Open Access
Add to BibSonomyAbstract
Single microring resonators have been used in applications such as wavelength multicasting and microwave photonics, but the dependence of the free spectral range with ring radius imposes a trade-off between the required GHz optical channel spacing, footprint and power consumption. We demonstrate four-channel all-optical wavelength multicasting using only 1 mW of control power, with converted channel spacing of 40-60 GHz. Our device is based on a compact embedded microring design fabricated on a scalable SOI platform. The coexistence of close resonance spacing and high finesse (205) in a compact footprint is possible due to enhanced quality factors (30,000) resulting from the embedded configuration and the coupling-strength dependence of resonance spacing, instead of ring size. In addition, we discuss the possibility of achieving continuously mode splitting from a single-notch resonance up to 40 GHz.
© 2014 Optical Society of America
1. Introduction
As optical signal processing progresses to overcome the limitations imposed by electronics in future high capacity communication networks [1], silicon microring resonators have been broadly employed to enable multiple functionalities such as optical modulators, high-order filters, optical buffers and optical logic circuits [2–7], preserving full compatibility with CMOS technology [8]. In this context, coupled microring configurations have been explored to conceive devices with specific amplitude and phase responses, demonstrating their high flexibility to perform spectral engineering [9–13].
A reduced footprint is usually desired to achieve low power consumption and high integration density in photonic circuitry [14], but the trade-off between ring-resonator diameter and free spectral range (FSR) may limit device performance in applications requiring multiple close-spaced channels. For instance, optical wavelength multicasting, which is used to improve traffic management in wavelength-division multiplexing (WDM) networks [15,16], and microwave photonics [17] operate with channels separated by GHz and could only be performed with single microrings with radius on the order of hundreds of micrometers, thus compromising low power consumption and small footprint. In such cases, a coupled ring configuration may provide the required channel spacing without increasing the overall footprint and even lowering the power consumption.
In this paper, we present an embedded coupled ring design that overcomes the FSR-footprint trade-off providing multiple GHz-spaced resonances with enhanced quality factors (Q). A quadruplet with sharp GHz-spaced resonances is identified and used to perform four-channel wavelength conversion with very low power consumption based on the two-photon absorption (TPA)-induced free carrier dispersion (FCD) [18,19]. In addition, the design efficiently couples clockwise (CW) and counter-clockwise (CCW) optical modes and may be used to achieve continuous mode splitting from a single-notch resonance up to 40 GHz.
The device architecture and schematic working principle are presented in Section 2, along with the analytical model based on the coupled mode theory (CMT) in time [20]. Section 3 presents the evolution of the transmission spectrum and relates the observed resonance spacing with the coupling coefficients between resonators. Section 4 is dedicated to the experimental demonstration of the low-power wavelength multicasting.
2. Device architecture and modeling
The design consists of two identical coupled rings embedded in an outer ring (Fig. 1). It enables an efficient coupling between CW and CCW traveling modes without introducing sidewall corrugation or quasi-gratings [19,21], which are associated with scattering losses. The incident light sin excites a CW mode on the outer ring a1cw, which feeds the CW modes on the embedded rings a2cw and a3cw (Fig. 1(b)). In the coupling region between the embedded rings, the CW mode of one ring couples into the other ring as a CCW mode (a3ccw and a2ccw). Finally, these CCW modes generate the CCW mode on the outer ring, a1ccw.
Fig. 1 (a) Optical microscopy of the device fabricated in SOI with radius R1 = 20 μm, R2 = 9.625 μm. The gap spacing is 200 nm in all coupling regions. (b) The direct coupling between embedded rings generates both clockwise (CW) and counter-clockwise (CCW) traveling modes, even if the incident light (sin) is coupled to only one direction.
The optical modes of the coupled system (supermodes) are determined using CMT. In this approach, the system dynamics is described by coupled linear equations, which can be written in matrix form as Ȧ = MA + S, where Ȧ is the time derivative of the optical mode vector A, M is the coupling matrix and S is the source vector. The supermode frequencies are derived from the eigenvalues of the coupling matrix. For slowly-varying mode amplitudes, a = ā∙exp(jωt), the system of equations read (the bar is omitted in the following)
where Δωi = ω – ωi is the detuning between the optical angular frequency ω and the bare resonance angular frequency ωi of the outer (i = 1) or embedded rings (i = 2). The coupling coefficient between rings i and j is κij (κij = κji for lossless coupling, as assumed), κext is the coupling coefficient between the outer ring and the bus waveguide, and μi is the mutual coupling coefficient between counter-propagating modes in the same ring. Γ1 = γ01 + γext is the total decay rate of the outer ring, where γext = κ2ext /2 = ωi /2Qext represent extrinsic losses, related to the external quality factor Qext, and γ0i = ωi /2Q0i is the intrinsic material and radiation losses, related to the intrinsic quality factor Q0i. The transmitted and reflected fields are related to the incident field sin by st = sin + jκext·a1cw and sr = jκext·a1ccw, respectively. The squared amplitude of these fields represents the power in the bus waveguide mode.This design is equivalent to configurations where three identical resonators are placed on the corners of an equilateral triangle [22,23], with two important distinctions. First, one of the rings has a different size, which is used here to exploit the Vernier effect in order to observe resonance tuning of one ring with respect to the others directly from the broadband transmission spectrum. Second, the two identical rings are embedded instead of externally coupled to the third one, which makes possible to introduce an add-drop port directly on the ring coupled to the bus waveguide.
3. Device characterization and spectral features
Our device was fabricated using a SOI platform at IMEC-EUROPRACTICE with ring dimensions R1 = 20 µm, R2 = 9.625 µm (Fig. 1(a)), and 200-nm gap between rings and between the outer ring and the waveguide. The effectively single mode (TE) waveguides consist of a silicon core (nSi = 3.45) with 220 nm x 450 nm cross-section on a 2-µm-thick layer of buried thermal SiO2 (nSiO2 = 1.45), and is covered with a 1-μm thick deposited SiO2 layer. The waveguide is butt-coupled to a GRIN-rod-lensed optical fiber using inverse nanotapers [24].
A good agreement between the CMT prediction and the experimental data is evidenced in Fig. 2. The detuning between the bare resonance wavelengths (frequencies) of the embedded rings with respect to the outer ring, λ2 – λ1 (ω2 – ω1), varies throughout the broadband spectral range of Fig. 2(a) due to the Vernier effect. As the detuning varies, the system undergoes different coupling regimes, which can be visualized in the anti-crossing diagram of Fig. 2(b). In this figure, the vertical axis corresponds to the horizontal axis of the broadband transmission spectrum (Fig. 2(a)), while the horizontal axis represents the detuning Δω2 between the supermode resonance frequency of the coupled system and the bare resonance ω2 (as defined in Eq. (1)). Since data account for different wavelengths, the coupling coefficients are also assumed to be dispersive in our CMT model, κ = κ0 + α∙(λ – λ0). The analytical plots assume κ012 = 260 GHz, κ013 = 250 GHz, κ023 = 210 GHz, α = 1.7 GHz·nm−1, and λ0 = 1520 nm, with maximum relative change in coupling coefficients between 60% and 80%. Despite the mismatch between experiment and simulation observed in Fig. 2(b) for higher wavelengths, this simple model succeeds in reproducing the general spectral features of the coupled device. κ023 is slightly smaller than κ012 and κ013, which results from the reduced interaction length between embedded rings when compared to the embedded-outer ring interaction length, caused by the opposite bend radius of the embedded rings [25]. In addition, if the embedded rings are not equally coupled to the outer ring (we assume κ13 = 0.9∙κ12), the CMT predicts an accidental anti-crossing, which is shown in the inset of Fig. 2(b). The coupling coefficient depends exponentially on the gap between waveguides [26], so a gap variation of 15 nm would suffice to induce the assumed 10% mismatch. In fact, for a perfectly symmetric design, mode degeneracy occurs when the three microrings are resonant and only four resonances are predicted, which is also expected for the triangular coupling configuration mentioned in the previous section [22]. Sidewall roughness was neglected (μm = 0) since mode splitting is not resolved for single (outer) ring resonances.
Fig. 2 (a) Broadband transmission spectrum or the coupled resonator design. The red (λ2) and blue (λ1) lines represent the bare resonances of the embedded and outer rings, respectively. The variable detuning (λ2–λ1) leads to multiple coupling regimes and is used to obtain an (b) anti-crossing diagram comparing the experimental points and the theoretical plot using CMT. Notice that the vertical axis of (b) corresponds to the horizontal axis of (a). Inset: accidental anti-crossing due to slightly asymmetric coupling between the embedded rings and the outer ring (κ13 = 0.9∙κ12). (c) Transmission spectra showing different resonance profiles: (i) a symmetric quadruplet is observed when only the embedded rings are resonant; (i-iv) as ω1 approaches ω2, the quadruplet is distorted and the outer ring resonance is mode-split (orange/purple dots).
The transmission spectra corresponding to selected points in the anti-crossing diagram are shown in Fig. 2(c), helping to visualize the interaction among the individual modes. When ω1 and ω2 are strongly detuned (case (i)), the outer ring does not feel the influence of the embedded rings and its transmission spectra presents a single-notch resonance (orange/purple dot). On the other hand, the CW and CCW modes of the two identical embedded rings are always coupled, resulting in a symmetric quadruplet. As ω1 approaches ω2 ((ii)-(v)), the coupling between embedded and outer rings gets stronger, exciting the CCW mode on the outer ring and causing mode splitting, while the quadruplet is distorted from its symmetric form.
The coexistence of close resonance spacing and high finesse in a compact footprint is only possible due to an embedded coupled configuration. For a single microring, the resonance spacing coincides with the FSR, given by FSR = λ2/(2πR∙ng) (R is the ring radius and ng is the index group), while F = FSR/δλ and Q = λ/δλ (λ and δλ are the resonance’s wavelength and linewidth). Therefore, to obtain the same resonance spacing and high finesse with a single ring, the ring radius would have to be approximately 225 μm, and the required loaded Q would be unattainable for a SOI microring (~700,000).
For our coupled design, the resonance spacing is no longer dictated by the ring size, but by the coupling strength. In addition, when these cavities are not resonant with the bus-coupled outer ring, bus-induced extrinsic loss is reduced, leading to enhanced Q in comparison with bus-coupled cavities [11].
A fitting of the quadruplet resonances (Fig. 3(a)) confirms high Q (30,000), close resonance spacing (40-60 GHz) and a moderate 9-dB extinction ratio. For comparison, the single-notch outer ring resonances have Q’s around 6,000, confirming fivefold Q-enhancement for the embedded configuration. Moreover, a high experimental finesse (F = 205) confirms the high field enhancement within the embedded rings, which can also be observed in the infrared images shown in Fig. 3(b).
Fig. 3 (a) Quadruplet resonances with close resonance spacing (40-60 GHz), high Q (30,000), moderate extinction ratio (9 dB) and high finesse (F = 205). (b) High field enhancement attested by infrared images. (c) Tunable mode-splitting originating from a single-notch resonance. The maximum resonance spacing observed is 0.35 nm (40 GHz).
Regarding the outer ring resonance, the continuous mode splitting observed as it is tuned close to resonance with the embedded rings (Fig. 3(c)) could be explored to perform actively tunable mode-splitting [27] from a single-notch resonance to a 40-GHz resonance splitting. This is an interesting capability with applications in optical switching, filtering, and reconfigurability [28], as well as for achieving continuously tunable slow to fast light [29].
In order to determine the dependence of resonance spacing with the different coupling coefficients, we show in Fig. 4(a) the electric field profile in the coupling region between the embedded rings (Fig. 4(b)), as obtained from 2D-Finite-Difference Time-Domain (FDTD) simulations. As can be seen in Fig. 4(c), the coupling is clearly anti-symmetric (blue-shifted anti-bonding) for resonances S1 and S2, while it is symmetric (red-shifted bonding) for resonances S3 and S4. Since the coupling of counter-propagating modes originates a blue-shifted anti-symmetric mode and a red-shifted symmetric mode [12], we identify S1-S3 and S2-S4 as pairs of modes split by counter-propagative coupling, mediated by κ23. If the embedded rings were not coupled internally, CCW modes would not be excited, S1 (S2) would degenerate with S3 (S4) and the resulting transmission spectrum would show a duplet instead of a quadruplet [11,30]. The additional splitting between resonances S1-S2 and S3-S4 accounts for the coupling between the identical embedded rings through the outer ring, mediated by κ12 and κ13. The optical power distribution shown in Fig. 4(d) confirms that the modes forming the quadruplet are spatially confined within the embedded rings, reducing the bus-induced extrinsic losses and therefore increasing the loaded Q’s.
Fig. 4 2D-FDTD simulations. (a) Transmission spectrum with a quadruplet of sharp resonances S1, S2, S3 and S4. (b) Coupling region between the embedded rings (solid rectangle) used to analyze the (c) electric field profile, showing anti-bonding (S1 and S2) and bonding (S3 and S4) coupling regimes. Plus ( + ) and minus (–) signs represent the maximum and minimum of the electric field. (d) The supermodes are spatially confined within the embedded rings for the quadruplet resonances, increasing their loaded Q’s.
4. Low power four-channel wavelength multicasting
All-optical modulation of silicon rings can be performed exploiting the resonance shift caused by TPA-induced FCD [18]. Dual-channel wavelength multicasting have been realized in silicon microrings using roughness induced mode-splitting [19], but a design that increases the number of converted channels with improved power consumption has not been reported. Since FCD is a broadband effect, it affects all the resonances similarly and the information carried by the control signal can be simultaneously converted to multiple probe signals with different wavelengths. We recall that free-carrier absorption (FCA) does not affect the conversion performance significantly [18].
The experimental setup is depicted in Fig. 5. Both control and probe light are generated by continuous wave (cw) tunable lasers. The control light is modulated with non-return-to-zero 27-1 pseudorandom bit sequence at 622 Mbit/s. Control and probe channels are coupled through a 90:10 coupler and launched into the waveguide. Insertion losses are approximately 7 dB. The control power launched into the waveguide is 0 dBm (1 mW) and the probe power is −12.5 dBm in each channel. The output of the microring resonator is filtered to separate control and converted signals, which are then amplified and individually analyzed.
Fig. 5 Experimental setup for four-channel wavelength multicasting. PC, polarization controller; PG, pattern generator; Mod, optical modulator; EDFA, erbium-doped fiber amplifier; VOA, variable optical attenuator; BPF, band-pass optical filter.
The control light wavelength λC is fixed at the shorter-edge of a sharp resonance located at 1547.9 nm and the probe wavelengths are tuned around the quadruplet resonances. When the probe wavelengths are located on resonance, the probe transmission increases as the high control signal (logic 1) generates free carriers and blue-shifts all the resonances, resulting in anon-inverted wavelength conversion (Fig. 6(a)) [18]. Accordingly, when the probe wavelength is located at the shorter-edge of the resonance, the probe transmission decreases as the resonances are blue-shifted, resulting in inverted wavelength conversion (Fig. 6(b)).
Fig. 6 Four-channel wavelength multicasting. Control and converted waveforms for (a) non-inverted and (b) inverted wavelength conversion at 622 Mbit/s. The control power is 0 dBm and the probe power is −12 dBm in each channel. Control and converted signal wavelengths are, respectively, λC = 1547.9 nm, λS1 = 1616.40 nm, λS2 = 1616.77 nm, λS3 = 1617.31 nm, and λS4 = 1617.65 nm.
These results show the advantage of using an embedded coupled design to achieve multiple wavelength conversion and thus multicasting at GHz channel spacing in a compact integrated device at very low power consumption. The control power required to achieve all-optical modulation based on resonance shift caused by FCD is proportional to VQ-3/2 [18], where V is the volume of the ring and Q is the quality factor. As discussed in the previous section, a SOI single microring with 50-GHz channel spacing should have a radius of the order of 225 μm, 10 times bigger than our device, requiring 10 times more power to achieve the same modulation, provided the same Q (30,000). We recall that such high Q was achieved due to the embedded configuration, so that a fair estimative of the power consumption for a similar single ring device should take into account its reduced Q, around 10,000 to agree with experimental Q’s of our single microrings. Thus, the power consumption is reduced by a factor of more than 50 when using an embedded coupled design in comparison to a single ring design for such a close channel spacing.
The time constant of this device is ~670 ps, which is dominated by the free carrier lifetime of intrinsic silicon (450 ps) [31]. This limits the maximum modulation rate to less than 1 Gbit/s. However, it has been experimentally demonstrated that much shorter free carrier lifetimes and thus much higher modulation rates can be achieved by employing a reverse-biased p-i-n junction [32] or by ion implantation [33,34]. In contrast to the duplet depicted in Fig. 3(c), where the channel spacing could be tuned by changing the resonance wavelength of the embedded or outer rings, in the quadruplet case channel spacing is dictated by the coupling strength and its accuracy is limited by fabrication precision.
5. Conclusion
In summary, we experimentally demonstrate quadruplet resonances presenting close resonance spacing (40-60 GHz), high-Q (30,000) and high finesse (205) simultaneously, in a 20-μm radius device. The device footprint can be further reduced to achieve higher field enhancement (and finesse) without compromising the resonance spacing, which is governed by the coupling strength between resonators. Our device is fabricated on a scalable integrated silicon platform, which makes it an interesting candidate to explore all-optical signal processing functionalities employed in WDM networks and microwave photonics. Here, this capability is demonstrated with four-channel wavelength multicasting based on the TPA-induced FCD, with 1 mW of control power.
In addition, this design represents an efficient way of coupling counter-propagating modes with no associated scattering losses. The possibility of creating and controlling mode-splitting in a range of approximately 0.3 nm (40 GHz) from a single-notch resonance is discussed, which would be useful for applications such as reconfigurable filtering and switching, and continuous slow to fast light in a compact and integrated platform.
Acknowledgments
The authors would like to thank H. L. Fragnito and P. Dainese for loaning the equipments to perform part of the experiments. This work was supported by Brazilian financial agencies CNPq, CAPES, and the Center for Optics and Photonics (CePOF) under Grant 05/51689-2, the National Institute for Science and Technology (FOTONICOM) under Grant 08/57857-2, and São Paulo Research Foundation (FAPESP).
References and links
1. M. Saruwatari, “All-optical signal processing for terabit/second optical transmission,” IEEE J. Sel. Top. Quantum Electron. 6, 1363–1374 (2000).
2. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Phot. Rev. 6(1), 47–73 (2012). [CrossRef]
3. S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. Poon, “Silicon photonics: from a microresonator perspective,” Laser Phot. Rev. 6(2), 145–177 (2012). [CrossRef]
4. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4(8), 518–526 (2010). [CrossRef]
5. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, “Very high-order microring resonator filters for WDM applications,” IEEE Photon. Technol. Lett. 16(10), 2263–2265 (2004). [CrossRef]
6. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007). [CrossRef]
7. Y. Tian, L. Zhang, R. Ji, L. Yang, P. Zhou, H. Chen, J. Ding, W. Zhu, Y. Lu, L. Jia, Q. Fang, and M. Yu, “Proof of concept of directed OR/NOR and AND/NAND logic circuit consisting of two parallel microring resonators,” Opt. Lett. 36(9), 1650–1652 (2011). [CrossRef] [PubMed]
8. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005).
9. L. Zhang, M. Song, T. Wu, L. Zou, R. G. Beausoleil, and A. E. Willner, “Embedded ring resonators for microphotonic applications,” Opt. Lett. 33(17), 1978–1980 (2008). [PubMed]
10. X. Zhou, L. Zhang, A. M. Armani, R. G. Beausoleil, A. E. Willner, and W. Pang, “Power enhancement and phase regimes in embedded microring resonators in analogy with electromagnetically induced transparency,” Opt. Express 21(17), 20179–20186 (2013). [CrossRef] [PubMed]
11. L. A. M. Barea, F. Vallini, G. F. M. de Rezende, and N. C. Frateschi, “Spectral engineering with CMOS compatible SOI photonic molecules,” IEEE Photonics J. 5(6), 2202717 (2013). [CrossRef]
12. S. V. Boriskina, “Photonic Molecules and Spectral Engineering,” in Photonic Microresonator Research and Applications, I. Chremmos, O. Schwelb, and N. Uzunoglu, eds. (Springer US, 2010), pp. 393–421.
13. Y. Hu, X. Xiao, H. Xu, X. Li, K. Xiong, Z. Li, T. Chu, Y. Yu, and J. Yu, “High-speed silicon modulator based on cascaded microring resonators,” Opt. Express 20(14), 15079–15085 (2012). [CrossRef] [PubMed]
14. L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,” Proc. SPIE 6125, 612502 (2006). [CrossRef]
15. R. Lin, W.-D. Zhong, S. K. Bose, and M. Zukerman, “Light-tree configuration for multicast traffic grooming in WDM mesh networks,” Photonic Netw. Commun. 20(2), 151–164 (2010). [CrossRef]
16. L. H. Sahasrabuddhe and B. Mukherjee, “Light trees: optical multicasting for improved performance in wavelength routed networks,” IEEE Commun. Mag. 37(2), 67–73 (1999). [CrossRef]
17. J. Yao, “Microwave Photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]
18. Q. Xu, V. R. Almeida, and M. Lipson, “Micrometer-scale all-optical wavelength converter on silicon,” Opt. Lett. 30(20), 2733–2735 (2005). [CrossRef] [PubMed]
19. Q. Li, Z. Zhang, F. Liu, M. Qiu, and Y. Su, “Dense wavelength conversion and multicasting in a resonance-split silicon microring,” Appl. Phys. Lett. 93(8), 081113 (2008). [CrossRef]
20. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
21. T. Wang, Z. Zhang, F. Liu, Y. Tong, J. Wang, Y. Tian, M. Qiu, and Y. Su, “Modeling of quasi-grating sidewall corrugation in SOI microring add-drop filters,” Opt. Commun. 282(17), 3464–3467 (2009). [CrossRef]
22. E. F. Franchimon, K. R. Hiremath, R. Stoffer, and M. Hammer, “Interaction of whispering gallery modes in integrated optical microring or microdisk circuits: hybrid coupled mode theory model,” J. Opt. Soc. Am. B 30, 1048–1057 (2013).
23. S. I. Schmid, K. Xia, and J. Evers, “Pathway interference in a loop array of three coupled microresonators,” Phys. Rev. A 84(1), 013808 (2011). [CrossRef]
24. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [PubMed]
25. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
26. H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984). Chap. 6.
27. A. H. Atabaki, B. Momeni, A. A. Eftekhar, E. S. Hosseini, S. Yegnanarayanan, and A. Adibi, “Tuning of resonance-spacing in a traveling-wave resonator device,” Opt. Express 18(9), 9447–9455 (2010). [PubMed]
28. W. S. Fegadolli, G. Vargas, X. Wang, F. Valini, L. A. M. Barea, J. E. B. Oliveira, N. Frateschi, A. Scherer, V. R. Almeida, and R. R. Panepucci, “Reconfigurable silicon thermo-optical ring resonator switch based on Vernier effect control,” Opt. Express 20(13), 14722–14733 (2012). [PubMed]
29. H. Shahoei and J. Yao, “Simultaneous slow light, fast light, and continues slow to fast light tuning in a microresonator via interaction of dual inputs,” Proc. SPIE 8007, 80070U (2011).
30. L. A. M. Barea, F. Vallini, P. F. Jarschel, and N. C. Frateschi, “Silicon technology compatible photonic molecules for compact optical signal processing,” Appl. Phys. Lett. 103(20), 201102 (2013). [CrossRef]
31. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]
32. S. F. Preble, Q. Xu, B. S. Schmidt, and M. Lipson, “Ultrafast all-optical modulation on a silicon chip,” Opt. Lett. 30(21), 2891–2893 (2005). [CrossRef] [PubMed]
33. N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, J. H. B. Deane, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, and G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” Opt. Express 16(24), 19779–19784 (2008). [CrossRef] [PubMed]
34. M. Waldow, T. Plötzing, M. Gottheil, M. Först, J. Bolten, T. Wahlbrink, and H. Kurz, “25ps all-optical switching in oxygen implanted silicon-on-insulator microring resonator,” Opt. Express 16(11), 7693–7702 (2008). [CrossRef] [PubMed]
