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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 25 — Dec. 10, 2007
  • pp: 16712–16718
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Compact 90° trench-based splitter for silicon-on-insulator rib waveguides

Yusheng Qian, Jiguo Song, Seunghyun Kim, and Gregory P. Nordin  »View Author Affiliations


Optics Express, Vol. 15, Issue 25, pp. 16712-16718 (2007)
http://dx.doi.org/10.1364/OE.15.016712


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Abstract

Compact silicon-on-insulator (SOI) rib waveguide 90° splitters based on narrow, high-aspect ratio (~10:1) trenches are designed and experimentally demonstrated. The splitter area is only 11 µm×11 µm. Splitter optical performance is investigated as a function of both trench width and refractive index of the trench fill material. We examine three trench fill materials, air (n=1.0), SU8 (n=1.57), and index matching fluid (n=1.733), and find good agreement between experimental measurement and three dimensional (3D) finite difference time domain (FDTD) simulation. A splitting ratio of 49/51 (reflection/transmission) is measured for an index fluid-filled trench 82nm wide.

© 2007 Optical Society of America

1. Introduction

The drive toward greater integration in planar lightwave circuits (PLCs) has motivated the development of high index, high index contrast (HIHIC) waveguide material systems such as silicon-on-insulator (SOI) [1

1. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, “Advances in Silicon-on-Insulator Optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938–947 (1998). [CrossRef]

3

3. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. 23, 401- (2005). [CrossRef]

] in order to decrease the minimum bend radius for bends and splitters. These waveguide elements impose the ultimate lower bound on device size for passive devices, as well as for many active devices. Single-mode SOI strip waveguides with rectangular cross section (~200 nm×~400 nm) have been shown to form particularly compact bends and splitters [2

2. Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004). [CrossRef] [PubMed]

,3

3. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. 23, 401- (2005). [CrossRef]

]. However, some applications [4

4. J. Liu, J. Yu, S. Chen, and Z. Li, “Integrated folding 4×4 optical matrix switch with total internal reflection mirrors on SOI by anisotropic chemical etching,” Photon. Technol. Lett. 17, 1187–1189 (2005). [CrossRef]

6

6. G. P. Nordin, J. W. Noh, and S. Kim, “In-plane photonic transduction for microcantilever sensor arrays,” in Nanoscale Imaging, Spectroscopy, Sensing, and Actuation for Biomedical Applications IV, Alexander N. Cartwright, Dav V. Nicolau, and Paul L. Gourley, Editors, Proceedings of SPIE Vol. 6447, pp. 64470J-1 to -8 (2007).

] require the use of rib waveguides in which silicon is etched to form a shallow ridge (see for example Fig. 1). In this case the in-plane refractive index contrast can be quite small which results in large bends and splitters when conventional curved waveguides are used. Bends based on an etched vertical interface and total internal reflection (TIR) have long been recognized as a way to dramatically reduce bend size for such waveguides [4

4. J. Liu, J. Yu, S. Chen, and Z. Li, “Integrated folding 4×4 optical matrix switch with total internal reflection mirrors on SOI by anisotropic chemical etching,” Photon. Technol. Lett. 17, 1187–1189 (2005). [CrossRef]

, 7

7. Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, “Integrated waveguide turning mirror on silicon-on-insulator,” Photon. Technol. Lett. 14, 68–70 (2002). [CrossRef]

9

9. Y. Qian, S. Kim, J. Song, and G. P. Nordin, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14, 6020–6028 (2006) [CrossRef] [PubMed]

]. However, comparably compact splitters have not been experimentally demonstrated.

Possible configurations for rib waveguide SOI splitters include Y-branches, multimode interference (MMI) couplers [10

10. C. S. Hsiao and L. Wang, “Design for beam splitting components employing silicon-on-insulator rib waveguide structures,” Opt. Lett. 30, 3153–3155 (2005). [CrossRef] [PubMed]

], and star couplers [11

11. A. Koster, E. Cassan, S. Laval, L. Vivien, and D. Pascal, “Ultracompact splitter for submicrometer silicon-on-insulator rib waveguides,” J. Opt. Soc. Am. A 21, 2180–2185 (2004). [CrossRef]

]. In each case the overall size of the splitter region is determined by the desired spacing between the two output waveguides. For example, a Y-branch with a 2° angle between the output waveguides requires a length of 1.1 mm to achieve a 40 µm waveguide separation. As discussed in Ref. 11, star couplers can be designed with a 9° angle between output waveguides, which reduces the required length to 250 µm for a 40 µm waveguide separation. Clearly, these approaches require significantly more area than do bends based on an etched trench and TIR [hereafter referred to as trench-based bends (TBB)] and therefore become the limiting factor in shrinking device size.

Calculations in Refs. 12–14 show that further dramatic size reduction of rib waveguide splitters can be realized with the use of narrow trenches and frustrated total internal reflection (FTIR). In this paper, we report the first experimental demonstration of compact SOI rib waveguide 90° splitters in which each splitter occupies an area of only 11 µm×11 µm. The addition of a single TBB can be used to re-direct one of the output waveguides to achieve any desired waveguide separation with little additional cost in size beyond what is required to route the waveguides. As an example, we demonstrate a splitter/bend combination for a 40 µm output waveguide separation in a total area of only 11 µm×50 µm. We also discuss the design of trench-based splitters (TBSs) using the three dimensional (3D) finite difference time domain (FDTD) method and fabrication of trenches with a nearly 10:1 aspect ratio. We further examine splitter reflection and transmission properties as a function of both trench width and refractive index of the trench fill material, and show good agreement between simulation and measurement. An 82 nm wide trench filled with index matching fluid is experimentally shown to have a reflection/transmission splitting ratio of 49/51 at a wavelength of 1550 nm.

2. SOI rib waveguide splitter design

For our application [6

6. G. P. Nordin, J. W. Noh, and S. Kim, “In-plane photonic transduction for microcantilever sensor arrays,” in Nanoscale Imaging, Spectroscopy, Sensing, and Actuation for Biomedical Applications IV, Alexander N. Cartwright, Dav V. Nicolau, and Paul L. Gourley, Editors, Proceedings of SPIE Vol. 6447, pp. 64470J-1 to -8 (2007).

] we require an SOI rib waveguide with a silicon layer thickness of 0.75 µm, etch depth of 0.1 µm, and rib width of 1.6 µm as shown in Fig. 1(a). For numerical simulation, the refractive indices of silicon and silicon dioxide are taken to be 3.476 and 1.444, respectively, at a wavelength of 1550 nm. The refractive index of the upper clad is the same as the material used to fill the splitter trenches. We consider three cases: trenches filled with (1) air (n=1.0), (2) SU8 (n=1.57), and (3) index matching fluid (n=1.733). In each case the SOI rib waveguide supports only the fundamental TE polarization mode (electric field in the plane) and therefore splitter design and measurement is performed only for TE polarization. Note that the in-plane core/clad refractive index contrast is quite small in each case (i.e., the effective index under the rib compared to the effective index in the slab). For example, with SU-8 overclad it is 0.84%, which translates into a 1.3 mm bend radius for a 90° degree bend with 98% optical efficiency.

Fig. 1. (a) Cross section of single mode SOI rib waveguide. (b) Splitter geometry.

Table 1. Splitter 3D FDTD simulation results

table-icon
View This Table

Figure 1(b) shows the TBS geometry. Light is incident in the input waveguide and split into reflection and transmission output waveguides by a narrow trench with width, W, and distance, D, with respect to the intersection of the waveguide centers. In all cases studied, light is incident at greater than the critical angle for TIR. However, since the trench is narrow enough that the exponentially decaying field is non-zero at the back interface of the trench, some of the light propagates into the transmission output waveguide while the rest is reflected into the reflection output waveguide. The splitting ratio can be controlled by the trench width, W, for a given refractive index of the trench fill material, or by the index of the trench fill material for a fixed trench width.

We employ a 3D FDTD method [15

15. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass., 1995).

, 16

16. J. Cai, G. P. Nordin, S. Kim, and J. Jiang, “Three-dimensional analysis of a hybrid photonic crystalconventional waveguide 90° bend,” Appl. Opt. 43, 4244–4249 (2004). [CrossRef] [PubMed]

] with Berenger perfectly matched layer (PML) boundary conditions [17

17. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

] to evaluate splitter design and performance for the three different trench fill materials. Our 3D FDTD code was developed in-house and validated for waveguide simulations to ensure that total power is conserved to within less than 0.5%. The trench width and total efficiency for a splitting ratio of 50/50 for each material is listed in Table 1 for D=0 (i.e., no Goos-Hanchen shift compensation). Note that as expected the highest refractive index fill material (n=1.733) results in the largest trench width (86 nm) for a 50/50 splitting ratio. We choose no Goos-Hanchen shift compensation for this comparison because we find little dependence of the total splitter efficiency on D. This is illustrated in Fig. 2 where the difference in splitter efficiency between D=0 and D=-76 nm (at which the peak efficiency occurs) is less than 0.3%.

Fig. 2. Total splitter efficiency (i.e., sum of transmitted and reflected power in waveguide modes divided by power in mode launched in 3D FDTD simulation) as a function of D [see Fig. 1(b) for definition of D] for SU8 trench fill and overclad.
Fig. 3. (a) Magnitude squared time-averaged magnetic field and (b) splitter efficiency as a function of trench width without Goos-Hanchen shift compensation for index matching fluid-filled case. The power in the incident waveguide mode for the simulations is normalized to unity such that the peak value of the magnitude squared time averaged magnetic field of the incident mode in (a) is 0.013. The fringes are due to interference between the incident and reflected modes.

Figure 3(a) shows the magnitude-squared time-averaged magnetic field in a plane 0.325 µm above the SiO2 layer for a splitter filled with index fluid and at a wavelength of 1550 nm (W=86 nm, D=0 nm). The splitting ratio and total efficiency as a function of trench width for the case of index matching fluid trench fill is shown in Fig. 3(b). As expected, the transmission decreases and the reflection increases as the trench width increases. Note also that the total efficiency decreases with increasing trench width. This is most likely due to out-of- plane divergence of the unconfined wave in the trench.

3. Fabrication

We use electron beam lithography (EBL) with a Nanometer Pattern Generation System (NPGS) (JC Nabity Lithography Systems) and field emission environmental scanning electron microscope (FEI/Philips XL30 ESEM-FEG) for trench patterning. We have previously shown that the alignment accuracy for EBL-patterned features is typically less than 40 nm [9

9. Y. Qian, S. Kim, J. Song, and G. P. Nordin, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14, 6020–6028 (2006) [CrossRef] [PubMed]

]. Our fabrication process is the same as reported in Ref. 9 for SOI TBBs. Since our features are very small (~80 nm) compared to the thickness of the ZEP 520A electron-beam resist (400 nm), a water soluble conductive polymer (aquaSAVE53za) is spin coated on top of the ZEP to prevent charging during EBL, which enhances patterning fidelity for fine features. The splitters are patterned with D=-76 nm to account for the Goos-Hanchen shift and then etched in an inductively coupled plasma reactive ion etcher (ICP RIE) (STS Advanced Silicon Etcher) to a depth of 0.75 µm using a C4F8 and SF6 etch chemistry. The ICP-RIE etch recipe for TBBs with wider Si trenches in Ref. 9 works well for the much narrower splitter trenches reported in this paper, although a longer etch time is required because of aspect ratio dependent etching (ARDE). After removing residual ZEP 520A, SU8 or index matching fluid is coated to fill the trenches and cover the waveguides.

Fig. 4. SEM images of (a) splitter, (b) roughness and verticality of etched sidewall, and (c) splitter/bend set after trench etch and before polymer coating.

A scanning electron microscope (SEM) image of a splitter that has an 82 nm trench width is shown prior to trench fill in Fig. 4(a), which is the smallest repeatable trench width we can fabricate for a 0.75 µm etch depth (i.e., nearly 10:1 aspect ratio). The circular etched regions at each end of the trench are intended to help to SU8 or index matching fluid infiltrate the trench. Figure 4(b) is a close-up view of the etched Si face showing smooth and vertical sidewalls.

Figure 4(c) shows a fabricated splitter with an additional 90° bend to turn the reflection output waveguide toward the exit face of the chip. The two output waveguides are separated by 40µm. The area of the splitter is only 11 µm×11 µm (not including the two circles). However, since 99% of the power in the waveguide mode is confined within a 4 µm lateral width of the waveguide, the splitter region can be as small as 4 µm×4 µm. The four patterns in the corners of the image are EBL alignment marks used to ensure accurate positioning of the trench relative to the waveguides [9

9. Y. Qian, S. Kim, J. Song, and G. P. Nordin, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14, 6020–6028 (2006) [CrossRef] [PubMed]

].

4. Experimental measurement and discussion

To characterize splitter optical properties, 1cm×1 cm die are fabricated, each with 20 single splitters such as the one shown in Fig. 4(c) and with sets of waveguides of equal length but different numbers of TBBs as discussed in Ref. 9 so that the bend efficiency can be measured. The splitters are fabricated with a range of trench widths. We use a super-luminescent light emitting diode (SLED) with a center wavelength of 1550 nm as a light source. Polarized output from the SLED is connected to one end of a polarization maintaining (PM) fiber with the other end of the fiber butt-coupled to an input waveguide. A single mode fiber is butt-coupled to an output waveguide to detect the optical power in an individual splitter output. Measurement of a single splitter involves maximizing the coupling of the input and output fibers to the input waveguide and one of the output waveguides using a Newport Autoalign system with three-axis translation stage stacks for each fiber and 50 nm movement resolution for each stage. The other splitter output is measured by moving the output fiber to the waveguide and adjusting the fiber’s position to maximize power coupled from the waveguide into the fiber.

Figure 5(a) compares the reflection and transmission splitting ratio (i.e., reflected or transmitted optical power divided by the sum of the two) as a function of the trench width for experimental measurement and 3D FDTD simulation for different trench fill materials. All measurements are made on the same die and with the same splitters. The width of each splitter trench is measured by nondestructive top-view SEM imaging. The widths vary from 82 nm to 116 nm. The optical properties of each splitter are first measured with only air as the trench fill material. Next, an SU8 film is applied and the splitter measurements are repeated. Finally, the SU8 film is stripped and index fluid is applied followed by again measuring the splitter properties.

Note that in all cases measurement results agree reasonably well with 3D FDTD simulation. As expected, for a given trench width more transmitted power is measured as the refractive index of the trench fill material increases. For SU8 the fabricated trench widths are not small enough to achieve a 50/50 splitting ratio. However, the refractive index of the index fluid is high enough that approximately 50/50 splitting is achieved at the smallest trench width of 82 nm. This is illustrated in Fig. 5(b) in which a 2D scan of the output fiber is shown. The result is a convolution of the fiber mode with the two output waveguides. The measured splitting ratio is 49/51 (reflection/transmission).

The total splitter optical efficiency, η, is measured based on

η=Psplitter_reflectionηBend+Psplitter_transmissionPStraight_waveguide
(1)

where ηBend is the optical efficiency of the bend, Psplitter_reflection and Psplitter_transmission are the measured splitter reflected and transmitted power, respectively, and PStraight _waveguide is the measured power through a straight waveguide. Psplitter_ reflection is divided by ηBend to account for the loss of the bend in the reflection path [Fig. 4(c)]. At λ=1550 nm, the bend efficiency is measured to be 90% (loss of -0.46 dB±0.06 dB/bend) from a set of equal length waveguides, each with a different number of bends, for TE polarization. The measured splitter efficiencies based on Eq. 1 are 78.4% (-1.06 dB±0.34 dB) for a trench with air fill; 72.4% (-1.40 dB±0.34 dB) for SU8; and 78.6% (-1.05 dB±0.48 dB) for index matching fluid.

Fig. 5. (a) Measured and 3D FDTD simulation results for reflection and transmission splitting ratio as a function of trench width for trench fills of air (n=1.0), SU8 (n=1.57), and index matching fluid (n=1.733) at λ=1550 nm. (b) 2D scan of output fiber at exit face of chip for a splitter with 82 nm trench width filled with index matching fluid.

5. Conclusions

Compact SOI rib waveguide 90° splitters have been designed and demonstrated. Splitters with trenches filled with air, SU8, or refractive index fluid are considered. EBL and ICP RIE processes are employed to fabricate the bends and splitters. Measured splitting ratios agree with 3D FDTD simulation results. A 49/51 (reflection/transmission) splitting ratio is achieved for a trench width of 82nm with index matching fluid as the trench fill material. The measured splitter efficiencies are 78.4%, 72.4%, and 78.6% for trench fills of air, SU8, and index fluid, respectively.

Acknowledgment

This work was supported in part by NSF grants IIS-0641973 and ECS-0602261, and DARPA grant N66001-04-8933.

References and Links

1.

B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, “Advances in Silicon-on-Insulator Optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938–947 (1998). [CrossRef]

2.

Y. A. Vlasov and S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004). [CrossRef] [PubMed]

3.

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology,” J. Lightwave Technol. 23, 401- (2005). [CrossRef]

4.

J. Liu, J. Yu, S. Chen, and Z. Li, “Integrated folding 4×4 optical matrix switch with total internal reflection mirrors on SOI by anisotropic chemical etching,” Photon. Technol. Lett. 17, 1187–1189 (2005). [CrossRef]

5.

I. Kiyat, A. Aydinli, and N. Dagli, “Low-power thermooptic tuning of SOI resonator switch,” Photon. Technol. Lett. 18, 364–366 (2006). [CrossRef]

6.

G. P. Nordin, J. W. Noh, and S. Kim, “In-plane photonic transduction for microcantilever sensor arrays,” in Nanoscale Imaging, Spectroscopy, Sensing, and Actuation for Biomedical Applications IV, Alexander N. Cartwright, Dav V. Nicolau, and Paul L. Gourley, Editors, Proceedings of SPIE Vol. 6447, pp. 64470J-1 to -8 (2007).

7.

Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, “Integrated waveguide turning mirror on silicon-on-insulator,” Photon. Technol. Lett. 14, 68–70 (2002). [CrossRef]

8.

S. Lardenois, D. Paskcal, L. Vivien, E. Cassan, and S. Laval, “Low-loss submicrometer silicon-on-insulator rib waveguides and corner mirrors,” Opt. Lett. 28, 1150–1152 (2003). [CrossRef] [PubMed]

9.

Y. Qian, S. Kim, J. Song, and G. P. Nordin, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14, 6020–6028 (2006) [CrossRef] [PubMed]

10.

C. S. Hsiao and L. Wang, “Design for beam splitting components employing silicon-on-insulator rib waveguide structures,” Opt. Lett. 30, 3153–3155 (2005). [CrossRef] [PubMed]

11.

A. Koster, E. Cassan, S. Laval, L. Vivien, and D. Pascal, “Ultracompact splitter for submicrometer silicon-on-insulator rib waveguides,” J. Opt. Soc. Am. A 21, 2180–2185 (2004). [CrossRef]

12.

L. Li, G. P. Nordin, J. M. English, and J. Jiang, “Small-area bends and beamsplitters for low-index-contrast waveguides”, Opt. Express 11(3), 282–290 (2003). [CrossRef]

13.

D. Goldring, E. Alperovich, U. Levy, and D. Mendlovic, “Analysis of waveguide-splitter-junction in high-index silicon-on-insulator waveguides,” Opt. Express 13, 2931–2940 (2005). [CrossRef] [PubMed]

14.

S. Kim, J. Jiang, and G. P. Nordin, “Design of compact polymer Mach-Zender interferometer and ring resonator with air trench structures,” Opt. Eng. 45, 054602 (2006). [CrossRef]

15.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass., 1995).

16.

J. Cai, G. P. Nordin, S. Kim, and J. Jiang, “Three-dimensional analysis of a hybrid photonic crystalconventional waveguide 90° bend,” Appl. Opt. 43, 4244–4249 (2004). [CrossRef] [PubMed]

17.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]

OCIS Codes
(130.0130) Integrated optics : Integrated optics
(130.1750) Integrated optics : Components
(230.1360) Optical devices : Beam splitters
(230.7370) Optical devices : Waveguides
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Integrated Optics

History
Original Manuscript: November 12, 2007
Revised Manuscript: November 28, 2007
Manuscript Accepted: November 29, 2007
Published: December 3, 2007

Citation
Yusheng Qian, Jiguo Song, Seunghyun Kim, and Gregory P. Nordin, "Compact 90° trench-based splitter for silicon-on-insulator rib waveguides," Opt. Express 15, 16712-16718 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-16712


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References

  1. B. Jalali, S. Yegnanarayanan, T. Yoon, T. Yoshimoto, I. Rendina, and F. Coppinger, "Advances in Silicon-on-Insulator Optoelectronics," IEEE J. Sel. Top. Quantum Electron. 4, 938-947 (1998). [CrossRef]
  2. Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004). [CrossRef] [PubMed]
  3. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, "Nanophotonic Waveguides in Silicon-on-Insulator Fabricated With CMOS Technology," J. Lightwave Technol.  23, 401- (2005). [CrossRef]
  4. J. Liu, J. Yu, S. Chen, and Z. Li, "Integrated folding 4x4 optical matrix switch with total internal reflection mirrors on SOI by anisotropic chemical etching," Photon. Technol. Lett. 17, 1187-1189 (2005). [CrossRef]
  5. I. Kiyat, A. Aydinli, N. Dagli, "Low-power thermooptic tuning of SOI resonator switch," Photon. Technol. Lett. 18, 364-366 (2006). [CrossRef]
  6. G. P. Nordin, J. W. Noh, and S. Kim, "In-plane photonic transduction for microcantilever sensor arrays," in Nanoscale Imaging, Spectroscopy, Sensing, and Actuation for Biomedical Applications IV, Alexander N. Cartwright, Dav V. Nicolau, and Paul L. Gourley, Editors, Proceedings of SPIE Vol. 6447, pp. 64470J-1 to -8 (2007).
  7. Y. Z. Tang, W. H. Wang, T. Li, and Y. L. Wang, "Integrated waveguide turning mirror on silicon-on-insulator," Photon. Technol. Lett. 14, 68-70 (2002). [CrossRef]
  8. S. Lardenois, D. Paskcal, L. Vivien, E. Cassan, and S. Laval, "Low-loss submicrometer silicon-on-insulator rib waveguides and corner mirrors," Opt. Lett. 28, 1150-1152 (2003). [CrossRef] [PubMed]
  9. Y. Qian, S. Kim, J. Song, and G. P. Nordin, "Compact and low loss silicon-on-insulator rib waveguide 90° bend," Opt. Express 14, 6020-6028 (2006) [CrossRef] [PubMed]
  10. C. S. Hsiao and L. Wang, "Design for beam splitting components employing silicon-on-insulator rib waveguide structures," Opt. Lett. 30, 3153-3155 (2005). [CrossRef] [PubMed]
  11. A. Koster, E. Cassan, S. Laval, L. Vivien, and D. Pascal, "Ultracompact splitter for submicrometer silicon-on-insulator rib waveguides," J. Opt. Soc. Am. A 21, 2180-2185 (2004). [CrossRef]
  12. L. Li, G. P. Nordin, J. M. English, and J. Jiang, "Small-area bends and beamsplitters for low-index-contrast waveguides", Opt. Express 11(3), 282-290 (2003). [CrossRef]
  13. D. Goldring, E. Alperovich, U. Levy, and D. Mendlovic, "Analysis of waveguide-splitter-junction in high-index silicon-on-insulator waveguides," Opt. Express 13, 2931-2940 (2005). [CrossRef] [PubMed]
  14. S. Kim, J. Jiang, and G. P. Nordin, "Design of compact polymer Mach-Zender interferometer and ring resonator with air trench structures," Opt. Eng. 45, 054602 (2006). [CrossRef]
  15. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Boston, Mass., 1995).
  16. J. Cai, G. P. Nordin, S. Kim, and J. Jiang, "Three-dimensional analysis of a hybrid photonic crystal-conventional waveguide 90o bend," Appl. Opt. 43, 4244-4249 (2004). [CrossRef] [PubMed]
  17. J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994). [CrossRef]

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