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Ring Resonator Gap Determination Design Rule and Parameter Extraction Method for Sub-GHz Resolution Whole C-Band Si_{3}N_{4} Integrated Spectrometer

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## Abstract

**:**

_{3}N

_{4}platform. The parameter extraction method is used to analyze the measured characterization data of the ring resonators. The results show good agreement within ~43 nm between the design rule and the gaps size determined by the parameters extracted from the measured data and provide experimental confirmation of the technological viability of the ring resonators required by the spectrometer.

## 1. Introduction

_{3}N

_{4}platform offers a compromise between these two extremes. One of the foci of recent research on Si

_{3}N

_{4-}based RR is the achievement of ultra-high Q ring resonators using ultra-low loss waveguides. Spencer et al. achieved intrinsic quality factor (Q

_{int}) values of 81 million by adjusting single mode coupling to multimode waveguide widths [17]. Careful reduction of scattering and absorption losses leads to a Si

_{3}N

_{4}ring resonator with 422 million intrinsic Q and 0.060 dB/m waveguide loss [18]. Recently, Liu et al. demonstrated a 720 million intrinsic Q resonator with 0.034 dB/m waveguide loss in a 200 mm wafer-scale CMOS-foundry compatible Si

_{3}N

_{4}process [19]. In addition, introducing a photonic crystal (PhC) within the ring resonator to affect the dispersion properties achieved high Q performance on a Si

_{3}N

_{4}platform [20,21].

_{3}N

_{4}/SiO

_{2}-based multi-project wafer (MPW) process offered by LioniX International was chosen for the fabrication of standalone add-drop ring resonators. The minimum gap size rule is applied to their design with a range of gaps targeting <6% power coupling. The fabricated ring resonator test structures are experimentally characterized, and the measured data is analyzed using the parameter extraction method. The results show good agreement between the design rule and parameters extracted from the measured data and provide experimental confirmation of the technological viability of the ring resonators required by the spectrometer.

## 2. Theory

#### 2.1. Parameter Extraction Method

#### 2.2. Dependence of Ring Resonator Coupling Coefficients on Gap

#### 2.3. Quality Factor and Finesse

## 3. Fabrication and Experimental Setup

_{00}and TM

_{00}modes through the straight waveguide. The straight waveguide loss of the TE

_{00}mode is ≤0.5 dB/cm, as specified by LioniX International. The TM polarization has a much larger propagation loss and bending loss and is therefore not supported. To facilitate optical characterization, the chip is pigtailed using polarization-maintaining fiber (PMF) arrays and wire bonded.

_{1}), 1.5 μm (RR

_{2}), 1.8 μm (RR

_{3}-RR

_{4}), and 2 μm (RR

_{5}—not shown in Figure 3a) to enable an assessment of the utility of the design rule. Each variant operates over the whole C band. Figure 3b shows the measured transmission spectrum of the RR

_{1}. A tunable laser (Agilent 81680A) capable of tuning over the whole C-band is utilized for characterizing the ring resonators. A polarization controller is utilized to maximize TE mode transmission. The input power to the device under test (DUT) is 0 dBm. The output is detected by an optical power sensor (Agilent 81632A) and analyzed by a lightwave measurement system (Agilent 8164A). It can be observed that resonant peak transmission at the drop port of the ring is almost constant at −5 dBm over the whole C band. The optical loss includes the pigtailed fiber-chip coupling losses, which can be estimated individually by using the alignment loop waveguides present in the chip. Each access waveguide is terminated by an integrated spot size converter (SSC) at the end facets of the chip.

## 4. Discussion

_{1}, which shows the shift of the resonant frequency over one FSR. Similar tuning behavior is observed for RR

_{2}, RR

_{3}, and RR

_{5}, which use an identical phase shifter configuration and thus provide similar linear I-V characteristics corresponding to a heater resistance of ~735 Ω. RR

_{4}uses a phase shifter, which is shorter in length and, thus, has a lower resistance of ~375 Ω. Figure 4b shows that a similar linear dependence between the resonant wavelength shift and applied power is maintained for all phase shifter configurations.

_{1}, RR

_{3}, RR

_{4}, and RR

_{5}are 193.4863, 193.4878, 193.4446, and 193.4678 THz, respectively. A linear fit has been achieved for all ring resonators with a noise-like residual with a root mean squared magnitude of 0.3536, 0.3489, 0.3673, and 0.3611 GHz for RR

_{1}, RR

_{3}, RR

_{4}, and RR

_{5,}respectively. To investigate the effect of coarser sampling on the validity of linear fitting, drop and through transmissions of the individual ring are measured over different wavelength spans with different resolutions at different times, and almost identical fitting has been observed. Quadratic fitting with the least squares method over these resonant frequencies over the corresponding span reveals a very small contribution of dispersion in the FSR evolution with wavelength, which is also evident from the linear fit.

- The effective index split of the two lowest-order local modes is found using a mode solver. The accuracy may be improved by increasing the number of local modes in the interaction;
- The difference data may be fitted to a suitable curve by a curve fitting toolbox. For an adiabatic curved coupler, the dependence of the effective index difference as a function of z is certainly a smooth bell-shaped curve, as in (21);
- The fitting will aid its numerical integration. If the asymptotic tails decay exponentially, it will allow an analytic integration of the tail region for $l\to \infty $. This will predict the overall power transfer matrix of the couplers based on proximate curved waveguides.

_{1}, RR

_{2}, and RR

_{3}.

_{5}, which has a smaller FSR of ~46.55 GHz. Sub-GHz bandwidth cannot be achieved for RR

_{1}. The loss $\gamma $ can be disentangled further into intrinsic ring waveguide loss and extrinsic coupler excess loss if the propagation and bending losses established by the process are known. LioniX International guarantees a straight waveguide loss <0.5 dB/cm with a typical value of ~0.2 dB/cm and negligible bending loss for its TriPleX™ ADS MPW process and lower waveguide loss for a dedicated run using stepper lithography. The losses extracted for RR

_{1}and RR

_{2}reveal that the straight waveguide loss is well below the upper limit. The loss also increases with the gap. These observations suggest a better waveguide loss figure has been achieved in the MPW run, and the fabricated ring coupler suffers from non-zero excess loss increasing with a gap. The excess loss per coupler is estimated on the basis of a straight waveguide loss of 0.2 dB/cm and negligible bending loss, which results in the maximum excess loss per coupler as follows: ~0.025 dB, ~0.05 dB, ~0.06 dB, ~0.085 dB, and ~0.055 dB for RR

_{1}, RR

_{2}, RR

_{3}, RR

_{4}, and RR

_{5}respectively.

_{5}than that of RR

_{3}, as RR

_{5}is located in a different location than the rest of the rings. The outlier is RR

_{4}. The loss for RR

_{4}is higher than RR

_{3}with the same coupler configuration, which suggests the additional loss and thus larger bandwidth is a consequence of the different phase shifter geometry. The geometries differ in length only as shown in Figure 3a; RR

_{3}has a phase shifter with a length of 2577.4 μm, whereas the phase shifter of RR

_{4}has a length of 1265.3 μm. Each phase shifter is formed by the Cr heater with Cr/Au electrical leads.

_{2}shows the largest deviation from its predicted coupling coefficient. A match between the measured coupling parameter for RR

_{2}and its corresponding gap from the prediction results in a gap of ~1.2429 μm instead of 1.2 μm. The difference is ~42.9 nm, which suggests that measurement points are well within the error bars due to fabrication uncertainty. LioniX International confirms that from 2022, the MPW process will be updated to the stepper lithography used for dedicated runs, which will substantially improve the loss and dimension uncertainty of the MPW process.

## 5. Conclusions

_{3}N

_{4}platform using an MPW process. A very good match between the predicted and measured coupling behavior has been found for all rings. The results suggest a ring resonator with a gap between 1.2 and 1.5 μm can meet the tight specifications perfectly while maintaining less loss. The parameter extraction method used to validate the design procedure is a single resonance-based method, which only needs intensity data from the through- and drop-path of the rings to disentangle the loss and coupling coefficients. The associated data analysis, with the assumptions of identical add- and drop couplers with adiabatic mode evolution, can solve the phase problem, which convolutes the separation of these parameters. The proposed method retrieves the complex transmission from an intensity-only measurement. The design rule and parameter extraction method can be adapted to other material platforms.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Bogaerts, W.; Dumon, P.; Thourhout, D.V.; Taillaert, D.; Jaenen, P.; Wouters, J.; Beckx, S.; Wiaux, V.; Baets, R.G. Compact wavelength-selective functions in silicon-on-insulator photonic wires. IEEE J. Sel. Top. Quantum Electron.
**2006**, 12, 1394–1401. [Google Scholar] [CrossRef] - Antonacci, G.; Elsayad, K.; Polli, D. On-Chip Notch Filter on a Silicon Nitride Ring Resonator for Brillouin Spectroscopy. ACS Photonics
**2022**, 9, 772–777. [Google Scholar] [CrossRef] - Xia, F.; Sekaric, L.; Vlasov, Y. Ultracompact optical buffers on a silicon chip. Nat. Photonics
**2007**, 1, 65–71. [Google Scholar] [CrossRef] - Ibrahim, T.; Grover, A.R.; Kuo, L.C.; Kanakaraju, S.; Calhoun, L.C.; Ho, P.T. All-optical AND/NAND logic gates using semiconductor microresonators. IEEE Photon. Technol.
**2003**, 15, 1422–1424. [Google Scholar] [CrossRef] - Ji, R.; Yang, L.; Zhang, L.; Tian, Y.; Ding, J.; Chen, H.; Lu, Y.; Zhou, P.; Zhu, W. Microring-resonator-based four-port optical router for photonic networks-on-chip. Opt. Express
**2011**, 19, 18945–18955. [Google Scholar] [CrossRef] - Fan, X.; White, I.M.; Zhu, H.; Suter, J.D.; Oveys, H. Overview of novel integrated optical ring resonator bio/chemical sensors. In Proceedings of the SPIE Laser Resonators Beam Control IX, San Jose, CA, USA, 14 February 2007. [Google Scholar]
- Xu, Q.; Manipatruni, S.; Schmidt, B.; Shakya, J.; Lipson, M. 12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulators. Opt. Express
**2007**, 15, 430–436. [Google Scholar] [CrossRef] - Jin, W.; Yang, Q.F.; Chang, L.; Shen, B.; Wang, H.; Leal, M.A.; Wu, L.; Gao, M.; Feshali, A.; Paniccia, M.; et al. Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high-Q microresonators. Nat. Photonics
**2021**, 15, 346–353. [Google Scholar] [CrossRef] - Ye, Z.; Twayana, K.; Andrekson, P.A. High-Q Si
_{3}N_{4}microresonators based on a subtractive processing for Kerr nonlinear optics. Opt. Express**2019**, 27, 35719–35727. [Google Scholar] [CrossRef] - Bogaerts, W.; Heyn, P.D.; Vaerenbergh, T.V.; Vos, K.D.; Selvaraja, S.K.; Claes, T.; Dumon, P.; Bienstman, P.; Thourhout, D.V.; Baets, R. Silicon microring resonators. Laser Photonics Rev.
**2012**, 6, 47–73. [Google Scholar] [CrossRef] - Mahmoud, M.; Cai, L.; Bottenfield, C.; Piazza, G. Lithium niobate electro-optic racetrack modulator etched in Y-cut LNOI platform. IEEE Photon. J.
**2018**, 10, 1–10. [Google Scholar] [CrossRef] - Chen, L.; Wood, M.G.; Reano, R.M. 12.5 pm/V hybrid silicon and lithium niobate optical microring resonator with integrated electrodes. Opt. Express
**2013**, 21, 27003–27010. [Google Scholar] [CrossRef] [PubMed] - Ahmed, A.N.R.; Shi, S.; Zablocki, M.; Yao, P.; Prather, D.W. Tunable hybrid silicon nitride and thin-film lithium niobate electro-optic microresonator. Opt. Lett.
**2019**, 44, 618–621. [Google Scholar] [CrossRef] [PubMed] - Grover, R.; Absil, P.P.; Van, V.; Hryniewicz, J.V.; Little, B.E.; King, O.; Calhoun, L.C.; Johnson, F.G.; Ho, P.T. Vertically coupled GaInAsP–InP microring resonators. Opt. Lett.
**2001**, 26, 506–508. [Google Scholar] [CrossRef] [PubMed] - Ibrahim, T.A.; Van, V.; Ho, P.T. All-optical time-division demultiplexing and spatial pulse routing with a GaAs/AlGaAs microring resonator. Opt. Lett.
**2002**, 27, 803–805. [Google Scholar] [CrossRef] [PubMed] - Bogaerts, W.; Bienstman, P.; Baets, R. Scattering at sidewall roughness in photonic crystal slabs. Opt. Lett.
**2003**, 28, 689–691. [Google Scholar] [CrossRef] - Spencer, D.T.; Bauters, J.F.; Heck, M.J.; Bowers, J.E. Integrated waveguide coupled Si
_{3}N_{4}resonators in the ultrahigh-Q regime. Optica**2014**, 1, 153–157. [Google Scholar] [CrossRef] - Puckett, M.W.; Liu, K.; Chauhan, N.; Zhao, Q.; Jin, N.; Cheng, H.; Wu, J.; Behunin, R.O.; Rakich, P.T.; Nelson, K.D.; et al. 422 Million intrinsic quality factor planar integrated all-waveguide resonator with sub-MHz linewidth. Nat. Commun.
**2021**, 12, 1–8. [Google Scholar] - Liu, K.; Jin, N.; Cheng, H.; Chauhan, N.; Puckett, M.W.; Nelson, K.D.; Behunin, R.O.; Rakich, P.T.; Blumenthal, D.J. Ultralow 0.034 dB/m loss wafer-scale integrated photonics realizing 720 million Q and 380 μW threshold Brillouin lasing. Opt. Lett.
**2022**, 47, 1855–1858. [Google Scholar] [CrossRef] - Ciminelli, C.; Innone, F.; Brunetti, G.; Conteduca, D.; Dell’Olio, F.; Tatoli, T.; Armenise, M.N. Rigorous model for the design of ultra-high Q-factor resonant cavities. In Proceedings of the 18th International Conference on Transparent Optical Networks (ICTON), Trento, Italy, 10–14 July 2016. [Google Scholar]
- Lu, X.; McClung, A.; Srinivasan, K. High-Q slow light and its localization in a photonic crystal microring. Nat. Photonics
**2022**, 16, 66–71. [Google Scholar] [CrossRef] - Kyotoku, B.B.; Chen, L.; Lipson, M. Sub-nm resolution cavity enhanced micro-spectrometer. Opt. Express
**2010**, 18, 102–107. [Google Scholar] [CrossRef] - Yurtsever, G.; Baets, R. Integrated spectrometer on silicon on insulator. In Proceedings of the 16th Annual Symposium of the IEEE Photonics Benelux Chapter, Ghent, Belgium, 1–2 December 2011. [Google Scholar]
- Xia, Z.; Eftekhar, A.A.; Soltani, M.; Momeni, B.; Li, Q.; Chamanzar, M.; Yegnanarayanan, S.; Adibi, A. High resolution on-chip spectroscopy based on miniaturized microdonut resonators. Opt. Express
**2011**, 19, 12356–12364. [Google Scholar] [CrossRef] [PubMed] - Xiang, C.; Morton, P.A.; Khurgin, J.; Morton, C.; Bowers, J.E. Widely tunable Si
_{3}N_{4}triple-ring and quad-ring resonator laser reflectors and filters. In Proceedings of the 2018 IEEE 15th International Conference on Group IV Photonics (GFP), Cancun, Mexico, 29–31 August 2018. [Google Scholar] - Zheng, S.; Cai, H.; Song, J.; Zou, J.; Liu, P.Y.; Lin, Z.; Kwong, D.-L.; Liu, A.-Q. A Single-Chip Integrated Spectrometer via Tunable Microring Resonator Array. IEEE Photon. J.
**2019**, 11, 1–9. [Google Scholar] [CrossRef] - Zheng, S.N.; Zou, J.; Cai, H.; Song, J.F.; Chin, L.K.; Liu, P.Y.; Lin, Z.P.; Kwong, D.L.; Liu, A.Q. Microring resonator-assisted Fourier transform spectrometer with enhanced resolution and large bandwidth in single chip solution. Nat. Commun.
**2019**, 10, 1–8. [Google Scholar] [CrossRef] [PubMed] - Li, Y.; Li, J.; Yu, H.; Yu, H.; Chen, H.; Yang, S.; Chen, M. On-chip photonic microsystem for optical signal processing based on silicon and silicon nitride platforms. Adv. Opt. Technol.
**2018**, 7, 81–101. [Google Scholar] [CrossRef] - Kita, D.M.; Lin, H.; Agarwal, A.; Richardson, K.; Luzinov, I.; Gu, T.; Hu, J. On-chip infrared spectroscopic sensing: Redefining the benefits of scaling. IEEE J. Sel. Top. Quantum Electron.
**2016**, 23, 340–349. [Google Scholar] [CrossRef] - Hasan, M.; Rad, M.; Hasan, G.M.; Liu, P.; Dumais, P.; Bernier, E.; Hall, T.J. Ultra-high resolution wideband On-chip spectrometer. IEEE Photon. J.
**2020**, 12, 1–17. [Google Scholar] [CrossRef] - Hasan, M.; Hasan, G.M.; Ghorbani, H.; Rad, M.; Liu, P.; Bernier, E.; Hall, T. Circuit design and integration feasibility of a high-resolution broadband on-chip spectral monitor. arXiv
**2021**, arXiv:2108.10121. [Google Scholar] - Zhuang, L.; Marpaung, D.; Burla, M.; Beeker, W.; Leinse, A.; Roeloffzen, C. Low-loss, high-index-contrast Si
_{3}N_{4}/SiO_{2}optical waveguides for optical delay lines in microwave photonics signal processing. Opt. Express**2011**, 19, 23162–23170. [Google Scholar] [CrossRef] - Yariv, A. Universal relations for coupling of optical power between microresonators and dielectric waveguides. Electron. Lett.
**2000**, 36, 321–322. [Google Scholar] [CrossRef] - Gifford, D.K.; Soller, B.J.; Wolfe, M.S.; Froggatt, M.E. Optical vector network analyzer for single-scan measurements of loss, group delay, and polarization mode dispersion. Appl. Opt.
**2005**, 44, 7282–7286. [Google Scholar] [CrossRef] - Heebner, J.E.; Wong, V.; Schweinsberg, A.; Boyd, R.W.; Jackson, D.J. Optical transmission characteristics of fiber ring resonators. IEEE J. Quantum Electron.
**2004**, 40, 726–730. [Google Scholar] [CrossRef] - Matres, J.; Ballesteros, G.C.; Mas, S.; Brimont, A.; Sanchis, P.; Marti, J.; Oton, C.J. Optical phase characterization of photonic integrated devices. IEEE J. Sel. Top. Quantum Electron.
**2013**, 20, 417–421. [Google Scholar] [CrossRef] - McKinnon, W.R.; Xu, D.-X.; Storey, C.; Post, E.; Densmore, A.; Delâge, A.; Waldron, P.; Schmid, J.H.; Janz, S. Extracting coupling and loss coefficients from a ring resonator. Opt. Express
**2009**, 17, 18971–18982. [Google Scholar] [CrossRef] [PubMed] - Roeloffzen, C.G.H.; Hoekman, M.; Klein, E.J.; Wevers, L.S.; Timens, R.B.; Marchenko, D.; Geskus, D.; Dekker, R.; Alippi, A.; Grootjans, R.; et al. Low-loss Si
_{3}N_{4}TriPleX optical waveguides: Technology and applications overview. IEEE J. Sel. Top. Quantum Electron.**2018**, 24, 1–21. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**(

**a**) Simulated transversal profile of the major electric field component E

_{x}of the TE

_{00}mode of the ADS waveguide, W = 1.1 μm is the top-width of the top stripe; (

**b**) effective index variation, and (

**c**) group index variation of first three modes with the width (W) of the waveguide.

**Figure 3.**(

**a**) Micrograph of different ring resonators. Each RR has the same radius, but different gaps. The minimum gaps of the ring waveguide and access waveguide are 1.2 μm, 1.5 μm, and 1.8 μm for RR

_{1}, RR

_{2}, RR

_{3}, and RR

_{4}, respectively. All rings are equipped with thermo-optic phase shifter heating elements, which cover almost the whole circumference of the ring waveguide except RR

_{4}, which covers less than half of the circumference; (

**b**) measured drop path transmission spectrum of the RR

_{1}over the whole C band.

**Figure 4.**(

**a**) Tuning spectra of RR

_{1}for different thermo-optic phase shifter applied voltage, (

**b**) resonant wavelength shifts of RR

_{1}, RR

_{2}, and RR

_{4}as a function of heater power, and (

**c**) linear fit to the multiplicity of resonant frequencies for RR

_{1}, RR

_{3}, RR

_{4}, and RR

_{5}.

**Figure 6.**Drop- and through-path transmission spectra for (

**a**,

**b**) RR

_{1}, (

**c**,

**d**) RR

_{2}, and (

**e**,

**f**) RR

_{3}. The measurements have been taken with 0.1 pm resolution using the abovementioned experimental setup. The reference frequency is 193.414 THz (1550 nm).

Gap (μm) | FWHM Bandwidth (GHz) | FSR (GHz) | Cross-Power Coupling Ratio (%) | Ring Transmission Loss (dB) | Quality Factor, Q | |
---|---|---|---|---|---|---|

RR_{1} | 1.2 | ~1.43 | ~49.4 | 7.46 | 0.12 | 135,258 |

RR_{2} | 1.5 | ~0.68 | ~49.7 | 2.33 | 0.17 | 284,469 |

RR_{3} | 1.8 | ~0.45 | ~49.55 | 0.64 | 0.19 | 429,867 |

RR_{4} | 1.8 | ~0.55 | ~49.8 | 0.68 | 0.24 | 351,671 |

RR_{5} | 2.0 | ~0.35 | ~46.55 | 0.29 | 0.18 | 552,640 |

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**MDPI and ACS Style**

Hasan, G.M.; Liu, P.; Hasan, M.; Ghorbani, H.; Rad, M.; Bernier, E.; Hall, T.J.
Ring Resonator Gap Determination Design Rule and Parameter Extraction Method for Sub-GHz Resolution Whole C-Band Si_{3}N_{4} Integrated Spectrometer. *Photonics* **2022**, *9*, 651.
https://doi.org/10.3390/photonics9090651

**AMA Style**

Hasan GM, Liu P, Hasan M, Ghorbani H, Rad M, Bernier E, Hall TJ.
Ring Resonator Gap Determination Design Rule and Parameter Extraction Method for Sub-GHz Resolution Whole C-Band Si_{3}N_{4} Integrated Spectrometer. *Photonics*. 2022; 9(9):651.
https://doi.org/10.3390/photonics9090651

**Chicago/Turabian Style**

Hasan, Gazi Mahamud, Peng Liu, Mehedi Hasan, Houman Ghorbani, Mohammad Rad, Eric Bernier, and Trevor J. Hall.
2022. "Ring Resonator Gap Determination Design Rule and Parameter Extraction Method for Sub-GHz Resolution Whole C-Band Si_{3}N_{4} Integrated Spectrometer" *Photonics* 9, no. 9: 651.
https://doi.org/10.3390/photonics9090651