Effect of boundary on refractive index of PDMS - OSA Publishing

Effect of boundary on refractive index of PDMS Ivan Martinček,1 Ivan Turek,2 and Norbert Tarjányi1,* 1

Department of Physics, Faculty of Electrical Engineering, University of Žilina, Univerzitná 1, Žilina 01026, Slovakia 2 Berlínska 4, Žilina 01008, Slovakia * [email protected]

Abstract: In this contribution we present some results of a study of a refractive index inhomogeneity near the boundary of polydimethylsiloxane (PDMS) samples. We have observed inhomogeneities of the refractive index at PDMS–glass, PDMS–brass, PDMS–Teflon, PDMS–polystyrene and PDMS–PDMS boundaries. The greatest changes of the refractive index were observed at the PDMS–PDMS boundary where an increase of the refractive index in a narrow region close to the boundary was observed. It gives the possibility for guiding light. The existence of such a waveguide was proved by the fact that the boundary also guided light when samples containing PDMS–PDMS boundaries had been bent. ©2014 Optical Society of America OCIS codes: (160.2710) Inhomogeneous optical media; (130.5460) Polymer waveguides.

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Received 2 Jun 2014; revised 30 Jul 2014; accepted 31 Jul 2014; published 4 Sep 2014

1 October 2014 | Vol. 4, No. 10 | DOI:10.1364/OME.4.001997 | OPTICAL MATERIALS EXPRESS 1997

1. Introduction Polydimethylsiloxane (PDMS) is an elastomer which is considered as a material for various photonic applications. PDMS is highly light-transparent in the visible spectral region and highly absorbent at some wavelengths in the near infrared region. It is chemically inert, biocompatible, thermally stable, permeable to gases when prepared in thin layers, isotropic in the basic state, homogeneous, able to absorb some solvents and oils, and simple to handle and manipulate. These properties make it attractive for different applications in different areas such as the electronics, plastics, textiles, automotive, and aerospace industries [1] and in microfluidic technology and photonics [2]. In photonics, PDMS is used for preparation of different photonic elements, for example lenses [3], diffraction gratings [4], Bragg gratings [5], optofluidic waveguides [6], multimode and singlemode waveguides [7,8], optical fibers and tapers [9], and so on. These elements are prepared by different advanced techniques such as proton beam writing [4], low-cost DUV irradiation [8], soft lithography [2], and so on. When some optical elements are prepared, knowledge of the optical properties of the material used is important. Many of the optical parameters of PDMS are known, for example its thermo-optic coefficient or the dependence of the refractive index and absorption on the wavelength [see for example [10]]. It is also well known that PDMS is an elastic material. The elasticity of PDMS is used, for example, in the construction of pressure sensors [11] or displacement sensors [12]. It has been observed that deformation of PDMS affects its optical parameters. A strong deformation dependence of its absorption coefficient and refractive index was stated in [13]. Therefore it follows that the deformation dependence of the optical parameters of the PDMS should be taken into account when PDMS is used for optical applications. PDMS is permeable to gases and easily absorbs some vapors and liquids [14]. This feature is used, for example, in solid-phase micro-extraction (SPME), where PDMS is used as a coating material for SPME fibers [15]. On the other hand, the gas and liquid absorption causes changes of the optical parameters of the PDMS. Also, the capillary forces acting during the polymerization of PDMS can change its refractive index. So, it is also necessary to take into account this effect when optical elements containing PDMS are designed. That is why we present the results of our study of the effect of the boundary on the refractive index of PDMS. For the preparation of all PDMS samples, we used silicone Sylgard 184 (Dow Corning) supplied as a two-part liquid component kit. After mixing the prepolymer (part A) and curing agent (part B) at a ratio of 10:1, the prepared elastomer was cured at a temperature of 22°C. 2. Description of experimental methods used During our work with PDMS, we noticed that in samples prepared as multiple layers the boundary between the layers could be seen although the layers were formed from the same mixture of the PDMS prepolymer and the curing agent. Moreover, we noticed that an area of refractive index inhomogeneity occurred in the vicinity of the layers’ boundaries. This led us to study the homogeneity of the PDMS samples near their interface. An illustrative image of the refractive index inhomogeneity can be obtained by photographing a suitable linear test object through the investigated PDMS sample (Fig. 1(a)). Such photographs make it possible to estimate the extent of the region in which the inhomogeneity occurs and also to roughly estimate the value of the refractive index gradient (Fig. 1(b)).

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Fig. 1. a) Observation of the inhomogeneity. b) Photograph of a test object through the sample.

As the gradient of the refractive index has only one component, some quantifiable results can be obtained using interferometric methods or by measuring the deviation of a light beam passing through the investigated sample near the boundary. The utilization of the latter method is satisfactory when the refractive index gradient is larger than 10−5cm−1. The scheme of the setup used based on the beam deviation is presented in Fig. 2(a). The equipment contains a semiconductor laser module (λ = 639 nm), an optical expander, which reduces the laser beam diameter from 1.5 mm to 0.3 mm, a table with a precision translation stage, and a screen with a ruler oriented in the direction of the refractive index gradient. The distance of the screen from the sample was 235 cm. The beam spot diameter in this distance was about 3 mm (Fig. 2(b)). This made it possible to determine a change of the beam angle of the order of 0.2 mrad.

Fig. 2. a) Measurement based on a beam deviation. b) Photo of the beam’s spot displayed on the screen.

Such precision can be achieved only when the change of the refractive index in the area of the beam does not radically enlarge the beam spot. That is why the beam diameter was decreased to 0.3 mm. This value is a result of a compromise between minimization of the interaction region and the effect of light diffraction. Such a width of the beam restricts the utilization of the method to areas that are not very close to the boundary. The interferometric investigation makes it possible to study the refractive index profile much closer to the boundary. We used a Mach–Zehnder interferometer for this study. The scheme of the arrangement used is shown in Fig. 3(a). From the photographs of the interference field (Fig. 3(b)), we were able to read refractive index changes of the order of

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10−5 (without using photometry) in samples of thickness 1 cm when a He-Ne laser (633 nm) was used.

Fig. 3. a) Scheme of the interferometer. stm – semi-transparent mirror, m – mirror. b) Detail of the photograph of interference field.

The interferometric setup used makes it possible to see finer details of the temporal development of the refractive index during the investigation in comparison with the method based on the beam deviation. The enclosed video (Fig. 4) illustrates the process of the temporal evolution of the refractive index distribution close to the boundary. The video was created by linking together the photographs of the interference field that were taken with frequency set to one picture per 2.5 minutes during 48 hours starting from the moment of pouring the mixture into a mold with a previously polymerized block of PDMS. The video is played-back with frequency 30 fps so one second represents approximately 77 minutes of the sample’s polymerization time.

Fig. 4. Single-frame excerpt from video recording of the temporal evolution of the refractive index distribution close to the boundary during polymerization (see Media 1).

3. Refractive index profile We have observed inhomogeneity of the refractive index distribution in the vicinity of PDMS–glass, PDMS–brass, PDMS–Teflon, and PDMS–PDMS boundaries. The most significant inhomogeneity was observed in the case of PDMS–PDMS boundaries. Such boundaries were prepared by adding a PDMS layer on a flat surface of another (already polymerized) PDMS sample. The “primary” and “secondary” layers were prepared from the same mixture of prepolymer and curing agent (parts A and B of the Sylgard 184 at a ratio of

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10:1). The observed dependence of the deviation angle (α) on the beam distance from the boundary (x) is presented in Fig. 5.

Fig. 5. Observed deviation of the beam in dependence on distance from the boundary.

When we assume the curvature of the beam in the investigated sample is so small that the difference between the optical length of the real beam and the beam taken as a straight line is negligible, then the difference in the phase Δφ of the wave at two close points at the end of the sample is Δϕ =

2π ∂n Δx d , λ ∂x

(1)

where d is the thickness of the sample, n is the refractive index, λ is wavelength of light, and Δx is the distance between the considered points. The phase difference Δφ means that the change in the wave vector’s direction turned to angle α  ∂n ( x )  d . (2)  ∂x  Equation (2) allows the refractive index gradient ∂n ∂x to be evaluated from the measured values of α(x) and the sample thickness d. The values of grad(n(x)) obtained in this way are shown in Fig. 6.

α ( x ) = arctg 

Fig. 6. Dependence of grad(n) on position x.

The values of the refractive index can be obtained from values of grad(n(x)) using the equation

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(

n ( x ) = if x < 0, n0 +  grad ( n ( x ) )dx, n0 +  x

x02

x01

x

)

grad ( n ( x ) )dx .

(3)

The values x01 and x02 in Eq. (3) are coordinates of the points in the primary and the secondary PDMS layers in which the refractive index value is equal to its value (n0) away from the interface. Equation (3) is valid if the primary value of the refractive index is the same in both parts of the sample. This assumption was confirmed by measuring the refractive index in both samples with a refractometer whose precision was about 5·10−4. The values of n(x) following from Eq. (3) are presented in Fig. 7.

Fig. 7. Dependence of the refractive index on position x.

The dependence drawn in Fig. 7 documents that the refractive index increases in the primary layer and decreases in the secondary layer from the bulk towards the boundary. When speaking about the spatial dependence of the refractive index we have to remark that the values presented in Fig. 7 close to the boundary follow from the extrapolation of the measured values. So the real values may be different in this region. The values given in the previous figures are the values of the refractive index of the samples after their full polymerization. For the sake of completeness, we also measured the dependence during the polymerization of the samples. The dependences presented in Fig. 8 show the evolution of the refractive index. The measurement was performed at room temperature.

Fig. 8. Illustration of the refractive index temporal evolution. Indication of the time is in hours. Insets show the time dependences of angle α for x = ± 0.4mm.

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It is interesting that in a short time after pouring the secondary mixture into the mold with the primary layer, the beam deviation was negative. The sign of the deviation changed approximately 20 hours after the second PDMS was poured on. During the polymerization, the speed of change of the refractive index decreased, and 50 hours after pouring, the increase in the refractive index practically stopped (the changes were smaller than the uncertainty of the measurement). So, one can say that the refractive index develops during the sample polymerization (according [16] the time of polymerization is 48 hours at 25°C). The inhomogeneity of the refractive index in the vicinity of the boundary also depends on the material of the mold in which the sample is prepared. The dependences presented in Fig. 9 illustrate this. The curves drawn in the figure show the dependences of the deviation angle near the PDMS–air boundary in two samples. One of them has been prepared in the glass mold and the second in a polystyrene mold.

Fig. 9. Comparison between the refractive index distributions near the surface of PDMS polymerized in a glass and in a polystyrene mold.

Although the dependences for the sample from the polystyrene mold show worse reproducibility, the influence of the mold material on the refractive index profile is clear (values obtained at three positions of the beam are plotted in the figure). As stated above, the measurement of the beam deviation cannot give any information on the refractive index in the region which is too close to the boundary. For investigation of the refractive index distribution in this region it is more convenient to use the interferometric methods. On the other hand, interferometric methods are not suitable for thick samples or samples with great changes of the refractive index. Figure 10 shows the interferograms of areas near the boundaries between PDMS and glass, brass, and Teflon and between brass and air. The samples were prepared by pouring the mixture into the divided glass mold with partitions made of above mentioned materials. The last interferogram illustrates the flatness of the mirrors of the interferometer. It follows from these interferograms that the changes in the refractive index in the vicinity of these boundaries are of the order of 10−4 (for thickness of the sample 5 mm and λ = 633 nm) and are restricted to a smaller region in comparison with the changes observed in the vicinity of the PDMS–PDMS boundary. These interferograms illustrate the effect of the boundary material on the refractive index distribution. The apparent differences in the shape of the interference fringes imply that the spatial distribution of the refractive index of PDMS depends on the material which is in contact with PDMS.

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Fig. 10. Interferograms of 1 cm thick samples in the molds.

4. The PDMS-PDMS boundary as a waveguide As already mentioned, the measurement based on the beam deviation cannot give information on the refractive index values very close to the boundary. That is why the curves in Figs. 6, 7, and 8 are discontinued at the boundary. When we accept the extrapolation of the refractive index dependence, we can expect a refractive index maximum in the vicinity of the boundary. This means that conditions for guiding light in this region are fulfilled. We observed the existence of a (multimodal) waveguide at the PDMS–PDMS boundary. The existence of the waveguide is confirmed by the fact that light was also guided when the sample containing such a waveguide was bent. Figures 11(a)–11(d) display the trajectories of the guided beam in a sample with no bending and with lesser and greater degrees of bending, respectively.

Fig. 11. Photographs of the guided beam in the bent sample.

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A particular (or total) irradiation of the beam occurs when the curvature is higher than a critical value (Fig. 11(e)). The centre of curvature was on the primary PDMS’s side in the situations displayed in Figs. 11(a)–11(e). When the sample is bent on the opposite side, the irradiation of the beam occurs at the bend, which is smaller than in the previous case. This is documented in Fig. 11(f). Such behavior corresponds to the sharp and slow decrease of the refractive index on the waveguide’s sides (see Fig. 7). One can also see the difference between beams irradiated into the sides. The “fan” shape of the beam irradiated into the secondary layer side is due to subsequent irradiation of the modes of the highest orders, which are not bound as fast as the modes of low orders. 5. Conclusion It follows from the observations and measurements performed that the refractive index inhomogeneity of the PDMS samples in the region surrounding the boundary is induced by at least two mechanisms: by diffusion of volatile molecules or radicals from or into polymerized material or by capillary intermolecular forces between the PDMS and the surrounding material. The influence of the latter mechanism is significantly weaker and is observable only when the first mechanism is absent. The slowness of the evolution of the inhomogeneity during the sample polymerization suggests that diffusion is the main mechanism of creation of the inhomogeneity. A refractive index profile with a local maximum near the boundary occurs in the samples prepared by subsequently created layers of PDMS. Such a profile causes the boundary itself to behave like an optical waveguide. The observed features of the refractive index distribution on the PDMS–PDMS boundary should be taken into account when monolithic PDMS optical waveguides are designed. On the other hand, knowledge of how the boundary affects the refractive index of PDMS may be useful when monolithic diffused optical waveguides are designed. Acknowledgment This work was supported by Slovak National Grant Agency under the projects Nos. VEGA 1/0491/14, 1/0528/12 and Slovak Research and Development Agency under the project No. APVV-0395-12 and the R&D operational program Centre of excellence of power electronics systems and materials for their components II. No. OPVaV-2009/2.1/02-SORO, ITMS 26220120046 funded by European regional development fund (ERDF).

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