We have designed, fabricated and characterized poly(dimethylsiloxane) (PDMS) single-mode rib waveguides. PDMS was chosen specifically for the core and cladding. Combined with the soft lithography fabrication techniques, it enables an easy integration of microoptical components for lab-on-a-chip systems. The refractive index contrast, Δ of 0.07% between the core and cladding for single-mode propagation was achieved by modifying the properties of the same base material. Alternatively, a higher refractive index contrast, Δ of 1.18% was shown by using PDMS materials from two different manufacturers. The fabricated rib waveguides were characterized for mode profile characteristics and confirmed the excitation of the fundamental mode of the waveguide. The propagation loss of the single-mode rib waveguide was characterized using the cutback measurement method at a wavelength of 635 nm and found to be 0.48 dB/cm for Δ of 0.07% and 0.20 dB/cm for Δ of 1.18%. Y-branch splitter of PDMS single-mode rib waveguide was further demonstrated.
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Poly(dimethylsiloxane) (PDMS) has been widely used for the fabrication of microfluidics and lab-on-a-chip (LOC) devices due to unique characteristic such as biocompatibility, low cost, and rapid prototyping capability by soft lithography . Most often, LOC devices depend on optical detection for sensing biochemical species [2,3] and the high transparency of PDMS in visible light thus motivates the monolithic integration of optical components with microfluidics in the same material. A range of LOC based microoptical components  such as 2D lenses , prisms , and waveguides [7,8] have been demonstrated. Among these components, PDMS waveguides have received considerable attention because of their potential for interfacing with other photonic or electronic devices and for producing mechanically robust microphotonic devices.
To date, several reported PDMS waveguides have been fabricated with large sizes (tens to hundreds of micrometers), hence featuring multimode behaviour. Such multimode PDMS waveguides have been integrated either in LOC devices [8,9] with core size of 125×125 µm2 and 250×250 µm2, or in optical interconnects in an electro-optical circuit board  with core size of 70×70 µm2. In comparison, single-mode waveguides provide higher versatility as basic building blocks in complex microphotonics devices such as such interferometers and biosensors. One of the essential criterions for producing single-mode waveguide is to reduce the waveguide core dimension to small sizes, on the order of micrometers. In addition, the previously reported approaches of fabricating multimode waveguides in PDMS involved tuning the refractive index difference either by modifying the PDMS curing process, which requires precise control of process parameters , or by attaching a -CH3 group to the silicon backbone, which produce two distinct materials through chemical processing , or by adding silicone oil to increase the refractive index .
In this paper, we design the single-mode rib waveguide based on the geometrical adjustment of the rib width, total waveguide height and slab height as first proposed by Soref et al. . The refractive indices for the cover, film and substrate used were of 1, 1.412, and 1.411, respectively for low refractive index contrast waveguide and 1, 1.429, and 1.412, respectively for high refractive index contrast waveguide. Based on the design results, we fabricated PDMS rib waveguides with small core size (<8 µm) by soft lithography. Here, we explore an alternative approach of creating a small refractive index difference (10-3) between core and cladding by diluting the PDMS precursor mixture with hexane as solvent and evaporating the solvent after complete curing for low refractive index contrast waveguide (Δ of 0.07%). Vaporization of the hexane creates void in the PDMS and produce a lower refractive index. This low refractive index difference enables small waveguide core dimensions in the range of about 5 to 10 µm, as required for single-mode operation. In dichotomy, the high refractive index contrast waveguide (Δ of 1.18%) was explored with refractive indices of 1, 1.429, and 1.411 for the cover, film and substrate. The mode profiles were studied in waveguides of 7.0, 5.5, 4.0 and 2.5 cm in lengths and their single-mode operation was established by mode field comparison of both the experimental and simulated values. The propagation loss was measured to be 0.48 dB/cm for Δ of 0.07% and 0.20 dB/cm for Δ of 1.18% at a wavelength of 635 nm. The propagation loss was largely attributed to the sidewall roughness scattering as PDMS has high transparency . The successful demonstration of Y-branch splitter indicates that the single-mode PDMS rib waveguide is a promising candidate for building microphotonic devices for LOC application.
2. Theoretical Design
Single-mode silicon-on-insulator rib waveguides (typically of width ≈5 µm) have been studied extensively by several groups [11–14]. Based on mode matching calculation, Soref et al.  has first proposed an expression related to their geometry (as shown in Fig. 1) to guarantee that they satisfied the single-mode condition, as follows:
where r is the ratio of slab height (h) to overall rib height (H), W/H is the ratio of waveguide width to overall rib height, and α=0.3. Later on, Pogossian et al.  suggested a more stringent value of α=0 based on an analytical effective-index design method. However, Lousteau et al.  using full-vectorial beam propagation method has demonstrated that this simple expression is insufficient to ensure single-mode behavior in rib waveguides. In addition, these analyses were limited to shallow rib height and did not provide enough information for deep ribs of large height (r<0.5). Hence, Chan et al.  extended the studies of single-mode condition for deep ribs (r<0.5) of small width (~1µm or less). Although these works have revealed some guidelines for the design of single-mode rib waveguides, they are limited only to SOI waveguides with a different set of refractive indices operating at near infrared wavelengths. This section highlights the main considerations for the design of PDMS rib waveguides with sizes on the order of a few micrometers (W>5 µm) that would exhibit single-mode behavior with low propagation loss in the visible light range.
The single-mode simulation was performed using Finite Difference Time Domain method (FDTD) in Apollo Photonics Software for a rib waveguide using pure PDMS (n=1.412) as core and modified PDMS (n=1.411) as cladding. A second set of simulation was repeated for PDMS (n=1.429) purchased from Gelest (OE-43) as core and PDMS (n=1.412) purchased from Dow Corning (Sylgard 184) as cladding. The simulation was carried out at a wavelength of 635 nm for fundamental, second and third order modes. The waveguide width (W) and rib height (H-h) were kept constant. The slab height (h) was increased in steps of 10 nm until the fundamental order mode is supported. Hence, the single-mode lower cutoff boundary could be found. As the slab height increased, the leakage of the fundamental mode to substrate increased and eventually it became a non-bounded mode. Therefore, the upper boundary limit can be found when the effective index of the fundamental mode is smaller than the cladding refractive index.
Figure 2 shows the TE and TM modes of the single-mode boundary for low refractive index contrast waveguide width of 8 µm, and with rib heights of 3 to 8 µm with a step of 1 µm. It is instructive to plot the graph in a different way using earlier results, as the rib height can be related to the thickness of the SU-8 mold whereas the slab height is determined by the residual layer left after blading away most of the PDMS in the soft lithography fabrication method. All higher order modes have been confirmed as radiation modes as their mode profile studies shows leakage to the substrate and the effective index of the mode propagation is lower than the cladding refractive index. For high refractive index contrast, the lower boundary is at 0.5 to 0.6 µm and a upper boundary greater than the low refractive index contrast waveguide. Thus, it was confirmed that these PDMS rib waveguide designs exhibit single-mode behavior.
The bending radius loss was simulated for the high refractive index contrast waveguides using FDTD and a Y-branch power splitter was designed for optimal branching length and gap. Figure 2b shows the bending radius loss for the high refractive index contrast and shows negligible loss for bending radius greater than 4000 µm.
Figure 3 shows the fabrication steps of the single-mode PDMS rib waveguide. The master mold for the soft lithography was prepared by patterning a 4.4 µm and 6.8 µm thick SU-8 2007 (MicroChem, NewtonMA, USA) photoresist spun on 8-inch silicon wafers. The patterned SU-8 was coated with a layer of fluorinated hydrocarbon by plasma decomposition of C4F8 to avoid sticking of the PDMS onto the SU-8 and also to reduce sidewall roughness.
For low refractive index contrast waveguide, the PDMS precursor mixture (Sylgard 184, Dow Corning) was prepared at a weight ratio of base to curing agent 10:1 and split into two portions. One portion of PDMS was further mixed with 10% w/w of hexane (Sigma-Aldrich, Inc.) to reduce its refractive index. The first precursor mixture of pure PDMS was poured on the SU-8 patterns to fill the trenches. The excess PDMS above the trenches was removed by blading it with cleanroom paper. This method has been demonstrated by Ryu et al. to produce in PDMS small features in the range of 5 µm . The blading process left a layer of PDMS on top of the SU-8 mold which formed the waveguide slab. Statistical studies of the slab height using microscope inspection gives 3 µm ± 1 µm and it is well within the acceptable region for single-mode region for the 8 µm width rib waveguide for rib height >4 µm. The precursor mixture in the SU-8 trenches was allowed to settle down to a uniform layer and was thereafter cured at 80°C for 2 hours. The second precursor mixture with added hexane was subsequently poured to form a thin layer and cured at room temperature (25 °C) for 48 hours. Cross-linked PDMS macromolecules diluted with hexane form a guest/host matrix configuration. The hexane can be subsequently removed through vaporization by heating the cured PDMS at 90°C (the boiling point of hexane is 78°C). Thus, the vaporization of hexane yielded void in the PDMS and produce a lower density of PDMS. This second PDMS layer fused together with the first one and formed the waveguide cladding layer. A thick layer of pure PDMS has to be cured over this layer to prevent the chip from warping due to the compressive stress induced after the hexane evaporation. The amount of Hexane was capped at 10% w/w because the 20% w/w of Hexane shows no further decrease of the refractive index and yet produces severe warping after evaporation. The third layer of pure PDMS precursor mixture was then poured to form a thick substrate layer.
For high refractive index contrast waveguide, the PDMS precursor mixture (OE-43, Gelest) was prepared at a weight ratio of base to curing agent 1:1. This PDMS precursor has a lower viscosity which allows spin coating on wafer to produce thin layer of PDMS down to 1 µm. The spin coated PDMS was cured at 55°C for 4 hours. Thereafter, the standard PDMS precursor mixture (Sylgard 184, Dow Corning) was cured over the thin layer of PDMS to form the cladding layer.
The refractive index was measured using the prism coupling method (Model 2010, Metricon Corporation) with a refractive index accuracy of ± 0.0002 on a thin PDMS film spin-coated at 6900 rpm for 60 s. Pre-cured PDMS was mixed with hexane at different composition and its refractive index was measured and compared with that of pure PDMS.
The propagation losses of the waveguides were measured with a cut-back method in which the PDMS waveguides are cut-back from 7.5 cm to 2.5 cm in 4 steps. The mode profile of the waveguide was studied using a collimated diode laser beam of wavelength 635 nm and butt-coupled into the waveguide through a 9/125 µm single-mode optical fiber. The image of the output end of the waveguide was focused with a 50× objective lens and captured on a CCD camera (Exwave, Sony, Japan). The resulting image was analyzed using Origin Software.
The Y-branch splitter was designed and fabricated based on the single-mode PDMS rib waveguide. The Y-branch was tested for splitting the power in the single-mode waveguide to a ratio 1:1 into both branching arm for a branch gap of 20 µm and 50 µm.
4. Results and Discussion
The measured refractive indices for both pure and hexane-modified PDMS materials are 1.412 and 1.411, respectively, resulting in a refractive index difference of 10-3 which has thus confirmed the effectiveness of the proposed scheme of refractive index tuning. Figure 4 shows the SEM images and microscope images of the fabricated single-mode waveguides.
The distribution of the mode fields resulting from FDTD and Beam Propagation Method (BPM) simulations for a PDMS rib waveguide 8 µm wide, with 6.8 µm rib height and 3.4 µm slab height are shown in Fig. 5a. From the pictures shown in Fig. 5a, it can observed that only the fundamental mode is bounded whereas the 2nd order mode is a radiation mode. The near-field pattern at the output of the waveguide was also studied, and the resulting cross-sectional intensity profiles in the xy-plane are shown in Fig. 5b. The Gaussian-fit diameters of the intensity profiles were approximately 8.9 µm in the x-direction and 8.8µm in the y-direction. These Gaussian diameters agrees well with the simulated results of 9.14 µm in the x-direction and 9.15 µm in the y-direction and thus confirmed that the waveguides works essentially as a single-mode waveguide at a wavelength of 635 nm.
Next, we evaluated the propagation loss of the PDMS rib waveguide for both types of waveguides. The intensity of the mode profile captured at the waveguide end was measured as a function of the length of the waveguide to determine the propagation loss and the results are shown in Fig. 6. The propagation loss of the single-mode waveguide was measured to be 0.48 dB/cm for low refractive index contrast waveguides (Δ=0.07%) and 0.20 dB/cm for high refractive index contrast waveguides (Δ=1.18%) at the wavelength of 635 nm. Propagation loss in a straight optical waveguide is generally attributable to the absorption of the material and scattering loss from the surface of the waveguide. PDMS has a low absorption and the simulation results indicated that the mode radiation loss should be in the order of only ~0.2 dB/cm. Therefore, the higher propagation loss measured in our low refractive index contrast PDMS single-mode waveguide might be due to the scattering from the sidewall roughness of the waveguide and low confinement factor in the waveguide [16,17]. This loss can be minimized through further optimization of the mold used in the soft lithography fabrication process. In addition, the improvement of confinement of light in the waveguide reduces the propagation loss as shown by the high refractive index contrast waveguides.
The Y-branch power splitter demonstrated the feasibility of producing bending waveguides for complex microphotonics devices. The Y-branch has a linear branching length of 1 mm and a branch gap of 20 µm and 50 µm. As shown in Fig. 7, the output of the Y-branch allows the waveguide to split power equally (1:1) in both waveguide branches.
Single-mode PDMS rib waveguides have been designed, fabricated and characterized. A refractive index difference of 10-3 between the core and cladding for single-mode waveguide has been produced by diluting the PDMS precursor with hexane. For a higher refractive index contrast, two PDMS precursor from different manufacturer were used for the core and cladding layer. The range of slab height for single-mode operation has been determined using FDTD simulations and further confirmed with BPM simulations. The mode profiles have shown single-mode propagation by both the simulation and measured data. The demonstration Y-branch power splitter based on the single-mode PDMS waveguides confirms that they can be used as basic building blocks for complex microphotonics devices.
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