## Abstract

We present a method to discriminate between analytes based on their size using multiple wavelengths in a Young interferometer. We measured the response of two wavelengths when adding 85 nm beads (representing specific binding), protein A (representing non-specific binding) and D-glucose (inducing a bulk change) to our sensor. Next, the measurements are analysed using a approach based on theoretical analysis, and a ratio-based analysis approach to discriminate between bulk changes and the binding of the different sized substances. Moreover, we were able to discriminate binding of 85 nm beads from binding of protein A (~2 nm) in a blind experiment using the ratio-based approach. This can for example be used to discriminate specific analyte binding of larger particles from non-specific binding of smaller particles. Therefore, we believe that by adding size-selectivity we can strongly improve the performance of the Young interferometer sensor and integrated optical interferometric sensors in general.

© 2016 Optical Society of America

## 1. Introduction

Integrated optical (IO) sensors are demonstrated to be a good analysis and detection tool for biosensing, mainly because of their high sensitivity, and their ability to measure real-time and label-free. Examples of IO sensors are grating couplers [1], resonant optical microcavity sensors [2–4], photonic crystal waveguide sensors [5,6] and interferometric sensors [7–11]. Interferometric biosensors use the evanescent field to detect refractive index (RI) changes induced by analyte binding. Extremely high RI sensitivities (~10^{−8} refractive index units (RIU)) are reported with interferometric sensors like the Mach-Zehnder interferometer [11] and the Young interferometer (YI) [9,10]. However, it is often not possible to fully use the high sensitivity capabilities of the sensor, because any RI change within the evanescent field will contribute to the measured signal. Next to the specific signal arising from specific binding of the analyte, signals originate from non-specific bound particles and RI changes in the fluid covering the waveguide (bulk). To discriminate specific binding from non-specific binding, selective chemical binding techniques are used in combination with washing steps. Differential measurements are used to cancel out bulk changes. Nevertheless, successful application of IO biosensors is still hampered by non-specificity due to bulk effects or non-specific adhesion. Therefore, a method was developed to reduce the contribution of non-specific binding to the measured signal [12]. The response to non-specific binding was reduced by a factor of hundred or more by tuning the evanescent fields of two different polarization modes such that the first 20-30 nm of the evanescent field were desensitized to reduce the contribution of non-specific binding. However, any RI change in this layer cannot be detected, resulting also in a reduction of the contribution due to specific binding. Moreover, a dual wavelength operation of an IO difference interferometer was used to distinguish binding of molecules from bulk changes or temperature changes [8]. Alternatively, dual polarization interferometry can be used to determine both the thickness and density (RI) of an adlayer [13,14]. Finally, we presented a theoretical description of a method called size-selective detection which can be used to discriminate between RI changes from binding of different sized particles and bulk changes (e.g. due to temperature changes) simultaneously [15]. Our theoretical analysis showed that it is possible to determine RI changes from multiple layers above the surface waveguide by measuring RI changes in the evanescent field at multiple wavelengths. Here, we present the experimental realisation of this theoretical analysis. We also present a new, more pragmatic, analysis approach which can be used to discriminate binding of particles from bulk changes and distinguish binding between different sized particles.

## 2. Materials and methods

#### 2.1 Young interferometer with multiple wavelengths

For the general theory of the working of the YI and how it can be used to determine multiple RI changes based on measurements with multiple wavelengths we refer to our theoretical article (Mulder et al. 2012). That article also showed that adding size-selectivity negatively affects the precision of the measured RI change. However, using three wavelengths to discriminate between RI changes at three different layers within the evanescent field and assuming a phase precision of 10^{−4} fringes and current waveguide specifications, the retained theoretical sensitivity is 1x10^{−6} RIU corresponding to 0.8 pg/mm^{2}, which is still comparable to the detection limits of other existing methods [16]. In the measurements shown in this contribution we discriminate between two substances of different sizes inducing a RI change by measuring the effective refractive index change $\Delta {N}_{eff}$ at two wavelengths (457 and 660 nm). Measurements with three wavelengths also showed that we could discriminate between three substances (see Appendix C), however results of $\Delta n$ became very noise because of enhancement of artefacts due to boundary effects of the shifting interference pattern (see Noise, drift and artefacts in measurements). For a successful application of these analysis approaches used to determine three independent $\Delta n$’s, artefacts and drift in $\Delta {N}_{eff}$ should be reduced significantly. All the experimental details about the setup are given in Appendix A.

#### 2.2 Measurement protocol

When a substance (with a different RI than the initial solution) is added to the evanescent field in the sensing window, this results in a RI change $\Delta n$ resulting in a $\Delta {N}_{eff}$. This $\Delta {N}_{eff}$ is determined by reading out the $\Delta \phi $ (in fringes) and multiplying it by the wavelength of the light source and dividing it by the sensing window length of the chip. This is done for the three wavelengths such that a $\Delta {N}_{eff}$ is determined for each wavelength. The substances that we measure with the sensor are 85 nm carboxylated polystyrene beads which bind to the sensor surface (representing specific binding of e.g. viruses which approximately this size), protein A (representing non-specific binding) which also binds to the sensor surface but is smaller (≈2 nm [17, 18]) and D-glucose which hardly binds to the sensor surface but induces a bulk change. These substances induce $\Delta n$’s at different places within the evanescent field and can therefore be discriminate from each other. In this case we discriminate between substances of different materials, but it is also possible to discriminate between substances of the same material as long as they are different in size. All the measurements are done using a 1x phosphate buffered saline (PBS) buffer to which the different samples were added. The measurements start with a baseline of approximately 400 s to determine the drift of $\Delta {N}_{eff}$ signal (can be caused e.g. by temperature fluctuations causing relative movement between chip and CCD camera or causing directly a $\Delta n$ at the sensing windows) which results in drift in $\Delta n$ (see Appendix E). Next, the measurements continue with a characterization step, containing an addition of 6.16 mg/ml D-glucose for 500 s to the PBS, which can be used to verify that the sensor responds as expected or to fit a theoretical model by changing waveguide parameters such that the determined curves of $\Delta n$ fulfil the expectations.

## 3. Theory

Usually, a YI is used to determine a $\Delta {N}_{eff}$ at a single wavelength. Consequently, an average $\Delta n$ is determined, based on any $\Delta n$ in the whole evanescent field. Measuring the $\Delta {N}_{eff}$ at multiple different wavelengths enables discrimination between multiple different $\Delta n$’s. Here, we shortly describe two analysis approaches which can be used for this: an approach based on theoretical analysis and a ratio-based analysis approach. A more detailed description of the ratio-based approach can be found in Appendix B.

#### 3.1 Approach based on theoretical analysis

Determining the $\Delta {N}_{eff}$ at two different wavelengths, enables the discrimination between $\Delta n$’s originating from two arbitrarily chosen layers within the evanescent field [15], using the following equation:

*j*layer (index

^{th}*l*stands for layer), the elements ${S}_{i,j}={\left(\partial {N}_{eff,{\lambda}_{i}}/\partial n\right)}_{j}$ of matrix $\overline{\overline{S}}$ are the theoretical sensitivity coefficients, which are the derivatives of ${N}_{eff}$ at the

*i*

^{t}^{h}wavelength with respect to

*n*occurring in the

*j*

^{th}layer and the element $\Delta {N}_{eff,i}$ of vector $\overline{\Delta {N}_{eff}}$ is the $\Delta {N}_{eff}$ at the

*i*wavelength. The sensitivity coefficients are determined by the structure of the waveguide (core thickness and RIs of the various layers of the waveguide), the wavelengths, the polarization and two arbitrarily chosen layers (within the evanescent field). The $\overline{\Delta {n}_{l}}$ can be determined by measuring $\overline{\Delta {N}_{eff}}$ and multiplying this by the inverse of matrix $\overline{\overline{S}}$. A homogeneous $\Delta {n}_{l}$ per layer is determined and therefore this method is less suitable for situations where $\Delta n$’s are induced in the same layer by different substances. However, assuming a low concentration of analytes, for example bulk effects can be cancelled out by subtraction of $\Delta n$ determined from multiple layers to finally arrive at an analyte concentration [15]. Nevertheless, this method requires tuning of many parameters to determine the correct values for the sensitivity coefficients that are required to determine the absolute value of $\Delta n$. Hence, this method is exact but in practice difficult to implement because of the many parameters that have to be tuned. This approach also requires more input than actually required, so therefore we developed a much more practical and easy to use ratio-based approach.

^{th}#### 3.2 Ratio-based approach

Here, we present the ratio-based analysis approach which uses the ratios of $\Delta {N}_{eff}$ at multiple wavelengths, caused by $\Delta n$’s originating from different substances $\Delta {n}_{s}$. Each substance with a different size which causes a $\Delta {n}_{s}$ in the evanescent field results in different $\Delta {N}_{eff}$’s for each wavelength because of the different electric field distributions of the respective wavelengths. The ratio of the $\Delta {N}_{eff}$ measured at two different wavelengths ${\lambda}_{k}$ and ${\lambda}_{l}$, induced by a substance *s _{m},* is defined as:

*s*), the vector $\overline{\Delta {N}_{eff}}$ is composed of the elements $\Delta {N}_{\text{eff,}{\lambda}_{\text{k}}}$, where $\overline{\overline{\Theta}}$ is a matrix with theoretical sensitivity coefficients of which the elements are given by ${\theta}_{k,m}=\partial {N}_{eff,{\lambda}_{k}}/\partial {n}_{{\text{s}}_{m}}\forall k=m$ and ${\theta}_{k,m}=0\forall k\ne m$, and the coefficients of matrix $\overline{\overline{R}}$ are given by ${r}_{k,m}={R}_{{\lambda}_{k}/{\lambda}_{m}}^{{s}_{m}}$. The experimental procedure is now as follows. First a characterization step is required to determine matrix $\overline{\overline{R}}$ by measuring the response of the sensor for each individual substance. The matrix ${\overline{\overline{\Theta}}}^{-1}$ can be regarded as a scaling matrix that allows to get absolute values of $\overline{\Delta {n}_{\text{s}}}$. When the coefficients of this matrix are unknown, ${\theta}_{k,m}\forall k=m$ can be set as 1 such that ${\overline{\overline{\Theta}}}^{-1}$ becomes the identity matrix, which means that $\overline{\Delta {n}_{\text{s}}}$ is fully determined by the measured ratios ${R}_{{\lambda}_{k}/{\lambda}_{m}}^{{s}_{m}}$. Without the scaling it is possible to compare the unscaled $\Delta {n}_{{\text{s}}_{m}}$ with $\Delta {n}_{{\text{s}}_{m}}$ of a different measurement. However, the amplitude of $\Delta {n}_{{\text{s}}_{m}}$ should not be compared with $\Delta {n}_{{\text{s}}_{n}}$as scaling is required. Now that we know the matrices of Eq. (3), we can use this equation. for analysis of a real experiment in which we add multiple substances simultaneously to the sensor to find the contribution of each substance independently.

_{m}An advantage of the ratio-based method is that direct discrimination between different substances is possible, also when $\Delta {n}_{s}$’s occur in same layer in the evanescent field, as long as the ratios in wavelengths are different from each other and as long as the substances do not influence each other’s response of the sensor. The analysis of two substances which induce a $\Delta {n}_{s}$ is relatively easy as only two ratios are determinable parameters which determine the shape of the signal of $\overline{\Delta {n}_{\text{s}}}$ over time. For three substances inducing a $\Delta {n}_{s}$, already six ratios need to be determined, illustrating the rapidly increasing complexity when increasing the number of distinguishable substances inducing a $\Delta {n}_{s}$. However, these ratios can be determined independently for each substance to discriminating these substances from each other.

The absolute value of $\overline{\Delta {n}_{\text{s}}}$ can be determined by combining the ratio-based approach with the theoretical model used for the approach based on the theoretical analysis. In this way ${\overline{\overline{\Theta}}}^{-1}$ can be determined. However, this requires again tuning of a lot of parameters. Therefore, it might be easier to determine scaling parameters for $\overline{\Delta {n}_{\text{s}}}$ using calibration experiments, which are usually also carried out by a single wavelength. Alternatively, this method can also be used as a quick screener, providing only a yes or no answer on the presence of the analyte and which therefore does not require knowing the absolute values of $\overline{\Delta {n}_{\text{s}}}$.

## 4. Results and discussion

First, we present the measured ratios ${R}_{{\lambda}_{k}/{\lambda}_{l}}^{{s}_{m}}$ for the individual substances which are used for the ratio-based approach to discriminate between these different-sized substances. Second, we present measurements in which two substances simultaneously induced a $\Delta n$ and the corresponding results obtained from both the approach based on theoretical analysis and the ratio-based analysis approach. Third, we demonstrate the power of the ratio-based approach in a blind experiment were the binding of 85 nm beads was discriminated from binding of protein A.

#### 4.1 Ratios of individual substances

Here, we present the measured ratios of $\Delta {N}_{eff}$ measured at different wavelengths for each individual substance which are used for the ratio-based approach in order to discriminate between these substances in the measurements presented in the next sections. We measured the ratios for two different wavelengths (${\lambda}_{1}$ = 457 nm and ${\lambda}_{2}$ = 660 nm), and three different substances: 85 nm carboxylated polystyrene beads (${R}_{660/457}^{\text{beads}}$ = 0.918 ± 0.045), protein A (${R}_{660/457}^{\text{protein}}$ = 0.680 ± 0.022) and D-glucose (${R}_{660/457}^{\text{glucose}}$ = 1.218 ± 0.016). The error margins of the ratios are determined by twice the standard deviation (95% confidence interval) of the measured ratios from different experiments. A more detailed description of how these ratios are determined is found in the Appendix B. The spread in the measured ratios might be caused by artefacts in the measurements (see section 4.4) or slightly different sensor surface properties from run-to-run due to unequal cleaning which can result in changes in binding as we use non-specific binding of the protein A and 85 nm beads. The ratios of the different substances are in principle independent of the substance concentration as long as the resulting surface concentrations are much smaller than a full monolayer coverage. When substances bind on top of each other this will result in a different ratio and therefore the proposed method is not valid anymore.

#### 4.2 Discrimination between two different-sized substances

In this section we present measurements where two of the three named different-sized substances (protein A, 85 nm beads and D-glucose which induces a homogeneous $\Delta n$ in the whole evanescent field of a few hundreds of nanometres) are discriminated from each other. First, 6.16 mg/ml D-glucose and 2.0 μg/ml protein A were added simultaneously to the sensor (see Fig. 1(a)) and $\Delta {N}_{eff}$ is measured at ${\lambda}_{1}$ = 457 nm and ${\lambda}_{2}$ = 660 nm. As a characterization step 6.16 mg/ml D-glucose only was added to the sensor, which results in an increase of the $\Delta {N}_{eff}$ as D-glucose has a higher *n* than PBS. As expected, the $\Delta {N}_{eff}$ is the highest at ${\lambda}_{2}$ as it is more sensitive to bulk changes (D-glucose does hardly bind to the surface) compared to ${\lambda}_{1}$. After applying a washing step, the $\Delta {N}_{eff}$ comes back to zero as the D-glucose bulk solution is completely replaced by PBS. After simultaneously adding D-glucose and protein A the $\Delta {N}_{eff}$ increases again differently at ${\lambda}_{1}$ compared to ${\lambda}_{2}$. For both $\Delta {N}_{eff}$’s the increase consist of a steep slope due to the bulk effect and a less steep slope due to the binding of the protein A to the surface. After again applying a washing step the signal drops due to the fact that the D-glucose and protein A in the bulk are replaced by PBS. The $\Delta {N}_{eff}$ does not go back to zero as protein A is left at the surface. In this case the $\Delta {N}_{eff}$ at ${\lambda}_{1}$ is higher than at ${\lambda}_{2}$ which is expected since shorter wavelengths are more confined to the core of the waveguide and have a relative larger field near the surface compared to the longer wavelengths. Therefore, the shorter wavelengths are more sensitive to changes close to the surface compared to longer wavelengths. Figure 1(d) shows a similar experiment where after addition of only 6.16 mg/ml D-glucose, 6.16 mg/ml D-glucose was added simultaneously with 1.0 μg/ml 85 nm beads. Figure 1(g) shows a similar measurement where after addition of only 6.16 mg/ml D-glucose,1.0 μg/ml protein A was added simultaneously with 2.0 μg/ml 85 nm beads respectively.

### 4.2.1 Protein A and D-glucose

Figure 1(b) shows the $\Delta n$ corresponding to Fig. 1(a) determined with the approach based on theoretical analysis. Assuming a homogeneous $\Delta n$ in the whole evanescent field for the D-glucose characterization step, the determined $\Delta {n}_{{l}_{1}}$ should be the same as $\Delta {n}_{{l}_{2}}$, independent of the arbitrarily chosen thickness of the layers. The *d _{core}*, which determines the theoretical sensitivity coefficients and therefore $\Delta n$, can be adjusted such that both $\Delta n$’s of both layers for the glucose step reach an equal level, independent of the selected layers. The best fit of $\Delta n$ was achieved by a

*d*of 61.8 nm. Other waveguide parameters were also tuned to fit the measurement data, but did not give better results. The $\Delta n$ for the first D-glucose step based on a

_{core}*d*of 61.8 nm is equal to 8.78x10

_{core}^{−4}RIU, which agrees well with the 8.88x10

^{−4}RIU determined from the $\Delta {N}_{eff}$ measured at a single wavelength (660 nm) assuming

*d*= 61.8 nm.

_{core}Next to the *d _{core}*, also the layer thickness of the first layer (

*d*), of which one can determine a $\Delta n$, can be adjusted. Changing

_{1}*d*results in a varying end level of $\Delta {n}_{{l}_{1}}$ and $\Delta {n}_{{l}_{2}}$ as layer 1 is defined from 0 -

_{1}*d*and layer 2 from

_{1}*d*- infinity. In the case of simultaneous addition of D-glucose and protein A, the expected end level of $\Delta {n}_{{l}_{2}}$ after the washing step back to PBS is zero. The layer thickness that provides the expected bulk levels for the experiment with the protein A and D-glucose is 3.5 nm, which is reasonably close to the determined height of an absorbed layer of protein A of approximately 1 nm [18] and 2.5 nm [17]. Assuming low concentrations and bulk changes occurring in both layers, the $\Delta {n}_{{l}_{2}}$was subtracted from $\Delta {n}_{{l}_{1}}$ resulting in a signal which should belong to only the protein A (see black dotted line in Fig. 1(b). The signal belonging to the protein A at the end of the measurement is equal to approximately a seventeenth of a full coverage of protein A.

_{1}The determined $\Delta n$ corresponding to Fig. 1(a) and based on the ratio-based approach is shown in Fig. 1(c). The ratios ${R}_{660/457}^{\text{protein}}$ and ${R}_{660/457}^{\text{glucose}}$ that were used for this ratio-based approach are the ratios measured for the individual substances. The $\Delta {n}_{\text{glucose}}$ fulfils the expectations as the signal goes up when D-glucose was added and comes down to the baseline when applying a washing step. The $\Delta {n}_{\text{protein}}$ goes up when protein A was added and slowly decreases after applying a washing step, which is probably be caused by partly desorption of the protein A from the sensor surface. However, $\Delta {n}_{\text{protein}}$ goes also slightly up when D-glucose was added. With an ${R}_{660/457}^{\text{glucose}}$ of 1.220 the $\Delta {n}_{\text{protein}}$ goes back to the expected level based on linear drift of $\Delta {n}_{\text{protein}}$. This slightly different ${R}_{660/457}^{\text{glucose}}$ remains within the error margins of the individually measured ratio for D-glucose, such that the difference can be explained by differences in response of the sensor per measurement. Amplitudes of $\Delta {n}_{\text{glucose}}$ should not be compared with $\Delta {n}_{\text{protein}}$ as scaling is required.

### 4.2.2 Beads and D-glucose

In a similar way as for the protein A and D-glucose, Fig. 1(d) was analysed with the theoretical model as shown in Fig. 1(e). The optimal result was realized based on a *d _{core}* of 63.4 nm and

*d*of 70 nm, which is lower than the expected 85 ± 6.5 nm. This might partly be explained by the fact that the beads are spherical and not cubical, as the response of the $\Delta {N}_{eff}$’s induced by a cubic shaped particle binding on the sensor surface is similar to the response of the $\Delta {N}_{eff}$’s induced by a larger spherical shaped bead binding on the same sensor surface. By subtracting the $\Delta {n}_{{l}_{2}}$ from $\Delta {n}_{{l}_{1}}$ and assuming low concentrations and bulk changes occurring in both layers it was again possible to determine a signal which should belong to only the beads. The determined $\Delta {n}_{{l}_{2}}-\Delta {n}_{{l}_{1}}$is equal to approximately 1.6x10

_{1}^{−3}RIU, which corresponds to a surface fractional coverage of the beads of approximately 0.2%.

Using the ratio-based approach, $\Delta {n}_{\text{glucose}}$ and $\Delta {n}_{\text{bead}}$ were determined, again based on the measured ratios of the individual substances. As expected, the $\Delta {n}_{\text{bead}}$ does not increase when adding D-glucose, increases when adding the beads and remains constant after applying a washing step. The $\Delta {n}_{\text{glucose}}$ reaches a level which is approximately the same as in Fig. 1(c) as expected because the added D-glucose concentrations were the same. However, after the washing step the $\Delta {n}_{\text{glucose}}$ is a bit lower than expected. An optimal result is given at ${R}_{660/457}^{\text{bead}}$ = 0.900 which again remains within measured error bars of ${R}_{660/457}^{\text{bead}}$.

### 4.2.3 Protein A and beads

For the measurement of simultaneous addition of beads and protein A the approach based on theoretical analysis is not very suitable, especially because $\Delta {n}_{{l}_{2}}$ is far from homogeneous as the evanescent field penetrates deeper than the thickness of the bead. Moreover, the expected end levels of the protein A and the beads are not known which was known for the bulk effect of the D-glucose. Consequently, the fitting of *d _{1}* is not feasible.

Using the ratio-based approach it is possible to discriminate between the protein A and the beads. The result based on ratios of ratios measured for the individual substances is shown in Fig. 1(i). As was mentioned, amplitudes between $\Delta {n}_{\text{protein}}$ and $\Delta {n}_{\text{bead}}$ should not be compared as scaling factors of substances are individual. However, $\Delta {n}_{\text{protein}}$ of Fig. 1(i) can be compared with $\Delta {n}_{\text{protein}}$ of Fig. 1(c). In Fig. 1(i) half of protein A was added to the sensor, but the measured $\Delta {n}_{\text{protein}}$ is only 1.6 times lower. An even lower signal of $\Delta {n}_{\text{protein}}$ is expected as now also beads can cover part of the surface where beads can bind. Furthermore, the $\Delta {n}_{\text{bead}}$ of Fig. 1(f) is approximately 2.6 times higher compared to $\Delta {n}_{\text{bead}}$ of Fig. 1(i), where the added beads concentration was two times lower. The differences might be explained that different chips and different stock solutions were used for the different measurements. Furthermore, all the measurements are based on the non-specific adhesion of the protein A and the beads to the sensor surface. Therefore, small differences between sensor surfaces can make a large difference. The result from D-glucose in which no binding is involved, the signals were in nice agreement with each other. Determined RI changes due to non-specific binding of particles and between different measurements should not be compared if not all the conditions (chip, stock solution, analysis parameters) of the measurements are the same.

Besides, Fig. 1(i) shows that using two ratios, excluding ${R}_{660/457}^{\text{glucose}}$, it is not possible to suppress the first D-glucose step from the protein and beads signal. Three wavelengths are required to discriminate between protein A, 85 nm beads and D-glucose in a single measurement, as presented in the Appendix C.

#### 4.3 Blind experiment

To approve the usability and verify the correctness of the ratio-based approach a blind experiment was carried out. Six combined samples of protein A (in the range of 0.1 - 1.0 μg/ml) and 85 nm beads (in the range of 0.4 - 4.0 μg/ml) were made and labelled by an independent person. Before measuring, the samples were carefully mixed to ensure homogeneous solutions. Next, the samples were measured in two measurement sets performed on the same waveguide using three measurement channels and one reference channel. In between the measurement sets the waveguides were cleaned using a cleaning protocol with can be found in Appendix G. A D-glucose characterization step was applied to verify the correct response at the different wavelengths. This resulted in a different ratio of the measured $\Delta {N}_{eff}$’s of 1.263 compared to the 1.218 ± 0.016. This can be explained by the fact that we used a different chip for this measurement which can have for example a slightly different *d _{core}*. To correct for this deviation, we changed the average measured ratios of the individual substances by multiplying them by $\text{1}.\text{263}/\text{1}.218$ and used this for the ratio-based approach to analyse this experiment. Figure 2(a) shows an example of a measurement with the D-glucose characterization step and adding sample A and Fib. 4b shows the corresponding determined $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{protein}}$ over time, which are read out at

*t*= 2400 s when the beads signal was constant. The expected values of $\Delta n$ based on linear drift (baseline determined between

*t*= 1320 s and

*t*= 1380 s) are subtracted from this ${n}_{t=2400s}$ and plotted as a function of the applied concentration in Fig. 2(c) and Fig. 2(d) for the 85 nm beads and the protein A respectively.

The applied bead concentration and the determined $\Delta {n}_{\text{bead}}$ show a linear trend which means the $\Delta {n}_{\text{bead}}$ was determined correctly using the ratio-based approach, assuming a linear relation between the number of beads in the sample and response of the sensor. Moreover, it shows that it is possible to do a calibration experiment to find the relations between the beads concentration and the response of the sensor. Furthermore, also a linear trend is seen between the measured $\Delta {n}_{\text{protein}}$ and the applied protein concentration. Only at higher applied protein A concentrations, the determined $\Delta {n}_{\text{protein}}$ flattens off, which can be explained by the fact that for these measurements the surface was saturated with protein A which can be seen in Fig. 2(b). That the signal of $\Delta {n}_{\text{bead}}$ still increases might be explained by the beads replacing the protein A of the surface. The be able to compare $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{protein}}$, the signals were both read out at the same time point. The blind experiment illustrates that the determined $\Delta {n}_{\text{substance}}$ can be compared with the $\Delta {n}_{\text{substance}}$ of a different experiment, when using the same measurement conditions (chip, stock solution, analysis parameters).

#### 4.4 Noise, drift and artefacts in measurements

Here, we shortly discuss the influence noise, drift and artefacts in $\overline{\Delta {N}_{eff}}$ on $\overline{\Delta n}$. All noise sources in the signal of $\overline{\Delta {N}_{eff}}$ are enhanced using the above named approaches, which means that they are stronger visible in $\overline{\Delta n}$. This can be explained by the matrix becoming more singular, resulting in enhancement of all kind of noise sources. Linear drift measured in $\Delta {N}_{eff}$’s (e.g. due to temperature changes causing relative movement between chip and CCD camera or causing directly a $\Delta n$ at the sensing windows) results in linear drift in $\Delta n$ of both layers (see Appendix E). For the measurements we assume linear drift and take this into account when fitting ${R}_{{\lambda}_{k}/{\lambda}_{l}}^{{s}_{m}}$ or waveguide parameters. Moreover, artefacts (fluctuations e.g. seen in Fig. 1(f) at *t* ≈500 s and 1000 s in $\Delta {n}_{\text{protein}}$, but better visible at discrimination between three substances using three wavelengths, see Appendix C) show up in $\overline{\Delta n}$. These artefacts are present in the signal of the $\Delta {N}_{eff}$’s, but are not visible because of the relatively higher slopes of $\Delta {N}_{eff}$ due to the fast addition of the sample. The artefacts are caused by boundary effects of the shifting interference pattern (see Appendix D). When inducing a linear $\Delta \phi $ in the interference pattern this results in a oscillation in the amplitude of the spatial frequency as it is not constant when the fringes move. It also results in a oscillation in $\Delta \phi $ which is directly related to $\overline{\Delta {N}_{eff}}$. Using a proper windowing function (e.g. Blackman-Nuttall) we were able to remove the oscillations from simulated shifting interference patterns. However, this was not sufficient for the measured data, possibly because of non-ideal properties of the lenses, the grating and beam shape (see Appendix D). Therefore, the artefacts in $\overline{\Delta {N}_{eff}}$can result in misfits of the fitted ${R}_{{\lambda}_{k}/{\lambda}_{l}}^{{s}_{m}}$or waveguide parameters. The spread in the determined *d _{core}*,

*d*and ${R}_{{\lambda}_{k}/{\lambda}_{l}}^{{s}_{m}}$ can be caused by especially the artefacts, resulting in a wrongly determined $\overline{\Delta n}$. The signal of $\overline{\Delta n}$ becomes especially very noisy in the case when discriminating between three $\Delta n$ ‘s based on three $\Delta {N}_{eff}$ ‘s (see Appendix C). To be able to use this method for three wavelengths to solve three independent $\Delta n$’s, the artefacts in the measurement should be reduced by for example testing if larger optical components reduce the artefacts.

_{layer}## 5. Summary and conclusions

By measuring the $\Delta {N}_{eff}$ at two different wavelengths it was possible to discriminate between two different substances inducing a $\Delta n$ in the evanescent field of the sensor. The binding of 85 nm beads or protein A was discriminated from D-glucose and the binding of 85 nm beads was discriminated from the binding of protein A. Using three $\Delta {N}_{eff}$’s to discriminate between three different substances inducing a $\Delta n$, the result became more noisy. For a successful application of these analysis approaches used to determine three independent $\Delta n$’s, the artefacts (due to boundary effects of the shifting interference pattern, see Appendix D) in $\Delta {N}_{eff}$should be reduced significantly. Alternatively, other techniques to improve specificity can be used next to size-selective detection. For example, to discriminate the binding of beads from binding of protein A and bulk changes due to D-glucose, D-glucose can also be added to the reference channel to cancel out the contribution due to D-glucose. In that case only two wavelengths are required to discriminate between binding of beads and proteins, resulting in less enhancement of noise.

Application of a approach based on theoretical analysis made it possible to discriminate between $\Delta n$’s occurring in different layers in the evanescent field, assuming a homogeneous $\Delta n$ in each layer. However, to determine the correct value for $\Delta n$, this method requires multiple parameters (e.g. the waveguide core thickness, waveguide RIs, layer thicknesses, wavelengths) to be tuned that is difficult and labour-intensive. Therefore, also a much more pragmatic ratio-based analysis approach is presented to discriminate between $\Delta n$’s induced by different substances. Moreover, this approach can be used for different substances inducing a $\Delta n$ in overlapping layers, which is not always possible with the approach based on theoretical analysis. Information on the absolute amplitude of $\Delta {n}_{s}$ is lost using the ratio-based approach, however for determining an analyte concentration calibration measurements can be performed which are usually also required using an YI with a single wavelength. 85 nm beads, D-glucose and protein A were discriminated from each other using this ratio-based approach. The working of the ratio-based approach was verified by a blind experiment with different samples containing different concentrations of protein A and beads. We could discriminated $\Delta {n}_{\text{bead}}$ from $\Delta {n}_{\text{protein}}$, resulting in an expected linear trend of the $\Delta {n}_{\text{bead}}$ with the applied concentration. So here we discriminate between protein A (≈2 nm large) and 85 nm beads, but this can raise the question what would be the minimal size difference of discriminable substances. It is very difficult to say something general about this as the minimal discriminable size difference depends on a number of parameters such as the amplitude of the signals of the substances and the amplitude of the noise, artefacts and drift of the phase signal. When a certain application is identified, then the sensor should be optimized to determine the limits of the device for the specific application in mind. Size-selective analyte detection can for example be used to discriminate specific analyte binding of larger particles from non-specific binding of smaller particles. Therefore, we believe that with measuring size-selectivity we can strongly improve the performance of our YI sensor and IO interferometric sensors in general. Especially the ratio-based approach is an easy approach to discriminate between different substances causing a $\Delta n$.

## Appendix A Experimental details

In this section we describe the experimental details of the setup which was used for the measurements presented in the main text and in the rest of the appendices.

#### A.1 Sample transportation

Samples are degassed by a 4-channel Degassi Classic degasser and transported to the sensor surface by a 4-channel Ismatec® Reglo Digital Peristaltic Pump with a flow rate of 100 μl/min towards the sensing windows of the waveguide structure. On top of these sensing windows a 100 μm high fluid cuvette is placed to transport the sample to the sensor with a laminar flow, which means that in the evanescent field that is used for detection the velocity is nearly zero and transport of the different substances is determined by diffusion.

#### A.2 Hardware

Measurements are performed in a 4-channel single-mode ridge waveguide YI sensor. The waveguide consists three layers: a PECVD SiO_{2} layer covering a LPCVD Si_{3}N_{4} 70 nm thick core on top of a thermal SiO_{2} substrate. A sensing window with a length *l* of 4 mm is created by etching away the PECVD SiO_{2} cover. Measurements are done with one single waveguide structure (chip) which is cleaned after each measurement (see Appendix G). The wavelengths 457, 561 (only used when discriminating between three substances) and 660 nm are chosen such that only zero order TE modes (in height) fit into the waveguide and such that wavelengths are well spread, which is required to achieve a good precision [15]. The different light sources are coupled into a single mode polarization maintaining (SMPM) fiber which can be positioned with respect to the waveguide using an *xyz*-stage to be able to quickly and sufficiently couple all wavelengths into the waveguide. The fiber tip is strengthened with a glass ferule which is positioned against the waveguide with a matching index gel in between them to prevent reflections at the interfaces which resulted in a oscillations of the phase signal. Figure 3 shows a schematic overview of the hardware of the setup.

#### A.3 Analysis

A Fast Fourier Transform (FFT) is applied to the interference patterns detected with the CCD camera. Different windows were applied to the interference patterns to prevent boundary effects (see Appendix D). Subsequently, spatial frequency peaks of the interference pattern are determined such that the phase change $\Delta \phi $ ($\propto \Delta {N}_{eff}$) of each channels pair can be read out. For the measurements we only use one channel pair combination (one measurement channel and one reference channel) and the rest is neglected, expect for the blind experiment for which we use all channels.

## Appendix B Ratio-based analysis approach

#### B.1 Effective refractive index ratios at various wavelengths

The ratios ${R}_{{\lambda}_{n}/{\lambda}_{m}}^{{s}_{m}}$ are experimentally determined for three different wavelengths (${\lambda}_{1}$=457 nm, ${\lambda}_{2}$=561 nm and ${\lambda}_{3}$=660 nm), and for three different substances: 85 nm carboxylated polystyrene beads, protein A and D-glucose (see Table 1), representing specific binding, non-specific binding and bulk changes respectively. Figure 4 shows an example of a measurement with D-glucose and 85 nm beads measured at ${\lambda}_{1}$=457 nm and ${\lambda}_{3}$=660 nm, illustrating the difference in ${R}_{660/457}$ for both substances. A single value for the ratio for a given substance is determined by calculating the mean value of the ratios over the time interval in which the ratios have a relatively stable value for that substance. In practice it was found that the time intervals that show a stable ratio correspond to intervals in which ${N}_{eff,{\lambda}_{1}}$ was between 80 - 100% of its maximum value for D-glucose, 20 - 100% for 85 nm beads and 10 - 100% for protein A. Therefore these intervals were applied for determination of all ratios.

Figure 5 shows all determined values of ${R}_{{\lambda}_{n}/{\lambda}_{m}}^{{s}_{m}}$ and their mean and corresponding 95% confidence interval (error bars, twice the standard deviation). The ratios ${R}_{{\lambda}_{n}/{\lambda}_{m}}^{{s}_{m}}$ and corresponding confidence intervals are also listed in Table 1.

#### B.2 Theory of ratio-based analysis method

Here, we derive Eq. (3) of the manuscript. When a substance *s _{m}* is added to the sensor it induces a $\Delta {n}_{{\text{s}}_{m}}$, this results in an effective refractive index change $\Delta {N}_{eff,{\lambda}_{k}}$ at ${\lambda}_{k}$. Assuming that the response of the sensor has a linear relationship with the amount of

*s*that is added to the sensor, this can be written as:

_{m}*s*. Assuming that substances do not influence each other’s response of the sensor, multiple substances inducing different ratios can be discriminated from each other using:

_{m}Next, we define the ratio of two $\Delta {N}_{eff}$’s measured at two wavelengths ${\lambda}_{k}$ and ${\lambda}_{l}$, induced by a substance *s _{m}* as:

## Appendix C Discrimination between three different-sized substances

To test if both analysis approaches are also applicable when using three wavelengths to discriminate three $\Delta n$’s induced by three different substances, D-glucose (6.16 mg/ml), 85 nm carboxylated polystyrene beads and protein A were added to the sensor after each other. The $\Delta {N}_{eff}$ was measured at ${\lambda}_{1}$=457 nm, ${\lambda}_{2}$=561 nm and ${\lambda}_{3}$=660 nm as shown in Fig. 6(a). Figure 6(b) shows the $\Delta n$ corresponding to Fig 6(a) determined with the approach based on theoretical analysis after fitting the *d _{core}*,

*d*and

_{1}*d*based on analysing the results based on two wavelengths. An example of this is shown in Fig. 6(c) where

_{2}*d*and

_{core}*d*were determined as 62.7 nm and 64 nm respectively, based on ${\lambda}_{1}$ and ${\lambda}_{3}$. It can be seen that at the D-glucose step the $\Delta {n}_{{l}_{1}}$ and $\Delta {n}_{{l}_{2}}$ are equal and when adding the beads at

_{2}*t*there is an increase of $\Delta {n}_{{l}_{1}}$ and $\Delta {n}_{{l}_{2}}$ stays approximately constant. Similarly, the fitting was done with ${\lambda}_{1}$ and ${\lambda}_{2}$, and for the combination of D-glucose and protein A and the combination of protein A and beads, based on the wavelength combination ${\lambda}_{1}$ with ${\lambda}_{2}$ and ${\lambda}_{1}$ with ${\lambda}_{3}$. This resulted in a

_{3}*d*= 62.55 ± 0.15 nm,

_{core}*d*= 5 ± 2 nm and

_{1}*d*= 60 ± 4 nm, illustrating that combinations of $\Delta {N}_{eff}$’s measured at different wavelengths give different fit values, indicating that the parameters in the theoretical model are probably not completely right and that artefacts (see Appendix D) play a significant role here. The result in Fig. 6(b) is based on the average values for

_{2}*d*,

_{core}*d*and

_{1}*d*and three wavelengths to discriminate between the three layers. The overall signals determined with the approach based on theoretical analysis based on three wavelengths/layers is much more noisy compared to the two wavelengths/layers case, which makes the optimization more difficult. The increase in noise, artefacts and drift can be explained by the fact the matrix to $\overline{\Delta {n}_{l}}$ from $\overline{\Delta {N}_{eff}}$ becomes more singular and therefore all noise sources are enhanced which was already shown by [15]. However, ignoring the noise, drift and artefacts, all signals increase roughly with the same amplitude when adding D-glucose at

_{2}*t*($\Delta {n}_{{l}_{1}}$ has a much higher amplitude, so is plotted on a different scale). When adding the beads, an increase in $\Delta {n}_{{l}_{1}}$ and $\Delta {n}_{{l}_{2}}$ is expected, but there is also an increase of $\Delta {n}_{{l}_{3}}$. Also when adding protein A at

_{1}*t*there is an unexpected decrease of $\Delta {n}_{{l}_{2}}$ and unexpected increase of $\Delta {n}_{{l}_{3}}$ as it was only expected that $\Delta {n}_{{l}_{1}}$ would increase. These things probably mean that the signals $\Delta {n}_{{l}_{1}}$, $\Delta {n}_{{l}_{2}}$ and $\Delta {n}_{{l}_{3}}$ are not sufficiently decoupled. Optimizing the theoretical matrix further is more complex compared to the two wavelengths/layers situation, because changing one parameter will result in change of all the signals $\Delta {n}_{{l}_{1}}$, $\Delta {n}_{{l}_{2}}$ and $\Delta {n}_{{l}_{3}}$, illustrating the complexity and limits of the approach based on theoretical analysis. Therefore, we ratio-based approach is better used for this analysis.

_{5}Figure 6(d) shows the determined $\overline{\Delta {n}_{\text{s}}}$ with the ratio-based approach. The ratios used for the analysis are again based on the determined ratios of $\Delta {N}_{eff}$ at the different wavelengths for the individual substances. Between *t _{1}* and

*t*only $\Delta {n}_{\text{glucose}}$ changes apart from some fluctuations seen for $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{protein}}$, which can be explained by boundary effects of the shifting interference pattern (see

_{2}*section 4.4 Noise, drift and artefacts in measurements*in main text). At

*t*the beads where added, but besides the increase of $\Delta {n}_{\text{bead}}$ there is also an increase of $\Delta {n}_{\text{protein}}$ and $\Delta {n}_{\text{glucose}}$ which means that the signals of $\overline{\Delta {n}_{\text{s}}}$ are not perfectly decoupled. This is also the case at

_{3}*t*when protein A is added to the sensor which mainly result in an increase of $\Delta {n}_{\text{protein}}$, but also in a small increase of $\Delta {n}_{\text{glucose}}$. Therefore, the ratios were also optimized by analysing the measurement based on two wavelengths/substances. An example is shown in Fig. 6(f), which shows that $\Delta {n}_{\text{protein}}$ was sufficiently decoupled from $\Delta {n}_{\text{glucose}}$ based on ${\lambda}_{1}$ and ${\lambda}_{3}$. Because only two wavelengths were used to discriminate between $\Delta {n}_{\text{protein}}$ and $\Delta {n}_{\text{glucose}}$ it was not possible to discriminate them from $\Delta {n}_{\text{bead}}$ which is shown between

_{5}*t*and

_{3}*t*where both $\Delta {n}_{\text{protein}}$ and $\Delta {n}_{\text{glucose}}$ increase. Figure 6(e) shows the result of $\overline{\Delta {n}_{\text{s}}}$ after optimization of the ratios which led to ${R}_{561/457}^{\text{protein}}$=0.837, ${R}_{660/457}^{\text{protein}}$=0.698, ${R}_{561/457}^{\text{bead}}$=0.967, ${R}_{660/457}^{\text{bead}}$=0.885, ${R}_{561/457}^{\text{glucose}}$=1.158 and ${R}_{660/457}^{\text{glucose}}$=1.215 from which ${R}_{660/561}^{{\text{s}}_{m}}$ can be calculated by dividing ${R}_{660/457}^{{\text{s}}_{m}}$ by ${R}_{561/457}^{{\text{s}}_{m}}$. All these values fall within the error margins of the experimentally determined ratios of the individual substances presented in Table 1. Using the slightly changed ratios, the three substances are nicely decoupled, illustrating that it is possible to discriminate between three different substances. However, the enhanced drift and artefacts in $\overline{\Delta {n}_{\text{s}}}$ makes it difficult to analyse these results. Moreover, when substances were added simultaneously (data not shown here) fitting based on two substances/two wavelengths is not possible. Therefore, the ratios used for the analysis should be measurable from measurements with the single substances and not be tuned afterwards. To realise this the spread in ratios should be reduced. More research is required to determine what the origin of the spread of the ratios is. In order to do this, it should be investigated if the spread can be explained by the artefacts or other noise sources of the measurements, the cleaning of the surfaces of the chip (larger spread is seen in binding of substances compared to bulk changes due to D-glucose) or the substances self (spread in protein A is smaller compared to beads). At least it is required to reduce the aforementioned artefacts which are enhanced too much when using three wavelengths to discriminate between three substances.

_{4}## Appendix D Artefacts in signal due to boundary effects of shifting interference pattern

Computer generated images of interference patterns (based on our four channel Young interferometer) were used to verify the correct working of the Labview program which is used to collect interference patterns and determine the corresponding phase changes during an experiment, to investigate artefacts when determining a phase change from a finite interference pattern and to test windowing functions to reduce artefacts. Calculations of the generated interference patterns are based on four point sources distanced at 60 μm, 80 μm and 100 μm, an imaged distance of 17.5 cm, and wavelengths of 457 nm and 660 nm. The generated images have a width of 1024 pixels, a height of 100 pixels and a dynamic range of 60000 counts and include shot noise (Poisson noise). To simulate a real experiment, a time varying $\Delta {N}_{eff}$ (~$\Delta \phi $) is introduced (see Fig. 7(a)). For each corresponding time point an image is calculated and stored for later analysis. Next, the Labview program loads the images, adds up the selected number of rows on which the interference patterns are imaged and subsequently adds 1024 zeros to increase spatial frequency resolution to improve phase readout. Optionally, a windowing function is applied before a Fast Fourier Transform (FFT) is executed. From the resulting spectrum, the phase and amplitude of the six different spatial frequencies are determined of which we now analyse one peak belonging to one channel pair. Figure 7(a) shows an example of the induced and calculated $\Delta {N}_{eff}$ for the two wavelengths. The same figure also shows the difference in $\Delta {N}_{eff}$between the induced and determined values. Figure 7(b) shows the determined amplitude and Fig. 7(c) shows the $\overline{\Delta {n}_{\text{substance}}}$ determined with the ratio-based approach based on the induced (ind) and determined (det) $\overline{\Delta {N}_{eff}}$. Figure 7(d), 7( e) and 7(f) show the $\overline{\Delta {N}_{eff}}$, the amplitude and the determined $\overline{\Delta {n}_{\text{substance}}}$ of a real measurement. Similar fluctuations (which we call artefacts) are seen in in the amplitude and $\overline{\Delta {n}_{\text{substance}}}$ when no windowing is applied on the simulated interference patterns. These artefacts are most prominent during (fast) changes in the induced $\Delta {N}_{eff}$.

To investigate this further, a linear $\Delta \phi $ (~$\Delta {N}_{eff}$) was induced and the peak-to-peak (pk-pk) values of the artefacts in $\Delta {N}_{eff}$ were determined to test the influence of the applied window on the size of the artefacts (both in amplitude and $\Delta \phi $ (~$\Delta {N}_{eff}$)). Figure 8(a) shows the linear $\Delta {N}_{eff}$ determined from the linear $\Delta \phi $, and the difference between the determined and induced $\Delta {N}_{eff}$ (=$\Delta {N}_{eff}$error, abbreviated as NE in the remainder of the text) for the case in which no window is applied and the case in which a in Labview build-in Blackman-Nuttall window is applied. Figure 8(b) shows the mean pk-pk values of the NE of different channel combinations, determined from $\Delta \phi $ measured at the spatial frequencies (sf) belonging to the channel combination in which a $\Delta n$ was generated in one of the channels as well as from the channel combinations in which no $\Delta n$ occurred (cross-talk, CT). To demonstrate the effect of windowing, results are plotted for different type of windows. For example, applying a Blackman-Nuttall or a Dolph-Chebyshev window, both CT and NE can be completely suppressed down to the shot-noise level as the artefacts were not visible above the shot-noise level.

Next, the use of different windows on real experimental data is evaluated. The mean pk-pk values of CT are similar to the mean pk-pk values of NE. Therefore, the mean pk-pk values of CT are used as a measure for the pk-pk values of NE for the real experiments, as it is not possible to determine the fluctuations in the measured signal of $\Delta {N}_{eff}$, because the slope ofthe measured signal is much higher than the slope of the artefacts. Also no induced $\Delta {N}_{eff}$ can be determined and consequently it is not feasible to determine the difference between a measured and induced $\Delta {N}_{eff}$ to determine the NE. Raw data (interference patterns) were saved and different windows were applied on the measured data. Figure 8(c) shows the fluctuations in $\Delta {N}_{eff}$ due to CT for a typical measurement where first D-glucose only (between *t* ≈500 and 1000 s) and subsequently D-glucose plus 85 nm beads (between *t* ≈1500 and 2000 s) were added simultaneously to the sensor. Figure 8(d) shows the pk-pk value of the first artefact in $\Delta {N}_{eff}$ (at *t* ≈500 - 700 s) due to CT as a function of the applied window. Applying different windows did not lead to significant differences in performance. Probably the measured interference patterns already contains a hardware-induced windowing. The non-ideal properties of the lenses, the grating and beam shape cause an ellipse-shaped image of the interference pattern as shown in Fig. 9. Before applying an FFT on the measured patterns, pixel intensities of each column in the recorded image are summed and therefore the ellipse-shaped image results in an interference pattern in which the intensities are suppressed at the edges which means that it already consists of a certain window. Furthermore, it was seen that different optics resulted in change in artefacts. Therefore, it should be tested if larger lenses and grating can reduce the artefacts in the signals of $\Delta {N}_{eff}$.

The analysis of an experiment with a two channel YI (two channels were blocked with a mask) showed similar artefacts as for a four channel YI, which means the artefacts are in the measured signal itself and not only induced by CT as there is only one spatial frequency peak for a two-channel YI.

## Appendix E Influence of drift on determined RI change

Here, we show simulations that were done to determine the influence of drift in a measured signal of $\Delta {N}_{eff}$ on the result of $\Delta n$. For the determination of $\Delta n$, the matrix of the ratio-based analysis approach is used together with ${R}_{660/457}^{binding}$ = 0.919, ${R}_{660/457}^{bulk}$ = 1.217. The influence of linear drift in $\Delta {N}_{eff}$ on $\Delta n$ is shown in Fig. 10. Linear drift in the signal $\Delta {N}_{eff}$ is translated to a linear drift in the result of $\Delta n$. The sign of the linear drift of $\Delta n$ is the determined by the sign and ratio of the drift of $\Delta {N}_{eff}$ at the different wavelengths. This can be explained from a theoretical perspective:

*c*and

_{1}*c*are constants which determine the amplitude of the linear drift of $\Delta {N}_{eff}$. One can see that this finally results in linear drift in the signal of $\overline{\Delta n}$ which is determined by the coefficients of the matrix

_{2}*M*and constants

*c*and

_{1}*c*.

_{2}## Appendix F Influence of input parameter values on the results for different analysis approaches

Calculating the value of $\Delta n$ in the applied approaches depends on the values of the various input parameters needed for the different approaches. Here, we investigate the sensitivity of the end-result on the parameter values. Figure 11 shows an experiment where first only D-glucose and later both 85 nm carboxylated polystyrene beads and D-glucose were added to the sensor, which is used for this investigation, and the corresponding determined $\Delta n$ which the approach based on the approach based on the theoretical analysis and the ratio-based analysis approach.

#### F.1 Approach based on theoretical analysis

The input parameters of the approach based on the theoretical analysis that were varied are *d _{core}* and

*d*Varying the

_{1}.*d*results in a varying level of both the value of $\Delta n$ of layer 1 and layer 2 at the D-glucose step. Independent of the layer thickness

_{core}*d*, the $\Delta n$ at the addition of only D-glucose should be the same in both layers, which is realized by choosing

_{1}*d*= 63 nm. Subsequently, the end level of both signals can be tuned by varying

_{core}*d*. The end level of the bulk should be zero, because there was no $\Delta n$ for the bulk compared to the starting situation were the bulk was also PBS. In the case of linear drift, the end level will not be zero but in line with the linear drift. This was realized with a

_{1}*d*= 65 nm, assuming a

_{1}*d*= 63 nm. Figure 11(b) shows the optimal result for $\Delta n$ based on

_{core}*d*= 63 nm and

_{core}*d*= 65 nm. Next, the

_{1}*d*and

_{core}*d*were varied and the change in $\Delta {n}_{{l}_{1}}-\Delta {n}_{{l}_{2}}$ (black dotted line in Fig. 11(b)) at

_{1}*t*= 1900 s was determined. Consequently, the deviation in terms of percentage compared to the correct value of $\Delta {n}_{{l}_{1}}-\Delta {n}_{{l}_{2}}$ at

*t*= 1900 s (based on

*d*= 63 nm and

_{core}*d*= 65 nm) was determined, which is shown in Fig. 12. When we assume the deviation in $\Delta {n}_{{l}_{1}}-\Delta {n}_{{l}_{2}}$ should be maximally 10% and we fix the parameters

_{1}*d*or

_{core}*d*and vary the other, this results in the dotted lines in Fig. 12. When both

_{1}*d*and

_{core}*d*result in a deviation of 10% then the final deviation in $\Delta {n}_{{l}_{1}}-\Delta {n}_{{l}_{2}}$ stays within the 20%. We assume that this deviation is acceptable but off course the limits of the acceptable deviation might be different for each application. For the

_{1}*d*this means that it should be determined with an maximal deviation of approximately ±1 nm. When this value is accurately determined it can be seen that the value of

_{core}*d*is less critical (a range of approximately 50 nm is fine). It should be noted that these deviations are determined for this specific case and at one time point. Deviations can be different when substances are different. Moreover, deviations in terms of percentage might be much larger when $\Delta {n}_{{l}_{1}}-\Delta {n}_{{l}_{2}}$ goes towards zero.

_{1}#### F.2 Ratio-based approach

Here, we determined the influence of the ratios ${R}_{660/457}^{bead}$ and ${R}_{660/457}^{\text{glucose}}$ on the end result of $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{glucose}}$. First, the best fit of $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{glucose}}$ was determined. This resulted in a ${R}_{660/457}^{\text{glucose}}$ = 1.220, having a zero level for the beads when only D-glucose was added. To fit the end level of the D-glucose with the expected value, assuming a constant linear drift, the ${R}_{660/457}^{bead}$ = 0.895. Subsequently, the ratios ${R}_{660/457}^{bead}$ and ${R}_{660/457}^{\text{glucose}}$ were varied. The deviation of $\Delta {n}_{\text{bead}}$ and $\Delta {n}_{\text{glucose}}$ (both at *t* = 1900 s) in terms of percentage compared with optimal fitted results are determined and shown in Fig. 13. When we assume a deviation in $\Delta {n}_{\text{bead}}$ of maximally 10% for a fixed ${R}_{660/457}^{bead}$, the ${R}_{660/457}^{\text{glucose}}$ should be between 1.192 and 1.254 (see dotted lines in Fig. 13(a)). This results in an difference of 0.062 which is higher than the deviation measured in ${R}_{660/457}^{\text{glucose}}$ of 0.032 (= ±0.016, see Table 1), which means that the spread measured in ${R}_{660/457}^{\text{glucose}}$ results in acceptable deviation in $\Delta {n}_{\text{bead}}$ based on the assumptions we made.

When we fix ${R}_{660/457}^{\text{glucose}}$ and assume again a maximal deviation of 10% in $\Delta {n}_{\text{bead}}$, the ${R}_{660/457}^{bead}$ should be between 0.859 and 0.925, which is equal to a difference of 0.066. When both ratios ${R}_{660/457}^{\text{glucose}}$ and ${R}_{660/457}^{bead}$ are varied with the deviation of 0.062 and 0.066 respectively, this result in a maximal deviation in $\Delta {n}_{\text{bead}}$ of 20%. The difference of 0.066 is lower than the response of the beads between measurements of 0.090 (= ±0.045, see Table 1). So the spread measured in ${R}_{660/457}^{bead}$ is not acceptable when we assume a maximal deviation in $\Delta {n}_{\text{bead}}$ of 20%. Therefore, more research is required to determine what the origin of the spread of the ratios is in order to reduce this spread. It should be investigated if the spread can be explained by the artefacts or other noise sources of the measurements, the cleaning of the surfaces of the chip (larger spread is seen in binding of substances compared to bulk changes due to D-glucose) or the substances self (spread in protein A is smaller compared to beads). Again, it should be determined for each application what the maximally allowed deviation is and it should be noted these deviations are determined for this specific case and at one time point in the graph of Fig. 11.

The deviation of $\Delta {n}_{\text{glucose}}$ was also determined as a function of ${R}_{660/457}^{bead}$ and ${R}_{660/457}^{\text{glucose}}$ in a similar way as for $\Delta {n}_{\text{bead}}$. This resulted in comparable maximum allowable values of ${R}_{660/457}^{bead}$ and slightly higher maximum allowable values of ${R}_{660/457}^{\text{glucose}}$ as shown in Fig. 13(b). For determination of $\Delta {n}_{\text{glucose}}$ within 20% accuracy, the ratio ${R}_{660/457}^{\text{glucose}}$ should be between 1.181 and 1.271 and the ratio ${R}_{660/457}^{bead}$ should be between 0.857 and 0.926. These values correspond to spreads of 0.090 for ${R}_{660/457}^{\text{glucose}}$ and 0.069 for ${R}_{660/457}^{bead}$. Again, the spread in the measurements for ${R}_{660/457}^{\text{glucose}}$ from measurement to measurement is lower than the required 0.090, so sufficient. The spread in ${R}_{660/457}^{bead}$ from measurement to measurement is again higher than the required 0.069. Consequently, to determine the $\Delta {n}_{\text{glucose}}$ within 20% accuracy, the spread ${R}_{660/457}^{bead}$ from measurement to measurement should be reduced. As was stated before, more research is required to determine the origin of the spread.

## Appendix G Cleaning protocol

As preferably the chip should be used in order to compare measurements, chips have to be reused and therefore cleaned sufficiently in between measurements. The following steps describe the cleaning procedure of the waveguide chips in between measurements:

- 1) rinse chip with water
- 2) rinse chip with acetone and wash chip with acetone and cotton (4x)
- 3) rinse chip with isopropanol (99.8%, filtered with 0.22 μm filter) and wash chip with same isopropanol and cotton (4x)
- 4) rinse chip with isopropanol (99.8%, filtered with 0.22 μm filter)
- 5) blow dry with instrumental air or nitrogen gas (N
_{2})

Fluorescent carboxylated beads were added to the sensor surface and after the measurement and after the cleaning protocol imaged with a fluorescence microscope to verify that the cleaning protocol was sufficient for removing the beads (see Fig. 14). As the protein A was not fluorescent and is smaller than the diffraction limit, the protein A could not be imaged and the cleaning protocol was not verified for the protein A. However, as we see that beads bind stronger to the surface than protein A (for protein A see more desorption after applying a washing step compared to the beads), we expect that the protein A is sufficiently removed from the surface using this cleaning protocol.

## Acknowledgments

We want to thank XiO Photonics for their help with the realisation of the fiber butt-end coupling and A. Sidhu for her help in preparing the samples of the blind experiments. This work is supported by NanoNextNL, a micro and nanotechnology consortium of the Government of the Netherlands and 130 partners.

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