Thermal tuning of Kerr frequency combs in silicon nitride microring resonators Xiaoxiao Xue,1,3 Yi Xuan,1,2 Cong Wang,1 Pei-Hsun Wang,1 Yang Liu,1 Ben Niu,1,2 Daniel E. Leaird,1 Minghao Qi,1,2 and Andrew M. Weiner1,2,4 1
School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA 2 Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA 3 [email protected] 4 [email protected]
Abstract: Microresonator based Kerr frequency comb generation has many attractive features, including ultrabroad spectra, chip-level integration, and low power consumption. Achieving precise tuning control over the comb frequencies will be important for a number of practical applications, but has been little explored for microresonator combs. In this paper, we characterize the thermal tuning of a coherent Kerr frequency comb generated from an on-chip silicon nitride microring. When the microring temperature is changed by ~70 °C with an integrated microheater, the line spacing and center frequency of the comb are tuned respectively by −253 MHz (−3.57 MHz/°C) and by −175 GHz (−2.63 GHz/°C); the latter constitutes 75% of the comb line spacing. From these results we obtain a shift of 25 GHz (362.07 MHz/°C) in the comb carrier-envelope offset frequency. Numerical simulations are performed by taking into account the thermo-optic effects in the waveguide core and cladding. The temperature variation of the comb line spacing predicted from simulations is close to that observed in experiments. The time-dependent thermal response of the microheater based tuning scheme is characterized; time constants of 30.9 μs and 0.71ms are observed. ©2015 Optical Society of America OCIS codes: (140.3945) Microcavities; (140.6810) Thermal effects; (190.3270) Kerr effect; (190.4380) Nonlinear optics, four-wave mixing.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9.
P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101(9), 093902 (2008). L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4(1), 41–45 (2010). J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8(5), 369–374 (2014). A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015). F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770– 776 (2011). S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84(5), 053833 (2011).
10. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6(7), 480–487 (2012). 11. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Modelocking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21(1), 1335–1343 (2013). 12. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013). 13. P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112(4), 043905 (2014). 14. Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1(3), 137–144 (2014). 15. W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39(10), 2920–2923 (2014). 16. P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015). 17. X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9(9), 594–600 (2015). 18. X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photonics Rev. 9(4), L23–L28 (2015). 19. S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114(5), 053901 (2015). 20. Y.-D. Hsieh, Y. Iyonaga, Y. Sakaguchi, S. Yokoyama, H. Inaba, K. Minoshima, F. Hindle, T. Araki, and T. Yasui, “Spectrally interleaved, comb-mode-resolved spectroscopy using swept dual terahertz combs,” Sci. Rep. 4, 3816 (2014). 21. J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014). 22. S. T. Cundiff, J. Ye, and J. L. Hall, “Optical frequency synthesis based on mode-locked lasers,” Rev. Sci. Instrum. 72(10), 3749 (2001). 23. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3(3), 031003 (2013). 24. H. Jung, K. Y. Fong, C. Xiong, and H. X. Tang, “Electrical tuning and switching of an optical frequency comb generated in aluminum nitride microring resonators,” Opt. Lett. 39(1), 84–87 (2014). 25. H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010). 26. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011). 27. T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004). 28. P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109(26), 263901 (2012). 29. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35(19), 3234–3236 (2010). 30. P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009). 31. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer, 2005). 32. C. L. Tien and T.-W. Lin, “Thermal expansion coefficient and thermomechanical properties of SiN(x) thin films prepared by plasma-enhanced chemical vapor deposition,” Appl. Opt. 51(30), 7229–7235 (2012). 33. J.-H. Zhao, T. Ryan, P. S. Ho, A. J. McKerrow, and W.-Y. Shih, “Measurement of elastic modulus, Poisson ratio, and coefficient of thermal expansion of on-wafer submicron films,” J. Appl. Phys. 85(9), 6421 (1999). 34. Y. Okada and Y. Tokumaru, “Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K,” J. Appl. Phys. 56(2), 314 (1984). 35. A. Arbabi and L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of Si3N4 and SiO(x) using microring resonances,” Opt. Lett. 38(19), 3878–3881 (2013). 36. A. C. Hryciw, R. D. Kekatpure, S. Yerci, L. Dal Negro, and M. L. Brongersma, “Thermo-optic tuning of erbiumdoped amorphous silicon nitride microdisk resonators,” Appl. Phys. Lett. 98(4), 041102 (2011). 37. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
38. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation,” J. Appl. Phys. 83(6), 3323 (1998). 39. S. Chongsawangvirod, E. A. Irene, A. Kalintsky, S. P. Tay, and T. P. Ellul, “Refractive Index Profiles of Thermally Grown and Chemically Vapor Deposited Films on Silicon,” J. Electrochem. Soc. 137(11), 3536 (1990). 40. J. Wang, Y. Xuan, A. M. Weiner, and M. Qi, “Fast and slow optical modulation of refractive index in a SiN microring,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper STh1M.8.
1. Introduction Microresonators offer potential as compact integrated comb sources in which comb generation arises due to the Kerr nonlinearity and cascaded four-wave mixing in the optical cavity [1–7]. Many efforts have been dedicated to exploring coherent comb states and increasing the comb spectral width [8–19]. Low-noise and phase-locked microresonator combs (microcombs) spanning tens to hundreds of nm have been demonstrated [11–13, 16– 19]. The tunability of frequency combs is important for many practical applications, such as high-resolution interleaved laser spectroscopy [20], wavelength-division multiplexed (WDM) coherent communications [21], and optical frequency synthesis [22]. Unlike mode-locked lasers based on bulk optics for which the oscillating frequencies can easily be controlled by moving the position of mirrors [22], the frequencies of microcombs are mainly determined by the material refractive index and the resonator geometry, which are hard to change once the microresonators are fabricated. Mechanical actuation was proposed in [23] to shift the microresonator mode frequencies and stabilize the comb line spacing. A lead-zirconatetitanate (PZT) element was attached to one end of a fused-quartz rod on which a high quality factor microresonator was fabricated. By changing the PZT voltage, the rod could be compressed, and the mode frequencies were shifted by 5 MHz/V (the free spectral range (FSR) of the rod resonator was around 32.6 GHz). Another method is electro-optic tuning which is applicable for microresonators made of materials with a strong Pockels effect. A tuning efficiency of 24 MHz/V was demonstrated for an aluminum nitride microring resonator with an FSR of 370 GHz [24]. For both mechanical actuation and electro-optic tuning, the tuning efficiency is small compared to the microresonator FSR, making it difficult to tune the microcomb over a range significant relative to the FSR. The thermo-optic effect, which is widely employed in microresonator based optical filters [25], allows tuning of individual comb frequencies over a much wider range. Reference [26] reported tuning of the comb lines from a fused silica microresonator over more than one FSR by directly shifting the pump laser frequency. Due to the temperature change caused by absorption in the microresonator, the thermally shifted resonance approximately follows the pump laser frequency, an effect generally named thermal self-locking [27]. However, the comb did not maintain a low-noise, phase-locked state as it was tuned. The reason is that the phase-locked states of microcombs are very sensitive to the pump-resonance detuning and can only be maintained over a limited detuning range. Because the detuning of the pump laser frequency with respect to the thermally shifted resonance does change for tuning based on thermal selflocking, phased-locked operation is not maintained. Recently, in our work on dark pulse mode-locking in normal-dispersion silicon nitride (SiN) microrings [17], we used a microheater to help tune the comb. The microring was thermally shifted by changing the voltage applied on the microheater in conjuction with tuning of the pump laser to maintain an approximately constant pump-resonance detuning. As a result, the comb was successfully tuned over 75% of the FSR with the phase-locked state maintained. In [17] a principal benefit of the thermal tuning was to study the relation between mode interactions and mode locking. In this paper, we present a detailed characterization of the microheater-based frequency tuning of this comb. The variation of the comb repetition rate (line spacing) versus pump laser frequency and temperature is investigated experimentally and is successfully modeled through simulations that consider the temperature
dependent refractive index changes of the core and cladding materials. The change of the carrier-envelope offset frequency is extracted from the data on repetition rate variation with pump frequency; tuning of the offset frequency by more than 25 GHz is observed. The thermal response time is also characterized and has a dominant component of 30.9 μs . Our results show that thermal tuning is a promising mechanism for comb center frequency tuning and for precise control of the line spacing and offset frequency. 2. Experimental setup and results The microring is fabricated with low-pressure chemical vapour deposition (LPCVD) SiN waveguides embedded in silicon dioxide (SiO2). The substrate is silicon. The cross-section dimension of the waveguide is 2 μm × 550 nm . The radius is 100 μm corresponding to an FSR of ~1.85 nm. The loaded quality factor (Q) is 7.7 × 105. A microheater is formed by depositing a layer of Au(300 nm)/Cr(5 nm) on the upper cladding right above the microring. The thickness of the upper cladding is 3.5 µm to avoid severe Q degradation that might be caused by proximity to the heater. The heater resistance with a geometry shown in the inset microscope image in Fig. 1 is ~291 Ω. By changing the voltage applied on the heater, the resonant wavelengths of the fundamental TE mode (which is pumped for comb generation) can be shifted with an efficiency of 0.82 nm/W. Another experiment is performed to evaluate the temperature change by heating the entire microring chip uniformly with a thermoelectric heat pump (not using the microheater) and probing the temperature with a thermistor. The efficiency of resonance shift versus temperature change is found to be ~21.1 pm/°C (−2.63 GHz/°C). We note though that one possible difference between using the microheater and heating the entire chip with the thermoelectric heat pump comes from the thermal expansion effect. When the microheater is used, the temperature increase is mainly restricted to the microheater covered area. The microring is surrounded by other parts of the chip that are not heated; this is expected to constrain thermal expansion relative to the case in which the whole chip is heated thermoelectrically. The thermal expansion coefficients of the different materials on the chip (SiN, SiO2, Si) are on the order of 10−6/°C. In comparison, the thermooptic coefficient of SiN (variation of refractive index with temperature) is on the order of 10−5/°C. Thus the contribution of thermal expansion should be relatively small (see more discussions at the beginning of the next section). Consequently we believe that comparing the resonant shifts obtained with the microheater to those obtained with the thermoelectric heat pump should provide a reasonable estimation of the local temperature changes induced via the microheater. The experimental setup for comb generation and characterization is illustrated in Fig. 1. The frequency of the pump laser is monitored by using a high-precision wavemeter. By optimizing the pump-resonance detuning at a pump power of ~1.7 W, a broadband frequency comb is generated and transitions to a low-noise phase-locked state. The details of the transition process which is related to dark pulse formation in the microring were discussed in [17]. To tune the comb, the pump laser wavelength and the microring are tuned in tandem in small steps (
School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA 2 Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA 3 [email protected] 4 [email protected]
Abstract: Microresonator based Kerr frequency comb generation has many attractive features, including ultrabroad spectra, chip-level integration, and low power consumption. Achieving precise tuning control over the comb frequencies will be important for a number of practical applications, but has been little explored for microresonator combs. In this paper, we characterize the thermal tuning of a coherent Kerr frequency comb generated from an on-chip silicon nitride microring. When the microring temperature is changed by ~70 °C with an integrated microheater, the line spacing and center frequency of the comb are tuned respectively by −253 MHz (−3.57 MHz/°C) and by −175 GHz (−2.63 GHz/°C); the latter constitutes 75% of the comb line spacing. From these results we obtain a shift of 25 GHz (362.07 MHz/°C) in the comb carrier-envelope offset frequency. Numerical simulations are performed by taking into account the thermo-optic effects in the waveguide core and cladding. The temperature variation of the comb line spacing predicted from simulations is close to that observed in experiments. The time-dependent thermal response of the microheater based tuning scheme is characterized; time constants of 30.9 μs and 0.71ms are observed. ©2015 Optical Society of America OCIS codes: (140.3945) Microcavities; (140.6810) Thermal effects; (190.3270) Kerr effect; (190.4380) Nonlinear optics, four-wave mixing.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9.
P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007). A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101(9), 093902 (2008). L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4(1), 41–45 (2010). J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010). T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011). B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8(5), 369–374 (2014). A. G. Griffith, R. K. W. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain, Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, and M. Lipson, “Silicon-chip mid-infrared frequency comb generation,” Nat. Commun. 6, 6299 (2015). F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5(12), 770– 776 (2011). S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84(5), 053833 (2011).
10. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6(7), 480–487 (2012). 11. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, and A. L. Gaeta, “Modelocking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21(1), 1335–1343 (2013). 12. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8(2), 145–152 (2013). 13. P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112(4), 043905 (2014). 14. Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1(3), 137–144 (2014). 15. W. Liang, A. A. Savchenkov, V. S. Ilchenko, D. Eliyahu, D. Seidel, A. B. Matsko, and L. Maleki, “Generation of a coherent near-infrared Kerr frequency comb in a monolithic microresonator with normal GVD,” Opt. Lett. 39(10), 2920–2923 (2014). 16. P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015). 17. X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9(9), 594–600 (2015). 18. X. Xue, Y. Xuan, P.-H. Wang, Y. Liu, D. E. Leaird, M. Qi, and A. M. Weiner, “Normal-dispersion microcombs enabled by controllable mode interactions,” Laser Photonics Rev. 9(4), L23–L28 (2015). 19. S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114(5), 053901 (2015). 20. Y.-D. Hsieh, Y. Iyonaga, Y. Sakaguchi, S. Yokoyama, H. Inaba, K. Minoshima, F. Hindle, T. Araki, and T. Yasui, “Spectrally interleaved, comb-mode-resolved spectroscopy using swept dual terahertz combs,” Sci. Rep. 4, 3816 (2014). 21. J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8(5), 375–380 (2014). 22. S. T. Cundiff, J. Ye, and J. L. Hall, “Optical frequency synthesis based on mode-locked lasers,” Rev. Sci. Instrum. 72(10), 3749 (2001). 23. S. B. Papp, P. Del’Haye, and S. A. Diddams, “Mechanical control of a microrod-resonator optical frequency comb,” Phys. Rev. X 3(3), 031003 (2013). 24. H. Jung, K. Y. Fong, C. Xiong, and H. X. Tang, “Electrical tuning and switching of an optical frequency comb generated in aluminum nitride microring resonators,” Opt. Lett. 39(1), 84–87 (2014). 25. H. Shen, M. H. Khan, L. Fan, L. Zhao, Y. Xuan, J. Ouyang, L. T. Varghese, and M. Qi, “Eight-channel reconfigurable microring filters with tunable frequency, extinction ratio and bandwidth,” Opt. Express 18(17), 18067–18076 (2010). 26. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107(6), 063901 (2011). 27. T. Carmon, L. Yang, and K. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004). 28. P. Del’Haye, S. B. Papp, and S. A. Diddams, “Hybrid electro-optically modulated microcombs,” Phys. Rev. Lett. 109(26), 263901 (2012). 29. R. Wu, V. R. Supradeepa, C. M. Long, D. E. Leaird, and A. M. Weiner, “Generation of very flat optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms,” Opt. Lett. 35(19), 3234–3236 (2010). 30. P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3(9), 529–533 (2009). 31. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Springer, 2005). 32. C. L. Tien and T.-W. Lin, “Thermal expansion coefficient and thermomechanical properties of SiN(x) thin films prepared by plasma-enhanced chemical vapor deposition,” Appl. Opt. 51(30), 7229–7235 (2012). 33. J.-H. Zhao, T. Ryan, P. S. Ho, A. J. McKerrow, and W.-Y. Shih, “Measurement of elastic modulus, Poisson ratio, and coefficient of thermal expansion of on-wafer submicron films,” J. Appl. Phys. 85(9), 6421 (1999). 34. Y. Okada and Y. Tokumaru, “Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K,” J. Appl. Phys. 56(2), 314 (1984). 35. A. Arbabi and L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of Si3N4 and SiO(x) using microring resonances,” Opt. Lett. 38(19), 3878–3881 (2013). 36. A. C. Hryciw, R. D. Kekatpure, S. Yerci, L. Dal Negro, and M. L. Brongersma, “Thermo-optic tuning of erbiumdoped amorphous silicon nitride microdisk resonators,” Appl. Phys. Lett. 98(4), 041102 (2011). 37. S. Johnson and J. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
38. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multiangle investigation,” J. Appl. Phys. 83(6), 3323 (1998). 39. S. Chongsawangvirod, E. A. Irene, A. Kalintsky, S. P. Tay, and T. P. Ellul, “Refractive Index Profiles of Thermally Grown and Chemically Vapor Deposited Films on Silicon,” J. Electrochem. Soc. 137(11), 3536 (1990). 40. J. Wang, Y. Xuan, A. M. Weiner, and M. Qi, “Fast and slow optical modulation of refractive index in a SiN microring,” in CLEO: 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper STh1M.8.
1. Introduction Microresonators offer potential as compact integrated comb sources in which comb generation arises due to the Kerr nonlinearity and cascaded four-wave mixing in the optical cavity [1–7]. Many efforts have been dedicated to exploring coherent comb states and increasing the comb spectral width [8–19]. Low-noise and phase-locked microresonator combs (microcombs) spanning tens to hundreds of nm have been demonstrated [11–13, 16– 19]. The tunability of frequency combs is important for many practical applications, such as high-resolution interleaved laser spectroscopy [20], wavelength-division multiplexed (WDM) coherent communications [21], and optical frequency synthesis [22]. Unlike mode-locked lasers based on bulk optics for which the oscillating frequencies can easily be controlled by moving the position of mirrors [22], the frequencies of microcombs are mainly determined by the material refractive index and the resonator geometry, which are hard to change once the microresonators are fabricated. Mechanical actuation was proposed in [23] to shift the microresonator mode frequencies and stabilize the comb line spacing. A lead-zirconatetitanate (PZT) element was attached to one end of a fused-quartz rod on which a high quality factor microresonator was fabricated. By changing the PZT voltage, the rod could be compressed, and the mode frequencies were shifted by 5 MHz/V (the free spectral range (FSR) of the rod resonator was around 32.6 GHz). Another method is electro-optic tuning which is applicable for microresonators made of materials with a strong Pockels effect. A tuning efficiency of 24 MHz/V was demonstrated for an aluminum nitride microring resonator with an FSR of 370 GHz [24]. For both mechanical actuation and electro-optic tuning, the tuning efficiency is small compared to the microresonator FSR, making it difficult to tune the microcomb over a range significant relative to the FSR. The thermo-optic effect, which is widely employed in microresonator based optical filters [25], allows tuning of individual comb frequencies over a much wider range. Reference [26] reported tuning of the comb lines from a fused silica microresonator over more than one FSR by directly shifting the pump laser frequency. Due to the temperature change caused by absorption in the microresonator, the thermally shifted resonance approximately follows the pump laser frequency, an effect generally named thermal self-locking [27]. However, the comb did not maintain a low-noise, phase-locked state as it was tuned. The reason is that the phase-locked states of microcombs are very sensitive to the pump-resonance detuning and can only be maintained over a limited detuning range. Because the detuning of the pump laser frequency with respect to the thermally shifted resonance does change for tuning based on thermal selflocking, phased-locked operation is not maintained. Recently, in our work on dark pulse mode-locking in normal-dispersion silicon nitride (SiN) microrings [17], we used a microheater to help tune the comb. The microring was thermally shifted by changing the voltage applied on the microheater in conjuction with tuning of the pump laser to maintain an approximately constant pump-resonance detuning. As a result, the comb was successfully tuned over 75% of the FSR with the phase-locked state maintained. In [17] a principal benefit of the thermal tuning was to study the relation between mode interactions and mode locking. In this paper, we present a detailed characterization of the microheater-based frequency tuning of this comb. The variation of the comb repetition rate (line spacing) versus pump laser frequency and temperature is investigated experimentally and is successfully modeled through simulations that consider the temperature
dependent refractive index changes of the core and cladding materials. The change of the carrier-envelope offset frequency is extracted from the data on repetition rate variation with pump frequency; tuning of the offset frequency by more than 25 GHz is observed. The thermal response time is also characterized and has a dominant component of 30.9 μs . Our results show that thermal tuning is a promising mechanism for comb center frequency tuning and for precise control of the line spacing and offset frequency. 2. Experimental setup and results The microring is fabricated with low-pressure chemical vapour deposition (LPCVD) SiN waveguides embedded in silicon dioxide (SiO2). The substrate is silicon. The cross-section dimension of the waveguide is 2 μm × 550 nm . The radius is 100 μm corresponding to an FSR of ~1.85 nm. The loaded quality factor (Q) is 7.7 × 105. A microheater is formed by depositing a layer of Au(300 nm)/Cr(5 nm) on the upper cladding right above the microring. The thickness of the upper cladding is 3.5 µm to avoid severe Q degradation that might be caused by proximity to the heater. The heater resistance with a geometry shown in the inset microscope image in Fig. 1 is ~291 Ω. By changing the voltage applied on the heater, the resonant wavelengths of the fundamental TE mode (which is pumped for comb generation) can be shifted with an efficiency of 0.82 nm/W. Another experiment is performed to evaluate the temperature change by heating the entire microring chip uniformly with a thermoelectric heat pump (not using the microheater) and probing the temperature with a thermistor. The efficiency of resonance shift versus temperature change is found to be ~21.1 pm/°C (−2.63 GHz/°C). We note though that one possible difference between using the microheater and heating the entire chip with the thermoelectric heat pump comes from the thermal expansion effect. When the microheater is used, the temperature increase is mainly restricted to the microheater covered area. The microring is surrounded by other parts of the chip that are not heated; this is expected to constrain thermal expansion relative to the case in which the whole chip is heated thermoelectrically. The thermal expansion coefficients of the different materials on the chip (SiN, SiO2, Si) are on the order of 10−6/°C. In comparison, the thermooptic coefficient of SiN (variation of refractive index with temperature) is on the order of 10−5/°C. Thus the contribution of thermal expansion should be relatively small (see more discussions at the beginning of the next section). Consequently we believe that comparing the resonant shifts obtained with the microheater to those obtained with the thermoelectric heat pump should provide a reasonable estimation of the local temperature changes induced via the microheater. The experimental setup for comb generation and characterization is illustrated in Fig. 1. The frequency of the pump laser is monitored by using a high-precision wavemeter. By optimizing the pump-resonance detuning at a pump power of ~1.7 W, a broadband frequency comb is generated and transitions to a low-noise phase-locked state. The details of the transition process which is related to dark pulse formation in the microring were discussed in [17]. To tune the comb, the pump laser wavelength and the microring are tuned in tandem in small steps (
