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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 10 — May. 7, 2012
  • pp: 11478–11486
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Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators

Xuezhe Zheng, Ying Luo, Guoliang Li, Ivan Shubin, Hiren Thacker, Jin Yao, Kannan Raj, John E. Cunningham, and Ashok V. Krishnamoorthy  »View Author Affiliations


Optics Express, Vol. 20, Issue 10, pp. 11478-11486 (2012)
http://dx.doi.org/10.1364/OE.20.011478


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Abstract

We show enhanced optical bistability induced by free carrier absorption from junction doping in substrate-removed silicon ring modulators. Such linear thermal effects dominate the loss in high-speed depletion silicon ring modulators. Optical bistability was observed with about 100 μW of input optical power. We further show that such thermal interactions causes data-dependent ring resonance shifts, and consequently severely degrade the data modulation quality at low speeds. The frequency response of this effect was measured to be about 100~200 kHz.

© 2012 OSA

1. Introduction

2. Optical bistability induced by self-heating from FCA in a depletion ring modulator

2.1High-speed tunable depletion ring modulator

A high-speed depletion ring modulator with good performance requires careful design of both the ring waveguide and the embedded PN junction [12

12. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Exp.19, 20435–20443 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-21-20435

]. Our ring modulator design was based on the Luxtera/Freescale 130nm SOI CMOS process. A ring radius of 7.5 μm was chosen in order to achieve a free spectral range (FSR) of ~12.8 nm to enable a 200GHz-spacing synthetic resonant comb structure uniformly covering the entire C-band [19

19. A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS Manufacturing to Reduce Tuning Requirements for Resonant Optical Devices,” IEEE Photon. J. 3, 567–579 (2011).

]. We optimized ring waveguide structure to enable a small ring size with low bending loss. The ring waveguide is designed with 380 nm width, 220 nm etch depth and 80nm Si slab thickness, as shown in Fig. 1(a)
Fig. 1 A tunable high-speed depletion silicon ring modulator. (a) Cross-section diagram of the ring waveguide high-speed section. (b) Photograph of the ring modulator.
.

A symmetric lateral PN junction is employed in the high-speed modulation waveguide. The doping density design is critical for modulator performance. The PN junction doping determines the depletion width and overlaps with the center of the optical mode. Hence, it has significant impact to the modulation depth and optical loss. The optical loss, in turn, determines the quality factor of the ring and the photon-lifetime-limited modulation bandwidth. Under the critical coupling condition, the photon-lifetime-limited modulator bandwidth is proportional to the waveguide loss, fO = cα/(πng), where c is the light speed in vacuum, α = αdop + αother is the effective waveguide loss, and ng~4.0 is the optical group index. αother introduced by waveguide bending, scattering, etc., is estimated to be about 6dB/cm for the waveguide we designed. Hence to achieve a desired photon-lifetime-limited modulation bandwidth, an appropriate junction doping density has to be selected to introduce the right amount of αdop. For photon-lifetime-limited modulation bandwidths of 10, 15 and 25 GHz, doping losses of about 12, 21, and 39 dB/cm are repectively required. For instance, a doping density of 3x1018 cm−3 was chosen for a 25Gigabits/s ring modulator design [20

20. R. Soref and B. Bennett, ““Electrooptical effect in silicon,”, IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

].

Although a ring resonator has periodic resonances, it is a narrow-band device with its resonance locations very sensitive to manufacturing tolerances and ambient temperature change. We integrated a doped silicon resistor directly onto the ring waveguide for efficient modulator wavelength thermal tuning. Two-thirds of the ring is made as a PN diode for high-speed modulation, while the upper-right 25% is N-type doped as a Si resistor for thermal tuning. The remaining 8% is undoped and used for isolation between the PN junction section and the doped resistor section.

A picture of a fabricated tunable depletion ring modulator is shown in Fig. 1(b). It demonstrated good performances in close agreement with the design targets. Figure 2(a)
Fig. 2 25G depletion ring modulator performance. (a) Spectra of one measured resonance of the ring modulator, indicating a Q of about 8000; (b) Optical “eye” diagram of the modulator for 20 Gbps PRBS 231-1 data modulation.
shows the spectra of one of its resonances around 1549 nm with good extinction ratio, from which we measured a loaded Q of about 8000. As expected, the modulator works at high-speed up to 25 Gbps. A clean open optical “eye” diagram for PRBS 231-1 data at 20 Gbps is shown in Fig. 2(b) with a measured dynamic extinction ratio of >7 dB.

The thermal tuning efficiency of the microring resonator has been tested by applying tuning power to the integrated Si resistor. The Si resistor has a resistance of about 750Ω. The resonant wavelength versus tuning power is plotted as diamonds with solid blue line in Fig. 3(a)
Fig. 3 Wavelength tuning efficiency improvement using back side substrate removal technique. (a) Tuning efficiency before (diamonds, blue line) and after (squares, pink line) substrate removal; (b) A picture of substrate removed tunable ring modulator taken from the substrate side with an etch pit window size of about 105μm × 105μm, seeing through the BOX layer.
, showing a tuning efficiency of 0.17nm/mW. With a backside local substrate-removal technique [21

21. J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18(18), 19055–19063 (2010). [CrossRef] [PubMed]

,22

22. I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron . (2012). doi: 10.1007/s11082-012-9577-9.

], its tuning efficiency can be improved by an order of magnitude. Figure 3(a) shows an improved tuning efficiency of ~1.02 nm/mW (6x) for a ring modulator with ~105μm × 105μm backside pit opening. A picture of the locally substrate-removed device with an etch pit window size of about 105μm × 105μm is shown in Fig. 3(b), taken from the substrate side of the chip through the buried oxide (BOX) layer.

2.2 Optical bistability induced by self-heating from FCA

As discussed above, the FCA loss from PN junction doping dominates the total round trip loss in a high-speed depletion-mode ring modulator. The absorbed optical power creates heat and results in a thermally-induced ring waveguide refractive index change. Because the optical field circulating inside a ring resonator is significantly enhanced due to resonance, the index change can be substantial. At resonance, the field enhancement factor (FE), defined as the ratio of field intensity inside of the ring and in the input bus waveguide, is about 1/κ, where κ is the coupling coefficient between the bus waveguide and the ring waveguide. Figure 4(a)
Fig. 4 (a) Q (blue line) and corresponding power enhancement factor (red line) in photon-life-time-limited rings; (b) Maximum heat power generated from junction doping FCA for ring modulators with different photon-lifetime-limited bandwidth at 1mW of input optical power.
shows the plot of the corresponding resonator Q and resonance power enhancement factor in the ring versus targeted photon-lifetime-limited bandwidth.

Assuming 1 mW of power is input to the ring modulator, and all absorbed optical power is converted to heat, Fig. 4(b) plots the heating power due to absorption in a doped ring modulator with different photon-lifetime-limited bandwidth. As explained above, the photon-lifetime-limited modulator bandwidth is proportional to the waveguide loss. Higher ring modulation speed requires a lower Q, and consequently higher effective loss. Due to limited waveguide loss, a higher junction doping density, therefore, has to be selected to achieve the desired total loss. At the same input power of 1 mW, we observe a monotonic increase of heating power in the ring modulator with respect to photon-lifetime-limited bandwidth. The figure also indicates that a heating power comparable to the input optical power can be generated from the doping absorption. For comparison, one can also calculate the TPA loss and the free carrier density generated by TPA under the same conditions. Using a TPA coefficient of 7.9 × 10−12 m/W [23

23. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

], we obtained a nonlinear absorption coefficient in the ring of less than 0.2 dB/cm for 10GHz to 30GHz depletion ring modulator designs with 1 mW of input optical power, which is orders of magnitude smaller than the linear FCA. Consequently, the carrier density produced by TPA would be lower than 1 × 1014cm−3. Hence, the nonlinear absorptions in such high-speed depletion ring modulators are negligible.

The thermal refractive index change from heating induced by the doping absorption will cause a red-shift in the ring resonance wavelength. This effect was clearly observed when we used a tunable laser to scan through one resonance of a 25G ring modulator with different powers, as plotted in Fig. 5(a)
Fig. 5 Measured ring resonance shift induced by junction doping absorption for a 25G depletion ring modulator with input power from −9.8dBm to −3.8dBm before substrate removal (a), and from −13.8dBm to −8.8dBm after substrate removal (b). Optical bistability observed at 100 μW input power from substrate removed ring modulator.
. With an input optical power of −9.8dBm to −3.8dBm, we observed a ring resonance shift of 68 pm, and a slight resonance distortion.

Local substrate removal techniques improve ring tuning efficiency. Effectively, more resonance wavelength shift can be achieved with less heating power. This enhancement also applies to the heating due to absorption because of increased ring thermal resistance. Figure 5(b) shows the self-heating enhancement from the same ring modulator with substrate removed, measured by wavelength scan using a tunable laser at different input power levels ranging from −13.8dBm to −8.8dBm. A maximum resonance shift of 102 pm was observed with significantly reduced input power. The measured enhancement compared to Fig. 5(a) is about 6x which agrees very well with the tuning efficiency improvement shown in Fig. 3(a). Both the on-resonance output power (Fig. 6(a)
Fig. 6 Both on-resonance output power (a) and resonance wavelength (b) show linear correlation to the input optical power.
) and resonance shift (Fig. 6b) shows linear correlation to the input power, as depicted in Fig. 6, confirming the dominance of the self-heating from FCA.

More direct evidence of ring bistability is the observation of a hysteresis loop in the transfer function (output power versus input power) of the ring resonator [14

14. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004). [CrossRef] [PubMed]

,15

15. Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31(3), 341–343 (2006). [CrossRef] [PubMed]

]. We experimentally verified such hysteresis by modulating the input laser power at a fixed wavelength while simultaneously monitoring the output power from the ring using a real time oscilloscope. The measurement results are shown in Fig. 7
Fig. 7 Hysteresis loop (right graph) due to optical bistability observed when laser wavelength approach ring resonance. Top green waveform X represents the input light modulation; the bottom yellow waveform Y is the ring output power measured using a receiver whose output is reversed in sign; and the middle is X versus Y.
, where the top green waveform X represents the input light modulation from about 30μW to 300μW, the bottom yellow waveform Y is the ring output power measured using a receiver whose output is reversed in sign, and the middle is X versus Y. The left graph is a screen shot of the waveforms when the laser wavelength is tuned to the right side away from the ring resonance, as A position shown in Fig. 2(a), while the right graph is for B position with laser wavelength close to the ring resonance. When the laser wavelength is positioned away from the ring resonance, the ring interacts little with the input laser. We observed clear linear correlation between the input signal and the ring output signal. When the laser wavelength is set closer to the ring resonance, as in B, the ring interacts strongly with the input laser light. The ring resonance is no longer stable because it depends on the amount of optical power circulating inside of the ring as discussed above. We observed a clear hysteresis loop of the ring output as we moved the input laser power up and down, indicating an optical bistability effect.

3. Impact to high-speed digital data transmission

As discussed above, the optical field circulating inside the ring affects the ring resonance due to FCA from PN junction doping. Hence, when using ring modulators for intensity modulation, the optical data itself will cause additional ring resonance shift on top of the shift from the applied electrical modulation signal. This data-dependent ring response could severely impair the quality of data modulation with symptoms like unstable “1” and “0” levels, and significantly reduced ER, especially for substrate-removed ring modulators with enhanced thermal tuning efficiency. Fortunately, it’s a thermal effect. Although the absorption happens instantly, it takes time for the absorbed energy to heat up the waveguide and change its refractive index. It has little impact to data modulation faster than the ring thermal response.

4. Discussion and conclusions

The plasma dispersion effect is the most common method of achieving high-speed optical modulation in silicon devices in which the concentration of free carriers changes the refractive index of silicon [20

20. R. Soref and B. Bennett, ““Electrooptical effect in silicon,”, IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

]. Both the real part and imaginary part of the refractive index changes due to such effect. Mechanisms such as carrier injection, depletion, and accumulation have been exploited. Carrier induced absorption exists in all these mechanisms.

FCA from doping in PIN carrier injection ring modulators can be smaller because the optical mode largely overlaps with the undoped intrinsic silicon waveguide. However, absorption from the injected carriers could be significant. We, therefore, expect to see a similar effect in forward-biased carrier injection ring modulators.

The ring resonance shifts in response to the self-heating from FCA, which causes nonlinear behavior and/or optical bistability. Such effects can be significantly enhanced in microring resonators with their local substrates removed in direct relation to their thermal tuning efficiency improvements. We demonstrated optical bistability with only 100 μW of optical input power.

Acknowledgements

This material is based upon work supported, in part, by DARPA under Agreement HR0011-08-9-0001. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. The authors thank Dr. Jagdeep Shah of DARPA MTO for his inspiration and support of this program. Approved for Public Release, Distribution Unlimited.

References and links

1.

A. V. Krishnamoorthy, Ron Ho, H. Xuezhe Zheng, Schwetman, P. Jon Lexau, Koka, I. GuoLiang Li, Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97(7), 1337–1361 (2009). [CrossRef]

2.

X. Zheng, P. Koka, H. Schwetman, J. Lexau, R. Ho, J. E. Cunningham, and A.V. Krishnamoorthy, “Silicon photonic WDM point-to-point network for multi-chip processor interconnects,” Group IV Photonics, 2008 5th IEEE International Conference on, pp. 380–382, 2008.

3.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]

4.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” IEEE J. Lightwave Tech. 15(6), 998–1005 (1997). [CrossRef]

5.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008). [CrossRef]

6.

H. L. R. Lira, S. Manipatruni, and M. Lipson, “Broadband hitless silicon electro-optic switch for on-chip optical networks,” Opt. Express 17(25), 22271–22280 (2009). [CrossRef] [PubMed]

7.

P. Dong, S. F. Preble, and M. Lipson, “All-optical compact silicon comb switch,” Opt. Express 15(15), 9600–9605 (2007). [CrossRef] [PubMed]

8.

X. Zheng, I. Shubin, G. Li, T. Pinguet, A. Mekis, J. Yao, H. Thacker, Y. Luo, J. Costa, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “A tunable 1x4 silicon CMOS photonic wavelength multiplexer/demultiplexer for dense optical interconnects,” Opt. Express 18(5), 5151–5160 (2010). [CrossRef] [PubMed]

9.

S. Manipatruni, L. Chen, and M. Lipson, “Ultra high bandwidth WDM using silicon microring modulators,” Opt. Express 18(16), 16858–16867 (2010). [CrossRef] [PubMed]

10.

P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express 17(25), 22484–22490 (2009). [CrossRef] [PubMed]

11.

G. Li, X. Zheng, J. Lexau, Y. Luo, H. Thacker, P. Dong, S. Liao, D. Feng, M. Asghari, J. Yao, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-power, high-performance Si photonic transmitter,” in Optical Fiber Communication Conference (OFC 2010), OMI2, 2010.

12.

G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Exp.19, 20435–20443 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-21-20435

13.

X. Zheng, F. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-Low Power Arrayed CMOS Silicon Photonic Transceivers for an 80 Gbps WDM Optical Link,” OFC/NFOEC 2011, PDPA1, 2011.

14.

V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004). [CrossRef] [PubMed]

15.

Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett. 31(3), 341–343 (2006). [CrossRef] [PubMed]

16.

L. W. Luo, G. S. Wiederhecker, K. Preston, and M. Lipson, “Power insensitive silicon microring resonators,” Opt. Lett. 37(4), 590–592 (2012). [CrossRef] [PubMed]

17.

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9623.

18.

M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Improvement of thermal properties of ultra-high Q silicon microdisk resonators,” Opt. Express 15(25), 17305–17312 (2007). [CrossRef] [PubMed]

19.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS Manufacturing to Reduce Tuning Requirements for Resonant Optical Devices,” IEEE Photon. J. 3, 567–579 (2011).

20.

R. Soref and B. Bennett, ““Electrooptical effect in silicon,”, IEEE J. Quantum Electron. 23(1), 123–129 (1987). [CrossRef]

21.

J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express 18(18), 19055–19063 (2010). [CrossRef] [PubMed]

22.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron . (2012). doi: 10.1007/s11082-012-9577-9.

23.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

24.

X. Zheng, P. Koka, M. O. McCracken, H. Schwetman, J. G. Mitchell, J. Yao, R. Ho, K. Raj, and A. V. Krishnamoorthy, “Energy-efficient error control for tightly-coupled systems using silicon photonic interconnects,” J. Opt. Commun. Netw. 3, A21–A31 (2011).

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(130.3120) Integrated optics : Integrated optics devices
(190.1450) Nonlinear optics : Bistability
(200.4650) Optics in computing : Optical interconnects
(130.4110) Integrated optics : Modulators

ToC Category:
Integrated Optics

History
Original Manuscript: March 7, 2012
Revised Manuscript: April 19, 2012
Manuscript Accepted: April 22, 2012
Published: May 4, 2012

Citation
Xuezhe Zheng, Ying Luo, Guoliang Li, Ivan Shubin, Hiren Thacker, Jin Yao, Kannan Raj, John E. Cunningham, and Ashok V. Krishnamoorthy, "Enhanced optical bistability from self-heating due to free carrier absorption in substrate removed silicon ring modulators," Opt. Express 20, 11478-11486 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11478


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References

  1. A. V. Krishnamoorthy, Ron Ho, H. Xuezhe Zheng, Schwetman, P. Jon Lexau, Koka, I. GuoLiang Li, Shubin, and J. E. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE97(7), 1337–1361 (2009). [CrossRef]
  2. X. Zheng, P. Koka, H. Schwetman, J. Lexau, R. Ho, J. E. Cunningham, and A.V. Krishnamoorthy, “Silicon photonic WDM point-to-point network for multi-chip processor interconnects,” Group IV Photonics, 2008 5th IEEE International Conference on, pp. 380–382, 2008.
  3. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics4(8), 518–526 (2010). [CrossRef]
  4. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” IEEE J. Lightwave Tech.15(6), 998–1005 (1997). [CrossRef]
  5. Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics2(4), 242–246 (2008). [CrossRef]
  6. H. L. R. Lira, S. Manipatruni, and M. Lipson, “Broadband hitless silicon electro-optic switch for on-chip optical networks,” Opt. Express17(25), 22271–22280 (2009). [CrossRef] [PubMed]
  7. P. Dong, S. F. Preble, and M. Lipson, “All-optical compact silicon comb switch,” Opt. Express15(15), 9600–9605 (2007). [CrossRef] [PubMed]
  8. X. Zheng, I. Shubin, G. Li, T. Pinguet, A. Mekis, J. Yao, H. Thacker, Y. Luo, J. Costa, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “A tunable 1x4 silicon CMOS photonic wavelength multiplexer/demultiplexer for dense optical interconnects,” Opt. Express18(5), 5151–5160 (2010). [CrossRef] [PubMed]
  9. S. Manipatruni, L. Chen, and M. Lipson, “Ultra high bandwidth WDM using silicon microring modulators,” Opt. Express18(16), 16858–16867 (2010). [CrossRef] [PubMed]
  10. P. Dong, S. Liao, D. Feng, H. Liang, D. Zheng, R. Shafiiha, C.-C. Kung, W. Qian, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Low Vpp, ultralow-energy, compact, high-speed silicon electro-optic modulator,” Opt. Express17(25), 22484–22490 (2009). [CrossRef] [PubMed]
  11. G. Li, X. Zheng, J. Lexau, Y. Luo, H. Thacker, P. Dong, S. Liao, D. Feng, M. Asghari, J. Yao, J. Shi, P. Amberg, N. Pinckney, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultralow-power, high-performance Si photonic transmitter,” in Optical Fiber Communication Conference (OFC 2010), OMI2, 2010.
  12. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Exp.19, 20435–20443 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-21-20435
  13. X. Zheng, F. Liu, J. Lexau, D. Patil, G. Li, Y. Luo, H. Thacker, I. Shubin, J. Yao, K. Raj, R. Ho, J. E. Cunningham, and A. V. Krishnamoorthy, “Ultra-Low Power Arrayed CMOS Silicon Photonic Transceivers for an 80 Gbps WDM Optical Link,” OFC/NFOEC 2011, PDPA1, 2011.
  14. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett.29(20), 2387–2389 (2004). [CrossRef] [PubMed]
  15. Q. Xu and M. Lipson, “Carrier-induced optical bistability in silicon ring resonators,” Opt. Lett.31(3), 341–343 (2006). [CrossRef] [PubMed]
  16. L. W. Luo, G. S. Wiederhecker, K. Preston, and M. Lipson, “Power insensitive silicon microring resonators,” Opt. Lett.37(4), 590–592 (2012). [CrossRef] [PubMed]
  17. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005). http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-23-9623 .
  18. M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Improvement of thermal properties of ultra-high Q silicon microdisk resonators,” Opt. Express15(25), 17305–17312 (2007). [CrossRef] [PubMed]
  19. A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS Manufacturing to Reduce Tuning Requirements for Resonant Optical Devices,” IEEE Photon. J.3, 567–579 (2011).
  20. R. Soref and B. Bennett, ““Electrooptical effect in silicon,”, IEEE J. Quantum Electron.23(1), 123–129 (1987). [CrossRef]
  21. J. E. Cunningham, I. Shubin, X. Zheng, T. Pinguet, A. Mekis, Y. Luo, H. Thacker, G. Li, J. Yao, K. Raj, and A. V. Krishnamoorthy, “Highly-efficient thermally-tuned resonant optical filters,” Opt. Express18(18), 19055–19063 (2010). [CrossRef] [PubMed]
  22. I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. (2012). doi: 10.1007/s11082-012-9577-9.
  23. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003). [CrossRef]
  24. X. Zheng, P. Koka, M. O. McCracken, H. Schwetman, J. G. Mitchell, J. Yao, R. Ho, K. Raj, and A. V. Krishnamoorthy, “Energy-efficient error control for tightly-coupled systems using silicon photonic interconnects,” J. Opt. Commun. Netw. 3, A21–A31 (2011).

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