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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 24 — Nov. 21, 2011
  • pp: 23658–23663
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Ultra-small silicon waveguide coupler switch using gap-variable mechanism

Yuta Akihama, Yoshiaki Kanamori, and Kazuhiro Hane  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 23658-23663 (2011)
http://dx.doi.org/10.1364/OE.19.023658


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Abstract

Submicron-wide silicon waveguide coupler with gap variable mechanism is proposed for a compact optical waveguide switch. Two freestanding silicon waveguides are placed parallel with a submicron gap. The gap is changed by electrostatic comb-drive micro-actuators to control the coupling coefficient of the coupler. The fabricated device consisted of the silicon waveguides of 400 nm in width and 260 nm in thickness. The total size of the switch was 100 μm wide and 150 μm long. Decreasing the gap between the waveguides to 110 nm, the output intensity at drop port became a maximum while the output intensity at through port became a minimum. The extension ratio of the switch output was 17 dB for the waveguide displacement of 300 nm.

© 2011 OSA

1. Introduction

Silicon waveguide circuits are promising for optical telecommunication devices and optical interconnection circuits [1

1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

]. Monolithic fabrication of silicon waveguides and silicon electronics is powerful for future integration in the opt-electronic systems. Due to the high refractive index of silicon (~3.5 at 1.5 μm wavelength), the silicon waveguide circuits can be miniaturized by a few orders of magnitude smaller than silica waveguide circuits. Submicron-wide silicon waveguide works as a single-mode waveguide of circuit with a bending radius as small as 1 μm [2

2. A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-oninsulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001). [CrossRef]

]. Several submicron-wide silicon waveguide devices such as waveguide splitter/coupler [3

3. S. Janz, P. Cheben, D. Dalacu, A. Delge, A. Densmore, B. Lamontagne, M.-J. Picard, E. Post, J. H. Schmid, P. Waldron, D.-X. Xu, K. P. Yap, and W. N. Ye, “Microphotonic elements for integration on the silicon-on-insulator waveguide platform,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1402–1415 (2006). [CrossRef]

,4

4. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photon. Technol. Lett. 17(3), 585–587 (2005). [CrossRef]

] and microring [5

5. P. Koonath, T. Indukuri, and B. Jalali, “Monolithic 3-D silicon photonics,” J. Lightwave Technol. 24(4), 1796–1804 (2006). [CrossRef]

] have been studied. Combining waveguide components, complex circuits such as arrayed waveguide device [6

6. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, “Arrayed waveguide grating of 70×60μm2 size based on Si photonic wire waveguides,” Electron. Lett. 41(14), 801–802 (2005). [CrossRef]

] have also been studied. In the case of functional devices, submicron-wide silicon waveguide switch using thermo-optical effect was reported [7

7. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1371–1379 (2006). [CrossRef]

]. Although the thermo-optical effect of silicon was larger than that of silica, the switch speed was relatively slow and some power was consumed by micro-heaters. Ultra-fast silicon waveguide light modulator using refractive index change of silicon by a carrier injection [8

8. W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007). [CrossRef] [PubMed]

] has attracted a strong attention for telecommunication and interconnection [9

9. C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006). [CrossRef]

]. The switch using the refractive index change of silicon by carrier injection also consumes a large power if it is used for a matrix switch.

Recently, a switch using a physical contact of submicron-wide waveguide with an electrostatic micro-actuator was demonstrated [10

10. E. Bulgan, Y. Kanamori, and K. Hane, “Submicron silicon waveguide optical switch driven by microelectromechanical actuator,” Appl. Phys. Lett. 92(10), 101110 (2008). [CrossRef]

]. Due to the small-size of silicon waveguide, a small misalignment and fabrication error generated a large optical loss, although the power consumption of the electrostatic micro-actuator was very small. Likewise, several functional devices using a gap-change of submicron-wide single-mode waveguides with an electrostatic micro-actuator were reported. Microring resonators were studied to change the coupling to bus-line waveguide [11

11. J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13(2), 202–208 (2007). [CrossRef]

,12

12. K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express 16(19), 14421–14428 (2008). [CrossRef] [PubMed]

]. Mach-Zehnder interferometer was also demonstrated by changing a path-length [13

13. T. Ikeda, K. Takahashi, Y. Kanamori, and K. Hane, “Phase-shifter using submicron silicon waveguide couplers with ultra-small electro-mechanical actuator,” Opt. Express 18(7), 7031–7037 (2010). [CrossRef] [PubMed]

]. Resonator tuning of 1D photonic crystal single-mode waveguide was also studied by changing the gap between the waveguides [14

14. X. Chew, G. Zhou, F. S. Chau, and J. Deng, “Nanomechanically tunable photonic crystal resonators utilizing triple-beam coupled nanocavities,” IEEE Photon. Technol. Lett. 23(18), 1310–1312 (2011). [CrossRef]

,15

15. X. Chew, G. Zhou, F. S. Chau, J. Deng, X. Tang, and Y. C. Loke, “Dynamic tuning of an optical resonator through MEMS-driven coupled photonic crystal nanocavities,” Opt. Lett. 35(15), 2517–2519 (2010). [CrossRef] [PubMed]

]. In the case of multi-mode waveguides, the gap change was also introduced for switching [16

16. M. W. Pruessner, K. Amarnath, M. Datta, D. P. Kelly, S. Kanakaraju, P.-T. Ho, and R. Ghodssi, “InP-based optical waqveguide MEMS switches with evanescent coupling mechanism,” J. Micromech. Syst. 14(5), 1070–1081 (2005). [CrossRef]

,17

17. M.-C. M. Lee, D. D. Hah, E. K. Lau, H. Toshiyoshi, and M. Wu, “MEMS-actuated photonic crystal switches,” IEEE Photon. Technol. Lett. 18(2), 358–360 (2006). [CrossRef]

]. However, for the silicon submicron-wide single-mode waveguide, there is no report on a directional coupler switch using a gap change with an electrostatic comb-drive actuator.

In the case of the electrostatic comb-drive micro-actuator [18

18. K. Takahashi, E. Bulgan, Y. Kanamori, and K. Hane, “Submicron comb-drive actuators fabricated on thin single crystalline silicon layer,” IEEE Trans. Ind. Electron. 56(4), 991–995 (2009). [CrossRef]

], the power consumption is calculated to be smaller than 1pJ for a single switching if we assume that all the energies stored in the mechanical spring and the electrostatic capacitor of the actuator were consumed by the resistor of wiring. For 1000 cycles of switching per a second, the actuator consumes 1nW. Therefore, the power consumption of the electrostatic comb-drive actuator is much smaller than those of the switches using the thermo-optical effect and carrier injection, where the power consumptions are larger than 1mW.

In this study, a submicron-wide silicon waveguide coupler switch using the ultra-small electrostatic comb-drive actuators is proposed. Changing the gap between the silicon waveguides of coupler, the input light is switched to the other waveguide. Being free from physical contact of waveguides, the optical loss of the switch is small and the power consumption is also low due to the capacitive operation. The design, fabrication, and characteristics of the proposed submicron-wide silicon waveguide coupler switch are reported.

2. Principle and fabrication

Figure 1(a)
Fig. 1 (a) Schematic diagram of gap-variable submicron-wide waveguide coupler, (b) Design of the coupler switch with electrostatic comb-drive actuators, (c) Schematic diagram of the whole device.
shows the schematic diagram of the structure of the proposed coupler switch consisting of two freestanding silicon single-mode waveguides. Figure 1(b) shows the detailed design of the proposed coupler switch. Figure 1(c) shows the whole layout of the optical components. The interaction region of the coupler is determined by the region where the gap of the two waveguides is narrower than the other region. When the gap between the two waveguide is much wider than the region of evanescent wave of the freestanding waveguides, there is no interaction of light propagating in an input waveguide. If the other waveguide approaches to the input waveguide as close as the modes of two waveguides become coupled, the input light transfers to the other waveguide by the coupling coefficient of unity under the maximum coupling condition. In the proposed device, the gap of coupler is controlled by electrostatic comb-drive actuators.

Using an analytical theory of coupler [19

19. K. Okamoto, Basis of Optical Waveguides Coronasha Ltd. (Tokyo) (1992).

,20

20. E. A. J. Marcatili, “Dielectric rectangular waveguide and dielectric coupler for integrated optics,” Bell Syst. Tech. J. 47(7), 2071–2102 (1969).

], the output intensityI1of light in an output waveguide (Output 1 at through port) and the output intensityI2in the other waveguide (Output 2 at drop port) is expressed for the lowest-mode wave of coupled two rectangular waveguides having the same cross-sectional profile by
I1=I0cos2(κl),I2=I0sin2(κl),
(1)
where I0is input intensity, κ and l are coupling coefficient and length, respectively. The coupling coefficient is expressed by

κ=2Δa(kxa)2(rxa)2(1+rxa)v3exp(rxg).
(2)

Here, g is the gap of waveguides. Δ and a are the relative refractive index difference and an half width of waveguide, respectively. kx and rxare the coefficients relating to wave vector and refractive index distribution, respectively, and ν is a normalized frequency. We select the width of waveguide to allow only a single lowest mode of waveguide, and thus we assume that the mode profile is that of the lowest TE mode since we introduce a TE-mode selector as shown in Fig. 1(c). Under our experimental conditions, the values of the parameters are as follows, Δ = 0.46, a = 200 nm, kx = 7.57x106 m−1, rx = 1.1x107 m−1, and ν = 2.70, respectively. Since the above equations are the approximations, we also carried out the simulations using the finite difference time domain method (FDTD, Crystal Wave) and the beam propagation method (BPM. Mode PROP) to confirm the mode profile and the coupling. From those evaluations, the coupling length is designed to be around 10 μm in the gap region form 100 nm to 300 nm. From the Eq. (1), the output intensities at drop and through ports oscillate with the decrease of gap.

The movable freestanding silicon waveguide of coupler is suspended by 1.3 μm wide and 8.0 μm long elliptical suspension bridges, which connect the movable waveguide to the suspension structures of actuators with 0.2 μm wide 1.6μm long silicon suspension arms as shown in Fig. 1(b). The distance between the two suspension bridges is 52 μm. The two actuators are identical in design and are used to support the long freestanding movable waveguide firmly. The other freestanding waveguide is fixed by the elliptical suspension bridges connected to substrate. These waveguides are 260 nm in thickness and 400 nm in width. The coupling length of the coupler is 10 μm and the initial gap is 1000 nm. The coupling part of the coupler is connected to two bent waveguides with a radius of 3.1 μm. The actuator consists of a pull-type comb-drive having 20 finger-pairs. Each finger is 1.73 μm long and 200 nm wide. The springs of actuator are double-folded type and each beam of the springs is 200 nm in width and 15 μm in length. The total spring constant of actuator is calculated to be 0.315 N/m. The electrostatic force of actuator is also theoretically estimated to be about 0.32 μN at the voltage of 23V. The maximum displacement of actuator is limited by a stopper of actuator at the displacement of 980 nm. Therefore, the minimum gap of coupler is designed to be 20 nm. A voltage is applied between the two regions of top silicon layer separated by etching as shown in Fig. 1(b).

The fabrication sequence is shown in Fig. 2
Fig. 2 Schematic diagram of fabrication process.
. A silicon on insulator (SOI) wafer with a 260 nm thick top silicon layer and a 2 μm thick buried oxide layer on a 625 μm thick silicon substrate was used. First, a 350 nm thick positive resist polymer (ZEON ZEP-520A) was coated on the SOI wafer, and it was exposed using an electron beam patterning machine (JEOL JBX-5000LS). After developing the resist polymer, the top silicon layer was etched by a fast atom beam (Ebara FAB-60ML). The resist polymer was removed by a H2SO4/ H2O2 solution. The SOI wafer was cleaved after partially dicing silicon substrate to obtain a facet of input waveguide for coupling light. Finally, the SiO2 layer was etched by a hydrofluoric acid vapor to obtain the freestanding structure of the proposed device.

The device characteristics were measured under a visible/infrared optical microscopy. A tunable laser (Agilent 81682A) was used as light source at the wavelength around 1.5 μm. For coupling the laser light to the end surface of the input port of the fabricated device, a lensed single mode fiber was used. The light intensities at the output ports (through and drop ports) were measured from the spot images of scattered light at the ends of waveguides using an IR camera (Goodruch SU32KTS-1.7RT) [13

13. T. Ikeda, K. Takahashi, Y. Kanamori, and K. Hane, “Phase-shifter using submicron silicon waveguide couplers with ultra-small electro-mechanical actuator,” Opt. Express 18(7), 7031–7037 (2010). [CrossRef] [PubMed]

].

3. Results and discussion

Figure 3(a)
Fig. 3 (a) A whole image of the gap-variable coupler switch, (b) a magnified image of the coupler region, (c) a magnified image of the gap between the waveguides.
shows a whole view of the fabricated device. The two actuators and the freestanding waveguides are well fabricated. The etched region below top silicon layer of SOI wafer is seen in pale color to be about 2.3 μm wide inside from the edge of the top silicon layer. Figure 3(b) shows a magnified image of the coupler region. The freestanding silicon waveguide coupler is fabricated well with a clear air gap. Figure 3(c) shows a magnified image of the gap between the coupler waveguides. The gap is measured to be 1110 nm, which is a little larger than the designed value. The waveguide is 380 nm wide, which is a little smaller than the design value. The surface roughness of the waveguide was evaluated from electron micrograph to be less than 15 nm.

The laser light at the wavelength of 1548 nm was used as input light, and the IR image of the output ports was obtained from the top of the device. Changing the voltage applied to the actuators, the intensities of light spots generated by the scattered light from the ends of the output waveguides varied by the displacement of the movable waveguide. Figure 4(a)
Fig. 4 (a) IR image of the ends of output waveguides at 0V and (b) that at 25.6V.
shows the IR image obtained at the voltage of 0V. Increasing the voltage from 0V, the intensity of light spot at through port decreased while that at drop port increased. At 25.6V, the intensity of light spot at the drop port becomes a maximum and that at the through port becomes a minimum as shown in Fig. 4(b).

Figure 5
Fig. 5 Output intensities as a function of displacement.
shows the output intensities measured as a function of the displacement of actuator. The output intensity at drop port increases with the decrease of the output intensity at through port, and they become equal at the gap of 180 nm. Further decreasing the gap, the output intensity at drop port becomes a maximum at the gap of 110 nm and the voltage of 25.6V, while the output intensity at through port becomes a minimum. Under the condition, the extinction ratio at the drop port is 17dB. Higher extension ration ratio is better for switch performance. The extension ratio of 30 dB was obtained in the thermo-optical interferometric switch [7

7. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1371–1379 (2006). [CrossRef]

]. The measured ratio in our experiment included a background intensity of the imaging camera, and thus it limited the dynamic range and the minimum measurable intensity compared to a fiber-optic measurement. The detailed investigation of our device using the fiber-optic measurement is also further needed.

Further decreasing the gap, the output intensities at the ports become equal again at the gap smaller than 100 nm. Before the contact of two waveguides, the measurement was stopped to prevent from sticking the waveguides. The relative displacement dependences of the output intensities at both ports are explained by the theoretical calculations as shown in Fig. 5. The theoretical curve was obtained by using the Eq. (2) with the waveguide parameters given in Sec.2. Although the 100% modulation is obtained in the theoretical calculation, the measured value is decreased by some influence such as small misalignment of waveguides due to residual stress of SOI layer. The deviation from the theoretical calculations may also be caused by background intensity of imaging system and loss of waveguides.

The response time of switch is generally limited by the first resonant frequency of actuator. We determine the resonant frequency by observing the vibration amplitude of actuator with a microscope while increasing the frequency of an ac voltage source. Since the resonant frequency of the actuator is measured to be 150 kHz, the response time is considered to be roughly 10 μsec. Due to the capacitive operation of electrostatic comb-drive, the power consumption is negligible compared with the case using thermal index variation of silicon waveguide by heater.

4. Conclusion

A submicron silicon waveguide coupler with a gap-variable mechanism was proposed for an ultra-small waveguide switch. The air gap of the coupler was varied by electrostatic comb-drive micro actuators. The proposed device was fabricated by electron beam lithography and silicon micromachining. The total size of the device was as small as a 150 μm square. The change of optical path was demonstrated by adjusting the voltage applied to the actuators. At the voltage of 25.6V, the extinction ratio of the switched light was 17dB at the gap of 110 nm. Due to the small size of the switch, a large scale matrix switch can be constructed by an array of the proposed switches. The proposed variable coupler can also be useful for variable splitter and attenuator in silicon submicron-wide waveguide circuits.

Acknowledgments

This work was supported by Japanese Ministry Grant-in-Aid and SCOPE. The device fabrication was carried out in MNC in Tohoku University.

References and links

1.

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006). [CrossRef]

2.

A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-oninsulator substrate,” Jpn. J. Appl. Phys. 40(Part 2, No. 4B), L383–L385 (2001). [CrossRef]

3.

S. Janz, P. Cheben, D. Dalacu, A. Delge, A. Densmore, B. Lamontagne, M.-J. Picard, E. Post, J. H. Schmid, P. Waldron, D.-X. Xu, K. P. Yap, and W. N. Ye, “Microphotonic elements for integration on the silicon-on-insulator waveguide platform,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1402–1415 (2006). [CrossRef]

4.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photon. Technol. Lett. 17(3), 585–587 (2005). [CrossRef]

5.

P. Koonath, T. Indukuri, and B. Jalali, “Monolithic 3-D silicon photonics,” J. Lightwave Technol. 24(4), 1796–1804 (2006). [CrossRef]

6.

K. Sasaki, F. Ohno, A. Motegi, and T. Baba, “Arrayed waveguide grating of 70×60μm2 size based on Si photonic wire waveguides,” Electron. Lett. 41(14), 801–802 (2005). [CrossRef]

7.

H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1371–1379 (2006). [CrossRef]

8.

W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express 15(25), 17106–17113 (2007). [CrossRef] [PubMed]

9.

C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006). [CrossRef]

10.

E. Bulgan, Y. Kanamori, and K. Hane, “Submicron silicon waveguide optical switch driven by microelectromechanical actuator,” Appl. Phys. Lett. 92(10), 101110 (2008). [CrossRef]

11.

J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron. 13(2), 202–208 (2007). [CrossRef]

12.

K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express 16(19), 14421–14428 (2008). [CrossRef] [PubMed]

13.

T. Ikeda, K. Takahashi, Y. Kanamori, and K. Hane, “Phase-shifter using submicron silicon waveguide couplers with ultra-small electro-mechanical actuator,” Opt. Express 18(7), 7031–7037 (2010). [CrossRef] [PubMed]

14.

X. Chew, G. Zhou, F. S. Chau, and J. Deng, “Nanomechanically tunable photonic crystal resonators utilizing triple-beam coupled nanocavities,” IEEE Photon. Technol. Lett. 23(18), 1310–1312 (2011). [CrossRef]

15.

X. Chew, G. Zhou, F. S. Chau, J. Deng, X. Tang, and Y. C. Loke, “Dynamic tuning of an optical resonator through MEMS-driven coupled photonic crystal nanocavities,” Opt. Lett. 35(15), 2517–2519 (2010). [CrossRef] [PubMed]

16.

M. W. Pruessner, K. Amarnath, M. Datta, D. P. Kelly, S. Kanakaraju, P.-T. Ho, and R. Ghodssi, “InP-based optical waqveguide MEMS switches with evanescent coupling mechanism,” J. Micromech. Syst. 14(5), 1070–1081 (2005). [CrossRef]

17.

M.-C. M. Lee, D. D. Hah, E. K. Lau, H. Toshiyoshi, and M. Wu, “MEMS-actuated photonic crystal switches,” IEEE Photon. Technol. Lett. 18(2), 358–360 (2006). [CrossRef]

18.

K. Takahashi, E. Bulgan, Y. Kanamori, and K. Hane, “Submicron comb-drive actuators fabricated on thin single crystalline silicon layer,” IEEE Trans. Ind. Electron. 56(4), 991–995 (2009). [CrossRef]

19.

K. Okamoto, Basis of Optical Waveguides Coronasha Ltd. (Tokyo) (1992).

20.

E. A. J. Marcatili, “Dielectric rectangular waveguide and dielectric coupler for integrated optics,” Bell Syst. Tech. J. 47(7), 2071–2102 (1969).

OCIS Codes
(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers
(250.5300) Optoelectronics : Photonic integrated circuits
(230.4685) Optical devices : Optical microelectromechanical devices

ToC Category:
Optoelectronics

History
Original Manuscript: August 4, 2011
Revised Manuscript: October 9, 2011
Manuscript Accepted: October 31, 2011
Published: November 7, 2011

Citation
Yuta Akihama, Yoshiaki Kanamori, and Kazuhiro Hane, "Ultra-small silicon waveguide coupler switch using gap-variable mechanism," Opt. Express 19, 23658-23663 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23658


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References

  1. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006). [CrossRef]
  2. A. Sakai, G. Hara, and T. Baba, “Propagation characteristics of ultrahigh-Δ optical waveguide on silicon-oninsulator substrate,” Jpn. J. Appl. Phys.40(Part 2, No. 4B), L383–L385 (2001). [CrossRef]
  3. S. Janz, P. Cheben, D. Dalacu, A. Delge, A. Densmore, B. Lamontagne, M.-J. Picard, E. Post, J. H. Schmid, P. Waldron, D.-X. Xu, K. P. Yap, and W. N. Ye, “Microphotonic elements for integration on the silicon-on-insulator waveguide platform,” IEEE J. Sel. Top. Quantum Electron.12(6), 1402–1415 (2006). [CrossRef]
  4. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photon. Technol. Lett.17(3), 585–587 (2005). [CrossRef]
  5. P. Koonath, T. Indukuri, and B. Jalali, “Monolithic 3-D silicon photonics,” J. Lightwave Technol.24(4), 1796–1804 (2006). [CrossRef]
  6. K. Sasaki, F. Ohno, A. Motegi, and T. Baba, “Arrayed waveguide grating of 70×60μm2 size based on Si photonic wire waveguides,” Electron. Lett.41(14), 801–802 (2005). [CrossRef]
  7. H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Si photonic wire waveguide devices,” IEEE J. Sel. Top. Quantum Electron.12(6), 1371–1379 (2006). [CrossRef]
  8. W. M. J. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express15(25), 17106–17113 (2007). [CrossRef] [PubMed]
  9. C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro26(2), 58–66 (2006). [CrossRef]
  10. E. Bulgan, Y. Kanamori, and K. Hane, “Submicron silicon waveguide optical switch driven by microelectromechanical actuator,” Appl. Phys. Lett.92(10), 101110 (2008). [CrossRef]
  11. J. Yao, D. Leuenberger, M.-C. M. Lee, and M. C. Wu, “Silicon microtoroidal resonators with integrated MEMS tunable coupler,” IEEE J. Sel. Top. Quantum Electron.13(2), 202–208 (2007). [CrossRef]
  12. K. Takahashi, Y. Kanamori, Y. Kokubun, and K. Hane, “A wavelength-selective add-drop switch using silicon microring resonator with a submicron-comb electrostatic actuator,” Opt. Express16(19), 14421–14428 (2008). [CrossRef] [PubMed]
  13. T. Ikeda, K. Takahashi, Y. Kanamori, and K. Hane, “Phase-shifter using submicron silicon waveguide couplers with ultra-small electro-mechanical actuator,” Opt. Express18(7), 7031–7037 (2010). [CrossRef] [PubMed]
  14. X. Chew, G. Zhou, F. S. Chau, and J. Deng, “Nanomechanically tunable photonic crystal resonators utilizing triple-beam coupled nanocavities,” IEEE Photon. Technol. Lett.23(18), 1310–1312 (2011). [CrossRef]
  15. X. Chew, G. Zhou, F. S. Chau, J. Deng, X. Tang, and Y. C. Loke, “Dynamic tuning of an optical resonator through MEMS-driven coupled photonic crystal nanocavities,” Opt. Lett.35(15), 2517–2519 (2010). [CrossRef] [PubMed]
  16. M. W. Pruessner, K. Amarnath, M. Datta, D. P. Kelly, S. Kanakaraju, P.-T. Ho, and R. Ghodssi, “InP-based optical waqveguide MEMS switches with evanescent coupling mechanism,” J. Micromech. Syst.14(5), 1070–1081 (2005). [CrossRef]
  17. M.-C. M. Lee, D. D. Hah, E. K. Lau, H. Toshiyoshi, and M. Wu, “MEMS-actuated photonic crystal switches,” IEEE Photon. Technol. Lett.18(2), 358–360 (2006). [CrossRef]
  18. K. Takahashi, E. Bulgan, Y. Kanamori, and K. Hane, “Submicron comb-drive actuators fabricated on thin single crystalline silicon layer,” IEEE Trans. Ind. Electron.56(4), 991–995 (2009). [CrossRef]
  19. K. Okamoto, Basis of Optical Waveguides Coronasha Ltd. (Tokyo) (1992).
  20. E. A. J. Marcatili, “Dielectric rectangular waveguide and dielectric coupler for integrated optics,” Bell Syst. Tech. J.47(7), 2071–2102 (1969).

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