1. Introduction

With the introduction of differential white-light spectral interferometry [1, 2] to label-free surface plasmon resonance (SPR) biosensing, we had expanded the dynamic range of SPR phase measurement to 1 × 10⁻² refractive index unit (RIU) and achieved refractive index resolution (RIR) of 2.2 × 10⁻⁷ RIU which is comparable to most laser based interferometric SPR systems [3–5]. Our “wide-dynamic range” is confined to the context of addressing the drawback of fixed incident-angle laser-based SPR phase measurement systems. However, the best RIR reported on SPR phase detection was up to 10⁻⁹ RIU [6] and those with 10⁻⁸ RIU [7, 8] are readily found in the literature. A recent review [9] explicitly listed the performance comparison between various SPR sensing schemes so it is believed that the combination of spectral interrogation with phase detection is the essential advancement for wide dynamic range highly sensitive SPR sensing.

However, there are two essential conditions for the SPR phase to be computed correctly, 1) the unwrapped phase must be continuous [10] and 2) the acquired interferogram should have good signal-to-noise ratio. The first requirement enables automated phase unwrapping [11] which is used to compute the true phase value, whereas the second requirement ensures that only sinusoidal signal is being processed. However, at optimal SPR coupling condition, there is an inherent difficulty in fulfilling these two requirements. The phase jump at the optimal wavelength is so sharp that the spectral phase itself becomes a discontinuity. Secondly, this is always accompanied by the most diminished reflection intensity so the recorded spectral interferogram is always overwhelmed by background noise. Thus, the issue becomes dilemmatic, as on one hand it is desirable to go for the highest RIR with optimal SPR coupling condition but on the other hand it is impossible to retrieve the correct SPR phase value.

In this paper, we propose a novel approach to alleviate the SPR phase measurement problem by introducing a temporal carrier to a common-path spectral interferometer, so that the ultimate refractive index resolution of our system may be significantly improved.

2. Theoretical investigation

To examine the theoretical ultimate RIR of the prism/gold/dielectric SPR system, we implemented the propagation matrix formulation [12] with numerical computation in MATLAB. RIR is wavelength dependent [2] and generally defined as

Table 1. Parameters and materials used for numerical calculation of ultimate RIR.

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Numerical phase responses of three different gold thicknesses, i.e. 48.0 nm, 51.6 nm and 53.4 nm are plotted in Fig. 1(a). The respective RIR were calculated with 1 × 10⁻⁴ RIU increment from 1.3300 to 1.3700 which corresponds to dynamic range of 4 × 10⁻² RIU and the numerical results are shown in Fig. 1(b). By observation of Fig. 1(a), the thickness of 51.6 nm produced the best SPR coupling condition so that it generates a phase discontinuity with sharp jump at the wavelength of 667.70 nm. On the contrary, while the thicknesses deviated from the optimal value, the phase response becomes moderate and continuous. As indicated by Fig. 1(b), the optimal thickness also produces RIR up to 1 × 10⁻⁸ RIU which is one order of magnitude better than those with less favorable values. This is in good agreement with our estimation and the predicted ultimate RIR is very encouraging.

 

Fig. 1 (a) Theoretical spectral phase response of a typical prism/gold/dielectric system with different gold thicknesses. The 51.6 nm gold layer produces the sharpest phase jump in comparison with those of 48.0 nm and 53.4 nm; (b) The theoretical refractive index resolution of the three layer system computed using parameters listed in Table 1 and the 51.6 nm gold produces the highest RIR.

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With regards to common-path SPR spectral interferometry, the spectral oscillation is introduced by the optical path difference (OPD) between the p- and s- polarizations traversing the system. Thickness of the birefringent crystal determines the OPD. According to our experience, the maximum OPD resolvable by the spectrometer is 140 microns. Using yttrium vanadate (YVO₄) crystal with birefringence of 0.24 to 0.21 from 532 nm to 808 nm, the thickness of crystal is designed and fabricated as 620 μm. In the case of SPR phase discontinuity, i.e. 51.6 nm of Fig. 1(a), it is impossible to unwrap the true spectral phase due to sign ambiguity [10, 11]. Therefore, we add the temporal carrier so that the phase computation and unwrapping can be performed in the time domain. To generate the temporal carrier, a liquid crystal (LC) modulator is introduced and aligned with the interferometric path. Half wave retardation between the two polarizations is achieved by the LC modulator at prescribed frequency. As the result, the spectral-temporal intensity recorded by each CCD pixel of the spectrometer can be expressed as

3. Experimental configuration

3.1 Experimental setup

A schematic of our setup is shown in Fig. 2. A 20W warm white light emitting diode was temperature controlled to ensure spectral stability. A broadband linear polarizer was the first element of the common-path interferometer. A swift liquid crystal variable retarder was aligned with the polarizer and synchronized with the prescribed sinusoidal wave to introduce the temporal carrier of 1 kHz. The spectrometer was configured with 0.05 nm resolution and integration time of 50 µs. An YVO₄ birefringent crystal was used to generate sufficient retardation between the two polarizations. A N-BK7 right-angle prism with 52 nm experimental thick gold coating was employed as the SPR couplers. The standard deviation of gold thickness was found to be ± 0.4 nm. A customized Teflon flow chamber was brought into contact with the gold film and the estimated sensing area was about 10 mm². Another piece of polarizer was used to recombine the two polarizations emerging from the SPR prism and the spectral-temporal signal was collected with the spectrometer operating in synchronized mode. To fulfill the isothermal requirement, all optical components and reagents were thermally shielded with an enclosure. A radiator was placed in proximity to the flow cell and a high precision temperature controller was used to stabilize the temperature to ± 0.005 °C for 24 hours prior to the experiment.

 

Fig. 2 Schematic of the common-path SPR spectral interferometer with the liquid crystal modulator which is synchronized with a prescribed sinusoidal reference signal to generate the temporal carrier and T.C. is the temperature controller.

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3.2 Verification of system performances

To demonstrate both high sensitivity and wide dynamic measurement range of the system, RIR was tested using minor change of sodium chloride (NaCl) solutions in a wide range of concentrations, i.e. from purified de-ionized water to 0.1% NaCl. Then the concentration changed from 2%, 6%, 7%, 8%, 12%, 14%, 15%, 18% to finally 19% with 0.1% increment between each step. Total of 10 trials were preformed. The solutions were obtained by repeated dilution and they were kept in sealed bottles with the interferometer before the experiment. The corresponding refractive index range was approximately 1.3333 to 1.3648 RIU [16] and the RIU changed from 1 × 10⁻⁴ to 3.15 × 10⁻² covering more than two orders of magnitude. To monitor the experimental phase fluctuation, purified de-ionized water was injected into the probe cell and the spectral phase is continuously measured over a period of 1 hour. The phase standard deviation was found to be 1.75 × 10⁻⁴ radian (approximately 0.01 degree).

4. Results and discussion

To demonstrate the phase discontinuity, the normalized spectral interferogram at optimal SPR coupling condition with 7% sodium chloride solution is shown in Fig. 3(a). It is obvious that at the optimal wavelength, fringe visibility becomes zero and the local interferogram, i.e. at 668.0 nm, is overwhelmed with background noise. So it is impossible to compute the spectral phase correctly using the same method previously described [1, 2]. On the other hand, we are able to collect the temporal waveform of 668.6 nm as indicated with arrow via the carrier technique. Our experimental result in Fig. 3(b) shows the normalized temporal waveform of 15 milliseconds. Although it is mixed with random noise, the sinusoidal carrier is still observable. When the NaCl concentration is increased to 7.1% (0.1% NaCl concentration difference), which corresponds to refractive index change of approximately 1.764 × 10⁻⁴ RIU, the normalized temporal wave of the same wavelength is shown in Fig. 3(c). After averaging all the temporal waveforms in the duration of one second and applying band-pass filter with a Hamming window from 0.998 to 1.002 kHz with fast Fourier transform (FFT), we retrieved the smoothed waveforms of 668.6 nm with 0.1% concentration change as shown in Fig. 3(d). It is obvious that the initial phase of the temporal waveform had significantly shifted upon the minor change of NaCl concentration. Phase computation is rather straightforward and we determined the phase change as 1.6643 radians at 668.6 nm. Using Eq. (2), we calculated the RIR to be approximately 2 × 10⁻⁸ RIU which is an order of magnitude improvement over our previous setup.

 

Fig. 3 (a) Experimental SPR spectral interferogram obtained with gold thickness of 52 ± 0.4 nm and 7% NaCl concentration, the reduced fringe visibility at the optimal wavelength about 668.0 nm is evident and the arrow indicates 668.6 nm with better signal; (b) Temporal waveform of 668.6 nm obtained with the carrier operating at 1 kHz; (c) With increment of the NaCl concentration by 0.1% to 7.1%, the temporal waveform shows phase shift; (d) After averaging and low-passed filtering, the reconstructed temporal waveform before and after 0.1% NaCl concentration change.

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To further demonstrate the wide dynamic measurement range, we performed the similar test with other concentrations. For each NaCl concentration change, a 0.1% increment was added to determine the RIR at each step. With the change of NaCl concentration, the SPR coupling wavelength shifts towards infrared, i.e. from 645.2 nm, 653.4 nm, 661.1 nm, 668.0 nm, 675.2 nm, 689.1 nm, 694.3 nm, 696.0 nm, 704.8 nm, to 707.5 nm finally. This is clearly shown in Fig. 4(a). As NaCl concentration changed from 7% to 19%, the optimal coupling wavelength changed from about 668.0 nm to approximately 707.5 nm. It is obvious that the fringe visibility at the optimal wavelengths is virtually zero. Using the temporal carrier, RIR was estimated over the whole dynamic range as shown in Fig. 4(b). Our system achieved 7 × 10⁻⁸ RIU for 0.1% to 2% NaCl concentration, it reached 4 × 10⁻⁸ RIU at 6%, then it became 2 × 10⁻⁸ RIU at 7% and 8%, after that the RIR decreased gradually from 3.5 × 10⁻⁸ RIU at 12% to 8 × 10⁻⁸ RIU at 19% finally. Generally, this is in good agreement with the theoretical calculation of Fig. 1(b) in which the RIR changes gradually from 2.5 × 10⁻⁸ RIU to the maximum of 1 × 10⁻⁸ RIU, then decreases steadily upon further refractive index increment. However, our experimental RIR is still less than the theoretical value and there are two reasons, 1) the experimental phase values were obtained from the adjacent wavelength where the phase change is less than those of the champion wavelength, 2) experimental thickness of our gold film was measured to be 52 ± 0.4 nm instead of 51.6 nm as used in the simulation.

 

Fig. 4 (a) Spectral interferograms of 7% and 19% sodium chloride solution shows that the optimal SPR coupling condition shifts towards infrared with increase of refractive index and our measurement range is able to follow the large RIU variation; (b) Estimated RIR of our system within the entire dynamic range of measurement.

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5. Conclusions

We have presented a novel common-path phase-sensitive surface plasmon resonance biosensor with temporal carrier modulation. It combines both wide dynamic measurement range and high detection sensitivity in a simple optical setup. To the best of our knowledge, this is the first time that a feasible solution is proposed to resolve the SPR spectral phase discontinuity for sensing applications. The scheme employs a liquid crystal modulator so that the differential spectral SPR phase information is acquired in the time domain. We have also experimentally demonstrated the wide dynamic range with sodium chloride solution of various concentrations and the detection limit is estimated from 2 × 10⁻⁸ to 8 × 10⁻⁸ RIU in a measurement range of 3 × 10⁻² RIU. Yet, the new optical setup supersedes its Michelson counterpart in term of simplicity, so we believe this is a significant contribution for practical SPR biosensing applications.