---
title: "Critical-angle refractometer enhanced by periodic multilayer coating"
authors: ["Valery N. Konopsky", "Elena V. Alieva"]
affiliation: "Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow region, 142190, RUSSIA."
journal: "Sensors and Actuators B: Chemical"
year: 2010
volume: "150"
issue: "2"
article_number: ""
pages: "794--797"
doi: "10.1016/j.snb.2010.07.034"
type: journal-article
site_group: "Biosensors based on optical surface modes"
url_abstract: "https://valery.konopsky.com/paper/SAB2010/SAB2010.htm"
url_pdf: "https://valery.konopsky.com/kvnlocal/SNB12488.pdf"
language: en
source_tex: "Z:\\ValeryData\\Valery_New\\my_articles\\Refractometer\\Sens_and_Act_B\\Manuscript\\Konopsky2SNB.tex"
source_pdf: "Z:\\ValeryData\\Valery_New\\my_articles\\Refractometer\\Sens_and_Act_B\\Published\\SNB12488.pdf"
---
## Abstract

We present a high-precision technique for determination of the refractive index (RI) of liquids and gases. The technique is based on standard critical-angle refractometry, which sensitivity is enhanced by deposition of an additional periodic multilayer stack on the interface between a prism and the medium under investigation. We show that this multilayer stack may be designed so that a reflectance change near the critical angle becomes much more sharp than the one in the standard refractometers. Test measurements of set of glucose concentrations in the water are presented and baseline noise of $9\!\times\!10^{-8}~\mathrm{RIU}/\sqrt{\mathrm{Hz}}$ is attained.

Refractometry ,RI based detector for chromatography ,On-line concentration monitoring ,Chemical sensor

# Introduction

Refractometry is a widely used detection method that has important applications in different domains. The refractive index (RI) of a solution is related to the concentration of dissolved materials and refractometry offers a simple, convenient and non-intrusive means of measuring concentration [1]. RI detectors are used for on-line concentration measurements in many analytical techniques, such as chromatography [2], for liquid separation monitoring, for chemical sensors and so on. RI based sensors have characteristics which make them attractive alternative to fluorescence and absorption based sensors. The most advantages property of RI based detectors is theirs universal response, because they do not demand that the analyte possesses specific properties, such as absorbance, fluorescence, or electrochemical activity.

# Working principle

Critical-angle refractometers [3, 4], such as classical Abbe refractometers, derive the RI of the sample under investigation by measuring the angle of total internal reflection (TIR) $\theta_\mathrm{TIR}$ from this sample. The sample RI $n_\mathrm{e}$ is then given by
``` math
\begin{equation}
    n_\mathrm{e}=n_0\sin(\theta_\mathrm{TIR})\, ,
\end{equation}
```
where $n_0$ is the RI of the prism in which the critical angle $\theta_\mathrm{TIR}$ is measured. If the incident angle is above the critical value and $n_0>n_\mathrm{e}$, then total reflection occurs from the external medium and $R(\theta_0)= 1\: \mathrm{at}\:  \theta_0>\theta_\mathrm{TIR}$, while at $\theta_0<\theta_\mathrm{TIR}$ some light is transmitted in the external medium and the reflection coefficient $R(\theta_0)$ is less than unity.

In idealized case, considering the lossless media and plane incident wave without divergence (i.e., infinite plane wave and infinite surface), one may expect that the derivative $\partial R(\theta_0)/\partial\theta_0$ would be equal to infinity at $\theta_0\equiv\theta_\mathrm{TIR}$ and the $\theta_\mathrm{TIR}$ value would be measured with the absolute precision. However, in the real world, the natural divergence of the optical beams (with a dimension $D$ and a wavelength $\lambda$) is at least $\lambda/D\!\sim\!10^{-4}\!-\!10^{-3}$ rad and even pure water has the imaginary part of its RI of the order of $\mathrm{Im}(n_\mathrm{e})\simeq 10^{-8}$, while optical glasses have $\mathrm{Im}(n_0)\simeq 3\!\times\!10^{-8}$. The pointed fundamental reasons and a lot of less fundamental reasons, such as surface imperfections, scattering and interference lead to a quite finite value of $\partial R(\theta_0)/\partial\theta_0$ at $\theta_0\simeq\theta_\mathrm{TIR}$. Therefore, the measurement precision of the $\theta_\mathrm{TIR}$ value and the sample RI value in the standard critical angle refractometry are limited as well.

In the present article we show that it is possible to increase considerably the sharpness of the reflection coefficient as a function of the incident angle near the critical angle (i.e., increase the derivative $\partial R(\theta_0)/\partial\theta_0$ at $\theta_0\le\theta_\mathrm{TIR}$) by appropriate multilayer coating of the prism. The physical reason for the sharp decreasing of the reflection coefficient immediately below the critical angle is the presence of a lossy optical surface mode at the external interface of the periodic multilayer stack. A small reflection coefficient below the critical angle is the result of a destructive interference between the reflected wave and the lossy surface wave that reradiated back to the prism with the corresponding rotation of its phase.

# Experimental

The sketch of the experimental setup is shown in Fig. 1. A light beam from fiber-coupled He-Ne laser ($\lambda=632.8\,\mathrm{nm,}\: P=0.2$ mW) is focused on a prism base by an objective with focal length $f=60$ mm. A glass plate with the one-dimensional photonic crystal (1D PC) structure deposited on its external side is fixed on the base of the prism by RI matching gel.

![The sketch of the experimental setup.](media/SAB2010/Fig1.eps)

*The sketch of the experimental setup.*

A flow cell is mounted on this coated glass plate. The flow cell is made from a glass slide with two holes in which two glass tubes are fitted, serving as inlet and outlet, respectively. An internal surface of this glass slide is frosted to avoid a reflection and an additional interference of the refracted beam (at $\theta_0<\theta_\mathrm{TIR}$). The inlet tube is connected to a small tank with the solution under study. Due to the force of gravity the solution flows to the outlet. The flow velocity is controlled by an elevation difference of the inlet tank level and the outlet end. The height of the cell is determined by the thickness of the Teflon film, which serves as a sealing gasket and as a spacer between the multilayer stack and the glass slide. We use the Teflon films with the thickness 1 mm and the corresponding flow cell volume is 100 $\mu$L. The dead volume of the flow cell system is approximately 25 $\mu$L. Gravity flows of water and glucose solutions are used with volumetric flow rate up to several mL/min.

The structure of the multilayer stack in the present experiments is as follows: substrate/$(LH)^{3}L'$/water, where $L$ is a $SiO_2$ layer with thickness $d_1=186.4$ nm, $H$ is a $Ta_2O_5$ layer with $d_2=115.2$ nm and $L'$ is a $SiO_2$ layer with $d_3=776.8$ nm. The $SiO_2/Ta_2O_5$ 7-layers structure (started and finished by $SiO_2$ layers) is deposited by magnetron sputtering. The prism and the glass plate substrate are made from BK-7 glass. The RIs of the substrate, $SiO_2$, $Ta_2O_5$ and water at $\lambda=632.8$ nm, are $n_0=1.515$, $n_1=n_3=1.47$, $n_2=2.07$ and $n_e=1.332$, correspondingly.

![The reflection coefficient of the plane wave from the prism with the multilayer coating (solid line – p -polarization), and without any coating (dashed line for p -polarization and dotted line for s -polarization).](media/SAB2010/Fig2.eps)

*The reflection coefficient of the plane wave from the prism with the multilayer coating (solid line – p -polarization), and without any coating (dashed line for p -polarization and dotted line for s -polarization).*

This 1D PC structure supports *p* -polarized (TM) optical surface wave [5, 6] at the excitation angles above the critical TIR angle. At the excitation angles below the critical angles this surface wave becomes a lossy wave and its surface propagation length is vanishing. But, nevertheless, part of energy of this wave is reradiated back to the prism with some phase shift. Due to the destructive interference between the reflected wave and the phase shifted reradiated wave the reflection coefficient $R(\theta_0)$ is diminish at the angles immediately below the TIR angle ($\theta_0\le\theta_\mathrm{TIR}$).

The intensity distribution of the reflected light is detected by a 512-pixels Hamamatsu photodiode array. The calculated reflection coefficient of our 1D PC structure for *p* -polarized light is shown in Fig. 2 by solid line. In the calculation we use plane waves and RIs with the next imaginary parts: $n_0=1.515+i\!\times\!3\!\times\!10^{-8}$ and $n_\mathrm{e}=1.332+i\!\times\!10^{-7}$.

The dashed line and the dotted line present the calculated reflection from a bare prism (without any coating) for *p* -polarized and *s* -polarized light respectively. One can see that the sharpness (and, therefore, 1st and 2nd derivatives) of the reflection coefficient is 5 times larger for the prism with the multilayer coating. This permits us to detect the position of the critical angles and its changes more precisely.

# Results and discussion

![The refractometer response to changes in glucose concentration in water. The corresponding glucose concentrations are shown in %(v/v). The measurement time is 1 s per point without posterior data averaging or smoothing. The bottom insert: noise of the baseline. The upper insert: the decrease of the solution RI in response to increase of flow velocity from 0.4 mL/min to 1.2 mL/min.](media/SAB2010/Fig3.eps)

*The refractometer response to changes in glucose concentration in water. The corresponding glucose concentrations are shown in %(v/v). The measurement time is 1 s per point without posterior data averaging or smoothing. The bottom insert: noise of the baseline. The upper insert: the decrease of the solution RI in response to increase of flow velocity from 0.4 mL/min to 1.2 mL/min.*

To demonstrate the sensitivity of this technique we have measured changes of RI of the water-glucose solution with different glucose concentrations. The results are presented in Fig. 3. The glucose concentrations are pointed in the figure. The light accumulation time is 1 s per point and no posterior data averaging or smoothing was done. On the bottom insert in Fig. 3 the baseline noise is depicted. The noise floor of the baseline is equal $\delta n_\mathrm{e}\simeq 9\!\times\!10^{-8}~\mathrm{RIU}/\sqrt{\mathrm{Hz}}$.

The upper insert magnifies an interesting dependence of the RI of the solution on its flow velocity. At $t=280$ sec the flow velocity was increased from 0.4 mL/min to 1.2 mL/min. One can see that the RI of the liquid is decreased on the value $2\!\times\!10^{-6}$ refractive index unit (RIU). We assume that this RI change is the result of the liquid temperature increase in response of an extra heat generation due to increase of a fluid friction, which is depended on the flow velocity. The change of the RI by $2\!\times\!10^{-6}$ corresponds to the change of the water temperature near surface by $0.02\,^0\mathrm{C}$.

# Conclusions

In this paper we have proposed and experimentally tested a new RI sensor with the RI sensitivity comparable or better then the RI sensitivity of modern label-free sensors and biosensors [7]. The attained baseline noise $9\!\times\!10^{-8}~\mathrm{RIU}$ corresponds to glucose concentration noise $10^{-4}\%$ ($=10^{-4}$ Brix) or $0.76\,\mu$g/mL. We suppose that intended applications of the device are in gas/liquid chromatography and possibly in chemical/concentration sensing rather than in the absolute determination of RIs.

# Acknowledgments

This work was financially supported in part by the Grant 09-02-00366-a from the Russian Foundation for Fundamental Researches.

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R. Falciai, A. Mignani, A. Vannini, Long period gratings as solution concentration sensors, Sens. Actuator B-Chem. 74 (1-3) (2001) 74–77.

S. Woodruff, E. Yeung, Refractive-index and absorption detector for liquid-chromatography based on Fabry-Perot interferometry, Anal. Chem. 54 (7) (1982) 1174–1178.

G. Meeten, A. North, Refractive-index measurement of absorbing and turbid fluids by reflection near the critical angle, Meas. Sci. Technol. 6 (2) (1995) 214–221.

Q. Song, C. Ku, C. Zhang, R. Gross, R. Birge, R. Michalak, Modified critical angle method for measuring the refractive-index of biooptical materials and its application to bacteriorhodopsin, J. Opt. Soc. Am. B-Opt. Phys. 12 (5) (1995) 797–803.

V. N. Konopsky, E. V. Alieva, Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface, Phys. Rev. Lett. 97 (25) (2006) 253904.

V. N. Konopsky, E. V. Alieva, Photonic crystal surface waves for optical biosensors, Anal. Chem. 79 (12) (2007) 4729–4735.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, Y. Sun, Sensitive optical biosensors for unlabeled targets: A review, Anal. Chim. Acta 620 (1-2) (2008) 8–26.

# Vitae

Valery N. Konopsky received the Ph.D. and M.S. degrees from the Moscow Institute of Physics and Technology in 1996 and 1993, respectively. During 1990–1993 he worked at Lebedev Physical Institute in Moscow and then, during 1993–1996, he worked at the Institute of Spectroscopy in Troitsk. Since 1996 he is a staff member of the Institute of Spectroscopy and currently he is a Senior Scientific Researcher, headed a group that is active in optical investigation of surfaces and surface nanostructures. His present research interests include surface optical waves, optical chemical sensors and biosensors.

Elena V. Alieva received the M.S. degrees from the Moscow Institute of Physics and Technology in 1976 and received her PhD in Physics and Mathematics from the Institute of Spectroscopy, Russian Academy of Sciences in 1980. Since 1988 she is a Senior Scientific Researcher at the Institute of Spectroscopy. Her current research interests include surface optics, surface electromagnetic waves and spectroscopy of surfaces and thin films.

## References

1. R. Falciai, A. Mignani, A. Vannini, Long period gratings as solution concentration sensors, Sens. Actuator B-Chem. 74 (1-3) (2001) 74--77.

2. S. Woodruff, E. Yeung, Refractive-index and absorption detector for liquid-chromatography based on Fabry-Perot interferometry, Anal. Chem. 54 (7) (1982) 1174--1178.

3. G. Meeten, A. North, Refractive-index measurement of absorbing and turbid fluids by reflection near the critical angle, Meas. Sci. Technol. 6 (2) (1995) 214--221.

4. Q. Song, C. Ku, C. Zhang, R. Gross, R. Birge, R. Michalak, Modified critical angle method for measuring the refractive-index of biooptical materials and its application to bacteriorhodopsin, J. Opt. Soc. Am. B-Opt. Phys. 12 (5) (1995) 797--803.

5. V. N. Konopsky, E. V. Alieva, Long-range propagation of plasmon polaritons in a thin metal film on a one-dimensional photonic crystal surface, Phys. Rev. Lett. 97 (25) (2006) 253904.

6. V. N. Konopsky, E. V. Alieva, Photonic crystal surface waves for optical biosensors, Anal. Chem. 79 (12) (2007) 4729--4735.

7. X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, Y. Sun, Sensitive optical biosensors for unlabeled targets: A review, Anal. Chim. Acta 620 (1-2) (2008) 8--26. thebibliography.

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