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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 13732–13737
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Efficient silicon wire waveguide crossing with negligible loss and crosstalk

Andrei V. Tsarev  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 13732-13737 (2011)
http://dx.doi.org/10.1364/OE.19.013732


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Abstract

Multiple optical elements utilize crossing of channel optical waveguides. This paper introduces efficient silicon wire waveguide crossing by means of vertical coupling of tapered Si wire with upper polymer wide strip waveguide through a silica buffer. Numerical simulations by 3D FDTD prove that optimal structure of 70 µm length can provide 98% efficiency for through pass and 99.9% efficiency for cross pass, as well as negligible back reflection (−50 dB) and cross talk (−70 dB). Proposed waveguide crossing on thin silicon-on-insulator CMOS compatible structures could find multiple applications in Photonics.

© 2011 OSA

1. Introduction

Current paper further evaluates the general idea of adiabatic interlayer coupling [1

1. K. Watanabe, Y. Hashizume, Y. Nasu, Y. Sakamaki, M. Kohtoku, M. Itoh, and Y. Inoue, “Low-loss three-dimensional waveguide crossings using adiabatic interlayer coupling,” Electron. Lett. 44(23), 1356–1357 (2008). [CrossRef]

] and implements it to design silicon wire waveguide crossing on SOI structures with polymer over guide, in order to provide negligible loss and crosstalk.

2. Waveguide crossing by vertical coupling with polymer upper channel waveguide

General idea of excellent waveguide crossing is to make possible optical beam to pass over the crossed channel waveguide [1

1. K. Watanabe, Y. Hashizume, Y. Nasu, Y. Sakamaki, M. Kohtoku, M. Itoh, and Y. Inoue, “Low-loss three-dimensional waveguide crossings using adiabatic interlayer coupling,” Electron. Lett. 44(23), 1356–1357 (2008). [CrossRef]

] by means of inverse tapers. Adiabatic inverted tapers are widely used as beam transformers for coupling Si wire waveguide with optical fiber [3

3. G. T. Reed, Silicon Photonics: The State of the Art (John Wiley & Sons, Ltd, 2008).

,4

4. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

,13

13. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]

18

18. J. K. Doylend and A. P. Knights, “Design and simulation of an integrated fiber-to-chip coupler for silicon-on-insulator waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1363–1370 (2006). [CrossRef]

]. Recently, vertical waveguide coupler with −0.2 dB loss is designed for TE single mode transmission from a bottom SOI channel waveguide to a top a-Si channel waveguide [19

19. R. Sun, M. Beals, A. Pomerene, J. Cheng, C. Y. Hong, L. Kimerling, and J. Michel, “Impedance matching vertical optical waveguide couplers for dense high index contrast circuits,” Opt. Express 16(16), 11682–11690 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11682. [CrossRef] [PubMed]

]. Impedance matching is provided by contra directed inverse tapers in the respective waveguides. This design is good for waveguide crossing but it needs an advanced technology for a-Si manufacturing of over layered waveguide, as well as carefully adjusting in space of two nano tapers. Current paper proposes and studies the design solution with polymer over layered waveguide, simpler from a technological point of view.

The proposed structure of cross coupler of Si wire waveguides is shown in Fig. 1a
Fig. 1 Design of cross coupler. a) General view (from the bottom) of the structure based by Si wire tapers vertically coupled with wide polymer waveguide. Buried oxide and Si substrate are not shown; b) Through pass transmitting efficiency T for Si wires of different cross section as a function of refractive index of upper waveguide in optimum structure.
. It contains two Si single mode wire waveguides with height h = 220 nm and width w = 450 nm on 2 μm buried oxide (BOX) silicon substrate with two contra directed inverse tapers [15

15. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-15-1302. [CrossRef] [PubMed]

], which are separated by a small distance Lg = 3 µm from taper ends. We use refractive indices 3.478 and 1.447 for silicon and BOX, respectively. The taper has a parabolic shape. It is characterized by a taper length L and a tip width d. The spacing between waveguide tips contains similar Si wire intersecting waveguides in cross direction (X). The waveguides are covered through spin-on 〉owable oxide (FOX) [20

20. C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) □lms produced by thermal curing,” J. Mater. Chem. 12(4), 1138–1141 (2002). [CrossRef]

] buffer with refractive index 1.4 and height Wg and by an upper strip waveguide of width W and height H built by polymer SU-8 (with refractive index Nw = 1.56 [21

21. C. Reardon, A. Di Falco, K. Welna, and T. Krauss, “Integrated polymer microprisms for free space optical beam deflecting,” Opt. Express 17(5), 3424–3428 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3424. [CrossRef] [PubMed]

,22] at optical wavelength 1.55 μm), which is situated just over the through pass Si wire (along Z). This refractive index 1.56 becomes suboptimum for the widely used Si wires with 220 × 450 nm2 cross section (see Fig. 1b). The final structure is additionally covered by FOX for protection of polymer waveguide from environment.

The proposed structure has been numerically investigated by three-dimensional finite difference time domain (FDTD) method by FullWave software [23

23. www.rsoftdesign.com, Rsoft Photonic CAD Suite, ver. 8.0, single license (2007).

]. We have used the same mesh size 50 nm for all simulations. It represents a trade-off between the computer power requirement and simulation accuracy which was 1% and 0.1% for absolute and relative power measurements, respectively. We launch and analyze propagation of fundamental mode of Si wire thought the structure and measure the relevant intensities, normalized to the input power for transmitted wave (T), back reflected wave (Back) and wave in the cross waveguide (Side), describing the crosstalk. Counter map of power transmittance is presented in Fig. 2
Fig. 2 Counter map of power transmittance through cross coupler of fundamental guided mode of Si wire waveguide. a) X-cut, b) Y-cut (due to symmetry we use half structure, X ≥ 0). 3D FDTD simulation. Lg = 3 μm, W = 1.5 μm, H = 1.7 μm, Wg = 200 nm, L = 30 μm, d = 160 nm.
.

Figure 3
Fig. 3 Power distribution in different cross-section. a) begin of structure (z = 4.5 μm) - the main of power is in the Si wire; b) middle of structure (z = 36.5 μm) - the main of power is in the upper polymer waveguide; c) end of structure (z = 72 μm) - the main of power is returned to the Si wire; 3D FDTD simulation. Lg = 3 μm, W = 1.5 μm, H = 1.7 μm, Wg = 200 nm, L = 30 μm, d = 160 nm.
presents the power distribution at different cross-sections. One can observe from Fig. 2 and Fig. 3 that the optical power is coupled up and down into the upper polymer waveguides by means of Si wire tapers, and thus it passes over the crossed Si wire waveguide.

For structure with optimal through pass parameters, the features of perpendicular cross pass architecture will be even better as X-directed waveguide has negligible coupling with other Si and polymer waveguides due to large distance separation, providing optical isolation. Note that propagation of optical wave along X produces too small cross scattering which is below the FDTD method sensitivity. In order to study the crossing for this case of extremely small loss, we have positioned 16 identical cross wires on the pass of X-directed waveguide. The total power transmittance is presented in Fig. 6b as additional curves (Cross(16)). From these data, it is possible to estimate total transmitting (−0.01 dB) and reflecting (−53 dB) coefficients for 16 wire crossing for Cross pass geometry. One has to mention that an error in measuring power amplitude for current 3D FDTD simulation is about 1%, thus corresponding value −0.04 dB could be regarded as the maximum of actual possible loss for the case of Si wire waveguide crossed by 16 Si wires. For the single wire crossing, the loss is smaller than this value by 16 times and thus transmitting efficiency could be better than 99.9%.

One has to point out this structure contains two coupled waveguides with drastically different refractive indices and sizes, thus it is not evident that it can provide the high efficiency of waveguide crossing for any set of device parameters. For the specific case of upper polymer waveguide, we find the set of structure parameters providing 98% power transmission. It is interesting that the power distribution in polymer waveguide at crossing point has an asymmetric structure (see Fig. 3b). It means that about 62% of total power is transmitted by the fundamental mode of polymer waveguide and, thus, the significant amount of power (38%) corresponds to other waveguide modes (first mode, radiated and evanescent). Thus we have different mechanisms of power coupling between single mode silicon wires to two-mode polymer waveguide. They could add constructively or destructively, thus making the coupling efficiency to be a complicated function of the structure parameters. It makes difficult to find an universal relation of the crossing performance on the waveguide geometry and the effective indexes of Si and polymer waveguides. Thus for different optical waveguide structures, one needs to complete the optimization procedure from the very beginning. For example, for the case of typical Si wire with h = 340 nm and w = 340 nm we have got suboptimum refractive Nw = 1.6 of the upper waveguide (see Fig. 1b). All other structure parameters are chosen the same as for optimized structure with h = 220 nm and w = 450 nm.

These simulations prove that the proposed structure can provide excellent crossing characteristics. We regard an ideal structure without propagation loss. Taking into account the small structure sizes (length 70 μm and width 3 μm), it does not make a significant error as the crossing loss (−0.1 dB) corresponds to “the effective per length” loss of about −14 dB/cm, which is much smaller propagation loss. The most important advantage of this optical element will be realized for the case of optical devices which implements multiple (up to hundreds) crossings in X directions and several crossings in Z directions. These structures could be manufactured by modern technology which is available in different nanophotonics centers [4

4. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

,6

6. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18(15), 16146–16155 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16146. [CrossRef] [PubMed]

,13

13. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]

,14

14. S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2927. [CrossRef] [PubMed]

,22].

4. Conclusion

Numerical experiments by 3D FDTD prove that vertical coupling through silica buffer of tapered Si wires and upper polymer waveguide could be used as low loss wire crossing with negligible crosstalk. It provides small power reflection (−50 dB) and scattering into crossing waveguide (−70 dB), as well as small loss for through pass (<0.1 dB) of fundamental guided mode. It has to be mentioned that loss for cross path is even smaller (<0.002 dB) due to a small coupling of crossed Si and polymer waveguides, which are separated from Si wire by silica buffer. New waveguide crossing could be manufactured by CMOS compatible technology and can find wide applications in silicon photonics and censoring for the cases if multiple and nondestructive waveguide crossing needed for high device performance.

Acknowledgments

The author thanks Company RSoft Design Group, Inc. [23] for providing user license and technical support for Rsoft Photonic CAD Suite 8.0 for FDTD simulations.

References and links

1.

K. Watanabe, Y. Hashizume, Y. Nasu, Y. Sakamaki, M. Kohtoku, M. Itoh, and Y. Inoue, “Low-loss three-dimensional waveguide crossings using adiabatic interlayer coupling,” Electron. Lett. 44(23), 1356–1357 (2008). [CrossRef]

2.

W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing,” Opt. Lett. 35(17), 2901–2903 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-17-2901. [CrossRef] [PubMed]

3.

G. T. Reed, Silicon Photonics: The State of the Art (John Wiley & Sons, Ltd, 2008).

4.

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

5.

P. Sanchis, J. V. Galan, A. Griol, J. Marti, M. A. Piqueras, and J. M. Perdigues, “Low-crosstalk in silicon-on-insulator waveguide crossings with optimized-angle,” IEEE Photon. Technol. Lett. 19(20), 1583–1585 (2007). [CrossRef]

6.

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18(15), 16146–16155 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16146. [CrossRef] [PubMed]

7.

D. Tanaka, Y. Ikuma, and H. Tsuda, “Low loss, small crosstalk offset crossing structure for large-scale planar lightwave circuits,” IEICE Electron. Express 6(7), 407–411 (2009). [CrossRef]

8.

W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32(19), 2801–2803 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-19-2801. [CrossRef] [PubMed]

9.

H. Chen and A. Poon, “Low-loss multimode-interference-based crossings for silicon wire waveguides,” IEEE Photon. Technol. Lett. 18(21), 2260–2262 (2006). [CrossRef]

10.

C.-H. Chiu and C.-H. Chiu, “Taper-integrated multimode-interference based waveguide crossing design,” IEEE J. Quantum Electron. 46(11), 1656–1661 (2010). [CrossRef]

11.

P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=ol-34-18-2760. [CrossRef] [PubMed]

12.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004). [CrossRef]

13.

T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]

14.

S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2927. [CrossRef] [PubMed]

15.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-15-1302. [CrossRef] [PubMed]

16.

D. Van Thourhout, G. Roelkens, R. Baets, W. Bogaerts, J. Brouckaert, P. P. P. Debackere, P. Dumon, S. Scheerlinck, J. Schrauwen, D. Taillaert, F. Van Laere, and J. Van Campenhout, “Coupling mechanisms for a heterogeneous silicon nanowire platform,” Semicond. Sci. Technol. 23(6), 064004 (2008). [CrossRef]

17.

I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review of fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997). [CrossRef]

18.

J. K. Doylend and A. P. Knights, “Design and simulation of an integrated fiber-to-chip coupler for silicon-on-insulator waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1363–1370 (2006). [CrossRef]

19.

R. Sun, M. Beals, A. Pomerene, J. Cheng, C. Y. Hong, L. Kimerling, and J. Michel, “Impedance matching vertical optical waveguide couplers for dense high index contrast circuits,” Opt. Express 16(16), 11682–11690 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11682. [CrossRef] [PubMed]

20.

C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) □lms produced by thermal curing,” J. Mater. Chem. 12(4), 1138–1141 (2002). [CrossRef]

21.

C. Reardon, A. Di Falco, K. Welna, and T. Krauss, “Integrated polymer microprisms for free space optical beam deflecting,” Opt. Express 17(5), 3424–3428 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3424. [CrossRef] [PubMed]

22.

http://www.microchem.com/products/su_eight.htm, SU-8 3000 Data Sheet.

23.

www.rsoftdesign.com, Rsoft Photonic CAD Suite, ver. 8.0, single license (2007).

24.

Handbook of Optics, http://refractiveindex.info/?group=CRYSTALS&material=Si.

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Integrated Optics

History
Original Manuscript: April 22, 2011
Revised Manuscript: June 14, 2011
Manuscript Accepted: June 17, 2011
Published: July 1, 2011

Citation
Andrei V. Tsarev, "Efficient silicon wire waveguide crossing with negligible loss and crosstalk," Opt. Express 19, 13732-13737 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-13732


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References

  1. K. Watanabe, Y. Hashizume, Y. Nasu, Y. Sakamaki, M. Kohtoku, M. Itoh, and Y. Inoue, “Low-loss three-dimensional waveguide crossings using adiabatic interlayer coupling,” Electron. Lett. 44(23), 1356–1357 (2008). [CrossRef]
  2. W. Shi, R. Vafaei, M. Á. G. Torres, N. A. F. Jaeger, and L. Chrostowski, “Design and characterization of microring reflectors with a waveguide crossing,” Opt. Lett. 35(17), 2901–2903 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-17-2901 . [CrossRef] [PubMed]
  3. G. T. Reed, Silicon Photonics: The State of the Art (John Wiley & Sons, Ltd, 2008).
  4. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]
  5. P. Sanchis, J. V. Galan, A. Griol, J. Marti, M. A. Piqueras, and J. M. Perdigues, “Low-crosstalk in silicon-on-insulator waveguide crossings with optimized-angle,” IEEE Photon. Technol. Lett. 19(20), 1583–1585 (2007). [CrossRef]
  6. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D.-X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18(15), 16146–16155 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-16146 . [CrossRef] [PubMed]
  7. D. Tanaka, Y. Ikuma, and H. Tsuda, “Low loss, small crosstalk offset crossing structure for large-scale planar lightwave circuits,” IEICE Electron. Express 6(7), 407–411 (2009). [CrossRef]
  8. W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Low-loss, low-cross-talk crossings for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 32(19), 2801–2803 (2007), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-32-19-2801 . [CrossRef] [PubMed]
  9. H. Chen and A. Poon, “Low-loss multimode-interference-based crossings for silicon wire waveguides,” IEEE Photon. Technol. Lett. 18(21), 2260–2262 (2006). [CrossRef]
  10. C.-H. Chiu and C.-H. Chiu, “Taper-integrated multimode-interference based waveguide crossing design,” IEEE J. Quantum Electron. 46(11), 1656–1661 (2010). [CrossRef]
  11. P. Sanchis, P. Villalba, F. Cuesta, A. Håkansson, A. Griol, J. V. Galán, A. Brimont, and J. Martí, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34(18), 2760–2762 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=ol-34-18-2760 . [CrossRef] [PubMed]
  12. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Low loss intersection of Si photonic wire waveguides,” Jpn. J. Appl. Phys. 43(2), 646–647 (2004). [CrossRef]
  13. T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,” IEEE J. Sel. Top. Quantum Electron. 11(1), 232–240 (2005). [CrossRef]
  14. S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-22-2927 . [CrossRef] [PubMed]
  15. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-15-1302 . [CrossRef] [PubMed]
  16. D. Van Thourhout, G. Roelkens, R. Baets, W. Bogaerts, J. Brouckaert, P. P. P. Debackere, P. Dumon, S. Scheerlinck, J. Schrauwen, D. Taillaert, F. Van Laere, and J. Van Campenhout, “Coupling mechanisms for a heterogeneous silicon nanowire platform,” Semicond. Sci. Technol. 23(6), 064004 (2008). [CrossRef]
  17. I. Moerman, P. P. Van Daele, and P. M. Demeester, “A review of fabrication technologies for the monolithic integration of tapers with III-V semiconductor devices,” IEEE J. Sel. Top. Quantum Electron. 3(6), 1308–1320 (1997). [CrossRef]
  18. J. K. Doylend and A. P. Knights, “Design and simulation of an integrated fiber-to-chip coupler for silicon-on-insulator waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1363–1370 (2006). [CrossRef]
  19. R. Sun, M. Beals, A. Pomerene, J. Cheng, C. Y. Hong, L. Kimerling, and J. Michel, “Impedance matching vertical optical waveguide couplers for dense high index contrast circuits,” Opt. Express 16(16), 11682–11690 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11682 . [CrossRef] [PubMed]
  20. C.-C. Yang and W.-C. Chen, “The structures and properties of hydrogen silsesquioxane (HSQ) □lms produced by thermal curing,” J. Mater. Chem. 12(4), 1138–1141 (2002). [CrossRef]
  21. C. Reardon, A. Di Falco, K. Welna, and T. Krauss, “Integrated polymer microprisms for free space optical beam deflecting,” Opt. Express 17(5), 3424–3428 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-5-3424 . [CrossRef] [PubMed]
  22. http://www.microchem.com/products/su_eight.htm , SU-8 3000 Data Sheet.
  23. www.rsoftdesign.com , Rsoft Photonic CAD Suite, ver. 8.0, single license (2007).
  24. Handbook of Optics, http://refractiveindex.info/?group=CRYSTALS&material=Si .

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