1. Introduction

Light based sensors are routinely used to analyze the composition of solids, fluids and gases. A common procedure is to use diffractometers or spectrophotometers in order to determine the chemical composition of a sample material. This kind of technology is reliable and routinely used but usually bulky and expensive. New possibilities for obtaining low cost, yet efficient, novel devices would be desirable. In the last 20 years, scientific research has shown a growing interest in realizing micro/nano structures in soft matter both for fundamental and industrial purposes [1–4]. One of the main challenges is to involve these materials in the biological/medical field to obtain very sensitive devices. Scientific literature is plenty of examples in this direction. An interesting one is offered by Broer et al. who have successfully realized holographically sculptured structures working as highly selective membrane [5]. Crawford has shown that by combining soft matter and nanotechnologies it is possible to open new frontiers in optically probing biological systems [6]. Finally, Sutherland et al. suggest the use of diffraction gratings as a way for detecting hazardous agents in the environment [7]. In this paper, we show how a binary diffraction grating realized with photoresist materials can perform as an accurate and sensitive device for measuring the refractive index of a medium. An eventual implementation of such a device can find application in the biological/medical field as a low-cost solution for performing self-made analysis or in the food and agro-industrial sector to make on-site quality checks of natural products (Oil or wine, etc.).

The very first bench-top laboratory refractometer is due to Ernst Abbe [8]. This device is very accurate but, due to the use of a prism (or a hemisphere), the interval of measurable refractive indices is limited to the refractive index by which the prism is made. Another common way to measure the refractive index of a medium is to use ellipsometric techniques [9]. The optical setup involves a He-Ne laser, a polarizer and a quarter wave-plate. However, in order to perform a reliable measurement, the medium needs to be spread on a very thin layer. This situation becomes cumbersome when probing the temporal behavior of a system. Another possibility is offered by the intracavity laser refractometry in reflection (ILRR), recently developed by Gonchukov et al. [10]. It is known that a slant reflection from an interface between two media introduces a phase shift between waves with different polarization. By measuring and comparing this shift with the one predicted by Fresnel theory, it is possible to estimate the refractive index of a medium put on the interface. A limit of this technique, is represented by the mode stability of the used laser. Moreover, the test medium needs to be put in direct contact with the glass interface where the reflection takes place.

In the following, we show another possibility to perform such measurement by using a holographic surface grating, written on a common polymethylmethacrylate substrate (PMMA or glass, or any other optically transparent material) by means of photoresist materials. In our scheme, the grating is put in optical contact with one of the faces of a prism-shaped PMMA hollow container that encloses the test material. The optical contact between the grating and the prism can be easily realized by using a refractive index matching fluid. Alternatively, directly patterning or imprinting the grating onto the external side of the hollow container can be implemented in order to improve the compactness of the device. This device (Fig. 1 ) is robust against laser mode instability and does not require the layering of the medium under investigation. The isosceles faces of the prism make an angle γ with the hypotenuse in contact with the grating. A collimated monochromatic beam (laser or collimated narrow band LED), incident on one of these faces, propagates throughout the medium (or air if the prism is empty) before arriving on the PMMA side where the grating is mounted. It is worth noting that, if the incident light is perpendicular to the entrance surface, whatever the medium inside the prism is, no refraction takes place at the PMMA/medium interface. This implies that, at the exit of the medium, the optical beam always makes an angle γ with the normal to the medium/PMMA interface. By propagating in the PMMA layer in contact with the grating, this beam is subject to refraction. The refracted angle α can be easily calculated by means of the Snell law [11]:

 

Fig. 1 Sketch of the device. A hollow prism contains tiny volumes of test materials and a diffraction grating is put in optical contact with one of its surfaces. Light is normally incident on the external surface of the prism and propagates without refraction throughout materials. The angle of incidence on the grating surface (α) and that of diffraction (β) are related to the refractive index n_mat of the test material.

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Here, n_mat and n_PMMA are respectively the refractive indices of the test material and of the PMMA. Because γ is fixed, the refractive index n_mat of the test material is directly related to the refracted angle α that is the incidence angle made by the optical beam on the grating surface (α_> in case n_mat>n_PMMA and α_< if n_mat<n_PMMA). If the periodicity Λ of the grating is known, by using the grating equation, it is easy to calculate the angle β by which this beam is diffracted by the grating.

If we indicate with m the considered diffracted order, β is given by:

From Fig. 2 , we can notice that the obtained behavior is, in first approximation, linear in the interval considered for n_mat. We can also write the angular variation of β respect to n_mat as the derivative:

 

Fig. 2 behavior of the diffracted angle made by the minus first order respect the grating normal versus the refractive index of the test material in the interval 1.00< n_mat<2.00.

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By considering that the previous is almost constant in the interval 1.00<n_mat<2.00, we deduce that an increase Δn_mat will correspond, in a linear way, to an angular shift Δβ of the diffracted order:

The minimum detectable Δn_mat represents the sensitivity of our device. By using a high-resolution CCD camera (or a linear array photodiode) it is possible to detect the angular shift Δβ of the diffracted beam through the corresponding spatial shift $\Delta x=L\cdot \Delta \beta$ where L is the distance between the grating and the CCD camera or the sensor. The typical pixel size of a high resolution CCD camera is as low as 10μm. By assuming this value as the minimum detectable spatial shift Δx and combining its expression with those in Eqs. (3) and (4) we estimate the sensitivity of the device as $\Delta n_{mat}^{\min }\approx {10}^{-4}$. In the previous, we considered L = 10cm and used the values reported above for the angle γ, the probe wavelength λ, the grating periodicity Λ and the refractive index n_mat. If a higher device sensitivity is necessary, it is enough to increase the distance L. In order to keep compact the size of an eventual device, it is convenient to fold the longer light path from the grating to the observation plane by using mirrors.

2. System design

The implementation of the system described above, requires an accurate design of the diffraction grating. Several parameters of the grating influence the behavior of the device. One of the most important is the periodicity Λ. This is directly related to the derivative of β with respect to n_mat [see Eq. (3)] and hence to the sensitivity of the device. Indeed, by considering the expression in Eq. (4), the higher the value of this derivative, the higher is the angular shift due to an n_mat variation, the better the device sensitivity. Once Λ is fixed, it is necessary to calculate the most convenient value for the prism angle γ. This choice has a consequence on the range of refractive indices detectable by the device. Indeed, it must be $\left(n_{mat}/n_{PMMA}\right)\sin \gamma \le 1$ otherwise the light coming from the medium is totally internally reflected by the medium/PMMA interface and cannot reach the grating. Finally, an important role is played by the intensity of the light diffracted by the grating: if this beam is too weak, it cannot be efficiently detected. The diffraction efficiency (η) is a measure of the diffractive power of a grating. It is defined as the ratio between the intensity of the desired diffracted beam and that of the incident beam. In general, η = f(α, λ, d, Δn) where α is the angle of incidence of the light on the grating, λ is the probe wavelength, d is the grating depth and Δn the refractive index modulation between the material by which the grating is made and air in our case. Taking into account the geometry illustrated in Fig. 1, the probe wavelength and the index modulation are fixed while it is possible to vary the prism angle (that is strictly related to the angle α) and the grating depth d. Simulations have been performed by using the commercially available software GSolver that is a rigorous diffraction grating efficiency calculation tool [12]. In the simulations we assumed our grating as a binary structure with 50% duty cycle, periodicity Λ = 500nm and light incoming from a PMMA layer. In Fig. 3 , obtained results are represented as a contour plot. It can be noticed that a grating depth d = 700nm and an angle α in the range 25° ÷ 55° can provide an optimal diffraction efficiency value of about 60-70%.

 

Fig. 3 Contour plot of the diffraction efficiency of the grating plotted as a function of the prism angle α and the grating depth d.

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It is worth to remind that the angle γ of the light incoming at the interface medium/PMMA is common to all considered media while the incidence angle α to the grating is not. Indeed, depending on the test material, this angle can assume all values up to α_max = 90°. For what concerns the minimum value for α (in case the test material is air), it can be chosen depending on the range of refractive indices we intend to investigate. We chose α_min = 32° which corresponds, for a grating depth d = 700nm, to the maximum achievable value for the diffraction efficiency (η = 70%). To this angle corresponds a prism angle γ = 52.25°. By using the condition $n_{mat}/n_{PMMA}\sin \gamma \le 1$ with this value for γ and n_PMMA = 1.491, the measurable range of refractive indices results 1.00≤n_mat≤1.88. In order to fabricate the grating with parameters as designed above, the procedure reported in [13] has been followed.

3. Device realization and characterization

For testing our idea, we prototyped the device by using the experimental set-up shown in Fig. 4(a) . A polarized He-Ne laser beam (λ = 633nm) is directed onto the hollow PMMA prism with an incidence angle γ respect the grating surface. Part of the beam is transmitted (0T) by the grating and part is diffracted (−1T) with an angle β. The grating is put in optical contact with the prism and both are mounted on a holder controlled by a translation and a rotation stage. By acting on the rotation stage it is possible to obtain the normal incidence of light on the entrance prism face. In Fig. 4(b), a photograph of the prism utilized for the experiment is reported, whereas a SEM image of the fabricated grating is shown in Fig. 4(c). The capacity of the device can be reduced or increased at will; in case a smaller volume is necessary, a smaller prism can be realized and, by conveniently reducing the spot size of the laser, the device functionalities remain the same. The fabricated grating has a periodicity Λ = 515nm which is compatible with results of simulations. In order to perform refractive index measurements, we estimated the angle by which light is diffracted by the grating by using the rotation stage where the sample is mounted. By substituting the measured value in Eq. (2), it is possible to calculate the refractive index value of the test material contained in the prism. Several media have been tested by using this method and obtained results, together with a comparison with corresponding refractive index values found in literature, are resumed in Table 1 . Obtained values are compatible with literature ones within the experimental error that we estimated in 10⁻². This sensitivity is way far from the one we predicted for our device (10⁻⁴) but, as anticipated above, in order to obtain such high sensitivity, it is necessary a more sophisticated implementation of the device that can be obtained by involving a high-resolution CCD camera for precisely measuring the position of the diffracted spot. Our aim, at the moment, was just to confirm the effectiveness of the technique and, in this view, obtained results are highly reliable.

 

Fig. 4 (a) Optical setup for device characterization; M, mirror; P1, P2 polarizers; S, sample; 0T, zero transmitted order; -1T, first transmitted order; α, incidence angle; β, diffracted angle. (b) Detail of the PMMA hollow prism used as a container for the test material. (c) SEM picture of the diffraction grating.

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Table 1. Measurements of the refractive index of several materials compared with corresponding values obtained with other techniques and found in literature

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4. Conclusions

In this paper, we have shown that by combining refraction and diffraction in an optical system it is possible to perform high sensitive analysis and refractive index measurements of a material in solid, liquid or gaseous phase. In more detail, the described system is represented by a diffraction grating put in optical contact with a hollow prism, used as a container of the test material. Probe light impinges on one of the prism faces and propagates throughout the test material. At the exit of the medium, the grating diffracts the light incident on it. The measurement of the diffracted angle can allow the calculation of the material refractive index with a sensitivity up to 10⁻⁴. An experimental implementation of this system has been set-up and the measurement of the refractive index of several materials has been taken. Even if this measurement has not been performed by using a high-resolution CCD camera, calculated values for the refractive indices are compatible, within the experimental error, with corresponding ones found in literature. An eventual device, based on this working principle can reveal itself as robust and low cost and find application in the healthcare or agroindustrial field. The main advantage of such a device is the absence of any contact between the grating surface and the test material. This preserves the grating functionalities ideally forever. Moreover, the simplicity and effectiveness of this sensor suggests a possible use as a research tool for measuring diffusion dynamics and local changes of the refractive index in the sample.