OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2996–3012
« Show journal navigation

XOR and XNOR operations at 12.5 Gb/s using cascaded carrier-depletion microring resonators

Lin Yang, Lei Zhang, Chunming Guo, and Jianfeng Ding  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2996-3012 (2014)
http://dx.doi.org/10.1364/OE.22.002996


View Full Text Article

Acrobat PDF (6239 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report the implementation of the XOR and XNOR logical operations using an electro-optic circuit, which is fabricated by CMOS-compatible process in the silicon-on-insulator (SOI) platform. The circuit consists of two cascaded add-drop microring resonators (MRRs), which are modulated through electric-field-induced carrier depletion in reverse biased pn junctions embedded in the ring waveguides. The resonance wavelength mismatch between the two nominally identical MRRs caused by fabrication errors is compensated by thermal tuning. Simultaneous bitwise XOR and XNOR operations of the two electrical modulating signals at the speed of 12.5 Gb/s are demonstrated. And 20 Gb/s XOR operation at one output port of the circuit is achieved. We explain the phenomena that one half of the resonance regions of the device are much more sensitive to the round-trip phase shift in the ring waveguides than the other half resonance regions. Characteristic graphs with logarithmic phase coordinate are proposed to analyze the sensitivity of the demonstrated circuit, as well as several typical integrated optical structures. It is found that our circuit with arbitrary chosen parameters has similar sensitivity to MRRs under the critical coupling.

© 2014 Optical Society of America

1. Introduction

Exclusive or (XOR) is a logical operation that outputs true whenever its two inputs differ with each other. The opposite of XOR is exclusive nor (XNOR), which outputs true whenever both inputs are the same. Such two logical operations are indispensable in digital communication and computing. The XOR operation can be employed in many occasions such as label processing [1

1. T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,” IEEE Photon. Technol. Lett. 13(7), 750–752 (2001). [CrossRef]

, 2

2. R. Clavero, J. M. Martínez, F. Ramos, and J. Martí, “All-optical packet routing scheme for optical label-swapping networks,” Opt. Express 12(18), 4326–4332 (2004). [CrossRef] [PubMed]

], parity checking [3

3. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity checker with bit-differential delay,” Opt. Commun. 162(1-3), 37–43 (1999). [CrossRef]

, 4

4. J. K. Rakshit, J. N. Roy, and T. Chattopadhyay, “Design of micro-ring resonator based all-optical parity generator and checker circuit,” Opt. Commun. 303, 30–37 (2013). [CrossRef]

], data encryption [5

5. M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. 34(9), 1315–1317 (2009). [CrossRef] [PubMed]

, 6

6. S. H. Jeon and S. K. Gil, “Optical implementation of triple DES algorithm based on dual XOR logic operations,” J. Opt. Soc. Korea 17(5), 362–370 (2013). [CrossRef]

], and pseudorandom number generation [7

7. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008). [CrossRef]

, 8

8. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010). [CrossRef]

]. With the aim of eliminating the optical-electronic-optical (OEO) conversion in optical communication system, all-optical XOR and XNOR logical operations attract most attentions [9

9. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). [CrossRef]

21

21. B. J. Eggleton, T. D. Vo, R. Pant, J. Schr, M. D. Pelusi, D. Yong Choi, S. J. Madden, and B. Luther-Davies, “Photonic chip based ultrafast optical processing based on high nonlinearity dispersion engineered chalcogenide waveguides,” Laser Photon. Rev. 6(1), 97–114 (2012). [CrossRef]

]. The semiconductor optical amplifier (SOA) is the most widely employed element to achieve these two operations [9

9. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). [CrossRef]

12

12. I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, N. Dutta, A. Piccirilli, J. Jaques, and C. R. Giles, “All-optical XOR and XNOR operations at86.4 Gb/s using a pair of semiconductor optical amplifier Mach-Zehnder interferometers,” Opt. Express 17(21), 19062–19066 (2009). [CrossRef] [PubMed]

]. The nonlinear behavior that is a drawback for the SOA as a linear amplifier makes it a good choice for an optically controlled optical gate [9

9. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). [CrossRef]

]. Other components that can be used to implement all-optical XOR and XNOR logic gates are periodically poled lithium niobate (PPLN) waveguide [13

13. C. Langrock, S. Kumar, J. E. McGeehan, A. E. Willner, and M. M. Fejer, “All-optical signal processing using χ(2) nonlinearities in guided-wave devices,” J. Lightwave Technol. 24(7), 2579–2592 (2006). [CrossRef]

15

15. A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. 35(23), 3955–3957 (2010). [CrossRef] [PubMed]

], highly nonlinear fiber (HNLF) [16

16. C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, and A. W. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. 17(6), 1232–1234 (2005). [CrossRef]

, 17

17. J. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multi-logic gate (XOR, AND, and OR) based on cross phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett. 22(16), 1199–1201 (2010). [CrossRef]

], silicon waveguides [18

18. F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011). [CrossRef] [PubMed]

, 19

19. C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express 19(21), 20681–20690 (2011). [CrossRef] [PubMed]

], and chalcogenide planar waveguide [20

20. T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett. 36(5), 710–712 (2011). [CrossRef] [PubMed]

, 21

21. B. J. Eggleton, T. D. Vo, R. Pant, J. Schr, M. D. Pelusi, D. Yong Choi, S. J. Madden, and B. Luther-Davies, “Photonic chip based ultrafast optical processing based on high nonlinearity dispersion engineered chalcogenide waveguides,” Laser Photon. Rev. 6(1), 97–114 (2012). [CrossRef]

].

From the development process of optical XOR and XNOR gates, it can be found that there is a general trend to achieve such functions in a more compact manner with low power consumption. Although there is a long history of pursuing all-optical information processing, there is a common view that electrical systems are adept in precise control and optical systems have an overwhelming advantage in massive information transfer. It is straightforward to come up with the idea that it may bring benefits to combine them together to do signal processing functions. In 2007, Hardy and Shamir proposed a logic paradigm called directed logic, which takes advantage of the propagation of light to carry out Boolean functions [22

22. J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007). [CrossRef] [PubMed]

]. As an original proposal, they did not specify which scheme to be employed to control the propagation of light. By taking advantage of the high refractive index contrast between silicon and silicon dioxide—and using silicon-on-insulator (SOI) wafers similar to those employed for advanced transistors—engineers can now construct micrometer-scale integrated optical circuits with complex functions and ultra-low power consumptions [23

23. M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A. E.-J. Lim, P. Guo-Qiang Lo, T. Baehr-Jones, and M. Hochberg, “The road to affordable, large-scale silicon photonics,” Opt. Photon. News 24(9), 32–39 (2013). [CrossRef]

]. The benefits that the SOI platform can offer us are silicon waveguides with small dimensions, low losses, high optical mode confinement, as well as the possibility of integrated with electrical controlling modules to form a highly integrated and complex system. Such a prospect will probably make traditional optical systems acquire a completely new outlook.

Since it is convenient to integrated electrical controlling parts with optical waveguides in the SOI platform, several prototype directed-logic devices have been proposed and demonstrated using silicon photonic devices [24

24. L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35(10), 1620–1622 (2010). [CrossRef] [PubMed]

28

28. L. Zhang, J. Ding, Y. Tian, R. Ji, L. Yang, H. Chen, P. Zhou, Y. Lu, W. Zhu, and R. Min, “Electro-optic directed logic circuit based on microring resonators for XOR/XNOR operations,” Opt. Express 20(11), 11605–11614 (2012). [CrossRef] [PubMed]

]. In all the demonstrations by far, microring resonators (MRRs) are employed to construct optical switches, which have tiny volume and high sensitivity to the phase vibration due to the multiple-beam interference mechanism in MRRs. Thermo-optic effect and electro-optic effect have been used to modulate the MRR-based optical switches. The thermo-optic effect has high tuning efficiency but low response time [24

24. L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35(10), 1620–1622 (2010). [CrossRef] [PubMed]

, 25

25. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef] [PubMed]

]. Thermal tuning is also adopted in electro-optic modulating circuits to compensate the fabrication errors. Up to now, only electric-field-induced carrier injection is adopted to construct directed logic circuits, which can just achieve several hundred Mb/s operations [26

26. C. Y. Qiu, X. Ye, R. Soref, L. Yang, and Q. F. Xu, “Demonstration of reconfigurable electro-optical logic with silicon photonic integrated circuits,” Opt. Lett. 37(19), 3942–3944 (2012). [CrossRef] [PubMed]

28

28. L. Zhang, J. Ding, Y. Tian, R. Ji, L. Yang, H. Chen, P. Zhou, Y. Lu, W. Zhu, and R. Min, “Electro-optic directed logic circuit based on microring resonators for XOR/XNOR operations,” Opt. Express 20(11), 11605–11614 (2012). [CrossRef] [PubMed]

]. Here in this paper, we report the demonstration of carrier-depletion directed logic circuit with the XOR and XNOR functions. Simultaneous bitwise XOR and XNOR operations at two output ports of the circuit with the speed of 12.5 Gb/s are demonstrated. And 20 Gb/s XOR operation at one output port of the circuit is achieved. We explain the phenomena that one half of the resonance regions of the device are much more sensitive to the round-trip phase shift in the ring waveguides than the other half resonance regions. Characteristic graphs with logarithmic phase coordinate are proposed to analyze the sensitivity of the demonstrated circuit, as well as several typical integrated optical structures.

It should be pointed out that the SOI platform not only offer us the convenience in integrating electrical controlling modules and optical waveguides, but also provide the possibility of achieving all-optical directed logic circuits with high efficiency and small volume due to the high optical mode confinement in silicon waveguides. We think that both the electro-optic and all-optic schemes have their own niche applications [29

29. R. Soref, “Reconfigurable integrated optoelectronics,” Adv. Optoelectron. 2011, 627802 (2011). [CrossRef]

, 30

30. Q. F. Xu and R. A. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19(6), 5244–5259 (2011). [CrossRef] [PubMed]

]. And the future work should focus on the implementation of directed logic circuits with more complex and more reconfigurable functions.

2. Design and fabrication

The schematic of the XOR/XNOR directed logic circuit based on two cascaded carrier-depletion MRRs is shown in Fig. 1 (a)
Fig. 1 (a) Schematic and (b) micrograph of the XOR/XNOR directed logic circuit based on two cascaded carrier-depletion microring resonators (CW: continuous wave, MRR: microring resonator, EPT: electrical pulse train, OPT: optical pulse train).
. The four ports of each MRR are denoted as input, through, add and drop according to their functions. Monochromatic light with the wavelength of λ coupled into the input and add ports will be directed to the through and drop ports (i.e. bypass the MRR), respectively, when the MRR is off-resonance at λ. And if the MRR is on-resonance at λ, light coupled into the input and add ports will be guided to the drop and through ports, respectively. The resonance status of each MRR is controlled by an electrical signal X and Y, respectively.

It can be noted in Fig. 1 that there are two arched segments in the waveguides connecting the four coupling areas of the two MRRs. Such two arched waveguides are designed on purpose to adjust the length difference between the two arms connecting the two MRRs, which has a remarkable impact on the response spectra of the device [25

25. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef] [PubMed]

]. We will discuss its impact in detail later in this paper.

The device is fabricated on an 8 in. (20.3 cm) silicon-on-insulator (SOI) wafer with 220-nm-thick top silicon and 2-μm-thick buried oxide layer. Rib waveguides with a height of 220 nm, a width of 400 nm and a slab thickness of 70 nm are used to construct the circuit, which only supports quasi-TE fundamental mode. The gaps between ring and straight waveguides are chosen to be 400 nm to achieve a balance between the extinction ratios of the drop and through ports of each MRR. The radii of the ring waveguides are both 10 μm. An elliptical structure (long axis = 6.25 μm, and short axis = 1.5 μm) is adopted to reduce the scattering at the crossing of the waveguides. 248-nm deep ultraviolet (UV) photolithography is used to define the device pattern. Inductively coupled plasma etching process is used to etch the top Si layer (Fig. 2 (a) and (b)
Fig. 2 Process flow of the device: (a) and (b) etching of the top Si layer by 150 nm and 70 nm, respectively, (c) and (d) p- and n-doping and through boron and phosphorus implantation, (e) and (f) p+- and n+-doping and through boron and phosphorus implantation, (g) deposition and etching of the TiN layer to form the microheater, (h) and (i) etching of the SiO2 layer to form the via holes to the PN diodes and microheaters, (j) deposition and etching of the Al layer to form the wires and pads, (k) deep etching to form the end-face of the spot size converters.
). Spot size converters (SSCs) are integrated on the input and output terminals of the waveguides to enhance the coupling between the waveguides and the fibers. The SSC is a 200-µm-long linearly inversed taper with 180-nm-wide tip.

After the waveguide is etched, two PN diodes are formed in the two ring waveguides. The p-type doping concentration is 1 × 1018/cm3 and the n-type doping concentration is 8 × 1017/cm3 (Fig. 2 (c) and (d)). The PN junction is designed to be an abrupt junction and the peak doping concentration for both p- and n-doping regions locates at the center of the rib waveguide in the vertical direction. In the lateral direction, the PN junction is right to the center of the rib waveguide with the offset of 40 nm. In other words, 220nm of the total width of 400 nm is p-doped, and the other 180 nm is n-doped. Such a doping profile makes the p-type depletion region have the maximum overlap with the optical mode in the ridge waveguide since the p-type carrier has a modulation effect around three times larger than the n-type carrier at such a doping concentration level [31

31. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, R. Min, and M. Yu, “Ultra-low-power carrier-depletion Mach-Zehnder silicon optical modulator,” Opt. Express 20(7), 7081–7087 (2012). [CrossRef] [PubMed]

]. Next, the anode (boron, p+ ~5.5 × 1020/cm3) and cathode (phosphorus, n+ ~5.5 × 1020/cm3) implants are formed (Fig. 2 (e) and (f)).

After the doping, a 1500-nm-thick silica layer is deposited on the Si layer as the separate layer (SL) by plasma enhanced chemical vapor deposition (PECVD). Then a 150-nm-thick titanium nitride (TiN) layer is sputtered on the SL and two microheaters are fabricated by deep UV photolithography and dry etching (Fig. 2(g)) [28

28. L. Zhang, J. Ding, Y. Tian, R. Ji, L. Yang, H. Chen, P. Zhou, Y. Lu, W. Zhu, and R. Min, “Electro-optic directed logic circuit based on microring resonators for XOR/XNOR operations,” Opt. Express 20(11), 11605–11614 (2012). [CrossRef] [PubMed]

]. Another silica layer of 300 nm is deposited by PECVD on the TiN heaters. Via holes to the PN diodes and microheaters are etched on the silica layer in two steps (Fig. 2 (h) and (i)). Then a 1000-nm-thick aluminum layer is sputtered and etched to be wires and pads connected to the microheaters and PN diodes (Fig. 2 (j)). Finally, the end-face of the SSC is exposed by a 110-µm-deep etching process as the world-to-chip interface (Fig. 2 (k)). The micrograph of the device is shown in Fig. 1(b). The 200-µm-long SSCs are not included in this micrograph. The two square pads located at the lower-left and lower-right of the micrograph have side lengths of 100 µm. The effective area of the device including the SSCs is about 1.4 × 0.4 mm2.

3. Experimental results

Broadband light from an amplified spontaneous emission (ASE) source is coupled into the device through a lensed fiber. The output light is collected by another lensed fiber and fed into the optical spectrum analyzer (OSA). A tunable voltage source is used to drive the microheater above the MRR with shorter resonance wavelength to make it resonate at the same wavelengths as the other MRR.

The response spectra at the two output ports of the device are shown in Fig. 3
Fig. 3 Response spectra obtained at the through and drop ports of the fabricated device with MRR1 being tuned by a heating voltage of 2.04 V to make it resonate at the same wavelength as MRR2 at the third resonance region.
, with MRR1 being tuned by a heating voltage of 2.04 V to align the resonance wavelengths of the two MRRs. As the two arms connecting the two MRRs have the same lengths, the first and the third resonance regions in Fig. 3 are degenerate, which has been shown and explained in [25

25. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef] [PubMed]

]. The spectra of the through ports at these two degenerate resonant regions should be flat due to the constructive interference between two light beams from two different paths [25

25. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef] [PubMed]

]. Shallow dips still appear at these two regions due to the difference of the two nominally identical connecting arms and MRRs caused by fabrication errors. The thermal tuning just aligns the resonance wavelengths of the two MRRs, their line shapes may still differ from each other.

3.1 Static characterization

The characterization of the static response spectra of the devices consists of two parts. Firstly, we characterize each MRR’s electro-optical response under different reverse biases. Since the two MRRs have similar resonance wavelengths, we tune MRR1 to resonate far away from MRR2 through heating. And then the responses at the through and drop ports of the device are recorded when different reverse biases from 0 V to 8 V are applied to both MRRs. The results in Fig. 4
Fig. 4 Spectra obtained at (a, b) the through port and (c, d) the drop port of the device. The left two figures are the responses of MRR1, which is thermally tuned to be resonant around 1552.4 nm. The right two figures are the responses of MRR2, which is resonant around 1550.6 nm.
show that the two MRRs have similar electro-optical response. The loaded quality factors (Q factors) of a single MRR at the through and drop ports are about 15,000 and 12,000, respectively. The shifts of the resonance wavelength are about 50 pm and 60 pm, respectively, when the reverse biases applied to the MRR are 4 V and 8 V.

Secondly, the static working statuses of the device are validated. The working wavelength is determined from the spectra when neither of the two MRRs is actuated (Fig. 3). The response spectra around the third resonance region in Fig. 3 are shown in detail in Fig. 5
Fig. 5 Response spectra obtained at (a-d) the through port and (e-h) the drop port of the device. Voltages applied to the two PN diodes are both 0 V in (a) and (e), 4 V and 0 V in (b) and (f), 0 V and 4 V in (c) and (g), and both 4 V in (d) and (h). The dashed arrow indicates the location of the working wavelength. In all cases, MRR1 has a heating voltage of 2.04 V.
. According to the aforementioned principle, a maximum (representing a ‘1’) and a minimum (representing a ‘0’) should be obtained at the through port and the drop port, respectively, when the two applied electrical signals are both at high level (0 V, representing ‘1s’). We choose 1550.64 nm as the working wavelength (Fig. 5 (a) and (e)). As shown in Fig. 5 (a-d), a maximum is obtained at the through port when the two applied electrical signals are both at low levels or high levels, and a minimum is obtained otherwise. As shown in Fig. 5 (e-h), a minimum is obtained at the drop port when the two applied electrical signals are both at low levels or high levels, and a maximum is obtained otherwise. Therefore, the XNOR and XOR operations are performed correctly at the through and drop ports of the device, respectively.

3.2 Dynamic operation

A monochromatic light at 1550.64 nm from a tunable laser is coupled into the device. Two user-defined non-return-to-zero (NRZ) signals with a period of 8 bits at the speed from 1 Gb/s to 20 Gb/s are applied to the two MRRs simultaneously. The two output optical signals are fed into a wideband sampling oscilloscope (Agilent DCA-X 860100D), which has 65 GHz optical and 80 GHz electrical plug-in modules. Since the oscilloscope has only one electrical port and one optical port, the two electrical signals applied to the two MRRs are measured separately, as well as the two output optical signals. The patterns of the two high-speed electrical signals are ‘00100101’ and ‘01001111’, respectively. Their XOR and XNOR operation results should be ‘01101010’ and ‘10010101’, respectively. Typical experimental results when the operation speed is 5Gb/s are shown in Fig. 6
Fig. 6 Typical experimental results when two 5 Gb/s electrical signals are applied to the two MRRs. (a) Signals applied to MRR1 with the repeated pattern of ‘00100101’. (b) Signals applied to MRR2 with the repeated pattern of ‘01001111’. (c) XOR operation result with the repeated pattern of ‘01101010’ at the drop port. (d) XNOR operation result with the repeated pattern of ‘10010101’at the through port.
, in which the patterns of the applied electrical signals and the output optical signals are marked. These waveforms are not aligned with each other at the time axis since they are measured one by one. It can be found from Fig. 6 (c) and (d) that the two logic operations are carried out correctly at the drop and through ports simultaneously.

It should be pointed out that the optical power of the monochromatic light from the tunable laser is about 3 dBm. After the coupling between the lensed fiber and the spot size converter, light injected to the silicon waveguide is about 0 dBm. Such a power level is too low to excite the nonlinear processes in the silicon waveguide, even with the enhancement of optical power in the ring cavity.

4. Discussion

4.1 Sensitivity analysis of the XOR/XNOR directed logic circuit

We will only analyze the behavior of the spectrum at the drop port. The sensitivity of the spectrum at the through port can be calculated in the same way. As a linear system, the circuit obeys the superposition principle. The output at the drop port (Ep3) can be decomposed into two parts. The first part comes from Ep1, which contribute to Ep3 via the drop function of MRR2. The second part comes from Ev1, which contribute to Ep3 via the through function of MRR2. So the expression of the electric field Ep3 can be written as follows.

Edrop=Ep3=t·(1α·exp(j·θ1))1α·t2·exp(j·θ1)×k2·α3/4·exp(j·3/4·θ2)1α·t2·exp(j·θ2)×exp(j·θs1)+k2·α1/4·exp(j·1/4·θ1)1α·t2·exp(j·θ1)×t·(1α·exp(j·θ2))1α·t2·exp(j·θ2)×exp(j·θs2)
(1)

Hear we do not consider the loss caused by the two connecting waveguides. The phase difference between the two terms of Eq. (1) is

Δφp3=arctan[α·sin(θ1)1α·cos(θ1)]arctan[α·sin(θ2)1α·cos(θ2)]+[34·θ214·θ1]+[θs2θs1]
(2)

When the two nominally identical MRRs are tuned to be resonant at the same wavelengths, θ1 equals to θ2, which means that the first two terms in Eq. (2) disappear. At the resonance wavelengths, we let θ1 and θ2 equal to 2, where the integer m is the resonance order. Since θ1, θ2, θs1 and θs2 are all proportional to their own waveguide length, θs1 and θs2 are proportional to θ1 and θ2. The proportionality factors are the ratio between the lengths of the connecting waveguides and the ring waveguides. We suppose that θs1θs2 are pmπ, where p is a real number. Then Eq. (2) can be simplified to

Δφp3=m×(p+1)×π
(3)

If p is an even number, the parity of the resonance order m will greatly affect the spectrum. If m is odd, Eq. (3) equals to π, the two constituent parts of Ep3 will interfere destructively with each other. Since the two terms in Eq. (1) have similar amplitudes, the destructive interference will produce trivial response, which is shown in the first and third resonance regions in Fig. 3. The small peak in the first resonance region is caused by small dissimilarity between the two MRRs, as well as the two connecting waveguides. If m is even, Eq. (3) equals to 0, the two constituent parts of Ep3 will interfere constructively with each other. The addition of the two terms in Eq. (1) will produce what we see in the second and fourth resonance regions in Fig. 3.

Since the two connecting waveguides in our device have the same length, the value of p is zero. So, half of the resonance regions are degenerate, and the other half are non-degenerate. We find from the static response spectra under different reverse biases (see Fig. 9
Fig. 9 The response spectra at the drop port under different reverse biases. (a) The second resonance region (non-degenerate). (b) The third resonance region (degenerate). The legends in the figures show the reverse voltages applied to MRR1 and MRR2, respectively.
) that only the degenerate resonance regions can be employed to achieve the XOR and XNOR operations. In other words, the degenerate resonance regions are much more sensitive to the tuning of the MRR than the non-degenerate regions. This is because at these regions, the two constituent parts interfere destructively with each other. When θ1 = θ2 = 2, the drop port will nominally output nothing at the degenerate resonance region’s center wavelength. And when any of θ1 or θ2 has a little variation, the balance will be broken. The misalignment of the two MRRs’ resonance wavelengths will produce a drastic increase of the output optical power. From Eq. (1), we can readily obtain the relation between the output optical power and the round-trip phase shifts in the MRRs. The results are presented in Fig. 10
Fig. 10 The sensitivities of the output at the drop port with different parity of the resonance order. (a) The resonance order m = 98, and p = 0. (b) The resonance order m = 99, and p = 0.
, where the round-trip amplitude transmission factor α and the cross-coupling coefficient k are taken to be 0.9856 (corresponding to an attenuation factor of 20 dB/cm in the ring waveguides) and 0.2 (t = 0.9798), respectively. The effective refractive index of the quasi-TE mode in typical sub-micron silicon waveguides is about 2.4 [32

32. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

]. Since the radii of the MRRs are 10 μm, the resonance order is calculated as 2πRneff/λ, which is about 100 around 1550 nm. We choose the resonance order to be 98 and 99 in Fig. 10 to show the impact of its parity on the sensitivity of the drop port’s output to the MRRs’ round-trip phase shift. In the calculations, we let θs1 = θs2 (p = 0). Figure 10 show that the sensitivity is much higher at the resonance point when the resonance order m is odd. When p is an odd integer, all the resonance regions have the sensitivities like that shown in Fig. 10(a), regardless of the parity of m.

As we have presented hereinbefore, the resonance wavelength change is about 50 pm when a reverse bias of 4 V is applied (see Fig. 4). And the free spectral range (FSR) of the MRR is about 10 nm. The round-trip phase shift is calculated to be about 0.01π. In consideration of that the device is much more sensitive around the resonance wavelength, we redraw Fig. 10 near the resonance point in Fig. 11
Fig. 11 The sensitivities of the output at the drop port with different parity of the resonance order. (a) The resonance order m = 98, and p = 0. (b) The resonance order m = 99, and p = 0. In the calculation, the cross-coupling coefficient k and the attenuation factor α are 0.2 and 20 dB/cm, respectively.
employing logarithmic coordinates in both the horizontal and vertical axes. In Fig. 11, we fix the value of θ2 to be 2, only considering the change of the output with the variation of the value of θ1. We can find from Fig. 11 that the roll-up factor of the output when m is odd is about 20 dB/decade. In the above calculations, the cross-coupling coefficient and the attenuation factor equal to 0.2 and 20 dB/cm, respectively. We can get the same roll-up factor of 20 dB/decade with other combinations of these two parameters (e.g. k = 0.3, attenuation factor = 10 dB/cm). The lower the attenuation factor is, the higher the degree of linearity the sensitivity graph shows. As shown in Fig. 11, the sensitivity of the output at the drop port is quite dependent on the parity of the resonance order. The radii of the microring resonators and the dispersion characteristic of the waveguides codetermine the locations of the odd and even resonance orders.

4.2 Sensitivity diagrams of typical photonic structures

4.2.1 All-pass microring resonator

The output of an all-pass MRR with only one access waveguide is [33

33. J. Heebner, R. Grover, and T. Ibrahim, Optical microresonators: theory, fabrication, and applications (Springer-Verlag, London, 2008), Chap. 3.

]

Ethrough=tα·exp(j·θ)1α·t·exp(j·θ)
(4)

All the parameters in Eq. (4) have the same meanings as those in Eq. (1). We can obtain the similar graph as Fig. 11, which is shown in Fig. 12
Fig. 12 Sensitivity diagram of all-pass MRR with the attenuation factor varying from 3 dB/cm to 50 dB/cm. For all the cases, the cross-coupling coefficient k equals to 0.2. Critical coupling condition is met when the attenuation factor equals to 28.22 dB/cm (α = t = 0.9798).
. In the calculations, the attenuation factor in the ring waveguide varies from 3 dB/cm to 50 dB/cm. And the cross-coupling coefficient k has a constant value of 0.2 (t = 0.9798). Critical coupling happens when the attenuation factor equals to 28.22 dB/cm, which makes the amplitude transmission factor α equal to the self-coupling coefficient t. It can be found from Fig. 12 that only a small range around the critical coupling point has a high sensitivity to the variation of the round-trip phase shift. It means that optical modulator based on such structure has to be work around the critical coupling point to make it have high efficiency and high extinction ratio. Compared Fig. 12 with Fig. 11, it can be found that the drop port of the circuit in Fig. 1 has a similar sensitivity to a all-pass MRR under critical coupling condition. Since the attenuation factor in Fig. 11 is arbitrarily chosen, it means that such a high sensitivity of our circuit is not susceptive to the attenuation factor in the ring waveguides. This feature can be used to enhance the sensitivity of bio-sensors based on MRRs [34

34. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

36

36. H. X. Yi, D. S. Citrin, and Z. P. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010). [CrossRef] [PubMed]

].

4.2.2 Add-drop microring resonator

The two outputs of an add-drop MRR with two access waveguides are [33

33. J. Heebner, R. Grover, and T. Ibrahim, Optical microresonators: theory, fabrication, and applications (Springer-Verlag, London, 2008), Chap. 3.

]

Ethrough=t1α·t2exp(j·θ)1α·t1·t2·exp(j·θ);Edrop=α1/2·k1·k2exp(j·θ/2)1α·t1·t2·exp(j·θ).
(5)

For the add-drop MRR with two symmetric coupling regions, critical coupling is approached when the attenuation factor is close to 0. This is because the critical coupling condition for the add-drop MRR is α = t1/t2. So the critical coupling condition can only be met when asymmetric coupling is adopted. We can find from Fig. 13 (a) that the extinction ratio of the through port is increased dramatically when the critical coupling condition is approached.

4.2.3 Mach-Zehnder interferometer

The output of a Mach-Zehnder interferometer (MZI) is

Eout=1/4×(α12+α22+2·α1·α2·cos(Δθ)).
(6)

In the above equation, α1 and α2 are the amplitude transmission factors in the two arms of the MZI. And ∆θ is the phase shift difference between the two arms. Since the MZI does not have an infinite impulse response (IIR) as the MRR, it is much less sensitive to the vibration of the phase shift. We draw its sensitivity graph in linear coordinate in Fig. 15 (a)
Fig. 15 Sensitivity diagrams of MZI in (a) linear coordinate, and (b) logarithmic coordinate. The length of one arm of the MZI is fixed to be 1000 μm, with the length of the other arm varying from 1000 μm to 200 μm with an interval of 200 μm. The legends in the figures show the length differences between the two arms. The attenuation factors in the two arms are both 20 dB/cm. The beam splitting and combining are assumed to be lossless.
, with the same data plot in logarithmic coordinate in Fig. 15 (b) to be compared with the property of MRRs shown in Figs. 13 and 14. The insensitivity of MZI to the phase shift makes the MZI-based optical modulators have much larger volume than MRR-based ones.

5. Conclusion

We implement XOR and XNOR operations using an electro-optic directed logic circuit based on two cascaded microring resonators. Simultaneous bitwise XOR and XNOR operations at 12.5 Gbit/s are demonstrated employing carrier-depletion modulation. And 20 Gbit/s XOR operation is achieved. The phenomenon that only half of the resonance regions can be employed to implement the logical operations is well explained. The graph with logarithmic phase coordinate is proposed to analyze the sensitivity of the spectra of the circuit as well as the sensitivity of typical photonic structures such as the all-pass MRR, the add-drop MRR and the MZI structures. Further efforts should be made to construct large-scale and reconfigurable directed logic circuits, in the electro-optic or all-optical manner.

Acknowledgment

This work has been supported by the National Natural Science Foundation of China (NSFC) under grants 61204061, 61235001, and 61377067 and by the National High Technology Research and Development Program of China under grants 2012AA012202 and 2013AA014203.

References and links

1.

T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,” IEEE Photon. Technol. Lett. 13(7), 750–752 (2001). [CrossRef]

2.

R. Clavero, J. M. Martínez, F. Ramos, and J. Martí, “All-optical packet routing scheme for optical label-swapping networks,” Opt. Express 12(18), 4326–4332 (2004). [CrossRef] [PubMed]

3.

A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity checker with bit-differential delay,” Opt. Commun. 162(1-3), 37–43 (1999). [CrossRef]

4.

J. K. Rakshit, J. N. Roy, and T. Chattopadhyay, “Design of micro-ring resonator based all-optical parity generator and checker circuit,” Opt. Commun. 303, 30–37 (2013). [CrossRef]

5.

M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. 34(9), 1315–1317 (2009). [CrossRef] [PubMed]

6.

S. H. Jeon and S. K. Gil, “Optical implementation of triple DES algorithm based on dual XOR logic operations,” J. Opt. Soc. Korea 17(5), 362–370 (2013). [CrossRef]

7.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2(12), 728–732 (2008). [CrossRef]

8.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4(1), 58–61 (2010). [CrossRef]

9.

K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. 6(6), 1428–1435 (2000). [CrossRef]

10.

N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron. 12(4), 702–707 (2006). [CrossRef]

11.

S. Kumar and A. E. Willner, “Simultaneous four-wave mixing and cross-gain modulation for implementing an all-optical XNOR logic gate using a single SOA,” Opt. Express 14(12), 5092–5097 (2006). [CrossRef] [PubMed]

12.

I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, N. Dutta, A. Piccirilli, J. Jaques, and C. R. Giles, “All-optical XOR and XNOR operations at86.4 Gb/s using a pair of semiconductor optical amplifier Mach-Zehnder interferometers,” Opt. Express 17(21), 19062–19066 (2009). [CrossRef] [PubMed]

13.

C. Langrock, S. Kumar, J. E. McGeehan, A. E. Willner, and M. M. Fejer, “All-optical signal processing using χ(2) nonlinearities in guided-wave devices,” J. Lightwave Technol. 24(7), 2579–2592 (2006). [CrossRef]

14.

J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Ultrafast all-optical three-input Boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate,” Opt. Lett. 33(13), 1419–1421 (2008). [CrossRef] [PubMed]

15.

A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. 35(23), 3955–3957 (2010). [CrossRef] [PubMed]

16.

C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, and A. W. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett. 17(6), 1232–1234 (2005). [CrossRef]

17.

J. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multi-logic gate (XOR, AND, and OR) based on cross phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett. 22(16), 1199–1201 (2010). [CrossRef]

18.

F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express 19(21), 20364–20371 (2011). [CrossRef] [PubMed]

19.

C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express 19(21), 20681–20690 (2011). [CrossRef] [PubMed]

20.

T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett. 36(5), 710–712 (2011). [CrossRef] [PubMed]

21.

B. J. Eggleton, T. D. Vo, R. Pant, J. Schr, M. D. Pelusi, D. Yong Choi, S. J. Madden, and B. Luther-Davies, “Photonic chip based ultrafast optical processing based on high nonlinearity dispersion engineered chalcogenide waveguides,” Laser Photon. Rev. 6(1), 97–114 (2012). [CrossRef]

22.

J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express 15(1), 150–165 (2007). [CrossRef] [PubMed]

23.

M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A. E.-J. Lim, P. Guo-Qiang Lo, T. Baehr-Jones, and M. Hochberg, “The road to affordable, large-scale silicon photonics,” Opt. Photon. News 24(9), 32–39 (2013). [CrossRef]

24.

L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett. 35(10), 1620–1622 (2010). [CrossRef] [PubMed]

25.

L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express 19(7), 6524–6540 (2011). [CrossRef] [PubMed]

26.

C. Y. Qiu, X. Ye, R. Soref, L. Yang, and Q. F. Xu, “Demonstration of reconfigurable electro-optical logic with silicon photonic integrated circuits,” Opt. Lett. 37(19), 3942–3944 (2012). [CrossRef] [PubMed]

27.

Y. Tian, L. Zhang, and L. Yang, “Electro-optic directed AND/NAND logic circuit based on two parallel microring resonators,” Opt. Express 20(15), 16794–16800 (2012). [CrossRef]

28.

L. Zhang, J. Ding, Y. Tian, R. Ji, L. Yang, H. Chen, P. Zhou, Y. Lu, W. Zhu, and R. Min, “Electro-optic directed logic circuit based on microring resonators for XOR/XNOR operations,” Opt. Express 20(11), 11605–11614 (2012). [CrossRef] [PubMed]

29.

R. Soref, “Reconfigurable integrated optoelectronics,” Adv. Optoelectron. 2011, 627802 (2011). [CrossRef]

30.

Q. F. Xu and R. A. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express 19(6), 5244–5259 (2011). [CrossRef] [PubMed]

31.

J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, R. Min, and M. Yu, “Ultra-low-power carrier-depletion Mach-Zehnder silicon optical modulator,” Opt. Express 20(7), 7081–7087 (2012). [CrossRef] [PubMed]

32.

Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett. 29(14), 1626–1628 (2004). [CrossRef] [PubMed]

33.

J. Heebner, R. Grover, and T. Ibrahim, Optical microresonators: theory, fabrication, and applications (Springer-Verlag, London, 2008), Chap. 3.

34.

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007). [CrossRef] [PubMed]

35.

D. X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, “Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding,” Opt. Express 16(19), 15137–15148 (2008). [CrossRef] [PubMed]

36.

H. X. Yi, D. S. Citrin, and Z. P. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010). [CrossRef] [PubMed]

OCIS Codes
(130.3750) Integrated optics : Optical logic devices
(250.5300) Optoelectronics : Photonic integrated circuits
(230.4555) Optical devices : Coupled resonators
(130.4815) Integrated optics : Optical switching devices

ToC Category:
Optics in Computing

History
Original Manuscript: December 13, 2013
Revised Manuscript: January 27, 2014
Manuscript Accepted: January 28, 2014
Published: January 31, 2014

Citation
Lin Yang, Lei Zhang, Chunming Guo, and Jianfeng Ding, "XOR and XNOR operations at 12.5 Gb/s using cascaded carrier-depletion microring resonators," Opt. Express 22, 2996-3012 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2996


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. Fjelde, A. Kloch, D. Wolfson, B. Dagens, A. Coquelin, I. Guillemot, F. Gaborit, F. Poingt, and M. Renaud, “Novel scheme for simple label-swapping employing XOR logic in an integrated interferometric wavelength converter,” IEEE Photon. Technol. Lett.13(7), 750–752 (2001). [CrossRef]
  2. R. Clavero, J. M. Martínez, F. Ramos, and J. Martí, “All-optical packet routing scheme for optical label-swapping networks,” Opt. Express12(18), 4326–4332 (2004). [CrossRef] [PubMed]
  3. A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity checker with bit-differential delay,” Opt. Commun.162(1-3), 37–43 (1999). [CrossRef]
  4. J. K. Rakshit, J. N. Roy, and T. Chattopadhyay, “Design of micro-ring resonator based all-optical parity generator and checker circuit,” Opt. Commun.303, 30–37 (2013). [CrossRef]
  5. M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett.34(9), 1315–1317 (2009). [CrossRef] [PubMed]
  6. S. H. Jeon and S. K. Gil, “Optical implementation of triple DES algorithm based on dual XOR logic operations,” J. Opt. Soc. Korea17(5), 362–370 (2013). [CrossRef]
  7. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008). [CrossRef]
  8. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010). [CrossRef]
  9. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron.6(6), 1428–1435 (2000). [CrossRef]
  10. N. Deng, K. Chan, C. K. Chan, and L. K. Chen, “An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWM in semiconductor optical amplifier,” IEEE J. Sel. Top. Quantum Electron.12(4), 702–707 (2006). [CrossRef]
  11. S. Kumar and A. E. Willner, “Simultaneous four-wave mixing and cross-gain modulation for implementing an all-optical XNOR logic gate using a single SOA,” Opt. Express14(12), 5092–5097 (2006). [CrossRef] [PubMed]
  12. I. Kang, M. Rasras, L. Buhl, M. Dinu, S. Cabot, M. Cappuzzo, L. T. Gomez, Y. F. Chen, S. S. Patel, N. Dutta, A. Piccirilli, J. Jaques, and C. R. Giles, “All-optical XOR and XNOR operations at86.4 Gb/s using a pair of semiconductor optical amplifier Mach-Zehnder interferometers,” Opt. Express17(21), 19062–19066 (2009). [CrossRef] [PubMed]
  13. C. Langrock, S. Kumar, J. E. McGeehan, A. E. Willner, and M. M. Fejer, “All-optical signal processing using χ(2) nonlinearities in guided-wave devices,” J. Lightwave Technol.24(7), 2579–2592 (2006). [CrossRef]
  14. J. Wang, J. Sun, X. Zhang, D. Huang, and M. M. Fejer, “Ultrafast all-optical three-input Boolean XOR operation for differential phase-shift keying signals using periodically poled lithium niobate,” Opt. Lett.33(13), 1419–1421 (2008). [CrossRef] [PubMed]
  15. A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett.35(23), 3955–3957 (2010). [CrossRef] [PubMed]
  16. C. Yu, L. Christen, T. Luo, Y. Wang, Z. Pan, L.-S. Yan, and A. W. Willner, “All-optical XOR gate using polarization rotation in single highly nonlinear fiber,” IEEE Photon. Technol. Lett.17(6), 1232–1234 (2005). [CrossRef]
  17. J. Qiu, K. Sun, M. Rochette, and L. R. Chen, “Reconfigurable all-optical multi-logic gate (XOR, AND, and OR) based on cross phase modulation in a highly nonlinear fiber,” IEEE Photon. Technol. Lett.22(16), 1199–1201 (2010). [CrossRef]
  18. F. Li, T. D. Vo, C. Husko, M. Pelusi, D.-X. Xu, A. Densmore, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical XOR logic gate for 40Gb/s DPSK signals via FWM in a silicon nanowire,” Opt. Express19(21), 20364–20371 (2011). [CrossRef] [PubMed]
  19. C. Husko, T. D. Vo, B. Corcoran, J. Li, T. F. Krauss, and B. J. Eggleton, “Ultracompact all-optical XOR logic gate in a slow-light silicon photonic crystal waveguide,” Opt. Express19(21), 20681–20690 (2011). [CrossRef] [PubMed]
  20. T. D. Vo, R. Pant, M. D. Pelusi, J. Schröder, D.-Y. Choi, S. K. Debbarma, S. J. Madden, B. Luther-Davies, and B. J. Eggleton, “Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals,” Opt. Lett.36(5), 710–712 (2011). [CrossRef] [PubMed]
  21. B. J. Eggleton, T. D. Vo, R. Pant, J. Schr, M. D. Pelusi, D. Yong Choi, S. J. Madden, and B. Luther-Davies, “Photonic chip based ultrafast optical processing based on high nonlinearity dispersion engineered chalcogenide waveguides,” Laser Photon. Rev.6(1), 97–114 (2012). [CrossRef]
  22. J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express15(1), 150–165 (2007). [CrossRef] [PubMed]
  23. M. Streshinsky, R. Ding, Y. Liu, A. Novack, C. Galland, A. E.-J. Lim, P. Guo-Qiang Lo, T. Baehr-Jones, and M. Hochberg, “The road to affordable, large-scale silicon photonics,” Opt. Photon. News24(9), 32–39 (2013). [CrossRef]
  24. L. Zhang, R. Q. Ji, L. X. Jia, L. Yang, P. Zhou, Y. H. Tian, P. Chen, Y. Y. Lu, Z. Y. Jiang, Y. L. Liu, Q. Fang, and M. B. Yu, “Demonstration of directed XOR/XNOR logic gates using two cascaded microring resonators,” Opt. Lett.35(10), 1620–1622 (2010). [CrossRef] [PubMed]
  25. L. Zhang, R. Q. Ji, Y. H. Tian, L. Yang, P. Zhou, Y. Y. Lu, W. W. Zhu, Y. L. Liu, L. X. Jia, Q. Fang, and M. B. Yu, “Simultaneous implementation of XOR and XNOR operations using a directed logic circuit based on two microring resonators,” Opt. Express19(7), 6524–6540 (2011). [CrossRef] [PubMed]
  26. C. Y. Qiu, X. Ye, R. Soref, L. Yang, and Q. F. Xu, “Demonstration of reconfigurable electro-optical logic with silicon photonic integrated circuits,” Opt. Lett.37(19), 3942–3944 (2012). [CrossRef] [PubMed]
  27. Y. Tian, L. Zhang, and L. Yang, “Electro-optic directed AND/NAND logic circuit based on two parallel microring resonators,” Opt. Express20(15), 16794–16800 (2012). [CrossRef]
  28. L. Zhang, J. Ding, Y. Tian, R. Ji, L. Yang, H. Chen, P. Zhou, Y. Lu, W. Zhu, and R. Min, “Electro-optic directed logic circuit based on microring resonators for XOR/XNOR operations,” Opt. Express20(11), 11605–11614 (2012). [CrossRef] [PubMed]
  29. R. Soref, “Reconfigurable integrated optoelectronics,” Adv. Optoelectron.2011, 627802 (2011). [CrossRef]
  30. Q. F. Xu and R. A. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express19(6), 5244–5259 (2011). [CrossRef] [PubMed]
  31. J. Ding, H. Chen, L. Yang, L. Zhang, R. Ji, Y. Tian, W. Zhu, Y. Lu, P. Zhou, R. Min, and M. Yu, “Ultra-low-power carrier-depletion Mach-Zehnder silicon optical modulator,” Opt. Express20(7), 7081–7087 (2012). [CrossRef] [PubMed]
  32. Q. F. Xu, V. R. Almeida, R. R. Panepucci, and M. Lipson, “Experimental demonstration of guiding and confining light in nanometer-size low-refractive-index material,” Opt. Lett.29(14), 1626–1628 (2004). [CrossRef] [PubMed]
  33. J. Heebner, R. Grover, and T. Ibrahim, Optical microresonators: theory, fabrication, and applications (Springer-Verlag, London, 2008), Chap. 3.
  34. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express15(12), 7610–7615 (2007). [CrossRef] [PubMed]
  35. D. X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, and J. H. Schmid, “Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding,” Opt. Express16(19), 15137–15148 (2008). [CrossRef] [PubMed]
  36. H. X. Yi, D. S. Citrin, and Z. P. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express18(3), 2967–2972 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited