## Fano-resonance-based Mach-Zehnder optical switch employing dual-bus coupled ring resonator as two-beam interferometer

Optics Express, Vol. 17, Issue 9, pp. 7708-7716 (2009)

http://dx.doi.org/10.1364/OE.17.007708

Acrobat PDF (994 KB)

### Abstract

A kind of Mach-Zehnder optical switch with a dual-bus coupled ring resonator as a two-beam interferometer is proposed and investigated. The analysis based on the transfer matrix method shows that a sharp asymmetric Fano line shape can be generated in the transmission spectra of such a configuration, which can be used to significantly reduce the phase change required for switching. Meanwhile, it can also be found that complete extinctions can be achieved in both switching states if the structural parameters are carefully chosen and the phase bias is properly set. Through tuning the phase difference between the arms of the Mach-Zehnder interferometer, complete extinction can be easily kept within a large range of the ring-bus coupling ratios in the OFF state. By properly modulating the phase change in the ring waveguide, the shift of the resonant frequency and the asymmetry of the transmission spectra can be controlled to finally enable optical switching with a high extinction ratio, even complete extinction, in the ON state. The switching functionality is verified by the finite-difference time-domain simulation.

© 2009 Optical Society of America

## 1. Introduction

1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. **15**, 998–1005 (1997). [CrossRef]

2. Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature **435**, 325–327 (2005). [CrossRef] [PubMed]

3. C. Kochar, A. Kodi, and A. Louri, “Proposed low-power high-speed microring resonator-based switching technique for dynamically reconfigurable optical interconnects,” IEEE Photon. Technol. Lett. **19**, 1304–1306 (2007). [CrossRef]

4. Y. Goebuchi, M. Hisada, T. Kato, and Y. Kokubun, “Optical cross-connect circuit using hitless wavelength selective switch,” Opt. Express **16**, 535–548 (2008). [CrossRef] [PubMed]

5. Y. Z. Sun and X. D. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express **16**, 10254–10268 (2008). [CrossRef] [PubMed]

6. G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. **17**, 1248–1254 (1999). [CrossRef]

7. J. Y. Yang, F. Wang, X. Q. Jiang, H. C. Qu, M. H. Wang, and Y. L. Wang, “Influence of loss on linearity of microring-assisted Mach-Zehnder modulator,” Opt. Express **12**, 4178–4188 (2004). [CrossRef] [PubMed]

8. X. B. Xie, J. Khurgin, J. Kang, and F. S. Chow, “Linearized Mach-Zehnder intensity modulator,” IEEE Photon. Technol. Lett. **15**, 531–533 (2003). [CrossRef]

9. J. F. Song, H. Zhao, Q. Fang, S. H. Tao, T. Y. Liow, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Effective thermo-optical enhanced cross-ring resonator MZI interleavers on SOI,” Opt. Express **16**, 21476–21482 (2008). [CrossRef] [PubMed]

10. S. Y. Cho and R. Soref, “Interferometric microring-resonant 2×2 optical switches,” Opt. Express **16**, 13304–13314 (2008). [CrossRef] [PubMed]

11. S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A **20**, 569–572 (2003). [CrossRef]

12. L. Y. Mario, S. Darmawan, and M. K. Chin, “Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching,” Opt. Express **14**, 12770–12781 (2006). [CrossRef] [PubMed]

## 2. The structure, and the expressions of the output electric fields

16. F. Xu and A. W. Poon, “Silicon cross-connect filters using microring resonator coupled multimode-interference-based waveguide crossings,” Opt. Express **16**, 8649–8657 (2008). [CrossRef] [PubMed]

*E*

_{i1}=0 or

*E*

_{i2}=0, has been widely used as an add-drop filter [17

17. C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. **35**, 1322–1331 (1999). [CrossRef]

*E*

_{i1}and

*E*

_{i2}are the electric fields of the input bus waveguides, while

*E*

_{o1}and

*E*

_{o2}represent that of the output bus waveguides. Since the bandwidth of the resonance is far smaller than the resonant frequency, the power coupling coefficients

*κ*

_{1}and

*κ*

_{2}can be considered as constants, where the superscripts represent the coupling regions. Assuming that the evanescent coupling is lossless,

*E*

_{o1}and

*E*

_{o2}can be determined through the transfer matrix approach and expressed as:

*j*= (-1)

^{1/2}.

*s*=

_{i}*κ*

_{i}^{1/2}is the ring-bus amplitude coupling coefficient, and

*c*= (1-

_{i}*κ*)

_{i}^{1/2}is the amplitude transmission coefficient, where

*i*= 1, 2.

*γ*= exp(-

*αL*/ 2) is the round-trip amplitude attenuation factor for a ring resonator with length

_{u}*L*and linear loss coefficient

_{u}*α*.

*φ*=

*βL*is the round-trip phase where

_{u}*β*is the propagation constant in the ring waveguide.

*φ*is equal to the sum of the phases

*φ*

_{1}in the upper semicircular waveguide with length

*L*

_{1}and the phase

*φ*

_{2}in the lower semicircle with length

*L*

_{2}, as shown in Fig. 1(b).

*m*is the quotient of

*L*

_{1}and

*L*, and

_{u}*n*is the quotient of

*L*

_{2}and

*L*. We have

_{u}*m*+

*n*= 1.

## 3. Fano-resonance transmission spectra in the OFF state

*E*

_{i1}and

*E*

_{i2}are equal. Assuming

*m*=

*n*=0.5, this device configuration is expected to exhibit a periodic spectral response. The period is 4

*π*according to Eq. (1). The transmission spectra

*I*

_{o1}= |

*E*

_{o1}|

^{2}and

*I*

_{o2}= |

*E*

_{o2}|

^{2}are shown in Fig. 2(a), when

*c*

_{1}= 0.9,

*c*

_{2}varies from 0.8 to 0.9 and

*γ*= 0.99. As it is known, the cavity is on resonance when

*φ*= 2

*qπ*(

*q*is an integer). It has been noted that the two-beam interference in the ring waveguide affects the resonant intensity. If the phase difference

*δ*= arg(

*E*

_{i1}/

*E*

_{i2}) is equal to zero and

*q*is even, the RRTBI can produce constructive interference and support resonance in the cavity (the even mode with respect to the mirror plane in Fig. 1(b)). When

*δ*=0 and

*q*is odd, the RRTBI can produce destructive interference and weaken resonance (the odd mode), so that the energy stored in the cavity drops. As a result, the power dissipation decreases.

*δ*, as shown in Fig. 2(c) and (d). When

*δ*= 0 or

*δ*=

*π*, the output profiles exhibit the symmetrical resonance dips, but the values of

*φ*for supporting the even and odd resonant modes are exchanged, as shown in Fig. 2(b). To illustrate the relationships in the transmission spectra around the two types of the resonant points, we define Δ

*φ*= −2

*πn*Δ

_{eff}L_{u}*λ*/

*λ*

_{0}

^{2}to denote the deviation of the phase, where Δ

*λ*is the wavelength detuning,

*λ*

_{0}is the resonant wavelength and

*n*is the effective refractive index of the ring waveguide. We define

_{eff}*I*and

_{oo}*I*to represent the transmission spectra in the range of 2

_{oe}*π*around the odd and even mode resonant points respectively. Considering

*I*and

_{oo}*I*are the functions of Δ

_{oe}*φ*and

*δ*, according to Eq. (1),

*I*(Δ

_{oo}*φ*,

*δ*) =

*I*(Δ

_{oe}*φ*,

*δ*+

*pπ*) is obtained, where

*p*is odd. Thus we just need to pay our attentions to the transmission spectra in the range −

*π*<Δ

*φ*<

*π*. The terms

*φ*

_{1}and

*φ*

_{2}in Eq. (1) can be replaced by 0.5Δ

*φ*.

*I*

_{o1}= 0 is assumed. Substituting

*E*

_{o1}=0 in Eq. (1),

*E*

_{i2}can be expressed as a function of

*E*

_{i1}:

*δ*, there are two values of Δ

*φ*symmetrical about the resonant frequency which satisfy Eq. (3). The positive value of Δ

*φ*is shown in Fig. 3(a). In the lossless case (

*γ*= 1), the value ranges of

*c*

_{1}and

*c*

_{2}derived from Eq.(3) are surrounded by the following curves, as shown in Fig. 3(a):

*c*

_{1}and

*c*

_{2}are set closer to the curves described by Eq. (4), Δ

*φ*drops to 0. The spectral profile finally turns to a symmetric resonance dip given by line F in Fig. 3(b). As

*c*

_{1}and

*c*

_{2}are chosen towards the curve given by Eq. (5), Δ

*φ*approaches to

*π*. While one of

*c*

_{1}and

*c*

_{2}wanes to zero, the other drops to 2

^{-1/2}, which means the corresponding coupling zone turns to a 3-dB coupler. In this case, the device is degraded to a conventional simple MZI.

*γ*= 1), the slopes of

*I*

_{o1}and

*I*

_{o2}at the resonant frequency (Δ

*φ*=0), can be derived from Eq. (1), respectively:

*δ*on the asymmetry.

*δ*= 0.5

*π*maximizes the gradients for a given pair of

*c*

_{1}and

*c*

_{2}. Moreover, for more oblique resonance spectra, the values of

*c*

_{1}and

*c*

_{2}have to be chosen to get closer to each other, and tend towards unit.

*I*

_{o1}=0 can be easily realized through biasing the phase difference

*δ*. This characteristic enables some high-extinction applications. Optical switch is one of such applications. In the next section, it will be shown that the ON state with

*I*

_{o2}=0 can be achieved by introducing a proper phase shift to the ring waveguide.

## 4. Fano-resonance transmission spectra in the ON state

*φ*to the ring waveguide, let’s tune the phase bias to have

_{d}*I*

_{o1}=0. For one thing, it is easy to understand that the phase shift

*φ*gives rise to a variation of the resonant frequency and the transmission spectra shift as shown in Fig. 5. To represent the deviation, we define Δ

_{d}*θ*= −2

*πn*Δ

_{eff}L_{u}*λ*/

*λ*

^{2}

_{0off}, where

*λ*

_{0off}is the resonant wavelength in the OFF state. For another thing, the changes in the maximums, the minimums, even the shapes, happen to the spectra. This is because the phase change in the ring waveguide alters the phase difference between the two interference paths in the RRTBI. For comparison, the phase change in the ring waveguide in a conventional REMZI just produces a shift of the transmission spectrum without the change in asymmetry. If these two functionalities, varying the asymmetry of the Fano-resonance spectra and shifting the resonant frequency, of the phase change in the ring waveguide can be matched, a complete switching can be achieved.

*I*

_{o2}= 0 in the ON state, we assume that the phase shift is applied to the lower semi-circle waveguide. Applying

*E*

_{o2}= 0 to Eq. (1),

*E*

_{i1}can be expressed as:

*φ*:

_{d}*γ*, the value ranges of

*c*

_{1}and

*c*

_{2}turn to a pair of curves. Figure 6 shows the relationships between the structural parameters and the phase change

*φ*. Based on the analysis in section 3, since the values of

_{d}*c*

_{1}and

*c*

_{2}increase and get closer to each other, the sharpness of the asymmetric Fano-resonance spectra increases. As a result,

*φ*and Δ

_{d}*φ*decrease. Accordingly, the energy stored in the cavity increases so that the output power decreases as shown in Fig. 7. Certainly, there is a tradeoff between the insertion loss and the required phase change.

*φ*>0.1

_{d}*π*, more than 93% of the modulation depth can be achieved. The small difference between the output powers

*I*

_{o1}and

*I*

_{o2}shown in Fig. 7, is because of the unequal ring-bus coupling ratios. The imbalance between the two coupling ratios results in different requirements of the energy stored in the cavity for the complete extinctions.

## 5. FDTD simulation

*n*in refractive index is introduced through the phase shifter. The parameters set for the simulation are described below. The radius of the ring resonator is 2μm and the waveguide width is 0.2μm. The refractive indices of the core and cladding are 3.477 and 1.444 respectively. The imaginary part of the refractive index of the ring waveguide is 2.025×10

^{-4}, which leads to

*γ*=0.99. The left and right gaps between the ring and the bus waveguides are 0.16μm and 0.147μm, which are used to obtain

*c*

_{1}= 0.896 and

*c*

_{2}= 0.869. The length of the phase shifter is a quarter of the ring waveguide. Figure 8(a) shows

*I*

_{o1}becomes zero after adjusting the phase difference between

*E*

_{i1}and

*E*, which leads to

_{i2}*δ*=0.41

*π*, when

*λ*=1.591μm. Tuned with Δ

*n*= 0.052 for the modulation length of about 3μm, the light is routed to the other output port as shown in Fig. 8(b). If the radius is increased to obtain a phase shifter with the length of more than 170μm, the required change in refractive index would be reduced to less than 0.001.

## 6. Conclusions

## Acknowledgments

## References and links

1. | B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. |

2. | Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature |

3. | C. Kochar, A. Kodi, and A. Louri, “Proposed low-power high-speed microring resonator-based switching technique for dynamically reconfigurable optical interconnects,” IEEE Photon. Technol. Lett. |

4. | Y. Goebuchi, M. Hisada, T. Kato, and Y. Kokubun, “Optical cross-connect circuit using hitless wavelength selective switch,” Opt. Express |

5. | Y. Z. Sun and X. D. Fan, “Analysis of ring resonators for chemical vapor sensor development,” Opt. Express |

6. | G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol. |

7. | J. Y. Yang, F. Wang, X. Q. Jiang, H. C. Qu, M. H. Wang, and Y. L. Wang, “Influence of loss on linearity of microring-assisted Mach-Zehnder modulator,” Opt. Express |

8. | X. B. Xie, J. Khurgin, J. Kang, and F. S. Chow, “Linearized Mach-Zehnder intensity modulator,” IEEE Photon. Technol. Lett. |

9. | J. F. Song, H. Zhao, Q. Fang, S. H. Tao, T. Y. Liow, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Effective thermo-optical enhanced cross-ring resonator MZI interleavers on SOI,” Opt. Express |

10. | S. Y. Cho and R. Soref, “Interferometric microring-resonant 2×2 optical switches,” Opt. Express |

11. | S. H. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A |

12. | L. Y. Mario, S. Darmawan, and M. K. Chin, “Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching,” Opt. Express |

13. | L. J. Zhou and A. W. Poon, “Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers,” Opt. Lett. |

14. | Y. Lu, J. Q. Yao, X. F. Li, and P. Wang, “Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach-Zehnder interferometer,” Opt. Lett. |

15. | R. G. J. Heebner and T. Ibrahim, |

16. | F. Xu and A. W. Poon, “Silicon cross-connect filters using microring resonator coupled multimode-interference-based waveguide crossings,” Opt. Express |

17. | C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. |

**OCIS Codes**

(130.2790) Integrated optics : Guided waves

(130.3120) Integrated optics : Integrated optics devices

(230.5750) Optical devices : Resonators

(130.4815) Integrated optics : Optical switching devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: March 5, 2009

Revised Manuscript: April 22, 2009

Manuscript Accepted: April 23, 2009

Published: April 24, 2009

**Citation**

Fan Wang, Xiang Wang, Haifeng Zhou, Qiang Zhou, Yinlei Hao, Xiaoqing Jiang, Minghua Wang, and Jianyi Yang, "Fano-resonance-based Mach-Zehnder optical switch employing dual-bus coupled ring resonator as two-beam interferometer," Opt. Express **17**, 7708-7716 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7708

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### References

- B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997). [CrossRef]
- Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, "Micrometre-scale silicon electro-optic modulator," Nature 435, 325-327 (2005). [CrossRef] [PubMed]
- C. Kochar, A. Kodi, and A. Louri, "Proposed low-power high-speed microring resonator-based switching technique for dynamically reconfigurable optical interconnects," IEEE Photon. Technol. Lett. 19, 1304-1306 (2007). [CrossRef]
- Y. Goebuchi, M. Hisada, T. Kato, and Y. Kokubun, "Optical cross-connect circuit using hitless wavelength selective switch," Opt. Express 16, 535-548 (2008). [CrossRef] [PubMed]
- Y. Z. Sun and X. D. Fan, "Analysis of ring resonators for chemical vapor sensor development," Opt. Express 16, 10254-10268 (2008). [CrossRef] [PubMed]
- G. Lenz and C. K. Madsen, "General optical all-pass filter structures for dispersion control in WDM systems," J. Lightwave Technol. 17, 1248-1254 (1999). [CrossRef]
- J. Y. Yang, F. Wang, X. Q. Jiang, H. C. Qu, M. H. Wang, and Y. L. Wang, "Influence of loss on linearity of microring-assisted Mach-Zehnder modulator," Opt. Express 12, 4178-4188 (2004). [CrossRef] [PubMed]
- X. B. Xie, J. Khurgin, J. Kang, and F. S. Chow, "Linearized Mach-Zehnder intensity modulator," IEEE Photon. Technol. Lett. 15, 531-533 (2003). [CrossRef]
- J. F. Song, H. Zhao, Q. Fang, S. H. Tao, T. Y. Liow, M. B. Yu, G. Q. Lo, and D. L. Kwong, "Effective thermo-optical enhanced cross-ring resonator MZI interleavers on SOI," Opt. Express 16, 21476-21482 (2008). [CrossRef] [PubMed]
- S. Y. Cho and R. Soref, "Interferometric microring-resonant 2x2 optical switches," Opt. Express 16, 13304-13314 (2008). [CrossRef] [PubMed]
- S. H. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators," J. Opt. Soc. Am. A 20, 569-572 (2003). [CrossRef]
- L. Y. Mario, S. Darmawan, and M. K. Chin, "Asymmetric Fano resonance and bistability for high extinction ratio, large modulation depth, and low power switching," Opt. Express 14, 12770-12781 (2006). [CrossRef] [PubMed]
- L. J. Zhou and A. W. Poon, "Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers," Opt. Lett. 32, 781-783 (2007). [CrossRef] [PubMed]
- Y. Lu, J. Q. Yao, X. F. Li, and P. Wang, "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach-Zehnder interferometer," Opt. Lett. 30, 3069-3071 (2005). [CrossRef] [PubMed]
- R. G. J. Heebner, and T. Ibrahim, Optical Microresonators (Springer, 2008).
- F. Xu and A. W. Poon, "Silicon cross-connect filters using microring resonator coupled multimode-interference-based waveguide crossings," Opt. Express 16, 8649-8657 (2008). [CrossRef] [PubMed]
- C. Manolatou, M. J. Khan, S. H. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, "Coupling of modes analysis of resonant channel add-drop filters," IEEE J. Quantum Electron. 35, 1322-1331 (1999). [CrossRef]

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