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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 12 — Jun. 11, 2007
  • pp: 7557–7563
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Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities

Marcel W. Pruessner, Todd H. Stievater, Mike S. Ferraro, and William S. Rabinovich  »View Author Affiliations


Optics Express, Vol. 15, Issue 12, pp. 7557-7563 (2007)
http://dx.doi.org/10.1364/OE.15.007557


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Abstract

Compact silicon-on-insulator (SOI) waveguide thermo-optically tunable Fabry-Perot microcavities with silicon/air Bragg mirrors are demonstrated. Quality factors of Q=4,584 are measured with finesse F=82. Tuning is achieved by flowing current directly through the silicon cavity resulting in efficient thermo-optic tuning over 2 nm for less than 50 mW applied electrical power. The high-Q cavities enable fast switching (1.9 μs rise time) at low drive power (<10 mW). By overdriving the device, rise times of 640 ns are obtained. Various device improvements are discussed.

© 2007 Optical Society of America

1. Introduction

Silicon-on-insulator (SOI) is a promising substrate material for high-speed electronics and increasingly finds application in optoelectronics. Thus, we can anticipate an eventual merging of the two fields on a common material platform. Application areas include high-speed microprocessors with optical interconnects, and optoelectronics for wavelength division multiplexing (WDM) with on-chip control circuits.

Silicon’s thermo-optic effect [1

1. G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28, 83–85 (1992). [CrossRef]

] is significantly larger than its electro-optic effect [2

2. R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

] and enables low-power switching via temperature dependent modulation of the refractive index. Therefore, the thermo-optic effect lends itself well to wavelength-division multiplexing (WDM) devices and components. A number of different silicon-based thermo-optic devices have been reported to date. Mach-Zehnder interferometer (MZI) switches with rise-/fall times of a few microseconds have been demonstrated with heating powers in the range of 100 mW [3–4

3. R. L. Espinola, M.-C. Tsai, James T. Yardley, and R. M. Osgood, “Fast and low-power thermo optic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003). [CrossRef]

]. By utilizing a multi-step voltage circuit to overdrive a thermo-optic switch, response times <1 μs have been achieved [5

5. M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermo optic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004). [CrossRef]

]. Sub-μs speeds with sub-mW switching power were demonstrated by differentially heating the two arms of a ≈100 μm long silicon strip waveguide MZI [6

6. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004). [CrossRef]

]. Finally, microring [7

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

], Fabry-Perot [8

8. C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry-Pérot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004). [CrossRef]

], and photonic crystal cavity [9

9. H. M. Chong and R. De La Rue, “Tuning of photonic crystal waveguide microcavity by thermooptic effect,” IEEE Photon. Technol. Lett. 16, 1528–1530 (2004). [CrossRef]

] resonators enable high-speed, low power switching due to their potential for high quality factor. However, such resonant thermo-optic switches have so far been limited in terms of speed or power consumption due to their large thermal mass [7

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

] or moderate Q-factor [8

8. C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry-Pérot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004). [CrossRef]

, 9

9. H. M. Chong and R. De La Rue, “Tuning of photonic crystal waveguide microcavity by thermooptic effect,” IEEE Photon. Technol. Lett. 16, 1528–1530 (2004). [CrossRef]

].

In this paper we present an SOI waveguide thermo-optic switch. Fast response time and low power are demonstrated by utilizing a high Q-factor Fabry-Perot resonator that is thermo-optically tuned by passing current directly through the silicon microcavity. The high-Q enables long effective optical interaction lengths in a compact device. In contrast, an MZI generally requires a long device for similar optical interaction length. Furthermore, passing current directly through the cavity enables rapid heating at low electrical powers, resulting in efficient and low-power tuning and high speed switching. We model and experimentally characterize our device and discuss alternate designs that may enable an order of magnitude improvement in terms of speed and power consumption.

2. Approach

In Fig. 2 we show infrared (IR) images of the optical cavity. The device was tested by coupling light into and out of the rib waveguide while sweeping the wavelength using a tunable laser. The sample had a LC=12 μm long cavity with W=5 μm wide rib (Q≈4,600). An IR camera (Sensors Unlimited) and IR objective (20x) oriented perpendicularly to the sample were used to image the cavity while sweeping the wavelength. The images clearly illustrate resonance [λ=λ0=1614.5 nm, Fig. 2(a)], as indicated by the high intensity inside the cavity.

At off-resonance [λ=1615.5 nm, Fig. 2(b)] little scattered light is seen with no light at the output.

Fig. 1. (a). Fabricated SOI waveguide Fabry-Perot cavity, (b) measured resonance spectrum and Q-factor for a LC=12 μm long cavity.
Fig. 2. (497 kB) Movie of infrared imaging of an optical cavity as the wavelength of light propagating through the rib waveguide is tuned: (a) on-resonance at λ=λ0=1614.5 nm (Q≈4,600) [Media 1], (b) off-resonance at λ=1615.5 nm. [Media 2]

In order to tune the devices, current flows directly through the optical cavity [Fig. 1(a)] similar to the MZI heating approach in Ref. [6

6. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004). [CrossRef]

]. Current flow results in Joule heating of the silicon cavity and thermo-optic resonance tuning. Our approach enables more efficient heating and tuning compared to using a thin-film heater on top of the cavity surface. This is significant for achieving fast and low power switching in devices with thick silicon layers (here t Silicon=4.7 μm), where there may be a large temperature gradient between the heater and the bottom of the silicon device layer. Low-power index tuning (Δn) and high-Q cavities enable fast switching for appropriate probe wavelengths, as will be shown.

In addition to the thermo-optic effect, our device may also enable tuning/switching via electro-optic effects, although these are known to be small in silicon. Soref et al. calculate an index change Δn≈-10-4 for an electric field E=106 V/cm (Kerr effect) [2

2. R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

]. The refractive index can also be modulated by free carriers, resulting in Δn≈-10-4 for a carrier injection ΔN≈1017 [2

2. R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

]. Although this latter effect can be significant, the expected free carrier injection in our measurements is ΔN<1015. Finally, the effect of free-carrier losses due to current injection is judged by observing the change in Q-factor during tuning, where any losses will lower the Q. In our measurements we did not observe any change in Q, as we will show.

3. Experimental results

For all measurements we set the polarization with the E-field perpendicular to the substrate. Lensed fibers are used to couple light to the waveguide and electrical probes supply the heating current to the device via the contact pads. Using the lensed fibers, we measured a fiber-waveguide coupling loss of αInsertion≈5 dB/facet. A typical Fabry-Perot cavity introduces an additional 5-6 dB of loss compared to an identical test waveguide with no cavity [11

11. M. W. Pruessner, Todd H. Stievater, and William S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32, 533–535 (2007). [CrossRef] [PubMed]

].

3.1 Thermo-optic tuning

A thermo-optic tuning measurement is shown in Fig. 3(a), and the extracted resonant peak and change in cavity index (Δn) vs. electrical power is shown in Fig. 3(b), indicating Δλ=2 nm tuning. We previously demonstrated Δλ=15 nm tuning in a low-Q cavity (Q≈700, I=2.2 mA heater current) [12

12. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Tunable Fabry-Perot waveguide microcavities with high index contrast mirrors, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2007), paper CThP3.

]. For our LC=12 μm long cavity, we measured a resistance R= 125 kΩ. The cavity index increases with electrical power, in agreement with silicon’s positive thermo-optic coefficient. The temperature increase is linear with ΔT=23.5 K at 42 mW power.

Silicon electro-optic effects generally decrease the cavity index with blueshift tuning [2

2. R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

, 13

13. B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, “Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes,” Opt. Express 15, 3140–3148 (2007). [CrossRef] [PubMed]

], in contrast to the observed redshift and positive Δn in Fig. 3. We observed little change in the full-width-half-maximum (FWHM) and Q-factor. Therefore, we conclude that current injected free carrier absorption losses are minimal for our measurements.

Fig. 3. (a). Measured tuning spectra with Lorentzian curve fit, (b) extracted wavelength shift and refractive index change vs. applied electrical power.

3.2 Thermo-optic attenuation

Fig. 4. (a). Measured resonances (λ0=1515.15 nm and λ0=1604.32 nm) with location of probes used in attenuation and switching measurements, b) attenuation vs. electrical power for the two resonances, where probe 1=1604.32 nm (Q=4,584) and probe 1=1575.73 nm (Q=2,626).

3.3 Thermo-optic switching

For switching, we set the wavelength to probe 1 or probe 2 and modulate the electrical power. Probe 1 is set to the resonant peak and probe 2 is set to the wavelength at which the optical power drops to -10 dB [Fig. 4(a)]. The choice of probe 1 or probe 2 affects the phase of the optical response to thermo-optic tuning. A current-voltage source (Keithley model 2400) was used along with a custom switching circuit that enabled voltage (current) pulses with 20 ns rise-/fall times. The electrical response time is thus much faster than any thermo-optic effect.

Figure 5 shows a typical switching measurement for probe 1=1604.31 nm and probe 2=1604.91 nm [defined in Fig. 4(a)], measured using a DC-125 MHz photodetector. Due to the thermo-optic redshift of the resonance, probe 2 is in phase with the applied electrical signal, while probe 1 is out of phase. The applied electrical power was an 11.5 mW square wave with a frequency f=1 kHz and 10 % duty cycle. For probe 1 the rise time (10–90 %) was t RISE, 1=1.9 μs and the fall time (90–10 %) was t FALL, 1=9.0 μs. Probe 2 resulted in t RISE, 2=7.3 μs and t FALL, 2=3.5 μs. Probe 1 exhibits a faster rise, whereas probe 2 has a faster fall time. This is the result of the different optical response with temperature for the two probes. The exponential response of the thermal time constant and the optical response for probes 1 and 2 results in the discrepancy in switching times for the probes.

Fig. 5. Switching measurement: (a) rise time, (b) fall time (probe 1 and probe 2). “Rise” (“fall”) refers to the optical response to the rising (falling) edge of the electrical signal. Lines: calculation, symbols: experiment.

4. Discussion

The switching measurements indicate high speed and large electrical bandwidth. The high Q, however, limits the optical bandwidth. One simple method to extend the optical bandwidth is to lower the Q-factor by decreasing the DBR reflectance. Another method for increasing the optical bandwidth is to tune the cavity resonance as required; low power tuning has already been achieved (see Fig. 3), and even larger tunability is possible [12

12. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Tunable Fabry-Perot waveguide microcavities with high index contrast mirrors, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2007), paper CThP3.

]. Although devices with large optical bandwidth can be realized, e.g. using photonic crystal waveguides [14

14. M. Tinker and J. -B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13, 7174–7188 (2005). [CrossRef] [PubMed]

], these devices require large heating and temperature shifts for switching and therefore do not present a significant advantage over resonant devices in terms of speed and power consumption.

We model our cavity temporal response as follows. Silicon’s thermo-optic coefficient is ΔnT≈+1.86×10-4/K [1

1. G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28, 83–85 (1992). [CrossRef]

] resulting in a redshift tuning with temperature increase (ΔT):

Δλ=ΔT(λ0nC)(ΔnΔT),
(1)

where n C=3.48 is the silicon cavity refractive index. The cavity temporal response is obtained by noting that Δλ is a function of the time-dependent temperature increase, ΔT:

ΔT(t)=T0(1etτ).
(2)

Here T 0 is the maximum temperature increase and τ is the thermal time constant given by:

τ=ρSicSiWC2κSiπ2,
(3)

where ρSi=2.33 g/cm3 is the silicon cavity mass density, c Si=0.7 J/g-K is the specific heat, κSi=1.3 J/cm-sec-K is the thermal conductivity, and W C=50 μm is the cavity width [Fig. 1(a)].

The thermal-temporal filter response is obtained from the time dependence of ΔT(t) and the Lorentzian lineshape of the Fabry-Perot cavity transmittance:

P0(ΔT)=P0[1+(λProbeλ0(ΔT)FWHM2)2],
(4)

where P 0 is the peak optical power, λProbe is the probe wavelength, FWHM is the resonance 3 dB bandwidth, and λ0T) is the tuned resonance. For a calculated thermal time constant τ=3.2 μs we find excellent agreement between measurement and experiment (Fig. 5). Although probes 1 and 2 exhibit different rise/fall times, the thermal time constant, τ, remains constant since it is determined by device geometry and not probe wavelengths.

One method to improve the device response is by overdriving (Fig. 6). We apply an electrical pulse with power significantly larger than the 8.4 mW required for -10 dB switching in Fig. 4(b), resulting in t RISE=640 ns for P=58.4 mW power (probe 1=1604.30 nm). The fall time, however, is increased to t FALL=22.4 μs compared to Fig. 5, since over-driving results in increased heating and hence a longer cooling time. Our thermal model with time constant τ=3.2 μs still gives accurate results for the rise time, but underestimates the fall time. This is likely the result of contact pad heating at high electrical powers, which our model does not take into account. Although the decreased rise time comes at the expense of an increased fall time, a two-step actuation can be used, as in Ref. [5

5. M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermo optic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004). [CrossRef]

]. A short high-voltage pulse followed by a low-voltage signal enables fast rise time [Fig. 6(a)], without increasing the fall time.

Fig. 6. Effect of overdriving on switching speed: a) rise time, b) fall time. Lines: calculation, symbols: experiment. Note the different time scales.

A number of other improvements can be made to the present devices. Higher Q-factors enable switching at lower powers with higher extinction. For example, in Fig. 4(b) the electrical power required to obtain -10 dB attenuation (switching) is 8.4 mW for probe 1=1604.32 nm (Q=4,584) and increases to 17.7 mW for probe 1=1575.73 nm (Q=2,626). A second approach makes use of a two-voltage step actuation to increase switching speed, as previously mentioned. Another design change is to reduce the cavity thermal time constant, τ=ρSi c Si W C 2/(κπ2), by reducing the cavity width, W C. For example, by shortening W C from the present 50 μm to 25 μm (10 μm) we decrease the thermal time constant to τ=800 ns (130 ns). Therefore, MHz-range thermal modulation appears possible. Finally, our high-Q cavities may also enable fast electro-optic (EO) switching [13

13. B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, “Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes,” Opt. Express 15, 3140–3148 (2007). [CrossRef] [PubMed]

] approaching GHz-range speeds. Although silicon EO effects are small [2

2. R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

], high-Q cavities enable long effective optical interaction lengths and large phase shifts in compact devices.

5. Summary

We demonstrated a compact thermo-optically tunable SOI waveguide Fabry-Perot microcavity. Thermo-optic tuning results in Δλ>2 nm (<50 mW electrical power). By appropriate choice of probe wavelength, thermo-optic attenuation (-25 dB) and optical switching was demonstrated with high speed (640 ns) and low power (<10 mW). Modeling enables accurate prediction of the temporal behavior. Design improvements were also discussed, potentially enabling MHz-range thermo-optic switching at mW-level powers.

Acknowledgments

References and links

1.

G. Cocorullo and I. Rendina, “Thermo-optical modulation at 1.5 μm in silicon etalon,” Electron. Lett. 28, 83–85 (1992). [CrossRef]

2.

R. A. Soref and B. R. Bennett, “Electro optical effects in silicon,” IEEE J. Quantum. Electron. QE-23, 123–129 (1987). [CrossRef]

3.

R. L. Espinola, M.-C. Tsai, James T. Yardley, and R. M. Osgood, “Fast and low-power thermo optic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003). [CrossRef]

4.

Y. Li, J. Yu, and S. Chen, “Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response,” IEEE Photon. Technol. Lett. 17, 1641–1643 (2005). [CrossRef]

5.

M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, “Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermo optic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004). [CrossRef]

6.

M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, “Submicrosecond submilliwatt silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004). [CrossRef]

7.

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

8.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact silicon tunable Fabry-Pérot resonator with low power consumption,” IEEE Photon. Technol. Lett. 16, 506–508 (2004). [CrossRef]

9.

H. M. Chong and R. De La Rue, “Tuning of photonic crystal waveguide microcavity by thermooptic effect,” IEEE Photon. Technol. Lett. 16, 1528–1530 (2004). [CrossRef]

10.

M. W. Pruessner, W. S. Rabinovich, T. H. Stievater, D. Park, and J. W. Baldwin, “Cryogenic etch process development for profile control of high aspect-ratio sub-micron silicon trenches,” J. Vac. Sci. Technol. B 25, 21–28 (2007). [CrossRef]

11.

M. W. Pruessner, Todd H. Stievater, and William S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32, 533–535 (2007). [CrossRef] [PubMed]

12.

M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Tunable Fabry-Perot waveguide microcavities with high index contrast mirrors, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2007), paper CThP3.

13.

B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, “Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes,” Opt. Express 15, 3140–3148 (2007). [CrossRef] [PubMed]

14.

M. Tinker and J. -B. Lee, “Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency,” Opt. Express 13, 7174–7188 (2005). [CrossRef] [PubMed]

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(160.6840) Materials : Thermo-optical materials
(230.1480) Optical devices : Bragg reflectors
(230.3120) Optical devices : Integrated optics devices
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides

ToC Category:
Optical Devices

History
Original Manuscript: March 27, 2007
Revised Manuscript: April 20, 2007
Manuscript Accepted: April 20, 2007
Published: June 5, 2007

Citation
Marcel W. Pruessner, Todd H. Stievater, Mike S. Ferraro, and William S. Rabinovich, "Thermo-optic tuning and switching in SOI waveguide Fabry-Perot microcavities," Opt. Express 15, 7557-7563 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-12-7557


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References

  1. G. Cocorullo and I. Rendina, "Thermo-optical modulation at 1.5 μm in silicon etalon," Electron. Lett. 28, 83-85 (1992). [CrossRef]
  2. R. A. Soref and B. R. Bennett, "Electro optical effects in silicon," IEEE J. Quantum. Electron. QE-23, 123-129 (1987). [CrossRef]
  3. R. L. Espinola, M.-C. Tsai, JamesT. Yardley, and R. M. Osgood, "Fast and low-power thermo optic switch on thin silicon-on-insulator," IEEE Photon. Technol. Lett. 15, 1366-1368 (2003). [CrossRef]
  4. Y. Li, J. Yu, and S. Chen, "Rearrangeable nonblocking SOI waveguide thermo optic 4×4 switch matrix with low insertion loss and fast response," IEEE Photon. Technol. Lett. 17, 1641-1643 (2005). [CrossRef]
  5. M. Harjanne, M. Kapulainen, T. Aalto, and P. Heimala, "Sub-μs switching time in silicon-on-insulator Mach-Zehnder thermo optic switch," IEEE Photon. Technol. Lett. 16, 2039-2041 (2004). [CrossRef]
  6. M. W. Geis, S. J. Spector, R. C. Williamson, and T. M. Lyszczarz, "Submicrosecond submilliwatt silicon-on-insulator thermooptic switch," IEEE Photon. Technol. Lett. 16, 2514-2516 (2004). [CrossRef]
  7. I. Kiyat, A. Aydinli, and N. Dagli, "Low-power thermo optical tuning of SOI resonator switch," IEEE Photon. Technol. Lett. 18, 364-366 (2006). [CrossRef]
  8. C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, "Compact silicon tunable Fabry-Pérot resonator with low power consumption," IEEE Photon. Technol. Lett. 16, 506-508 (2004). [CrossRef]
  9. H. M. Chong, and R. De La Rue, "Tuning of photonic crystal waveguide microcavity by thermooptic effect," IEEE Photon. Technol. Lett. 16, 1528-1530 (2004). [CrossRef]
  10. M. W. Pruessner, W. S. Rabinovich, T. H. Stievater, D. Park and J. W. Baldwin, "Cryogenic etch process development for profile control of high aspect-ratio sub-micron silicon trenches," J. Vac. Sci. Technol. B 25, 21-28 (2007). [CrossRef]
  11. M. W. Pruessner, ToddH. Stievater, and William S. Rabinovich, "Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors," Opt. Lett. 32, 533-535 (2007). [CrossRef] [PubMed]
  12. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, "Tunable Fabry-Perot waveguide microcavities with high index contrast mirrors, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2007), paper CThP3.
  13. B. Schmidt, Q. Xu, J. Shakya, S. Manipatruni, and M. Lipson, "Compact electro-optic modulator on silicon-on-insulator substrates using cavities with ultra-small modal volumes," Opt. Express 15, 3140-3148 (2007). [CrossRef] [PubMed]
  14. M. Tinker and J. -B. Lee, "Thermal and optical simulation of a photonic crystal light modulator based on the thermo-optic shift of the cut-off frequency," Opt. Express 13, 7174-7188 (2005). [CrossRef] [PubMed]

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