## Tuning of resonance-spacing in a traveling-wave resonator device

Optics Express, Vol. 18, Issue 9, pp. 9447-9455 (2010)

http://dx.doi.org/10.1364/OE.18.009447

Acrobat PDF (1102 KB)

### Abstract

In this work a traveling-wave resonator device is proposed and experimentally demonstrated in silicon-on-insulator platform in which the spacing between its adjacent resonance modes can be tuned. This is achieved through the tuning of mutual coupling of two strongly coupled resonators. By incorporating metallic microheaters, tuning of the resonance-spacing in a range of 20% of the free-spectral-range (0.4nm) is experimentally demonstrated with 27mW power dissipation in the microheater. To the best of our knowledge this is the first demonstration of the tuning of resonance-spacing in an integrated traveling-wave-resonator. It is also numerically shown that these modes exhibit high field-enhancements which makes this device extremely useful for nonlinear optics and sensing applications.

© 2010 OSA

## 1. Introduction

1. R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1678–1687 (2006). [CrossRef]

2. Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express **17**(4), 2247–2254 (2009). [CrossRef] [PubMed]

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science **317**(5839), 783–787 (2007). [CrossRef] [PubMed]

5. A. H. Atabaki, M. Soltani, S. Yegnanarayanan, A. A. Eftekhar, and A. Adibi, “Optimization of Metallic Micro-Heaters for Reconfigurable Silicon Photonics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

7. L. Chen, N. Sherwood-Droz, and M. Lipson, “Compact bandwidth-tunable microring resonators,” Opt. Lett. **32**(22), 3361–3363 (2007). [CrossRef] [PubMed]

3. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express **16**(7), 4881–4887 (2008). [CrossRef] [PubMed]

8. J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, “All-fiber comb filter with tunable free spectral range,” Opt. Lett. **30**(16), 2062–2064 (2005). [CrossRef] [PubMed]

9. Y. G. Han, X. Y. Dong, J. H. Lee, and S. B. Lee, “Wavelength-spacing-tunable multichannel filter incorporating a sampled chirped fiber Bragg grating based on a symmetrical chirp-tuning technique without center wavelength shift,” Opt. Lett. **31**(24), 3571–3573 (2006). [CrossRef] [PubMed]

## 2. Device proposal and simulation results

10. M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express **15**(8), 4694–4704 (2007). [CrossRef] [PubMed]

*λ*

^{2}/

*Ln*where

_{g};*λ*is the resonance wavelength,

*L*is the optical length of resonator, and

*n*is the group index sensed by the traveling wave. Since in conventional microring, microdisk, or racetrack TWRs,

_{g}*n*cannot be tuned in a wide range, FSR of these resonators is almost fixed. This very fundamental property of resonators calls for an indirect approach for the tuning of the spacing of adjacent resonant modes. In this work, we exploit the mode-splitting properties of a strongly coupled TWR device to achieve dynamic tuning of the spacing of resonant modes.

_{g}*κ*

^{2}. The structures in Figs. 1(b) and 1(c) are called single-point-coupled and two-point-coupled resonator structures, respectively. Figure 1(d) shows the amount of resonance-frequency splitting normalized to the FSR of each single resonator versus the power coupling coefficient of DCs (i.e.,

*κ*

^{2}). Appendix A contains the details of the derivation of resonance condition for both devices. These simulations are performed for two identical silicon-on-insulator (SOI) coupled racetrack resonators composed of waveguides with effective refractive index and group index of 2.5 and 4.25, respectively.

13. J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express **12**(1), 90–103 (2004). [CrossRef] [PubMed]

^{5}is assumed for the SOI racetrack resonators with effective refractive index and group index of 2.5 and 4.25, respectively; corresponding to waveguides with a width of 480 nm and thickness of 230 nm buried under SiO

_{2}cladding. The length of each single resonator is considered to be 245 µm and the lower resonator is coupled to an external bus waveguide with a power coupling coefficient of

_{0}= 1.55 µm) normalized to the FSR of the uncoupled resonator. Figures 2(a) (2(d)), 2(b) (2(e)), and 2(c) (2(f)) show the spectra for single-point-coupled (two-point-coupled) resonator structures for power coupling coefficients of

*κ*

^{2}= 0,

*κ*

^{2}= 0.5, and

*κ*

^{2}= 1, respectively. The “2x” sign next to the drops in the transmission spectra indicates the presence of two degenerate modes at that particular frequency. It is observed that as the coupling coefficient increases from zero, the initially degenerate modes split and reach their maximum splitting for

*κ*

^{2}= 1. For the single-point-coupled structure with

*κ*

^{2}= 1, in each round-trip, electromagnetic field from one resonator completely couples to the second resonator with the addition of a phase shift of π/2 [12] and after traveling the second resonator, it couples back into the first resonator with an additional phase of π/2. As a result, the coupled-resonator device is equivalent to one resonator with twice the length of each single resonator with a total phase of π introduced in its roundtrip-phase. This is observed in Fig. 2(c) where the FSR of the coupled-resonator is half the FSR of each single resonator (Fig. 2(a)) and the resonances are shifted by half of an FSR because of the additional π phase. For the two-point-coupled structure the interference between the two arms of the balanced MZI formed between the resonators, determines the effective mutual coupling between them. For example, at

*κ*

^{2}= 0.5, the MZI has complete power coupling between the two resonators with the addition of a π/2 phase on the field amplitudes (excluding the propagation phase term). Hence, this structure acts exactly the same as the single-point-coupled structure with

*κ*

^{2}= 1; and as result, transmission spectra in Figs. 2(c) and 2(e) are the same. However, in the two-point-coupled structure, for

*κ*

^{2}= 1, the MZI has zero power coupling between the two resonators; hence, the two resonators are decoupled with an addition of a total phase of π introduced in the roundtrip-phase of each resonator as a result of the MZI phase (excluding propagation phase term in the straight part of the MZI).

*κ*

^{2}= 0. Therefore, by looking at the evolution of modes in Figs. 2(d) to 2(f), it is observed that as

*κ*

^{2}is increased, even and odd supermodes travel half of an FSR in opposite directions and a net splitting of one whole FSR is observed in this structure. The arrows in Figs. 2(b) and 2(e) show the direction of the shift in the resonance modes as coupling coefficients in coupling points are increased.

*κ*

^{2}and consequently the effective length of the device changes. For example if the mutual coupling between the two resonators changes from one to zero, the effective length of the device changes from 2

*L*to

_{res}*L*, where

_{res}*L*is the length of each resonator. Hence, within each resonator roundtrip, the mode experiences different levels of loss as the effective coupling between the two resonators changes. However, as the coupling to the bus waveguide is fixed within each roundtrip, different levels of extinction are observed at the resonance for different coupling strengths between the resonators. This is indicative of different levels of field enhancement in the device (e.g.: maximum enhancement is achieved at zero extinction or critical coupling condition). As field enhancement is one of the more important measures in many sensing and nonlinear optics applications, the effect of resonator mutual coupling on field enhancement is studied in section 4 in detail.

_{res}## 3. Fabrication and experimental results

_{2}-based chemistry. After this step, 1 µm SiO2 is deposited using plasma-enhanced chemical-vapor-deposition (PECVD) and microheater patterns are defined by a lift-off process using ZEP and electron-beam evaporation. Optimized microheaters with rapid reconfiguration have been developed to achieve sub-microsecond reconfiguration [5

5. A. H. Atabaki, M. Soltani, S. Yegnanarayanan, A. A. Eftekhar, and A. Adibi, “Optimization of Metallic Micro-Heaters for Reconfigurable Silicon Photonics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.

^{2}= 0.42, assuming the two couplers are identical. Intrinsic Q of the modes of the coupled-resonator structure is also measured to be 70,000.

_{2}(Fig. 4), coupling between the two resonators can be tuned. Figure 5(b) depicts the normalized transmission spectra of the two coupled resonance modes in the vicinity of λ = 1.601 µm for three different levels of power dissipation in heater H

_{2}. The number next to each spectrum is the power dissipation in the microheater. Similar tuning results are obtained for other FSRs in Fig. 5(a). Horizontal axis in Fig. 5(b) shows the wavelength detuning from the center of the coupled modes (or supermodes). It is observed that as the phase mismatch between the arms of the interferometer is increased (through applying heat), coupling between the resonators and consequently the mode spacing between the coupled modes is decreased. In addition to the change in the resonator coupling strengths, resonance wavelength of the upper resonator is red-shifted while heating the upper interferometer arm. This causes the center of the two coupled resonant modes (even and odd supermodes) to be red-shifted as their spacing is reduced. Here, this red-shift is compensated by introducing an appropriate wavelength offset to the experimental data, so that the centers of coupled-modes in each transmission spectrum match. In practice, by simultaneous tuning of all fabricated heaters, center wavelength of two resonators can remain unchanged while their mutual coupling is tuned. Figure 6 shows the change in resonance wavelength spacing of the even and odd coupled-modes for the structure in Fig. 4 for different power dissipations in heater H

_{2}. It is observed that 0.4 nm change in wavelength spacing between coupled modes is achieved by dissipating 27 mW in H

_{2.}This amount of change is equivalent to 20% of the FSR of the uncoupled resonators.

## 4. Discussion

_{2}, proves that the resonator-based device in Fig. 4 can be used for a large set of signal conditions in applications like nonlinear optics in which signals with different wavelengths interact. By tuning the mode spacing, we can achieve resonance condition and simultaneous field enhancement for the involved signals. The amount of field-enhancement is an important characteristic which determines the device performance and needs to be addressed for any proposed device. As our proposed resonator structure is composed of an interferometer in addition to resonators, its field-enhancement characteristic is expected to be different compared to a simple resonator. Using a similar transfer-matrix approach as in Ref [13

13. J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express **12**(1), 90–103 (2004). [CrossRef] [PubMed]

*κ*

^{2}= 0.7; and the power coupling coefficient for the coupling of the bus waveguide to the lower resonator is

^{5}). The intensity enhancements shown in Fig. 7 are denoted by

*a*and defined by the ratio of the intensity of the field of each resonant mode inside the resonator to the intensity of the field at the input waveguide. Subscripts 1 and 2 determine the fields in the bottom resonator (R

_{1}) and the top resonator (R

_{2}), respectively. Also, the modes with lower and higher frequency are called even and odd mode, respectively. Figure 7 shows that as the MZI phase difference increases, the amount of enhancement of the even (odd) mode in R

_{1}increases (decreases) until φ = 0.8π. As φ further increases, R

_{2}becomes decoupled from R

_{1}; the field in R

_{2}drops to zero; and the enhancement of both even and odd modes increases in R

_{1}. The reason for this high increase in the field-enhancement is because of the decrease in the effective length of the coupled-resonator system as the resonators are decoupled. This decrease in the effective length results in the decrease of the mode-volume of the structure, which directly translates into a higher field enhancement. In simulations, as φ approaches π, even and odd modes gradually overlap and become numerically indistinguishable. In Fig. 7, the dashed lines connect the last simulation point for which even and odd modes were distinguishable (i.e., φ = 0.95π) to the limiting case of zero coupling (i.e., φ = π), where the two modes completely overlap. It is observed that in each resonator (R

_{1}and R

_{2}) both even and odd modes exhibit field enhancement simultaneously. This confirms that waves in resonance with these modes exhibit enhanced nonlinear interaction. However, this enhancement varies as the resonance frequency spacing is tuned and this has to be taken into account for any application.

## 5. Conclusion

## Appendix A. Resonance condition of the coupled-resonator device

13. J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express **12**(1), 90–103 (2004). [CrossRef] [PubMed]

**T**is the transfer matrix of a general DC coupling the two resonators in which

*θ*is the propagation phase, and

_{c}*t*and

_{c}*κ*are the amplitude through and cross-coupling coefficients, respectively. Also, through the feedback path from

_{c}*L*is the length of each resonator and

*β*is propagation constant of resonators. By combining Eqs. (1) and (2) we haveand by substituting for

**T**from Eq. (1) in Eq. (3), the following eigenvalue equation for the resonance frequency of the coupled-resonator device is derived:Here,

2. Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express **17**(4), 2247–2254 (2009). [CrossRef] [PubMed]

*t*

^{2}and

*κ*

^{2}, respectively. For the coupler in the single-point-coupled resonator (Fig. 1(b)), we haveand for the MZI coupler in the two-point-coupled resonator (Fig. 1(c)), we have,where,

## Acknowledgments

## References and links

1. | R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. |

2. | Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express |

3. | A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express |

4. | A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science |

5. | A. H. Atabaki, M. Soltani, S. Yegnanarayanan, A. A. Eftekhar, and A. Adibi, “Optimization of Metallic Micro-Heaters for Reconfigurable Silicon Photonics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4. |

6. | M. A. Popovic, T. Barwicz, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Transparent Wavelength Switching of Resonant Filters,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CPDA2. |

7. | L. Chen, N. Sherwood-Droz, and M. Lipson, “Compact bandwidth-tunable microring resonators,” Opt. Lett. |

8. | J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, “All-fiber comb filter with tunable free spectral range,” Opt. Lett. |

9. | Y. G. Han, X. Y. Dong, J. H. Lee, and S. B. Lee, “Wavelength-spacing-tunable multichannel filter incorporating a sampled chirped fiber Bragg grating based on a symmetrical chirp-tuning technique without center wavelength shift,” Opt. Lett. |

10. | M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express |

11. | M. Soltani, S. Yegnanarayanan, Q. Li, and A Adibi, “Systematic Engineering of Waveguide-Resonator Coupling for Silicon Microring/Microdisk/Racetrack Resonators: Theory and Experiment,” (accepted, IEEE J. Quantum Electron. (to appear)). |

12. | H. A. Haus, |

13. | J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(230.5750) Optical devices : Resonators

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: March 22, 2010

Revised Manuscript: April 19, 2010

Manuscript Accepted: April 20, 2010

Published: April 21, 2010

**Citation**

Amir H. Atabaki, Babak Momeni, Ali A. Eftekhar, Ehsan S. Hosseini, Siva Yegnanarayanan, and Ali Adibi, "Tuning of resonance-spacing in a traveling-wave resonator device," Opt. Express **18**, 9447-9455 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9447

Sort: Year | Journal | Reset

### References

- R. Soref, “The Past, Present, and Future of Silicon Photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006). [CrossRef]
- Q. Li, M. Soltani, S. Yegnanarayanan, and A. Adibi, “Design and demonstration of compact, wide bandwidth coupled-resonator filters on a siliconon- insulator platform,” Opt. Express 17(4), 2247–2254 (2009). [CrossRef] [PubMed]
- A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008). [CrossRef] [PubMed]
- A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]
- A. H. Atabaki, M. Soltani, S. Yegnanarayanan, A. A. Eftekhar, and A. Adibi, “Optimization of Metallic Micro-Heaters for Reconfigurable Silicon Photonics,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CThB4.
- M. A. Popovic, T. Barwicz, F. Gan, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kärtner, “Transparent Wavelength Switching of Resonant Filters,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CPDA2.
- L. Chen, N. Sherwood-Droz, and M. Lipson, “Compact bandwidth-tunable microring resonators,” Opt. Lett. 32(22), 3361–3363 (2007). [CrossRef] [PubMed]
- J. Magné, P. Giaccari, S. LaRochelle, J. Azaña, and L. R. Chen, “All-fiber comb filter with tunable free spectral range,” Opt. Lett. 30(16), 2062–2064 (2005). [CrossRef] [PubMed]
- Y. G. Han, X. Y. Dong, J. H. Lee, and S. B. Lee, “Wavelength-spacing-tunable multichannel filter incorporating a sampled chirped fiber Bragg grating based on a symmetrical chirp-tuning technique without center wavelength shift,” Opt. Lett. 31(24), 3571–3573 (2006). [CrossRef] [PubMed]
- M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15(8), 4694–4704 (2007). [CrossRef] [PubMed]
- M. Soltani, S. Yegnanarayanan, Q. Li, and A Adibi, “Systematic Engineering of Waveguide-Resonator Coupling for Silicon Microring/Microdisk/Racetrack Resonators: Theory and Experiment,” (accepted, IEEE J. Quantum Electron. (to appear)).
- H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).
- J. Poon, J. Scheuer, S. Mookherjea, G. Paloczi, Y. Huang, and A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express 12(1), 90–103 (2004). [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.