Abstract

We demonstrate the generation of amplitude-shift-keying (ASK) optical signals using a system of parallel microring resonators. By independently modulating two symmetric microring resonators arranged in a Mach-Zehnder configuration, we realize the generation of three levels. The proposed scheme can be extended to any number of logic levels, which effectively increases the data rate of an optical link using slower modulators. Here, we separately utilize thermo-optic and ultrafast all-optical modulation schemes to generate ASK signals on a silicon photonic chip.

©2010 Optical Society of America

1. Introduction

Recent innovations and breakthroughs in silicon photonics are paving the way for the realization of high speed on-chip optical interconnects [1,2]. Transfer of information between components requires that data be superimposed on the optical carrier signal by electro-optic modulation. Numerous high performance silicon electro-optic modulators have been demonstrated which generate non-return-to-zero (NRZ) encoding at bit-rates as high as 40 Gbps [3,4]. However, there are numerous other optical modulation formats which could yield improved performance of the optical links such as better Signal/Noise ratio, reduced non-linearity or even higher bit-rates [5]. Some recent examples of alternate encodings on a silicon photonic platform are the use of ring resonators to convert non-return-to-zero (NRZ) to pseudo-return-to-zero (PRZ) in order to aid clock recovery and the generation of return-to-zero-differential-phase-shift-keying (RZ-DPSK) signals with improved chirp [6,7].

Here, we propose a scheme for generating amplitude-shift-keying (ASK) format in order to significantly increase the bit-rate of on-chip optical links. In an ASK signal, multiple logic levels are used to encode information, which effectively increases the bit-rate of an optical link [8]. Here, we generate three amplitude level signals using a pair of symmetric microring resonators arranged in parallel in a Mach-Zehnder configuration as seen in Fig. 1 . The device works by splitting the input light into two separate paths with a 3-dB coupler. When the light is on resonance with the rings, it is coupled to the drop ports where it constructively interferes at the output port. If one ring resonator is shifted off-resonance, the output of the system is halved because only half of the light transfers to the output port as illustrated in Fig. 1 (b), and if both ring resonators are shifted off-resonance, then there is no field at the output port, as shown in Fig. 1 (c). Therefore, with two ring resonators we can generate three states. So, in general N + 1 amplitude levels can be realized by N ring resonators cascaded in parallel.

 figure: Fig. 1

Fig. 1 The principle of operation of the device is illustrated - (a) two unmodulated ring resonators result in amplitude level 1. (b) Modulating one ring (blue) resonator independently results in amplitude level 2 and (c) modulating both ring resonators results in amplitude level 3.

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The operation of the structure can be understood by considering the transmission of an individual ring resonator to the drop port, which is given by coupled mode theory [9]

Tdrop=e2γκ12κ22(1t1t2eγ)2+4t1t2eγsin2[θ]
In Eq. (1), e is the field transmission per round in the ring, κ1 and κ2 are the coupling coefficients at add and drop ports respectively,t1,2=1κ1,22, θ=πn2πR/λ is phase the mode accumulates in one round trip (n is the refractive index, λ is the resonant wavelength). Equation (1) has a peak value when θ=m2πand quickly drops off to zero for any other values (i.e. off-resonance) [9]. Therefore the overall transmission of our structure can be modeled by
T=m=1NuTdropmN
In Eq. (2), N is the total number of ring resonators in parallel and u takes on a value of one/zero when the individual rings are on/off resonance, respectively.

2. Demonstration of ASK Modulation using Thermo-optic Tuning

As a proof of concept of the generation of amplitude-shift-keying optical signals using silicon ring resonators, here we use thermo-optic tuning of the structure shown in Fig. 1. The device is fabricated on 250 nm thick hydrogenated-amorphous silicon deposited using plasma enhanced chemical vapor deposition technique (PECVD) at 400°C onto 3 microns of thermally grown oxide. The ring resonators are patterned using electron-beam lithography followed by an etch using an inductively coupled plasma (ICP) chlorine etching system. The process flow involved in the fabrication of the microrings structure is illustrated in Fig. 2 . The ring resonator waveguides are 460 nm wide, have a diameter of 10 µm and are spaced 40 µm apart as seen in Fig. 3 (a) . The device is clad with 600 nm of PECVD silicon dioxide to protect the optical mode, but is thin enough to ensure efficient coupling of heat to the silicon waveguides [10]. The heat is supplied by Nickel-Chromium heaters that are patterned on top of the 600 nm oxide. The heaters are 2 µm wide and are defined using standard optical lithography and lift-off of 80 nm thick sputtered nickel-chromium film. An optical microscope image of the device with heaters is shown in Fig. 3(b).

 figure: Fig. 2

Fig. 2 Process flow in the fabrication of a-Si:H microring resonators with resistive heaters

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 figure: Fig. 3

Fig. 3 (a) SEM image of the fabricated device. (b) Optical microscope image of the device with heaters

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The thermo-optic generation of ASK signals is achieved using the experimental setup shown in Fig. 4 . Heat is applied to each ring resonator which effectively shifts its resonance. The thermo-optic co-efficient in hydrogenated-amorphous silicon at room temperature is measured to be n/T=2.4×104K1 [11]. The change in amplitude of the optical field at the drop port due to the applied heat can be modeled based on Eq. (2).

 figure: Fig. 4

Fig. 4 Experimental set-up to measure simultaneous thermootpic switching of two ring resonators. The two rings are switched individually using the thermo-optic effect by applying square wave electrical pulses at 100 Hz to produce modulated signal observed on an oscilloscope.

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The measured shift in resonance of one of the ring resonators is shown in Fig. 5 where we observe a 0.14 nm/mW shift from the applied electric power. By driving this single resonator at 100 Hz with a 2 Vpp electronic signal, we see in Fig. 6(a) that two amplitude levels are generated from the structure. The high level is where both ring resonators are in resonance with the input light and the ~0.5 level is generated when one ring resonator is shifted off-resonance due to the application of heat.

 figure: Fig. 5

Fig. 5 Thermal tuning of resonant wavelengths is achieved by applying heat to the individual rings.

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 figure: Fig. 6

Fig. 6 (a). Temporal response of the system due to the modulation of one resonator. The other resonator is always on resonance. (b) Modulating both resonators generates three amplitude levels on a single carrier.

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In order to generate three amplitude levels, both ring resonators are modulated simultaneously. As seen in Fig. 6(b) when both rings are on resonance, a “1” is generated, when one is off-resonance, a “0” is generated and lastly when both are off resonance, a “-1” is generated. Note that “-1” and “1” can be reversed if the wavelength of the light is such that it is off-resonance when no heat is applied. Therefore, it is observed that with two ring resonators it is possible to generate up to three different amplitude levels on a single optical carrier. This scheme can simply be scaled up to more logic levels by adding additional ring resonators and splitters to the system.

3. ASK Modulation using all-optical switching

In order to demonstrate the operation of the ASK modulation scheme at ~Gbps data rates, we used an all-optical modulation scheme similar to those previously demonstrated [12].

A detailed schematic of the pump-probe all-optical modulation set-up is shown in Fig. 7 . The pump source is a mode-locked Ti-sapphire laser generating 100 fs pulses centered at 810 nm with an 80 MHz repetition rate. A β-barium borate crystal is used to generate second harmonic pulses centered at 405 nm. A beam-splitter and a pair of fiber collimators are used to couple the 405 nm pulses into a pair of optical fibers. The second harmonic pulses are absorbed by the silicon waveguides and generate photoexcited carriers. These photo-excited carriers change the effective index of the ring resonators which shifts the resonances [9]. We should note in this experiment, we used an identical crystalline-silicon device. The probe signal obtained from a tunable continuous wave laser using a tapered lens fiber passes through a polarization controller and is coupled on and off the silicon chip using adiabatic inverse tapers [13]. The output from the chip is detected using a 20 GHz photodetector and sampling oscilloscope.

 figure: Fig. 7

Fig. 7 Measurement set-up to generate all-optically modulated ASK signals. The two pump pulses are delayed by 200 ps to enable the demonstration of three switching levels. PC: Polarization Controller

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To achieve the modulation, we initially operate the system with the probe signal slightly off-resonance as indicated in Fig. 8(a) . The system does not transmit in this state which corresponds to the first logic level of the system. The system is modulated to the next logic level by switching one ring resonator on resonance using a pump pulse, which causes the transmission of the system to rise to half its maximum, corresponding to the second logic level. However, before the carriers can completely recombine, the second ring resonator is switched on-resonance after a delay of ~200 picoseconds. This results in the maximum transmission of the system corresponding to the third logic level as indicated in Fig. 8(b). The switching speed of the system is limited by the free-carrier recombination lifetime which can be improved by incorporating p-i-n diodes to sweep out the carriers, thereby improving the data-rate of the overall system [14].

 figure: Fig. 8

Fig. 8 (a). The resonances of the individual resonators and through port of the entire system. Here we use a probe wavelength that is slightly blue-shifted off-resonance. (b) Three level temporal response of the system by switching two ring resonators with a 200 ps delay.

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4. Conclusion

In summary, we have demonstrated generation of three-level amplitude-shift-keying optical signals (ASK) using a pair of silicon microring resonators using thermal and all-optical modulation. This scheme can also be implemented using electro-optic modulators recently demonstrated by others [1,3]. This would enable an increase in the spectral efficiency of single optical carriers in an on-chip optical communication link. However, drawbacks of ASK are that the number of levels that can be utilized is limited by the signal/noise ratio of the optical link and the amplitude levels need to be discriminated at the receiver. We believe that with the recent implementation of on-chip transceivers and low loss waveguides, the integration of the necessary circuitry with sufficient S/N is possible for at least a three-level ASK format [1,15,16].

Acknowledgements

This work is supported in part by the NSF under grant ECCS-0903448 and by the Semiconductor Research Corporation under contract SRC-2009-HJ-2000. The work was also partially supported by NSF grant ECCS-0824103. This work was performed in part at the Cornell Nanoscale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECS – 0335765).

References and links

1. L. Chen, K. Preston, S. Manipatruni, and M. Lipson, “Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors,” Opt. Express 17(17), 15248–15256 (2009). [CrossRef]   [PubMed]  

2. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008). [CrossRef]   [PubMed]  

3. 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(6), 3140–3148 (2007). [CrossRef]   [PubMed]  

4. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007). [CrossRef]   [PubMed]  

5. P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006). [CrossRef]  

6. L. Zhou, H. Chen, and A. W. Poon, “On-Chip NRZ-to-PRZ Format Conversion Using Narrow-Band Silicon Microring Resonator-Based Notch Filters,” J. Lightwave Technol. 26(13), 1950–1955 (2008). [CrossRef]  

7. L. Zhang, Y. Li, J. Yang, R. G. Beausoleil, and A. E. Willner, “Creating RZ Data Modulation Formats Using Parallel Silicon Microring Modulators for Pulse Carving in DPSK,” in C (Optical Society of America, 2008), paper CWN4.

8. R. Ramaswami, and K. N. Sivarajan, Optical Networks: A Practical Perspective, (Morgan Kaufmann, 2002)

9. Q. Xu, “Controlling the flow of light on chip with microring- resonator-based silicon photonic devices,” (PhD Thesis, Cornell University 2007)

10. N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008). [CrossRef]   [PubMed]  

11. F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001). [CrossRef]  

12. 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]  

13. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef]   [PubMed]  

14. 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]  

15. P. J. Winzer, and R. J. Essiambre, “Receivers for advanced optical modulation formats,” in Lasers and Electro-Optics Society, 2003. LEOS 2003. The 16th Annual Meeting of the IEEE, 27–28 Oct. 2003.

16. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009). [CrossRef]   [PubMed]  

References

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  1. L. Chen, K. Preston, S. Manipatruni, and M. Lipson, “Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors,” Opt. Express 17(17), 15248–15256 (2009).
    [Crossref] [PubMed]
  2. Q. Xu, D. Fattal, and R. G. Beausoleil, “Silicon microring resonators with 1.5-microm radius,” Opt. Express 16(6), 4309–4315 (2008).
    [Crossref] [PubMed]
  3. 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(6), 3140–3148 (2007).
    [Crossref] [PubMed]
  4. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15(2), 660–668 (2007).
    [Crossref] [PubMed]
  5. P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
    [Crossref]
  6. L. Zhou, H. Chen, and A. W. Poon, “On-Chip NRZ-to-PRZ Format Conversion Using Narrow-Band Silicon Microring Resonator-Based Notch Filters,” J. Lightwave Technol. 26(13), 1950–1955 (2008).
    [Crossref]
  7. L. Zhang, Y. Li, J. Yang, R. G. Beausoleil, and A. E. Willner, “Creating RZ Data Modulation Formats Using Parallel Silicon Microring Modulators for Pulse Carving in DPSK,” in C (Optical Society of America, 2008), paper CWN4.
  8. R. Ramaswami, and K. N. Sivarajan, Optical Networks: A Practical Perspective, (Morgan Kaufmann, 2002)
  9. Q. Xu, “Controlling the flow of light on chip with microring- resonator-based silicon photonic devices,” (PhD Thesis, Cornell University 2007)
  10. N. Sherwood-Droz, H. Wang, L. Chen, B. G. Lee, A. Biberman, K. Bergman, and M. Lipson, “Optical 4x4 hitless slicon router for optical networks-on-chip (NoC),” Opt. Express 16(20), 15915–15922 (2008).
    [Crossref] [PubMed]
  11. F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
    [Crossref]
  12. 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]
  13. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
    [Crossref] [PubMed]
  14. 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]
  15. P. J. Winzer, and R. J. Essiambre, “Receivers for advanced optical modulation formats,” in Lasers and Electro-Optics Society, 2003. LEOS 2003. The 16th Annual Meeting of the IEEE, 27–28 Oct. 2003.
  16. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
    [Crossref] [PubMed]

2009 (2)

2008 (3)

2007 (2)

2006 (1)

P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

2005 (1)

2004 (1)

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]

2003 (1)

2001 (1)

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Almeida, V. R.

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]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[Crossref] [PubMed]

Barrios, C. A.

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]

Beausoleil, R. G.

Bergman, K.

Biberman, A.

Cardenas, J.

Chen, H.

Chen, L.

Chetrit, Y.

Ciftcioglu, B.

Della Corte, F.

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Essiambre, R. J.

P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

Fattal, D.

Izhaky, N.

Lee, B. G.

Liao, L.

Lipson, M.

Liu, A.

Manipatruni, S.

Montefusco, M.

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Moretti, L.

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Nguyen, H.

Panepucci, R. R.

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]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[Crossref] [PubMed]

Paniccia, M.

Poitras, C. B.

Poon, A. W.

Preble, S. F.

Preston, K.

Rendina, I.

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Robinson, J. T.

Rubin, D.

Rubino, A.

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

Schmidt, B.

Schmidt, B. S.

Shakya, J.

Sherwood-Droz, N.

Wang, H.

Winzer, P. J.

P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

Xu, Q.

Zhou, L.

Appl. Phys. Lett. (1)

F. Della Corte, M. Montefusco, L. Moretti, I. Rendina, and A. Rubino, “Study of the thermo-optic effect in hydrogenated amorphous silicon and hydrogenated amorphous silicon carbide between 300 and 500 K at 1.55 um,” Appl. Phys. Lett. 79(2), 168–170 (2001).
[Crossref]

J. Lightwave Technol. (1)

Nature (1)

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]

Opt. Express (6)

Opt. Lett. (2)

Proc. IEEE (1)

P. J. Winzer and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006).
[Crossref]

Other (4)

L. Zhang, Y. Li, J. Yang, R. G. Beausoleil, and A. E. Willner, “Creating RZ Data Modulation Formats Using Parallel Silicon Microring Modulators for Pulse Carving in DPSK,” in C (Optical Society of America, 2008), paper CWN4.

R. Ramaswami, and K. N. Sivarajan, Optical Networks: A Practical Perspective, (Morgan Kaufmann, 2002)

Q. Xu, “Controlling the flow of light on chip with microring- resonator-based silicon photonic devices,” (PhD Thesis, Cornell University 2007)

P. J. Winzer, and R. J. Essiambre, “Receivers for advanced optical modulation formats,” in Lasers and Electro-Optics Society, 2003. LEOS 2003. The 16th Annual Meeting of the IEEE, 27–28 Oct. 2003.

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Figures (8)

Fig. 1
Fig. 1 The principle of operation of the device is illustrated - (a) two unmodulated ring resonators result in amplitude level 1. (b) Modulating one ring (blue) resonator independently results in amplitude level 2 and (c) modulating both ring resonators results in amplitude level 3.
Fig. 2
Fig. 2 Process flow in the fabrication of a-Si:H microring resonators with resistive heaters
Fig. 3
Fig. 3 (a) SEM image of the fabricated device. (b) Optical microscope image of the device with heaters
Fig. 4
Fig. 4 Experimental set-up to measure simultaneous thermootpic switching of two ring resonators. The two rings are switched individually using the thermo-optic effect by applying square wave electrical pulses at 100 Hz to produce modulated signal observed on an oscilloscope.
Fig. 5
Fig. 5 Thermal tuning of resonant wavelengths is achieved by applying heat to the individual rings.
Fig. 6
Fig. 6 (a). Temporal response of the system due to the modulation of one resonator. The other resonator is always on resonance. (b) Modulating both resonators generates three amplitude levels on a single carrier.
Fig. 7
Fig. 7 Measurement set-up to generate all-optically modulated ASK signals. The two pump pulses are delayed by 200 ps to enable the demonstration of three switching levels. PC: Polarization Controller
Fig. 8
Fig. 8 (a). The resonances of the individual resonators and through port of the entire system. Here we use a probe wavelength that is slightly blue-shifted off-resonance. (b) Three level temporal response of the system by switching two ring resonators with a 200 ps delay.

Equations (2)

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T d r o p = e 2 γ κ 1 2 κ 2 2 ( 1 t 1 t 2 e γ ) 2 + 4 t 1 t 2 e γ sin 2 [ θ ]
T = m = 1 N u T d r o p m N

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