Two integrated Young’s interferometer (YI) sensors based on long-range surface plasmon polariton (LRSPP) waveguides are presented. The first sensor is single-channel and based on a Y-junction splitter, and the other is multi-channel and based on a corporate feed structure. The multichannel YI enables simultaneous and independent phase-based monitoring of refractive index changes in multiple channels. The diverging output beams from the waveguides are overlapped in the far field to form interference patterns which are then post-processed using the fast Fourier transform (FFT) algorithm to extract phase values. The sensing capability of these YIs was demonstrated through sequential injection of solutions with increasing refractive index into the sensing channels. A detection limit of ∼ 1 × 10−6 RIU was obtained for both LRSPP based YIs, a significant improvement over measurements from similar structures using attenuation-based sensing.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Interferometry has been demonstrated as among the most sensitive optical interrogation methods available for label-free biosensing applications.  Numerous works on optical fiber interferometers have been reported, [2–5] but integrated waveguides are more compact, mechanically stable and can be mass-produced in planar technology. Besides, waveguide interferometers are less influenced by effects such as temperature variations and mechanical vibrations because the waveguides are usually located very close to each other and subject to similar perturbations.  Integrated waveguide interferometers can generally be classified into various groups according to their configuration, namely Mach-Zehnder , Young , Fabry-Perot , differential , dual polarization , and bimodal waveguide . The interferometric sensors usually have at least one sensor arm which interacts with the sample of interest and a reference arm which is either insulated from the environment or interacts with a reference/control sample. Any change of the sample on the sensing channel shifts the phase of the sensing beam compared to the reference arm.
The first demonstration of an integrated Young’s interferometer (YI) biosensor based on dielectric waveguides was reported in 2000 , where the two beams from a single-channel Y-junction were superimposed to produce interference fringes at the detector. The adsorption of molecules was indicated by a lateral shift of the interference fringes. Similar YI biosensors were presented by other research groups [8, 14, 15]. There are also reports of multichannel integrated YIs based on dielectric waveguides [16, 17]. In this work, we report multichannel integrated YI biosensors based on plasmon waveguides implemented as gold stripe geometrical structures which support the propagation of long-range surface plasmon polaritons (LRSPPs) for high-sensitivity. Advantageously, gold is not too reactive yet presents a highly suitable surface for chemical functionalization on which, e.g., a well-packed self-assembled monolayer of alkanethiol can be formed via incubation . Furthermore, gold is also suitable for toposelective functionalization using electrochemical techniques .
Surface plasmon polariton (SPP) based biosensors are very sensitive, compact, label-free and provide real-time responses. SPPs are transverse-magnetic electromagnetic waves propagating along a metal-dielectric interface . Various methods have been introduced to excite SPPs, such as prism-based configurations  or gratings . LRSPPs, which have a symmetrical electric field distribution along the metal-dielectric interfaces, propagate along thin metal stripes embedded in dielectric, allowing the design of various integrated plasmon devices . Integrated structures operating with LRSPPs such as Y-junctions, S-bends, and couplers can be excited by butt-coupling to an optical fibre  or via grating coupling .
Recently, plasmonic interferometry has attracted increasing interest for refractive index sensing [26,27] and medical imaging . Mach-Zehnder refractometric sensors using LRSPP waveguides were realised [29–31], and although highly sensitive, the performance of the sensors were affected by imperfect input coupling and fabrication defects in the structure. Previously, Y-junction  and multichannel  waveguides have been demonstrated to perform bulk and protein sensing through intensity interrogation. We build on this work, as well as work on multichannel YI sensors implemented in dielectric waveguides , to demonstrate the ability of LRSPP waveguides to act as high sensitivity multichannel YI sensor.
2. Principle of operation
A YI operates based on the generation of an interference pattern created by overlapping two or more coherent light beams. In this paper, the divergent output beams of multichannel LRSPP waveguides overlap with one another to form an interference pattern. When there are more than two output beams, the final interference pattern is a superposition of individual interference patterns due to the overlapping of divergent beams of a specific waveguide pair.
Two LRSPP biosensors, namely the Y-junction and corporate-feed multichannel biosensors, were implemented as YI devices in this work. The LRSPP waveguide used in both biosensors consists of a thin Au stripe 5 μm wide and 35 nm thick embedded in optically-infinite CYTOP claddings (a fluoropolymer with a refractive index close to that of biologically compatible fluids). The structure supports a single long-range mode (LRSPP), and its modal properties on this waveguide can be found in our previous work [33,34], but are summarised here for convenience: the effective index of the LRSPP is neff = 1.338 + j1.71 × 10−4, its mode power attenuation is MPA = 7.1 dB/mm, and its diameter is 7 μm (the mode profile is approximately circular). The whole structure is supported by a silicon wafer. The linear length of the Y-junction structure is 3.5 mm and the corporate-feed multichannel waveguide is 4.6 mm long. The length of the fluidic channels which define the sensing regions are 1.65 mm in all cases.
The Y-junction waveguide as shown in Fig. 1 is a single-channel Young interferometer. A fluidic channel is defined over one arm of the Y-junction by etching the top cladding to expose the surface of the Au stripe. The other arm remains cladded and acts as a reference channel. When there is a refractive index change in the sensing channel (due to a change in the bulk index of the sensing fluid or to the formation of a biochemical adlayer on the waveguide), a spatial shift Δx along the camera surface will occur in the interference pattern.
Figure 2 shows the corporate-feed multichannel structure, which has four sensing channels defined by etches on waveguides 1, 2, 5 and 6, along with two reference channels as the cladded waveguides 3 and 4. The corporate feed structure is formed by cascading two Y-junction splitters to a first Y-junction structure. A pair of couplers are implemented on each branch of the first Y-junction to obtain a small amount of power for referencing purposes. The distance between each waveguide pair (ith and jth channels) and the end facet dij is different so that the output beams from these channels will have different optical path lengths at the interfering position. Each spatial frequency kij will correspond to interference between the waveguide pair separated by dij producing a distinct peak in the amplitude plot of the Fourier-transformed interference pattern. As a result, the corresponding phase difference Δφij between each waveguide pair can be extracted independently from other waveguide pairs. The distances between the six output channels are d12 = d56 = 40 μm, d23 = 74 μm, d34 = 44 μm, and d45 = 72 μm. The distances d12 and d56 were selected to be the same to produce equal power splitting in these Y-junctions. To ensure negligible bend losses, S-bend structures with bend radii between 4 and 5 mm were used to separate the output waveguides . There are 13 possible spatial frequencies corresponding to 13 different combinations of distances between waveguide pairs. Our corporate-feed YI has two reference channels, which adds redundancy (reliability), which will assist in compensating drifts in the set-up .
In general, the irradiance distribution of the interference pattern at the interfering position can be written as Eq. (1) is modulated by the intensity profile of the waveguide outputs a(x), which can be approximated by a Gaussian distribution . Thus, the resulting distribution is given by
The phase difference Δφij is written for bulk sensing:29].
In the case of our corporate-feed YI shown in Fig. 2(a) (N = 6), waveguides 1, 2, 5 and 6 are the sensing channels and waveguides 3 and 4 are the reference channels. When a sensing solution is introduced into the sensing channels, the phase changes, Δφ13, Δφ14, Δφ23, ΔΦ24, Δφ35, Δφ45, Δφ36 and Δφ46, will be of interest.
Our first experimental setup is illustrated in Fig. 3(a). A semiconductor laser diode operating at the wavelength of 1310 nm with TM polarization was butt-coupled into the input of the LRSPP waveguides via a polarization-maintaining single-mode optical fibre (PM-SMF). Initially, a microscope objective was placed such that its focus was located on the output end facet, such that individual outputs from the waveguides can be easily distinguished, as shown in Figs. 1(a) and 2(a). Then the distance L between the chip end facet and the objective lens was slowly increased until the output divergent beams overlapped one another on the front side of the microscope objective. The collimated interference pattern thus produced was directed to an infrared camera (7290A, MicronViewer) and captured using frame-grabber software (LBA-710PC, Ophir Spiricon). The recorded interference pattern was then analysed using a MATLAB script exploiting a fast-Fourier transform (FFT) routine. The spatial frequencies of waveguide pairs show up as different peaks in the amplitude plot of the fast-Fourier-transformed interference pattern. The phase difference between each waveguide pair was taken as the phase of the spectral coefficient at the corresponding spatial frequency (Eq. (2)).
An improvement to the setup to increase the spatial frequency resolution was made by inserting a plano-convex lens (f = 60 mm, NA = 0.21, Edmund Optics) between the microscope objective and the camera, as shown in Fig. 3(b). The outputs from the chip were first magnified and collimated using the 20× objective. The plano-convex lens was inserted after the objective to force the magnified and collimated beams to diverge and overlap on the detector of the camera. The distance between the focal length of the plano-convex lens and the detector of the camera is set to L = 11 cm so that all spatial frequencies of the corporate-feed multichannel YI could be uniquely identified. The interference patterns were recorded using the frame-grabber software and post-processed using MATLAB.
4. Results and discussion
The calculated interference patterns for our Y-junction YI and our corporate feed YI along the detection surface are plotted in Figs. 4(a) and 4(b), respectively. The intensity was computed using Eq. (2) by considering identical output powers from all channels and no refractive index differences between the channels (Δφij = 0). The influence of the limited aperture of the waveguide is approximated by a simple Gaussian model a(x) following the field intensity distribution of the fundamental mode supported by an optical fiber, illustrated as the dashed curves in Figs. 4(a) and 4(b).
The spectral magnitude and phase of the interference pattern can be determined by Fourier transforming the intensity distribution described by Eq. (1):Appendix). The first term in Eq. (5) is the DC component which represents the average amplitude across the interference pattern. The transform produces a mirror copy of peaks in the magnitude plot which represents the number of unique spatial frequencies. The magnitude plots for the Y-junction and the corporate-feed multichannel YIs are shown in Fig. 5. The fundamental frequency of the transform was circular-shifted and zero-centered for ease of visualization . The theoretical result was obtained by fast Fourier transform (FFT) of the computed intensity distributions shown in Fig. 4, whereas the experimental magnitude plots were Fourier-transformed from the interference patterns captured using the setup illustrated in Fig. 3(b) (and discussed further below). The spectral frequencies in Fig. 5 were normalized to facilitate comparisons in the relative position of the theoretical and experimental spectral frequencies. The phase differences Δφij can be extracted from the phase part of the Fourier coefficients at specific spatial frequencies identified from the magnitude plot. The phase values correspond to the phase difference between waveguide pairs.
To demonstrate the sensing capability of our YIs, bulk sensing experiments were conducted at an operating wavelength of λ0 = 1310 nm, where the sensing channels of the YIs were injected with solutions of different refractive index and the corresponding phase differences were measured. A microfluidic jig, as discussed previously , was integrated into the setup to allow the continuous flow of solutions over the sensing channels. Solutions of a different refractive index were prepared by adjusting the percent concentration by mass (w/w) of distilled deionized water (DDI H2O) and glycerol (Gly). The range of refractive index was selected to be slightly above that of CYTOP (n = 1.3348) to reduce the intensity of the background light at the waveguide outputs.
First, three solutions ranging in refractive index from nc = 1.336 to 1.340 in steps of Δnc = 2 × 10−3 were injected sequentially into the fluidic channel of the Y-junction YI using the setup shown in Fig. 3(a), and the interference patterns were recorded at 1s intervals. Each solution was injected again in reverse sequence to examine the repeatability of the experiment. The recorded interference patterns were post-processed by taking a horizontal cutline across the centre of each interference pattern and applying a 1D Fourier-transform to the extracted intensity distribution. The phase change over time thus obtained is plotted in Fig. 6(a) and noted to be noisy. Although the interference pattern is 1D (along x - see Eq. (1)) we applied a two-dimensional (2D) FFT to the recorded full interference patterns, and found that the noise in the signal was reduced significantly, as can be seen in Fig. 6(a). The 2D discrete Fourier transform for an N×M grid in x and y directions respectively is given by Eq. (6) is separable and can be modified to be Eq. (7) corresponds to the 1D Fourier transform across each row of the interference pattern. In other words, the 2D FFT is actually realized by a 1D FFT along each row, followed by a 1D FFT along each column. Compared to a one-dimensional cross-section, a 2D image provides more data points for analysis along with smoothing over imperfections or background noise in the pattern, caused, for example, by dust particles on the camera detector, or diffraction due to the glass faceplate in front of the camera’s detector.
Signal fluctuations due to fluid exchange are an important indicator in phase-based sensing to identify if a phase difference greater than 2π occurs due to the change in refractive index. If so, phase unwrapping must be performed to recover the actual phase difference. Using Eq. (4) and signal fluctuations observed during fluidic exchanges, the refractive index change Δnc = 2 × 10−3 corresponds to a phase difference greater than 2π. Thus, phase unwrapping is required to recover the full phase difference. Figure 6(b) plots the unwrapped relative phase difference due to the introduction of the three solutions (nc = 1.336, 1.338, and 1.340) into the sensing channel of the Y-junction YI. The phase difference for the case of the first solution injected was used as the baseline (zero reference) - the phase differences relative to this case are plotted. Similar phase differences were reproduced during the second cycle of solution exchanges. Ideally, there is no refractive index perturbation in the reference channel as different solutions are injected, so the refractive index difference between the waveguide pair (sensing, reference) is Δn12 = nc − 1.3348 where 1.3348 is the refractive index of CYTOP at λ0 = 1310 nm which clads the reference waveguide. From Eq. (4) we write for our Y-junction YI:
To determine the bulk sensitivity of the Y-junction YI, a series of eleven solutions in smaller steps (Δnc = 2×10−4) ranging from nc = 1.3370 to 1.3390 was prepared and injected sequentially into the fluidic channel. Due to the small refractive index step and the limited resolution of our commercial refractometer, two “stock solutions” with nc = 1.337 and nc = 1.339 were first prepared, then mixed according to ratio in volume using a pipette to produce the rest of the series. The refractive index values of the 2 stock solutions were verified by a prism-coupler based instrument (Model 2010, Metricon) to an accuracy of ±5 × 10−4. Figure 7(a) plots the phase difference over time for each solution, relative to the first one injected (used as the baseline). The range of solutions was selected to reveal more than one period (2π) of phase difference. The relative phase difference increases due to the increase in the refractive index difference Δn12 between the reference channel (1) and the sensing channel (2) of the Y-junction.
Due to the small difference in the distances between the output channels in the corporate-feed YI and the fixed camera resolution, some of the spectral components could not be identified independently from one another using setup 1 sketched in Fig. 3(a). Signal analysis techniques such as zero padding and windowing do not improve the frequency resolution but only interpolate over more samples to improve the accuracy of the extracted phase information . Thus, the setup was modified as discussed in the Section 3 to improve the spectral resolution. The same bulk sensing experiment was repeated for the Y-junction YI using setup 2, shown in Fig. 3(b). Figure 7(b) plots the relative phase difference over time during the introduction of the eleven solutions ranging from nc = 1.3370 to 1.3390. Similar bulk steps were observed where the phase difference increases as the refractive index of the solutions increases.
By considering Eq. (9), the bulk modal sensitivity of the sensing waveguide used in the Y-junction YI can be determined from the slope of a linear fit to the measurements of Fig. 8 which yields 3676.4 rad/RIU. To ensure accurate fitting, we considered the two sets of measurement data obtained with Δnc = 2 × 10−4 and the intercept was forced to yield the refractive index of CYTOP, following Eq. (9). The bulk modal sensitivity ∂neff/∂nc is thus determined as 0.46, a value slightly lower than reported previously.
The standard deviation of the phase difference over time during the flow of solution was measured as σ = 0.005 rad. Therefore, the detection limit of our Y-junction YI for bulk sensing is 1.36 × 10−6 RIU at a limiting signal-to-noise ratio of SNR = 1, and 4.07 × 10−6 RIU considering SNR = 3. This detection limit is about 4× better than observed for attenuation-based bulk sensing using an identical Y-junction structure .
Figure 9 demonstrates the formation of interference patterns for the corporate-feed YI using setup 2 (Fig. 3(b)), produced by slowly varying the distance L from the convex lens to the camera. The outputs from the corporate-feed multichannel waveguide are initially collimated, yielding six beams, each of different power, as shown in Fig. 9(a), obtained when there is no convex lens placed after the microscope objective. A convex lens is then inserted. The beams approach each other for L < f (Fig. 9(b)), where f is the focal length of the convex lens. They overlap at the focal point for L = f (Fig. 9(c)). For L > f, the beams diverge and form an interference pattern on the camera (Fig. 9(d)).
The corporate-feed YI has 13 unique combinations of channel distance dij which produce well-separated and distinct peaks in the magnitude plot of the Fourier-transformed interference pattern (see Fig. 5(b)). As a result, each waveguide pair acts as a “two-channel sensor” where their phase difference can be monitored simultaneously and independently. Given our current design of microfluidic channels and assembly, a solution injected into the chip will simultaneously cover sensing channels 1, 2, 5 and 6 (Fig. 2(b)). Thus, we expect a phase difference for these channels relative to the reference channels 3 or 4. There should be no phase difference between sensing channel pairs or between the reference channels.
Since the output channel distances dij and the wavelength λ0 are constant, the spatial frequency corresponding to interference between channels i and j kij = dij/(λ0L) depends on L, the distance between the focus of the plano-convex lens and the camera (Fig. 3 (b)). Evaluating Eq. (5), we found that the peaks of the corporate-feed Young’s interferometer are well separated for L = 11 cm. At the same time, the waveguide pair corresponding to each peak in the magnitude plot of the Fourier-transformed interference pattern was determined by introducing a refractive index difference between one waveguide pair at a time. The phase value at each spatial frequency can then be extracted to determine the phase difference during bulk sensing experiments.
Three DDI H2O/Gly sensing solutions of refractive index nc = 1.336, 1.338, and 1.340 were injected sequentially into the fluidic channels of the corporate-feed YI and the measured relative phase difference between each waveguide pair is plotted in Fig. 10. The waveguide pairs 1–2 and 5–6 share the same peak in the magnitude plot of the FFT interference pattern because the channels are output from Y-junctions which have the same distance between their waveguide pairs (d12 = d56). The same observation holds with regards to waveguide pairs 1–5 and 2–6.
The experimental results are in good agreement with theoretical expectations. When a DDI H2O/Gly sensing solution of refractive index slightly higher than CYTOP was injected into the sensing channels, a similar phase difference was observed for all waveguide pairs comprising a sensing channel and a reference channel, as shown in Figs. 10(c), 10(d), 10(f), 10(g), 10(h), 10(i), 10(k) and 10(l). The remaining waveguide pairs showed a null phase difference (as expected) with fluctuations less than 0.15 radians as seen in the inset of Fig. 10, possibly caused by cross-talk between channel pairs . No significant drift was observed during the bulk sensing experiments and the repeatability of the measurements was confirmed by injecting the solutions in reverse sequence.
The measured phase difference between all waveguide pairs comprising a sensing channel and a reference channel are very close to one another as represented by the error bars in Fig. 11(a), confirming the repeatability across sensing channels. From Fig. 11(a) the bulk sensitivity of the corporate-feed YI is determined as 3150 rad/RIU (through fitting) and the detection limit is 2.41 × 10−6 RIU (for SNR = 1), and is 7.23 × 10−6 RIU (for SNR = 3), for a baseline noise of σ = 0.008 rad. The bulk detection limit improves by 3.5× compared to attenuation-based bulk sensing using identical corporate-feed multichannel waveguides .
As the refractive index of the injected solutions increases, the measured phase difference begins to deviate from the expected linear response because the sensing waveguides become increasingly asymmetric and lossy. The lower output power form weaker fringes in the interference patterns increases error.
Figure 12 plots the measured bulk response of a similar corporate-feed YI but this time for eight solutions ranging in refractive index from nc = 1.3370 to 1.3384 in smaller steps of Δnc = 2 × 10−4. The relative phase difference pattern for all waveguide pairs is similar to those in Fig. 10. However, negative phase differences are seen here, in Figs. 12(d), 12(i), 12(k) and 12(l). This is in accordance with expectations because the phase difference Δφij is directly proportional to the refractive index difference defined as Δnij ≡ nj − ni. Thus for waveguide pairs with the ith channel as the sensing channel, the refractive index difference becomes increasingly negative as the refractive index of the injected solution increases. Conversely, the relative phase difference for waveguide pairs with the jth channel as the sensing channel increases as the refractive index of the injected solution increases. Waveguide pairs 1–3 and 3–6 show opposite trends from expected. This error is probably due the uncertainty in the distance between the focal length of the plano-convex lens and the detector of the camera, L. The value of L is difficult to measure accurately due to the camera construction where the detector in the camera is positioned behind a borosilicate glass faceplate of thickness 2.4 mm (± 0.3 mm), located approximately 16.5 mm from the front flange of the C-mount . Figure 11(b) plots the measured phase difference as a function of the refractive index of the injected solutions in steps of Δnc = 2 × 10−4. We used the absolute value of the phase difference for all waveguide pairs in constructing this plot. The variation across waveguide pairs is represented by the error bars. By fitting to this data, the bulk sensitivity of the corporate-feed YI is determined as 3718.4 rad/RIU with a standard deviation of σ = 0.01 rad, implying a detection limit of 2.69 × 10−6 RIU at a SNR = 1 and 4.07 × 10−6 at a SNR = 3.
The bulk sensitivity and detection limit of both the Y-junction and corporate-feed YIs are summarized in Table 1. In general, using a bulk step of Δnc = 2 × 10−4 produces smaller phase differences which and no phase unwrapping is necessary making it easier to determine the sensitivity. Theoretically, both structures should produce the same phase sensitivity because the sensing waveguides are of identical design throughout, but experimentally this was not the case. The corporate-feed YI had a slightly higher sensitivity than the Y-junction YI, but the detection limit was also higher due to a noisier baseline signal. In general, the detection limits of our YI sensors are worse than obtained for Mach-Zehnder interferometers using similar structure , likely due to the poor quality of the infrared camera (vidicon) and imperfections in fabrication which cause background light to interfere with the output modes. A detection limit below 10−7 can be obtained by optimising the design and improving the fabrication of the structures. The distances between the six output channels could also be optimised to generate more distinct spectral peaks.
Two designs for integrated Young’s interferometers using LRSPP waveguides were presented: one based on a Y-junction structure for single-channel phase sensing, and the other based on a corporate-feed structure for multi-channel phase sensing. We theoretically described the operational principles of the YIs and showed experimentally the ability of both designs to perform bulk sensing. The bulk sensing experiments were performed using two experimental setups where the latter improves the spatial resolution of the interference pattern via the addition of a convex lens. The measured responses of the YI sensors are in good agreement with theoretical predictions. The detection limits of our YIs are in general 3 to 4 times better than those obtained from the same structures, but used under intensity interrogation. The sensitivity and detection limit could be improved by using longer sensing channels and better detection hardware in the interrogation set-up. Further improvements on the corporate-feed design would include increasing the distance between the outputs of waveguide pairs (dij) to allow better separation of the spectral frequencies. By altering the design of the microfluidic jig and channels, simultaneous sensing of different sensing solutions or biomarkers can be achieved.
Appendix: Fourier-transformed irradiance distribution of interference pattern
From Eq. (1) in the main text, the irradiance distribution of the interference pattern is given by:
The authors gratefully acknowledge Oleksiy Krupin and Anthony Olivieri for assistance in carrying out the experiments.
1. P. Kozma, F. Kehl, E. Ehrentreich-Förster, C. Stamm, and F. F. Bier, “Integrated planar optical waveguide interferometer biosensors: A comparative review,” Biosens. Bioelectron. 58, 287–307 (2014). [CrossRef] [PubMed]
2. B. Huang, S. Xiong, Z. Chen, S. Zhu, H. Zhang, X. Huang, Y. Feng, S. Gao, S. Chen, W. Liu, and Z. Li, “In-fiber Mach-Zehnder interferometer exploiting a micro-cavity for strain and temperature simultaneous measurement,” IEEE Sens. J. 19, 5632–5638 (2019). [CrossRef]
3. W.-M. Zhao and Q. Wang, “A high sensitivity refractive index sensor based on three-level gradient structure S-tapered fiber mode-mode interferometer,” Measurement 139, 49–60 (2019). [CrossRef]
4. J. Villatoro, V. P. Minkovich, V. Pruneri, and G. Badenes, “Simple all-microstructured-optical-fiber interferometer built via fusion splicing,” Opt. Express 15, 1491–1496 (2007). [CrossRef] [PubMed]
5. A. Wang, H. Xiao, J. Wang, Z. Wang, W. Zhao, and R. G. May, “Self-calibrated interferometric-intensity-based optical fiber sensors,” J. Light. Technol. 19, 1495 (2001). [CrossRef]
7. R. G. Heideman, R. P. H. Kooyman, and J. Greve, “Performance of a highly sensitive optical waveguide Mach-Zehnder interferometer immunosensor,” Sens. Actuators B: Chem. 10, 209–217 (1993). [CrossRef]
8. A. Ymeti, J. S. Kanger, R. Wijn, P. V. Lambeck, and J. Greve, “Development of a multichannel integrated interferometer immunosensor,” Sens. Actuators B: Chem. 83, 1–7 (2002). [CrossRef]
10. C. Tyszkiewicz and T. Pustelny, “Differential interferometry in planar waveguide structures with ferronematic layer,” Opt. Appl. 34, 507–514 (2004).
12. D. Duval, A. B. González-Guerrero, S. Dante, J. Osmond, R. Monge, L. J. Fernández, K. E. Zinoviev, C. Domínguez, and L. M. Lechuga, “Nanophotonic lab-on-a-chip platforms including novel bimodal interferometers, microfluidics and grating couplers,” Lab Chip 12, 1987–1994 (2012). [CrossRef] [PubMed]
13. A. Brandenburg, R. Krauter, C. Künzel, M. Stefan, and H. Schulte, “Interferometric sensor for detection of surface-bound bioreactions,” Appl. Opt. 39, 6396–6405 (2000). [CrossRef]
14. K. Schmitt, B. Schirmer, C. Hoffmann, A. Brandenburg, and P. Meyrueis, “Interferometric biosensor based on planar optical waveguide sensor chips for label-free detection of surface bound bioreactions,” Biosens. Bioelectron. 22, 2591–2597 (2007). [CrossRef]
16. A. Ymeti, J. S. Kanger, J. Greve, P. V. Lambeck, R. Wijn, and R. G. Heideman, “Realization of a multichannel integrated Young interferometer chemical sensor,” Appl. Opt. 42, 5649–5660 (2003). [CrossRef] [PubMed]
17. A. Wikerstål, “Multi-channel solutions for optical labelfree detection schemes based on the interferometric and grating coupler principle,” Phd thesis, Albert Ludwig University of Freiburg (2001).
18. C. D. Bain, E. B. Troughton, Y. T. Tao, J. Evall, G. M. Whitesides, and R. G. Nuzzo, “Formation of monolayer films by the spontaneous assembly of organic thiols from solution onto gold,” J. Am. Chem. Soc. 111, 321–335 (1989). [CrossRef]
19. M. Tencer, O. Krupin, B. Tezel, and P. Berini, “Electrochemistry of au-sam-protein stacks,” J. Electrochem. Soc. 160, H22–H27 (2013). [CrossRef]
20. S. A. Maier, Plasmonics: Fundamentals and applications (Springer Science & Business Media, 2007).
21. L. Yang, J. Wang, L.-z. Yang, Z.-D. Hu, X. Wu, and G. Zheng, “Characteristics of multiple Fano resonances in waveguide-coupled surface plasmon resonance sensors based on waveguide theory,” Sci. Rep. 8, 2560 (2018). [CrossRef] [PubMed]
23. R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Light. Technol. 24, 477–494 (2006). [CrossRef]
24. P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photon. 1, 484–588 (2009). [CrossRef]
26. P. I. Nikitin, A. A. Beloglazov, V. E. Kochergin, M. V. Valeiko, and T. I. Ksenevich, “Surface plasmon resonance interferometry for biological and chemical sensing,” Sens. Actuators B: Chem. 54, 43–50 (1999). [CrossRef]
29. A. Khan, O. Krupin, E. Lisicka-Skrzek, and P. Berini, “Mach-Zehnder refractometric sensor using long-range surface plasmon waveguides,” Appl. Phys. Lett. 103, 111108 (2013). [CrossRef]
30. H. Fan and P. Berini, “Bulk sensing using a long-range surface-plasmon dual-output Mach-Zehnder interferometer,” J. Light. Technol. 34, 2631–2638 (2016). [CrossRef]
31. H. Fan and P. Berini, “Bulk sensing using a long-range surface-plasmon triple-output Mach-Zehnder interferometer,” J. Opt. Soc. Am. B 33, 1068–1074 (2016). [CrossRef]
33. W. R. Wong, H. Fan, F. R. M. Adikan, and P. Berini, “Multichannel long-range surface plasmon waveguides for parallel biosensing,” J. Light. Technol. 36, 5536–5546 (2018). [CrossRef]
34. W. R. Wong, O. Krupin, F. R. Mahamd Adikan, and P. Berini, “Optimization of long-range surface plasmon waveguides for attenuation-based biosensing,” J. Light. Technol. 33, 3234–3242 (2015). [CrossRef]
37. J. S. Kanger, V. Subramaniam, P. H. J. Nederkoorn, and A. Ymeti, “A fast and sensitive integrated Young interferometer biosensor,” in Advanced Photonic Structures for Biological and Chemical Detection, X. Fan, ed. (Springer, 2009), pp. 265–295. [CrossRef]
38. MathWorks, MATLAB Function Reference (R2018b) (2018).
39. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Pearson, 2017).
40. D. Donnelle and B. Rust, “The fast Fourier transform for experimentalists. part I. concepts,” Comput. Sci. Eng. 7, 80–88 (2005). [CrossRef]
41. Sofradir EC Inc., MicronViewer 7290A Frequently Asked Questions (2013).