef] [PubMed]
- 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]
- 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]
- J. Kushibiki and N. Chubachi, “Material characterization by line-focus-beam acoustic microscope,” Trans. Sonics Ultrason.32(2), 189–212 (1985). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.