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

Optics Express, Vol. 22, Issue 3, pp. 2996-3012 (2014)

http://dx.doi.org/10.1364/OE.22.002996

Acrobat PDF (6239 KB)

### 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

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]

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]

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. 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]

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]

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. 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]

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]

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]

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]

## 2. Design and fabrication

*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.

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]

*1*’ makes the MRR to be off-resonance. While in the current work, the carrier-depletion modulation is employed, which tunes the MRR to be off-resonance when a negative voltage is applied to the PN diode. In this case, a logic ‘

*0*’ makes the MRR to be off-resonance.

*λ*, when no electrical signals are applied. When the electrical signal is at low level, the applied voltage is negative, which tunes the MRR to be off-resonance through extracting carriers from the PN diode. And when the electrical signal is at high level, the applied voltage is 0 V, which does not change the resonance status of the MRR. So if the two applied electrical signals are same (both at high or low level), the input light will be directed to the

*through*port of the circuit. If the two applied electrical signals are different (one is at high level and the other one is at low level), the input light will be directed to the

*drop*port of the circuit. This means that we can achieve the XOR and XNOR operations of the two applied electrical signals at the

*drop*and

*through*ports, respectively. All the four situations are summarized in Table 1. It should be noted that the denotation of the output ports of the circuit is different from that in the previous work [28

**20**(11), 11605–11614 (2012). [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]

*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)). 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.

^{18}/cm

^{3}and the n-type doping concentration is 8 × 10

^{17}/cm

^{3}(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]

^{+}~5.5 × 10

^{20}/cm

^{3}) and cathode (phosphorus, n

^{+}~5.5 × 10

^{20}/cm

^{3}) implants are formed (Fig. 2 (e) and (f)).

**20**(11), 11605–11614 (2012). [CrossRef] [PubMed]

^{2}.

## 3. Experimental results

_{1}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]

*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

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

### 3.1 Static characterization

_{1}to resonate far away from MRR

_{2}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 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.

*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 ‘

*1*s’). 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

*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, 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.

*0*s’, and negative spikes between two consecutive ‘

*1*s’, which also appear in our previous work and has been well explained [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]

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

## 4. Discussion

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

**20**(11), 11605–11614 (2012). [CrossRef] [PubMed]

### 4.1 Sensitivity analysis of the XOR/XNOR directed logic circuit

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

_{1}and MRR

_{2}to be

*θ*

_{1}and

*θ*

_{2}, respectively. And we consider that the round-trip amplitude transmission factor of the two MRRs to be identical, which is represented by

*α*in Fig. 8. The single-pass phase shifts in the connecting waveguides of S

_{1}and S

_{2}are denoted to be

*θ*

_{s1}and

*θ*

_{s2}, respectively. The four coupling regions are supposed to be identical, which are describe by lumped self- and cross-coupling coefficients

*t*and

*k*. These parameters of

*θ*

_{1},

*θ*

_{2},

*θ*

_{s1}and

*θ*

_{s2}are all wavelength-dependent. And

*α*is considered to be wavelength-independent. In the previous work, we just calculate the static response spectra of the circuit, where

*θ*

_{1}always equals to

*θ*

_{2}[25

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

*θ*

_{1}and

*θ*

_{2}.

*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 (

*E*

_{p3}) can be decomposed into two parts. The first part comes from

*E*

_{p1}, which contribute to

*E*

_{p3}via the drop function of MRR

_{2}. The second part comes from

*E*

_{v1}, which contribute to

*E*

_{p3}via the through function of MRR

_{2}. So the expression of the electric field

*E*

_{p3}can be written as follows.

*θ*

_{1}equals to

*θ*

_{2}, which means that the first two terms in Eq. (2) disappear. At the resonance wavelengths, we let

*θ*

_{1}and

*θ*

_{2}equal to 2

*mπ*, where the integer

*m*is the resonance order. Since

*θ*

_{1},

*θ*

_{2},

*θ*

_{s1}and

*θ*

_{s2}are all proportional to their own waveguide length,

*θ*

_{s1}and

*θ*

_{s2}are proportional to

*θ*

_{1}and

*θ*

_{2}. The proportionality factors are the ratio between the lengths of the connecting waveguides and the ring waveguides. We suppose that

*θ*

_{s1}−

*θ*

_{s2}are

*pmπ*, where

*p*is a real number. Then Eq. (2) can be simplified to

*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

*E*

_{p3}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

*E*

_{p3}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.

*p*is an odd number, the parity of the resonance order

*m*will not affect the spectrum. The value of Eq. (3) always equals to

*0*, the two constituent parts of

*E*

_{p3}will interfere constructively with each other at every resonance regions. Such characteristic has been analyzed in our previous work, where the other port is discussed [25

**19**(7), 6524–6540 (2011). [CrossRef] [PubMed]

*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) 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

*θ*

_{1}=

*θ*

_{2}= 2

*mπ*, the

*drop*port will nominally output nothing at the degenerate resonance region’s center wavelength. And when any of

*θ*

_{1}or

*θ*

_{2}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, 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]

*π*∙

*R*∙

*n*

_{eff}/

*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

*θ*

_{s1}=

*θ*

_{s2}(

*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*.

*θ*

_{2}to be 2

*mπ*, only considering the change of the output with the variation of the value of

*θ*

_{1}. 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

*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. 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

*α*=

*t*

_{1}/

*t*

_{2}. 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.

*k*

_{1}in Fig. 14 (a) coincide. It means that for a certain

*k*

_{1}, the sensitivity does not change with the loss in the ring, as long as the critical coupling is satisfied. It can be found that, for different

*k*

_{1}, the roll-up and roll-off factors have almost the same amplitudes, which are measured to be about 20 dB/decade at the through port and −20 dB/decade at the drop port, respectively. It has the same value as a simple first order network such as the RC circuit. This is because both the MRR around the resonate frequency and the RC circuit have lorentzian line shapes.

#### 4.2.3 Mach-Zehnder interferometer

*α*

_{1}and

*α*

_{2}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), 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

## Acknowledgment

## 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. |

2. | R. Clavero, J. M. Martínez, F. Ramos, and J. Martí, “All-optical packet routing scheme for optical label-swapping networks,” Opt. Express |

3. | A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All-optical parity checker with bit-differential delay,” Opt. Commun. |

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. |

5. | M. P. Fok and P. R. Prucnal, “All-optical encryption based on interleaved waveband switching modulation for optical network security,” Opt. Lett. |

6. | S. H. Jeon and S. K. Gil, “Optical implementation of triple DES algorithm based on dual XOR logic operations,” J. Opt. Soc. Korea |

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 |

8. | I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics |

9. | K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. Quantum Electron. |

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. |

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 |

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 |

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. |

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. |

15. | A. Bogoni, X. Wu, Z. Bakhtiari, S. Nuccio, and A. E. Willner, “640 Gbits/s photonic logic gates,” Opt. Lett. |

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. | 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. |

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. | 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 |

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. |

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. |

22. | J. Hardy and J. Shamir, “Optics inspired logic architecture,” Opt. Express |

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. | 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. |

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 |

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. |

27. | Y. Tian, L. Zhang, and L. Yang, “Electro-optic directed AND/NAND logic circuit based on two parallel microring resonators,” Opt. Express |

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 |

29. | R. Soref, “Reconfigurable integrated optoelectronics,” Adv. Optoelectron. |

30. | Q. F. Xu and R. A. Soref, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express |

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 |

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. |

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 |

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 |

36. | H. X. Yi, D. S. Citrin, and Z. P. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express |

**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

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### References

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