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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 14690–14695
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Ten Gbit/s ring resonator silicon modulator based on interdigitated PN junctions

Melissa Ziebell, Delphine Marris-Morini, Gilles Rasigade, Paul Crozat, Jean-Marc Fédéli, Philippe Grosse, Eric Cassan, and Laurent Vivien  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 14690-14695 (2011)
http://dx.doi.org/10.1364/OE.19.014690


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Abstract

10 Gbit/s silicon modulator based on carrier depletion in interdigitated PN junctions is experimentally demonstrated. The phase-shifter is integrated in a ring resonator, and high extinction ratio larger than 10 dB is obtained in both TE and TM polarizations. VπLπ of about 2.5 V × cm and optical loss lower than 1 dB are estimated. 10 Gbit/s data transmission is demonstrated with an extinction ratio of 4 dB.

© 2011 OSA

1. Introduction

Silicon photonics has generated an increasing interest in the recent years, as it can revolutionize global data communication [1

1. S. Koehl, A. Liu, and M. Paniccia, “Integrated silicon photonics: harnessing the data explosion,” Opt. Photon. News 22(3), 24–39 (2011). [CrossRef]

]. The silicon modulator is among the main challenging building blocks, and intensive work has been carried on for a few years. Carrier depletion-based structures using reverse-biased diodes are most used to achieve high speed and reliable refractive index variations in silicon. Different silicon modulators have been demonstrated, integrated in Mach Zehnder interferometers [2

2. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]

8

8. F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express 19(12), 11804–11814 (2011). [CrossRef] [PubMed]

] or in ring resonators [9

9. F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009). [CrossRef] [PubMed]

,10

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]

]. In all experimental demonstrations up to now, junctions have always been oriented parallel to the light propagation direction, with vertical [2

2. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]

] or lateral [3

3. D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed]

10

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]

] orientations. As the space charge extension modulation due to carrier depletion is limited, typically around 100 nm, the design of the modulator relies firstly on the optimization of the overlap between the optical mode and the effective depleted region in either PN or PIPIN diodes. Secondly, the trade-off among modulation efficiency, rapidity and optical loss has to be carried out [11

11. G. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010). [CrossRef]

]. To increase the modulation efficiency, an alternative solution is to change the orientation of the diode and consequently to use interdigitated PN junctions orthogonally oriented to the direction of light propagation (i.e. waveguide direction). In such configuration, the optical mode propagates through successive depleted regions, which maximizes the interaction between the light and the regions where refractive index variation occurs. Some numerical simulations were carried out on a similar structure by Li et al [12

12. Z.-Y. Li, D.-X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J.-Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

]. We present in this paper the first experimental demonstration of interdigitated PN silicon modulator integrated in a ring resonator.

2. Device Design and Fabrication

A schematic view of the device is shown in Fig. 1(a)
Fig. 1 (a) and (b) Top views of the ring resonator reporting the series of P and N regions along the ring (c) Schematic 3D view of the phase shifter with periodically PN junctions along the waveguide. P+ and N+ regions between the waveguide and the contacts are not represented here for clarity purposes. White-colored regions in the waveguide represent non-intentionally doped silicon (d) Optical microscope view of the fabricated ring resonator modulator. The silicon rib waveguide width is 420 nm, the height is 390 nm and the etching depth is 290 nm, respectively. The lengths of P and N regions are 400 nm and 300 nm, respectively. Ring resonator radius is 50 µm.
1(c). The silicon rib waveguide width is 420 nm, the height is 390 nm and the etching depth is 290 nm. This geometry was chosen in order to optimize mode confinement in the waveguide [7

7. G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, F. Milesi, P. Grosse, D. Bouville, E. Cassan, and L. Vivien, “High extinction ratio 10 Gbit/s silicon optical modulator,” Opt. Express 19(7), 5827–5832 (2011). [CrossRef] [PubMed]

] and to ensure quasi-TE and -TM single mode propagations at a wavelength of 1.55 µm.

The modulator used a ring resonator with a radius of 50 µm in order to avoid losses due to waveguide bending. Due to the coupling region between the ring and the waveguide where it is not possible to place metallic contact, the successive P/N diodes were not integrated all along the ring (perimeter 314 µm-long), but only in a 292 µm long waveguide. Light coupling in the ring was achieved by placing a straight waveguide 200 nm away from one edge of the ring. When light propagates along the ring, the optical mode successively crosses both P and N regions. Optical and electrical simulations allowed us to set the lengths and doping concentration of P and N regions at 400 nm/4 × 1017 cm−3 and 300 nm/1 × 1018 cm−3, respectively. These values were chosen in order to have a large number of PN diodes in the optical path, ensuring large space charge extension variations when a reverse bias from 0 to 10 volts is applied to the diodes.

The optical modulator was fabricated on a 200 mm SOI wafer with a 2 μm-thick buried oxide (BOX) layer and a 400 nm-thick crystalline silicon film. Deep-UV optical lithography and ion implantations were used to obtain highly doped P+ and N+ regions between the active region and the contacts. For hard mask purposes, SiO2 was then deposited by LPCVD. The waveguides were patterned using Deep-UV lithography. After etching the hard mask with reactive ion etching, boron and phosphorus implantations were performed to obtain P and N doped layers in the waveguide, followed by thermal annealing. Finally, Ti/TiN/AlCu/Ti/TiN metal stack was deposited onto the wafer, and the electrodes were patterned and etched down to the SiO2 cap layer. The process used was fully compatible with SOI CMOS technology and could be transferred in high-volume microelectronic manufacturing. Optical microscope view of the fabricated device is shown in Fig. 1(d).

3. Characterization

The normalized transmission of the modulator as a function of the wavelength is plotted in Fig. 2
Fig. 2 Normalized transmission of ring resonator modulator as a function of the wavelength for different applied reverse bias for (a) TE polarization: maximum ER = 11dB at 1546.695 nm and (b) TM polarization: maximum ER = 10 dB at 1549.71 nm.
for reverse bias equal to 0, 5 and 10 V, for both TE and TM polarizations. It can be noted that the periodic interleaved junctions do not introduce any grating effect as predicted in [12

12. Z.-Y. Li, D.-X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J.-Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

]. The quality factor of the ring resonator can be estimated to be approximately 20 000 in TE polarization and 25 000 in TM polarization for a reverse bias of 5 V. Large redshift is obtained due to carrier depletion with the increase of reverse bias. In addition, the resonance depth increases due to the decrease of the losses caused by the free carrier absorption in the ring. Extinction ratios as high as 11 dB in TE and 10 dB in TM were obtained between 0 and −10 V.

The effective index variations and the figure of merit VπLπ of the active region were deduced from the wavelength resonance shifts and are reported in Fig. 3
Fig. 3 (a) Effective index variation as a function of the reverse bias deduced from Fig. 2. (b): VπLπ as a function of the reverse bias deduced from (a). Both TE and TM polarizations are reported.
. For a reverse bias of 10V, Δneff reaches 1.5 × 10−4 and 2 × 10−4 for TE and TM polarizations, respectively. The evolution of VπLπ is reported in Fig. 3(b), and shows a larger phase shift efficiency at low reverse bias which corresponds to a large Δneff(V) slope. VπLπ varies from 2.5 to 4.9 V × cm and from 2.5 to 4.2 V × cm for TE and TM polarizations, respectively. The largest phase modulation efficiency for TM polarization is due to a larger confinement of the optical mode in the rib waveguide, where carrier depletion occurs. Indeed the filling factor of the optical mode in the region under the rib of the waveguide has been calculated by mode solver and varies from 83% for TE mode to 88% for TM mode.

The on-chip insertion loss (when the modulator is on the ‘ON’ state) was estimated to be ~6 dB (excluding coupling loss), including ~5 dB from the 5 mm-long passive waveguides used to guide the light on the chip, and ~1 dB excess loss from the coupling in the ring modulator. The specific amount of loss from the ring resonator and the passive waveguides was estimated by comparing the transmission of a waveguide with a ring resonator to the transmission of contiguous waveguides without ring resonators.

High-speed performance of the modulator was analyzed by measuring optical eye diagrams. A Centellax G2P1A pattern generator was used to obtain 10 Gbit/s PRBS signal with a 210-1 pattern length. The PRBS output signal passed through a driver amplifier, which produced electrical voltage peak-to-peak of 6.3 V. As the impedance of the ring resonator does not match to 50 ohms impedance, we connected the output of the driver to a power divider, with one output linked to a 50 Ω load. The second output was connected to a bias tee used to add a −5 V DC bias to the RF signal, in order to always reverse-bias the diode. The DC + RF signals then fed the ring resonator, using high-speed ground-signal-ground probes. The presence of the power divider decreased the peak-to-peak voltage to less than 5V. The output light from the modulator was passed through an Erbium Doped Fiber Amplifier (EDFA), and a tunable wavelength filter was used to suppress the noise due to the amplified spontaneous emission of the EDFA. Light was then detected using 86100C Agilent oscilloscope with 86106B optical module. The measured 10 Gbit/s eye diagram for both TE and TM input polarizations are reported in Fig. 4
Fig. 4 10 Gbit/s optical eye diagram (a): TE polarization, (b): TM polarization.
. An extinction ratio of 4 dB and 2.7 dB at 10 Gbit/s was measured for TE and TM polarizations, respectively. The dynamic extinction ratios were slightly decreased in comparison with the DC extinction ratios. Indeed, around 5 dB is deduced from Fig. 2 for a 5V peak-to-peak signal. This difference could probably be attributed to RF signal attenuation in the cables, connectors, and bias tee.

Moreover, the presence of the 50 Ω load in parallel to the RF line of the electrical signal applied to the ring is also responsible for power dissipation [8

8. F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express 19(12), 11804–11814 (2011). [CrossRef] [PubMed]

]. A square 5 V peak-to-peak voltage is responsible for 125 mΩ of power consumption in the load, which corresponds to 12.5 pJ/bit at 10 Gbit/s. This value can also be decreased by reducing the applied RF voltage. It is important to mention, that the largest power consumption contribution comes from the load, as the energy required to charge and discharge the capacitance is only a small fraction of the total energy required to drive the modulator.

4. Discussion

In this periodically interdigitated PN junction modulator, the phase modulation efficiency depends only on the P and N regions lengths and on their doping concentrations. For this first experimental demonstration, the lengths of the P and N doped regions were 400 nm and 300 nm, respectively, and the targeting P and N doped concentrations were 4 × 1017 cm−3 and 1 × 1018 cm−3, respectively. These values were chosen to optimize modulation efficiency and maintaining low optical loss. Space charge extension as a function of the reverse bias can be analytically described [13

13. G. Rasigade, D. Marris-Morini, M. Ziebell, E. Cassan, and L. Vivien, “Analytical model for depletion-based silicon modulator simulation,” Opt. Express 19(5), 3919–3924 (2011). [CrossRef] [PubMed]

], assuming the space charge regions are completely empty. The phase shift was evaluated by calculating the effective index variations between the cases where doped regions were deserted or not, and by multiplying it with the total length of deserted regions. This method predicts a VπLπ equal to 1.4 V × cm for TE polarization and 1.2 V × cm for TM polarization, while 2.5 V × cm is experimentally obtained. To understand the discrepancy with experimental results, we performed S-parameters measurements to deduce the capacitance of the ring resonator as a function of the reverse bias from 0 to 10 V. A capacitance varying from 54 to 38 fF was deduced. The comparison with theoretical evaluation of the modulator capacitance indicated that the actual doping concentrations were lower than targeted values. With a P doped concentration of 4 × 1017 cm−3 and a N-doped concentration of 1 × 1018 cm−3, the capacitance of the modulator should vary from 220 to 64 fF. This reduction in doping concentration is responsible for the moderate efficiency of the device; for that reason, targeted doping concentrations need to be improved in future fabrications. Interdigitated-based phase shifters will then reach at least the same efficiency as the more “classical” lateral PN diodes-based devices (VπLπ of 1.5 V × cm in [10

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]

] and 1.4 V × cm in [5

5. N.-N. Feng, S. Liao, D. Feng, P. Dong, D. Zheng, H. Liang, R. Shafiiha, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High speed carrier-depletion modulators with 1.4V-cm VπL integrated on 0.25 µm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]

]).

Finally, the modulator based on interdigitated diodes discussed in this paper can present a large advantage in comparison with other structures regarding the fabrication process. Indeed, the position of the junction inside the waveguide is much more tolerant to shifts due to mask alignment. One perspective for fabrication is to obtain self-aligned diodes by first doping the total active region by P implantation for example and then doping the N part of the diodes. The alignment tolerance of this lithography step for the N part of the diode can create a random shift of the junction position; however, even 100 or 200 nm shift of the junction in the waveguide direction will not influence the phase shifter efficiency for the interdigitated diode modulator.

5. Conclusion

In conclusion, we reported the first experimental demonstration of a carrier depletion silicon modulator based on interdigitated PN junctions. The structure was integrated in a ring resonator with a radius of 50 µm. High modulation was obtained in both TE and TM polarizations, with DC extinction ratio larger than 10 dB. VπLπ as low as 2.5 V × cm was obtained in both TE and TM polarizations and it is theoretically predicted that this value can decreased down to 1.2 V × cm with optimized doped regions. Excess optical loss lower than 1 dB were measured. Finally, high-speed operation was analyzed thanks to 10 Gbit/s eye diagram measurements. A clearly open eye diagram was obtained, with 4 dB extinction ratio using 5 V peak-to-peak RF signal. This new active region has a large potential for performance increase in terms of efficiency and rapidity.

Acknowledgments

The research leading to these results has received funding from the European Community under grant agreement n° 224312 HELIOS and from the French ANR under project SILVER.

References and links

1.

S. Koehl, A. Liu, and M. Paniccia, “Integrated silicon photonics: harnessing the data explosion,” Opt. Photon. News 22(3), 24–39 (2011). [CrossRef]

2.

L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]

3.

D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed]

4.

T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon modulators an germanium photodetectors on SOI: monolithic integration, compatibility and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]

5.

N.-N. Feng, S. Liao, D. Feng, P. Dong, D. Zheng, H. Liang, R. Shafiiha, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High speed carrier-depletion modulators with 1.4V-cm VπL integrated on 0.25 µm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]

6.

J. W. Park, J.-B. You, I. G. Kim, and G. Kim, “High-modulation efficiency silicon Mach-Zehnder optical modulator based on carrier depletion in a PN Diode,” Opt. Express 17(18), 15520–15524 (2009). [CrossRef] [PubMed]

7.

G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, F. Milesi, P. Grosse, D. Bouville, E. Cassan, and L. Vivien, “High extinction ratio 10 Gbit/s silicon optical modulator,” Opt. Express 19(7), 5827–5832 (2011). [CrossRef] [PubMed]

8.

F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express 19(12), 11804–11814 (2011). [CrossRef] [PubMed]

9.

F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009). [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. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010). [CrossRef]

12.

Z.-Y. Li, D.-X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J.-Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]

13.

G. Rasigade, D. Marris-Morini, M. Ziebell, E. Cassan, and L. Vivien, “Analytical model for depletion-based silicon modulator simulation,” Opt. Express 19(5), 3919–3924 (2011). [CrossRef] [PubMed]

OCIS Codes
(130.0250) Integrated optics : Optoelectronics
(130.4110) Integrated optics : Modulators

ToC Category:
Integrated Optics

History
Original Manuscript: May 9, 2011
Revised Manuscript: June 23, 2011
Manuscript Accepted: July 8, 2011
Published: July 15, 2011

Citation
Melissa Ziebell, Delphine Marris-Morini, Gilles Rasigade, Paul Crozat, Jean-Marc Fédéli, Philippe Grosse, Eric Cassan, and Laurent Vivien, "Ten Gbit/s ring resonator silicon modulator based on interdigitated PN junctions," Opt. Express 19, 14690-14695 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14690


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References

  1. S. Koehl, A. Liu, and M. Paniccia, “Integrated silicon photonics: harnessing the data explosion,” Opt. Photon. News 22(3), 24–39 (2011). [CrossRef]
  2. L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky, and M. Paniccia, “40 Gbit/s silicon optical modulator for high speed applications,” Electron. Lett. 43(22), 1196–1197 (2007). [CrossRef]
  3. D. J. Thomson, F. Y. Gardes, G. T. Reed, F. Milesi, and J.-M. Fédéli, “High speed silicon optical modulator with self aligned fabrication process,” Opt. Express 18(18), 19064–19069 (2010). [CrossRef] [PubMed]
  4. T.-Y. Liow, K.-W. Ang, Q. Fang, J.-F. Song, Y.-Z. Xiong, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Silicon modulators an germanium photodetectors on SOI: monolithic integration, compatibility and performance optimization,” IEEE J. Sel. Top. Quantum Electron. 16(1), 307–315 (2010). [CrossRef]
  5. N.-N. Feng, S. Liao, D. Feng, P. Dong, D. Zheng, H. Liang, R. Shafiiha, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “High speed carrier-depletion modulators with 1.4V-cm VπL integrated on 0.25 µm silicon-on-insulator waveguides,” Opt. Express 18(8), 7994–7999 (2010). [CrossRef] [PubMed]
  6. J. W. Park, J.-B. You, I. G. Kim, and G. Kim, “High-modulation efficiency silicon Mach-Zehnder optical modulator based on carrier depletion in a PN Diode,” Opt. Express 17(18), 15520–15524 (2009). [CrossRef] [PubMed]
  7. G. Rasigade, M. Ziebell, D. Marris-Morini, J. M. Fédéli, F. Milesi, P. Grosse, D. Bouville, E. Cassan, and L. Vivien, “High extinction ratio 10 Gbit/s silicon optical modulator,” Opt. Express 19(7), 5827–5832 (2011). [CrossRef] [PubMed]
  8. F. Y. Gardes, D. J. Thomson, N. G. Emerson, and G. T. Reed, “40 Gb/s silicon photonics modulator for TE and TM polarisations,” Opt. Express 19(12), 11804–11814 (2011). [CrossRef] [PubMed]
  9. F. Y. Gardes, A. Brimont, P. Sanchis, G. Rasigade, D. Marris-Morini, L. O’Faolain, F. Dong, J. M. Fédéli, P. Dumon, L. Vivien, T. F. Krauss, G. T. Reed, and J. Martí, “High-speed modulation of a compact silicon ring resonator based on a reverse-biased pn diode,” Opt. Express 17(24), 21986–21991 (2009). [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. Rasigade, D. Marris-Morini, L. Vivien, and E. Cassan, “Performance evolutions of carrier depletion silicon optical modulators: from PN to PIPIN diodes,” IEEE J. Sel. Top. Quantum Electron. 16(1), 179–184 (2010). [CrossRef]
  12. Z.-Y. Li, D.-X. Xu, W. R. McKinnon, S. Janz, J. H. Schmid, P. Cheben, and J.-Z. Yu, “Silicon waveguide modulator based on carrier depletion in periodically interleaved PN junctions,” Opt. Express 17(18), 15947–15958 (2009). [CrossRef] [PubMed]
  13. G. Rasigade, D. Marris-Morini, M. Ziebell, E. Cassan, and L. Vivien, “Analytical model for depletion-based silicon modulator simulation,” Opt. Express 19(5), 3919–3924 (2011). [CrossRef] [PubMed]

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