Thermal tuning of Kerr frequency combs in silicon …fsoptics/articles/...Thermal tuning of Kerr frequency combs in silicon nitride microring resonators Xiaoxiao Xue,1,3 Yi Xuan,1,2

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

1School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, Indiana 47907-2035, USA

2Birck Nanotechnology Center, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907, USA [email protected] [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. 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).

2. 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).

3. 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).

4. 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).

5. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).

6. B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8(5), 369–374 (2014).

7. 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).

8. 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).

9. 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).

#253388 Received 6 Nov 2015; revised 18 Dec 2015; accepted 20 Dec 2015; published 8 Jan 2016 © 2016 OSA 11 Jan 2016 | Vol. 24, No. 1 | DOI:10.1364/OE.24.000687 | OPTICS EXPRESS 687

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 erbium-doped 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, multi-angle 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-zirconate-titanate (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 self-locking, 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 30.9μs . 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 thermo-optic 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 (<0.01 nm). The phase-locked state can be maintained for each pump wavelength targeted, which was checked first by monitoring the comb intensity noise and further verified through line-by-line pulse shaping. The spectral tuning results reported in [17], replotted for better visualization of the power variation of the main comb lines close to the pump, are shown in Fig. 2. The comb center wavelength (corresponding to the pump laser wavelength) is tuned from 1549 nm to 1550.4 nm with an increment of 0.1 nm. Very little change in the spectral envelope of the comb occurs during this process.


Fig. 1. Experimental setup for microcomb generation and tuning characterization. The inset microscope image shows the silicon nitride microring integrated with a microheater. The comb line spacing (frep) is measured by using two independent methods: electro-optic (EO) down-conversion and comb-assisted spectroscopy. PC: polarization controller; EDFA: erbium-doped fiber amplifier; EOM: electro-optic modulator; PD: photodetector; BPs: radio-frequency bandpass filters with center frequencies of 22 MHz, 30 MHz, and 75 MHz.

Fig. 2. Comb spectra when the pump laser wavelength is tuned from 1549 nm to 1550.4 nm with an increment of 0.1 nm. The spectrum with pump at 1549 nm is plotted in dark blue while the other spectra are plotted in light blue. The voltage applied on the microheater is adjusted to maintain the phase-locked state after each tuning step.

The comb line spacing ( repf ) is around 231 GHz which is too high to detect for

commercial photodetectors. To precisely measure repf , we use two independent methods and

compare their results for high confidence. The first method is electro-optic (EO) down-conversion [28]. The comb is sent to cascaded optical modulators, a configuration similar to


that used for flat EO comb generation [29]. By optimizing the amplitude and phase of the radiofrequency (RF) signal that drives the modulators, multiple sidebands are generated which fill in the gaps between Kerr comb lines. The RF drive at frequency

RF 19.000000 GHzf = is generated from a commercial microwave source with an accuracy of

± 2 kHz. The zoom-in comb spectra before and after EO modulation are shown in Fig. 3(a). The 6-th modulation sidebands from adjacent Kerr comb lines get very close to each other. Their beat frequency IFf is detected by a photodetector and measured by a RF spectrum

analyzer. An example spectrum of the down-converted beat note is shown in Fig. 3(b). The Kerr comb line spacing is then calculated by rep RF IF12f f f= + (note that the RF frequency is

chosen that RF rep12 f f< , thus the sign of IFf is positive rather than negative).

The second method is frequency-comb-assisted spectroscopy which has previously been used to characterize microresonator dispersion [30] and subcomb formation [10]. The microcomb is combined with a tunable continuous-wave laser that is scanned in frequency, and the resulting beat notes are detected by a photodetector. An RF bandpass filter with a center frequency of 22 MHz is placed after the photodetector, and its output is recorded by a real-time oscilloscope running in peak-detect mode. When the scanning laser moves across each microcomb line, two high amplitude markers corresponding to 22 MHz away from the comb line are captured. In the same way, the scanning laser is combined with a 250-MHz self-referenced fiber comb to generate a series of reference markers (two narrowband RF bandpass filters with center frequencies of 30 MHz and 75 MHz are used after the photodetector). The relative frequencies of the Kerr combs can then be derived based on the reference markers (see Fig. 4). The microcomb line spacing is obtained by linearly fitting the microcomb frequencies versus line number. The uncertainty of the repf obtained in this way

is ± 20 kHz which is estimated by considering the measurement error of each comb frequency ( ± 1 MHz) in curve fitting.

Fig. 3. (a) Zoom-in spectra of the comb without (upper) and with (lower) electro-optic (EO) modulation when the pump laser wavelength is 1549.3 nm. The modulation frequency

RF 19.000000 GHzf = . (b) Beat note of the 6th modulation sidebands from adjacent

microcomb lines (marked with red dashed rectangles in (a)). The resolution bandwidth is 5

kHz. The down-converted intermediate frequency ( IFf ) corresponding to zero in (b) is

3.185582 GHz. The microcomb line spacing is then calculated by

rep RF IF12 231.185582 GHzf f f= + = .


Fig. 4. (a) Zoom-in view of frequency markers resulting from the scanning laser beating with the reference fiber comb (upper) or with the microcomb (lower). Peak75, peak30, peak22: outputs from the RF bandpass filters with center frequencies of 75 MHz, 30 MHz, and 22 MHz, respectively. (b) Measured relative frequencies of the Kerr comb lines in the C band when the pump laser wavelength is 1549.3 nm. The comb spacing is obtained by linearly fitting the comb frequencies versus the comb numbers, giving

rep 231.185603 GHzf = .

The plots of repf versus temperature and pump frequency are shown in Fig. 5(a). The

temperature ranges from about 45°C, which is the temperature estimated in the microring due to heating by the pump laser alone, to about 115°C with the microheater activated. The results measured with two independent methods agree with each other very well, with a root-mean-square deviation of ± 80 kHz. The variation of repf is characterized by a slope of 1.36

MHz/GHz versus pump frequency, or −3.57 MHz/°C versus temperature. The uncertainty estimated based on the residuals in linear fitting is ± 1.89 kHz/GHz ( ± 4.97 kHz/°C). We also characterized the temperature dependent FSR change for the microresonator by measuring its resonant frequencies with low probe power. The results are also shown in Fig. 5(a). The change of comb line spacing follows the cavity FSR quite well. There is a small shift between them which we attribute to the frequency detuning between the pump laser and the cavity resonance in comb generation. We then extracted the comb carrier-envelope offset frequency ( ceof ) according to the equation rep ceof mf f= + where f is the frequency of one of the

comb lines (here we choose the pump) and m is an integer [31]. Figure 5(b) shows the variation of ceof in the comb tuning process, showing a slope of −137.67 MHz/GHz versus

pump frequency or 362.07 MHz/°C versus temperature. The uncertainty estimated based on the residuals in linear fitting is ± 1.58 MHz/GHz ( ± 4.16 MHz/°C). It is interesting to note that ceof approaches zero when the pump laser frequency is around 193.5 THz. The ability to

achieve close-to-zero ceof may be an important enabler for experiments seeking to detect and

stabilize the offset frequency of a microcomb for applications such as optical frequency synthesis, because it admits the use of low-frequency electronics.


Fig. 5. (a) Variation of mode spacing versus temperature and center mode frequency. For the comb measurement, center mode frequency means the pump laser frequency, and mode spacing means the comb line spacing. For the thermally tuned cavity measurement, center mode frequency means the frequency of the resonance which is pumped in comb generation, and mode spacing means the localized free spectral range. (b) Comb carrier-envelope offset frequency versus temperature and pump laser frequency.

3. Theoretical analysis and discussion

There are two effects that are responsible for the thermal tuning: 1) the thermal expansion effect, i.e. the dimension of the ring changes slightly with temperature; and 2) the thermo-optic effect, i.e. the refractive indices of the core and cladding materials change with temperature. The thermal expansion coefficients for the different materials on our microchip are respectively SiN: 3~4 × 10−6/°C [32], SiO2: 0.5~4.1 × 10−6/°C [33], Si: 2.6 × 10−6/°C [34]. In comparison, the thermo-optic coefficient of SiN is generally 2~3 × 10−5/°C [35]. The contribution of thermal expansion should therefore be relatively small. Furthermore, since heating is applied in our experiments only in a small area in the vicinity of the microring, thermal expansion of the microring should be suppressed, at least in part, because it is surrounded by unheated material. Therefore, as reported in previous literature [35, 36], we neglect the thermal expansion effect in our following analysis.

The resonant frequency ( f ) of the microring satisfies the following equation


p22

fn Lk

c

ππ= ⋅ (1)

where pn is effective phase index, c is the light speed in vacuum, L is the circumference of

the ring, and k is an integer. Taking the derivative of both sides of Eq. (1) with respective to temperature, we can get

p pp 0

n nf fn f

T T f T

∂ ∂ ∂ ∂+ + ⋅ = ∂ ∂ ∂ ∂ (2)

The thermal tuning efficiency of f is then

p

g

dd

d d

nf f

T T n= − ⋅ (3)

where gn is effective group index given by g p pn n f n f= + ∂ ∂ .

The comb line spacing is given by

repg

cf

n L= (4)

The thermal tuning efficiency of repf is thus

rep g rep

g

d d

d d

f n f

T T n= − ⋅ (5)

The thermal tuning efficiency of ceodf is then

rep g pceo

g

d d dd d

d d d d d

f n nf f fm

T T T T T n

= − ≈ − ⋅

(6)

We retrieve the thermo-optic coefficients of the core (SiN) and cladding (SiO2) materials from Eq. (3) using a method similar to that reported in [35], i.e. solving the following equations

p,TE p,TE claddingcoreTE TE

g,TE core cladding

ddd

d d d

n n nnf f

T n n T n T

∂ ∂= − ⋅ + ⋅ ∂ ∂

(7)

p,TM p,TM claddingcoreTM TM

g,TM core cladding

ddd

d d d

n n nnf f

T n n T n T

∂ ∂= − ⋅ + ⋅ ∂ ∂

(8)

Here the thermal tuning efficiencies of the two fundamental polarization modes are measured in experiments; and the sensitivities of the effective phase refractive indices to the core and cladding refractive indices are calculated in simulations using a freely available software package (MIT Photonic Band) [37]. The refractive index of the SiN core material is measured by performing spectroscopic ellipsometry on a SiN film (deposited using a process similar to that used to fabricate the microring in Fig. 1). For the SiO2 cladding we use data typical of thermal silicon oxide [38] (here we neglect the small difference between CVD oxide and thermal oxide which is generally <2% [39]). At room temperature, the Sellmeier equations for SiN and SiO2 are as follows


2

2core 2 2

2.92571

0.14664n

λλ

= +−

(9)

2

2 2cladding 2 2

0.819961.3000 0.01082

0.10396n

λ λλ

= + −−

(10)

where λ is the vacuum wavelength in µm. The refractive indices at 1.55 µm for SiN and SiO2 are 1.988 and 1.448 respectively. The parameters and computed thermo-optic coefficients are listed in Table 1. The computed thermo-optic coefficients are 2.96 × 10−5/°C for SiN and 0.61 × 10−5/°C for SiO2, which are comparable to the results reported previously [35]. We also computed the thermo-optic coefficients based on data taken for the first higher-order TE and TM modes. The results were very close to those obtained from the fundamental TE and TM modes (3.00 × 10−5/°C for SiN and 0.57 × 10−5/°C for SiO2), which shows good reliability for this procedure. With the material thermo-optic coefficients, we assume a small temperature change in simulations and compute the effective phase indices at different wavelengths. The effective group index is then calculated according to g p pd dn n nλ λ= − ,

and the thermal coefficient is found to be gd dn T = 2.81 × 10−5/°C for the fundamental TE

mode (which is the mode pumped for comb generation in our experiments). According to Eq. (5), the thermal tuning efficiency of repf is calculated to be −3.15 MHz/°C, which is within

~12% of our experimental observation (−3.57 MHz /°C). The deviation may be attributed to the difference between the parameters used in simulations and the real material parameters and by our neglect of the thermal expansion effect. These results demonstrate the ability to reasonably model the variation of the microcomb repetition rate with temperature. However, modeling of the offset frequency is more difficult: according to Eq. (6), uncertainties in

repd df T are multiplied by a large integer m, where 837m = for our comb.

From Eq. (3), we note that the thermal tuning efficiency of the comb center frequency is independent of the microresonator dimension for the same resonant frequency. In our experiments the tuning range is 175 GHz (~75% of the FSR), which is limited by the current handling capability of the microheater. We anticipate that full-FSR tuning would be achieved with optimized microheater designs. Nevertheless, the demonstrated tuning range is already enough for applications, such as WDM fiber communications, that generally require a line spacing smaller than in our demonstration (e.g., WDM fiber communication uses channel spacings such as 25 GHz, 50 GHz, or 100 GHz). We can also see from Eq. (6) that the thermal tuning efficiency of the comb carrier-envelope offset frequency is independent of the microresonator dimension. The ceof is shifted by 25 GHz as the temperature is changed by 70

°C in our experiments. This tuning range is enough for full ceof control in f-2f self-

referencing experiments which are usually performed with line spacings well below 25 GHz. Note that the interaction between the different transverse modes is not considered in our

thermal tuning analysis. The broadband comb after the mode-locking transition is related to dark pulse action in the cavity which is mainly determined by the properties of the fundamental TE mode. Furthermore, the frequency location of the mode interaction involved in comb initiation in this paper (around 1656 nm) is far from the pump. The weak mode interaction does not affect the comb repetition rate and offset frequency significantly. This coincides with the fact that simulation results reasonably close to measurements can be obtained without considering the mode interaction. However, when strong mode interaction occurs at frequencies close to the pump, the comb repetition rate and offset frequency may be affected. Furthermore, because the different transverse modes have slightly different thermal tuning rates, the effects of mode interaction may change with temperature. These cases are reserved for future research.


Table 1. Parameters for retrieving the thermo-optic coefficients

Parameter Value

Measured TEf , TMf ~193.5 THz

Measured TEd df T −2.632 GHz/°C

Measured TMd df T −2.330 GHz/°C

Simulated g,TEn , g,TMn 2.059, 2.076

Simulated p,TEn , p,TMn 1.774, 1.706

Simulated p,TE coren n∂ ∂ 0.915

Simulated p,TE claddingn n∂ ∂ 0.155

Simulated p,TM coren n∂ ∂ 0.770

Simulated p,TM claddingn n∂ ∂ 0.365

Computed cored dn T 2.96 × 10−5/°C (2.45 × 10−5/°C in [35])

Computed claddingd dn T 0.61 × 10−5/°C (0.95 × 10−5/°C in [35])

4. Thermal response time

The response time of the microheater based tuning scheme is characterized with the setup shown in Fig. 6(a). The wavelength of a probe laser is tuned to one edge of the resonance. The optical power is very low so that the probe laser does not induce self-heating of the microring. A rectangular dithering voltage ( sV ) is applied on the microheater. Due to the

thermal shifting, the optical power after the microring is modulated. The amplitude of sV is

carefully selected such that the modulation remains in the linear region. The modulated optical power after the microring is converted to a voltage ( oV ) through a photodetector and

recorded on an oscilloscope. Figure 6(b) shows the waveforms of sV and oV . The thermal

response time can be obtained by fitting the falling edge of oV with exponential functions.

We find that there are two response components, one of which is substantially faster than the other. The fitted edge of oV is given by

( ) ( ) ( ) ( ) ( )o 2 1 1 2 1 2 1 2 2exp expV t V V V t V V tα τ α τ= + − − + − − (11)

where 1V and 2V are the voltage at the start and end of the fitted edge; 1α and 2α are the

relative amplitude of the two responses and satisfy 1 2 1α α+ = ; 1τ and 2τ are response times.

Here the origin of time t is chosen at the start of the edge. Figure 6(c) shows the measured and fitted curves of one falling edge. The retrieved parameters are: 1 0.91α = , 2 0.09α = ,

1 30.9μsτ = , 2 0.71msτ = . We believe that the fast thermal response is due to the thermo-

optic effect; the slow response may be associated with temperature changes over a larger region of the chip for which thermal expansion becomes more significant. Note that the amplitude of the slow response is an order smaller than that of the fast response, which agrees with our estimation of the thermal expansion effect. The ca. 30 µs fast thermal response is likely limited by the 3.5 µm buffer layer separating the microheater from the microring. Thermal response as fast as 0.25 µs was reported in experiments in which heating was induced optically directly inside a silicon nitride microring [40].


Fig. 6. (a) Setup for measuring the thermal response time. (b) Upper: dithering voltage applied on the microheater; lower: output voltage of the photodetector. (c) Measured and fitted falling edge at the output of the photodetector.

5. Summary

In summary, we have investigated the thermal tuning of a Kerr frequency comb from a SiN microring which maintains phase-locked operation while tuning over 75% of the free spectral range. The variations of the comb line spacing and carrier-envelope offset frequency versus the temperature are characterized experimentally. With a 70 °C temperature change, the comb center frequency is shifted by −175 GHz and the offset frequency is shifted by 25 GHz. Numerical simulations are performed by taking into account of the thermo-optic effect of the core and cladding materials; the temperature variation of the line spacing predicted from simulations is close to that observed in experiments. These results show that thermal tuning is a promising tool for tuning of the center frequency of a comb and for precise control of its line spacing and offset-frequency.

Acknowledgment

This work was supported in part by the Air Force Office of Scientific Research under grant FA9550-12-1-0236 and FA9550-15-1-0211, by the DARPA PULSE program through grant W31P40-13-1-0018 from AMRDEC, and by the National Science Foundation under grant ECCS-1509578.


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