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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 14 — Jul. 6, 2009
  • pp: 11739–11746
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Design and fabrication of Poly(dimethylsiloxane) single-mode rib waveguide

Jack Sheng Kee, Daniel Puiu Poenar, Pavel Neuzil, and Levent Yobas  »View Author Affiliations


Optics Express, Vol. 17, Issue 14, pp. 11739-11746 (2009)
http://dx.doi.org/10.1364/OE.17.011739


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Abstract

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.

© 2009 OSA

1. Introduction

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 [1

1. S. K. Sia and G. M. Whitesides, “Microfluidic devices fabricated in poly(dimethylsiloxane) for biological studies,” Electrophoresis 24(21), 3563–3576 (2003). [CrossRef]

]. Most often, LOC devices depend on optical detection for sensing biochemical species [2

2. B. Kuswandi, J. Nuriman, J. Huskens, and W. Verboom, “Optical sensing systems for microfluidic devices: a review,” Anal. Chim. Acta 601(2), 141–155 (2007). [CrossRef]

,3

3. E. Verpoorte, “Chip vision-optics for microchips,” Lab Chip 3(3), 42N–52N (2003).

] 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 [4

4. Q. Kou, I. Yesilyurt, V. Studer, M. Belotti, E. Cambril, and Y. Chen, “On-chip optical components and microfluidic systems,” Microelectron. Eng. 73, 876–880 (2004). [CrossRef]

] such as 2D lenses [5

5. S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003). [CrossRef]

], prisms [6

6. A. Llobera, R. Wilke, and S. Büttgenbach, “Poly(dimethylsiloxane) hollow Abbe prism with microlenses for detection based on absorption and refractive index shift,” Lab Chip 4(1), 24–27 (2004). [CrossRef]

], and waveguides [7

7. B. G. Splawn and F. E. Lytle, “On-chip absorption measurements using an integrated waveguide,” Anal. Bioanal. Chem. 373(7), 519–525 (2002). [CrossRef]

,8

8. D. A. Chang-Yen, R. K. Eich, and B. K. Gale, “A monolithic PDMS waveguide system fabricated using soft-lithography techniques,” IEEE J. Lightwave Technol. 6(6), 2088–2093 (2005). [CrossRef]

] 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

8. D. A. Chang-Yen, R. K. Eich, and B. K. Gale, “A monolithic PDMS waveguide system fabricated using soft-lithography techniques,” IEEE J. Lightwave Technol. 6(6), 2088–2093 (2005). [CrossRef]

,9

9. J. S. Kee, D. P. Poenar, P. Neuzil, and L. Yobas, “Monolithic Integration of Poly(dimethylsiloxane) Waveguides and Microfluidics for On-Chip Absorbance Measurements,” Sens. Actuators B Chem. 134(2), 532–538 (2008). [CrossRef]

] with core size of 125×125 µm2 and 250×250 µm2, or in optical interconnects in an electro-optical circuit board [10

10. S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical-optical circuit boards,” Int. J. Electron. Commun. 61(3), 163–167 (2007) (AEU). [CrossRef]

] 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 [8

8. D. A. Chang-Yen, R. K. Eich, and B. K. Gale, “A monolithic PDMS waveguide system fabricated using soft-lithography techniques,” IEEE J. Lightwave Technol. 6(6), 2088–2093 (2005). [CrossRef]

], or by attaching a -CH3 group to the silicon backbone, which produce two distinct materials through chemical processing [9

9. J. S. Kee, D. P. Poenar, P. Neuzil, and L. Yobas, “Monolithic Integration of Poly(dimethylsiloxane) Waveguides and Microfluidics for On-Chip Absorbance Measurements,” Sens. Actuators B Chem. 134(2), 532–538 (2008). [CrossRef]

], or by adding silicone oil to increase the refractive index [10

10. S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical-optical circuit boards,” Int. J. Electron. Commun. 61(3), 163–167 (2007) (AEU). [CrossRef]

].

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. [11

11. R. A. Soref, J. Schmidtchen, and K. Petermann, “Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971 (1991). [CrossRef]

]. 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 [16

16. F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994). [CrossRef]

]. 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

Fig. 1. Cross-sectional view and geometrical parameters of a PDMS rib waveguide.

WHα+r1r2
(1)

for

0.5r1.0
(2)

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. [12

12. S. P. Pogossian, L. Vescan, and A. Vonsovici, “The Single-Mode Condition for Semiconductor Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 16(10), 1851 (1998). [CrossRef]

] suggested a more stringent value of α=0 based on an analytical effective-index design method. However, Lousteau et al. [13

13. J. Lousteau, D. Furniss, A. B. Seddon, T. M. Benson, A. Vukovic, and P. Sewell, “The Single-Mode Condition for Silicon-on-Insulator Optical Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 22(8), 1923–1929 (2004). [CrossRef]

] 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. [14

14. S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-Mode and Polarization-Independent Silicon-on-Insulator Waveguides with Small Cross Section,” IEEE J. Lightwave Technol. 23(6), 2103–2111 (2005). [CrossRef]

] 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.

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.

Fig. 2. Simulation results of the design of the single-mode waveguide operating at a wavelength of 635 nm; a) Single-mode region with cutoff boundary lines for low refractive index contrast waveguide with an 8 µm width rib waveguide b) Bending radius loss for high refractive index contrast waveguide with 8 µm width, 4.5 µm rib height and 3.5 µm slab height.

3. Experimental

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 [15

15. K. S. Ryu, X. Wang, K. Shaikh, and C. Liu, “A Method for Precision Patterning of Silicone Elastomer and Its Applications,” IEEE J. Microelectromech. Syst. 13(4), 568–575 (2004). [CrossRef]

]. 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.

Fig. 3. Schematic diagram of the fabrication process of the PDMS-based single-mode rib waveguide.

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.

Fig. 4. Images of rib waveguides fabricated in PDMS: a) SEM image of an array of waveguides; b) Microscope image of the face end of waveguide c) SEM image of a single rib waveguide.
Fig. 5. Beam profile studies on straight PDMS single-mode rib waveguides at a z-position of 5.5 cm: a) Simulation results of both FDTD for mode 1 & 2 and BPM; b) Face end image of output waveguide captured by CCD.

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

16. F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994). [CrossRef]

,17

17. F. Ladouceur, “Roughness, Inhomogeneity, and Integrated Optics,” IEEE J. Lightwave Technol. 15(6), 1020–1025 (1997). [CrossRef]

]. 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.

Fig. 6. Measured propagation loss in the fabricated PDMS rib waveguides.
Fig. 7. Y-branch power splitter output face end image; a) Branch gap of 20 µm and ;b) Branch gap of 50 µm.

5. Conclusions

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.

References and links

1.

S. K. Sia and G. M. Whitesides, “Microfluidic devices fabricated in poly(dimethylsiloxane) for biological studies,” Electrophoresis 24(21), 3563–3576 (2003). [CrossRef]

2.

B. Kuswandi, J. Nuriman, J. Huskens, and W. Verboom, “Optical sensing systems for microfluidic devices: a review,” Anal. Chim. Acta 601(2), 141–155 (2007). [CrossRef]

3.

E. Verpoorte, “Chip vision-optics for microchips,” Lab Chip 3(3), 42N–52N (2003).

4.

Q. Kou, I. Yesilyurt, V. Studer, M. Belotti, E. Cambril, and Y. Chen, “On-chip optical components and microfluidic systems,” Microelectron. Eng. 73, 876–880 (2004). [CrossRef]

5.

S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003). [CrossRef]

6.

A. Llobera, R. Wilke, and S. Büttgenbach, “Poly(dimethylsiloxane) hollow Abbe prism with microlenses for detection based on absorption and refractive index shift,” Lab Chip 4(1), 24–27 (2004). [CrossRef]

7.

B. G. Splawn and F. E. Lytle, “On-chip absorption measurements using an integrated waveguide,” Anal. Bioanal. Chem. 373(7), 519–525 (2002). [CrossRef]

8.

D. A. Chang-Yen, R. K. Eich, and B. K. Gale, “A monolithic PDMS waveguide system fabricated using soft-lithography techniques,” IEEE J. Lightwave Technol. 6(6), 2088–2093 (2005). [CrossRef]

9.

J. S. Kee, D. P. Poenar, P. Neuzil, and L. Yobas, “Monolithic Integration of Poly(dimethylsiloxane) Waveguides and Microfluidics for On-Chip Absorbance Measurements,” Sens. Actuators B Chem. 134(2), 532–538 (2008). [CrossRef]

10.

S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical-optical circuit boards,” Int. J. Electron. Commun. 61(3), 163–167 (2007) (AEU). [CrossRef]

11.

R. A. Soref, J. Schmidtchen, and K. Petermann, “Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971 (1991). [CrossRef]

12.

S. P. Pogossian, L. Vescan, and A. Vonsovici, “The Single-Mode Condition for Semiconductor Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 16(10), 1851 (1998). [CrossRef]

13.

J. Lousteau, D. Furniss, A. B. Seddon, T. M. Benson, A. Vukovic, and P. Sewell, “The Single-Mode Condition for Silicon-on-Insulator Optical Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 22(8), 1923–1929 (2004). [CrossRef]

14.

S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-Mode and Polarization-Independent Silicon-on-Insulator Waveguides with Small Cross Section,” IEEE J. Lightwave Technol. 23(6), 2103–2111 (2005). [CrossRef]

15.

K. S. Ryu, X. Wang, K. Shaikh, and C. Liu, “A Method for Precision Patterning of Silicone Elastomer and Its Applications,” IEEE J. Microelectromech. Syst. 13(4), 568–575 (2004). [CrossRef]

16.

F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994). [CrossRef]

17.

F. Ladouceur, “Roughness, Inhomogeneity, and Integrated Optics,” IEEE J. Lightwave Technol. 15(6), 1020–1025 (1997). [CrossRef]

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.7390) Optical devices : Waveguides, planar
(130.5460) Integrated optics : Polymer waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: March 25, 2009
Revised Manuscript: May 15, 2009
Manuscript Accepted: May 16, 2009
Published: June 29, 2009

Virtual Issues
Vol. 4, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Jack Sheng Kee, Daniel Puiu Poenar, Pavel Neuzil, and Levent Yobas, "Design and fabrication of Poly(dimethylsiloxane) single-mode rib waveguide," Opt. Express 17, 11739-11746 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11739


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References

  1. S. K. Sia and G. M. Whitesides, “Microfluidic devices fabricated in poly(dimethylsiloxane) for biological studies,” Electrophoresis 24(21), 3563–3576 (2003). [CrossRef]
  2. B. Kuswandi, J. Nuriman, J. Huskens, and W. Verboom, “Optical sensing systems for microfluidic devices: a review,” Anal. Chim. Acta 601(2), 141–155 (2007). [CrossRef]
  3. E. Verpoorte, “Chip vision-optics for microchips,” Lab Chip 3(3), 42N–52N (2003).
  4. Q. Kou, I. Yesilyurt, V. Studer, M. Belotti, E. Cambril, and Y. Chen, “On-chip optical components and microfluidic systems,” Microelectron. Eng. 73, 876–880 (2004). [CrossRef]
  5. S. Camou, H. Fujita, and T. Fujii, “PDMS 2D optical lens integrated with microfluidic channels: principle and characterization,” Lab Chip 3(1), 40–45 (2003). [CrossRef]
  6. A. Llobera, R. Wilke, and S. Büttgenbach, “Poly(dimethylsiloxane) hollow Abbe prism with microlenses for detection based on absorption and refractive index shift,” Lab Chip 4(1), 24–27 (2004). [CrossRef]
  7. B. G. Splawn and F. E. Lytle, “On-chip absorption measurements using an integrated waveguide,” Anal. Bioanal. Chem. 373(7), 519–525 (2002). [CrossRef]
  8. D. A. Chang-Yen, R. K. Eich, and B. K. Gale, “A monolithic PDMS waveguide system fabricated using soft-lithography techniques,” IEEE J. Lightwave Technol. 6(6), 2088–2093 (2005). [CrossRef]
  9. J. S. Kee, D. P. Poenar, P. Neuzil, and L. Yobas, “Monolithic Integration of Poly(dimethylsiloxane) Waveguides and Microfluidics for On-Chip Absorbance Measurements,” Sens. Actuators B Chem. 134(2), 532–538 (2008). [CrossRef]
  10. S. Kopetz, D. Cai, E. Rabe, and A. Neyer, “PDMS-based optical waveguide layer for integration in electrical-optical circuit boards,” Int. J. Electron. Commun. 61(3), 163–167 (2007) (AEU). [CrossRef]
  11. R. A. Soref, J. Schmidtchen, and K. Petermann, “Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27(8), 1971 (1991). [CrossRef]
  12. S. P. Pogossian, L. Vescan, and A. Vonsovici, “The Single-Mode Condition for Semiconductor Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 16(10), 1851 (1998). [CrossRef]
  13. J. Lousteau, D. Furniss, A. B. Seddon, T. M. Benson, A. Vukovic, and P. Sewell, “The Single-Mode Condition for Silicon-on-Insulator Optical Rib Waveguides with Large Cross Section,” IEEE J. Lightwave Technol. 22(8), 1923–1929 (2004). [CrossRef]
  14. S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-Mode and Polarization-Independent Silicon-on-Insulator Waveguides with Small Cross Section,” IEEE J. Lightwave Technol. 23(6), 2103–2111 (2005). [CrossRef]
  15. K. S. Ryu, X. Wang, K. Shaikh, and C. Liu, “A Method for Precision Patterning of Silicone Elastomer and Its Applications,” IEEE J. Microelectromech. Syst. 13(4), 568–575 (2004). [CrossRef]
  16. F. P. Payne and J. P. R. Lacey, “A theoretical analysis of scattering loss from planar optical waveguides,” Opt. Quantum Electron. 26(10), 977–986 (1994). [CrossRef]
  17. F. Ladouceur, “Roughness, Inhomogeneity, and Integrated Optics,” IEEE J. Lightwave Technol. 15(6), 1020–1025 (1997). [CrossRef]

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