This work reports the real-time observation of the thermo-optical dynamics in silica microsphere resonators based on the dispersive time stretch technique. In general, the thermo-optical dynamics of silica microsphere resonators, including the thermal refraction and thermal expansion, can be characterized by the resonance wavelength shift, whose duration is at the millisecond timescale. However, this fast wavelength shift process cannot be directly captured by conventional spectroscopy, and only its transmission feature can be characterized by a fast-scanning laser and an intensity detector. With the advance of the time-stretch spectroscopy, whose temporal resolution is up to tens of nanoseconds, the thermo-optical dynamics can be observed in a more straight-forward way, by utilizing the pump-probe technology and mapping the resonance wavelength to the time domain. Here, the thermo-optical dynamics are explored as a function of the power and the scanning rate of the pump laser. Theoretical simulations reproduce the experimental results, revealing that the thermo-optical dynamics of silica microsphere resonators is dominated by the fast thermo-optical effect and the slow heat dissipation process to the surroundings, which leads to gradual regression of the resonance wavelength. This work provides an alternative solution for studying the thermo-optical dynamics in whispering gallery mode microresonators, which would be crucial for future applications of microresonator photonic systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Ultrahigh quality factors (Q) and small mode volumes of whispering-gallery-mode (WGM) optical microresonators, with the capability of significantly enhancing the intro-cavity light energy density, make it an ideal platform for a wide range of applications, such as microlasers [1,2], optomechanical oscillators [3–5], microcombs [6–9], sensors [10–14], and parity-symmetric systems [15,16]. Ultrahigh-Q microresonators with the ability to boost light-matter interaction provide an excellent platform for studying nonlinear optical phenomena [17–21], such as the nonlinear thermo-optical dynamics [22–24]. The absorption by the cavity material converts a small fraction of light into heat, which results in the resonance wavelength shift via the thermal refraction and expansion. Although it is conventionally considered as the detrimental feature, the thermo-optical dynamics can be exploited to determine the heat exchange rate between the microresonator and the external environment. By recording the resonance wavelength, it has successfully characterized the thickness of the adsorbed water layer and the desorption rate, and obtained the absolute values of thermal accommodation coefficients of different gases at low pressures [25,26]. Thermal induced change of the mode effective refractive index has been widely used as a resonance wavelength tuning method for WGM microresonators [27,28]. Also, the thermal self-locking method has been well applied to realize rare-earth  and Brillouin microlasers .
Conventional investigation of the thermo-optical dynamics is performed by monitoring the transmission feature of a WGM microresonator. By controlling the wavelength sweeping speed, the sweeping direction and the power of the scanning laser, different transmission features including thermo-optical linewidth broadening , linewidth compression  and oscillation [32–36] have been reported. However, it cannot directly observe the fast resonance wavelength shift induced by the thermo-optical effect in real-time, which usually occurs at the millisecond timescale. There is an ultrafast spectroscopy technique proposed, called dispersive time-stretch . This time-stretch method has been applied to study complex ultrafast nonlinear phenomena, such as soliton explosions [38,39], wavelength evolution dynamics  and dissipative soliton molecule dynamics [41,42] in ultrafast fiber lasers. By introducing the pump-probe technology and utilizing the temporal dispersion to perform the wavelength-to-time mapping, it can reveal the resonance wavelength shift with a temporal resolution up to tens of nanoseconds. Therefore, the dispersive time-stretch technique enables the exploration of the thermo-optical dynamics of the WGM microresonators in a more straight-forward way, which is inaccessible by conventional means.
In this work, we present an alternative approach that observes the thermo-optical dynamics in silica microsphere resonators based on the time-stretch spectroscopy. It can realize a straight-forward investigation of the thermo-optical effect, which induces the fast resonance wavelength shift process. Different thermo-optical processes have been experimentally observed as a function of the power and the scanning rate of the pump laser. A thermo-dynamic model, which considered both the fast thermo-optical effect and the slow heat dissipation process of the microsphere resonators, is established to simulate the thermo-optical dynamics. The theoretical results are consistent with the experimental results. This exploration could pave the way toward real-time observation of the thermo-optical dynamics in WGM microresonators, which would be crucial for future applications of microresonator photonic systems.
2. Device characterization and experimental setup
As shown in the inset of Fig. 1, a silica microsphere resonator with a diameter of about 25 μm is used in our experiments. The microsphere resonator possesses ultrahigh Q factors due to its smooth surface of the cavity, which helps suppress the scattering loss. As a result, for a specific mode with TE polarization, the microsphere resonator exhibits a loaded Q factor of 6×107 at the resonance wavelength around 1522.2 nm as shown in Fig. 1.
The experimental setup performing real-time observation of the thermo-optical dynamics of the microsphere resonator is shown in Fig. 2. In the upper branch, a tunable continuous-wave laser driven by an arbitrary waveform generator (AWG) is periodically scanning back and forth around 1522.2 nm in a jagged trajectory. This swept pump light is coupled into the microsphere resonator through a tapered fiber to excite the thermo-optical dynamics, with the coupling state carefully controlled by adjusting the gap between the microsphere and the microfiber. A digital storage oscilloscope with a 125-MHz photo-detector (PD1) is used to record the pump transmission. In the lower branch, a pulsed source with 20-MHz repetition rate and 14-nm spectral bandwidth acts as a spectral probe to show the thermo-optical dynamics of the microresonator. To enable real-time recording of transient resonance wavelength shifts, the probe pulses are stretched by a dispersion compensation fiber (DCF) with –2.31 ns/nm dispersion to perform wavelength-to-time mapping. The temporal resolution decided by the repetition rate of the pulsed source is 50 ns, which is fast enough for capturing the thermo-optical effect induced resonance wavelength shift. The spectral resolution limited by the group velocity dispersion of the dispersive element is 83.3 pm. The resolution of the wavelength drift measurement decided by the sampling rate and the dispersive element is 5.4 pm. A 0.1-nm-bandwidth optical notch filter at 1550 nm imparts a wavelength mark onto the probe spectrum as a reference. Obviously, the average power of the probe light fed into the microfiber should be low enough (∼6 μW) so that its thermal impact on the microsphere is negligible. The temporally mapped probe spectrum which contains multiple resonance wavelengths, is separated from the pump light by a wavelength division multiplexer, and subsequently captured by a 33-GHz photo-detector (PD2) and another channel of the oscilloscope.
3. Theoretical analysis
As the pump wavelength scans from short wavelength to long wavelength, accumulated thermal effect in the microsphere leads to the increased temperature of silica. Since both the thermo-optical and thermal expansion coefficient are positive, the resonance wavelength of the microsphere resonator shows a red-shift, which means that the thermal nonlinear effect can be analyzed by the temperature variation of the cavity.
According to the formula of the N-th resonance wavelength (λr), we get the function of the resonance wavelength with respect to the cavity temperature:
According to the law of conservation of energy, the net heat generated in the microsphere resonator is equal to the net heat inflow (qi) minus the net heat outflow (qo):
As shown in Fig. 3(b), the red line is the pump wavelength as a function of time with a scanning speed of 0.031 nm/ms. The pump wavelength is firstly swept from short wavelength to long wavelength. When the pump wavelength is swept into the resonance dip of the cold cavity (λp = 1522.23 nm, t = 6.5 ms), there will accumulates a large power and thus a lot of heat in the microsphere resonator. The thermo-optical effect induced the change of the RI and cavity radius, leading to a red-shift of the resonance wavelength. The scanning direction of the pump wavelength is the same as the resonance wavelength shift induced by the thermo-optical effect, thus the pump wavelength needs longer time to match the resonance wavelength, which leads to an asymmetric and broadened transmission spectrum (blue line). In Fig. 3(c), the red line is the measured resonance wavelength shift of the microsphere resonator, and the black line is the thermal variation in the microsphere resonator calculated by Eqs. (2)–(5). The temperature of the microsphere resonator increases from t = 6.5 ms to t = 9 ms and the resonance wavelength has a red-shift of 80 pm. When t is larger than 9 ms, the pump wavelength exceeds the resonance dip, which leads to the decrease of the temperature of the cavity, and the resonance wavelength starts to present a blue-shift. The blue-shift process needs longer time (from 9 ms to 16 ms) than that of the red-shift process, because the microsphere used in our experiments has a small diameter of 25 μm. The small microsphere results in a slower heat dissipation process as the heat is dissipated into the environment through the cavity surface. In addition, the advantage of using a small microsphere is that it can achieve more pronounced thermal nonlinear effect at a low pump power and a clean mode excitation in the 30-GHz scan range, so that the thermal effect can dominate the resonance wavelength shift. For the case where the thermal effect is relatively weak, other high-order effects, such as Kerr effect and mode coupling, should be considered . From Fig. 3(c), it can be seen that the simulation results agree well with the experimental results. The parameters used in the simulations are P0/Cp = 5.8×10−4 °C/ms, λ0 = 1522.23 nm, Q = 6×107, K/Cp = 2.8×10−5 s−1, and Pp = 0.6 mW.
4. Experimental results and discussion
The probe spectrum that contains multiple resonance wavelengths of the cold cavity (without pump light) was firstly measured by an optical spectrum analyzer and the dispersive time stretch technique. As shown in Fig. 3(a), the measured optical spectrum (red line) is well mapped to the temporal waveform (blue line). The wavelength-to-time mapping relation calculated from Fig. 3(a) is –2.3 ns/nm, which matches the dispersion value (–2.31 ns/nm) of the DCF. After calibrating the wavelength-to-time mapping factor, the drift amount of the resonance wavelength (e.g., resonance wavelength A at 1554.37 nm) can be obtained from the temporal spectra by measuring the time shift off the reference notch, which has a fixed wavelength λref. Figure 3(b) presents the scanning pump wavelength variation (red line) and the transmission feature (blue line) when the pump laser is swept at 62.5 Hz under 0.6-mW output power. With the ultrafast spectral measurement performance of the time-stretch technique, we can track the real-time drifting of the resonance wavelength, as shown in Fig. 3(c). It can be seen that as the pump wavelength approaches the resonance dip (t = 6.5 ms), the microsphere resonator starts to be heated up so that the resonance wavelength shifts away from the initial resonance wavelength of the cold cavity (from 6.5 ms to 9 ms). As long as the pump wavelength is on the blue side of the resonance dip, heating continues. When the pump wavelength exceeds the resonance dip, the cavity comes off the resonance, and cooling starts. While in the down scan process, the resonance wavelength does not shift upward because of the scan rate across the cavity lineshape is sufficiently fast to prevent the accumulation of the heat. Therefore, the triangular resonance wavelength response in the up scan of the heat generation and the subsequent heat dissipation process, both of which constitute the key features of the thermo-optical dynamics in microsphere resonators.
To further characterize the thermo-optical dynamics of the microsphere resonator under different conditions, we explore the influences of the pump power and the wavelength scan rate on the resonance wavelength shift. Figures 4(a)–4(e) show the measured thermo-optical dynamics of the microsphere resonator at different pump powers and the corresponding simulation results. Comparing the thermo-optical dynamics shown in Figs. 4(a)–4(e), significant thermal variation can be observed when the pump power was further increased to 0.5 mW while keeping the wavelength scan rate of 100 Hz unchanged. The duration for the resonance wavelength shift returning back to the initial resonance wavelength becomes longer as the pump power increases. This is because more pump light is converted to a larger temperature variation in the cavity, and subsequently brings a larger resonance wavelength shift to the microsphere resonator. Moreover, it can be seen that a set of corresponding simulation results reproduce the experimental results.
Figure 5 shows the similar results for different wavelength scan rates while keeping a fixed 1 mW pump power. As seen from Figs. 5(a)–5(h), when the scan rate gradually decreased, the resonance wavelength shift and thermal variation increased significantly. For example, at a lower scan rate (50 Hz), the thermo-optical dynamics becomes even more prominent, and the maximum resonance wavelength shift can reach 70 pm. In Figs. 6(a) and 6(b), the measured resonance wavelength shift as a function of the pump power and wavelength scan rate are presented. Each experimental point has been measured with the same accuracy, which is presented by the error indicator. It can be seen from Fig. 6(a) that a definitive resonance wavelength shift can be stably detected starting from a power of 0.1 mW. In addition, in the same figure we show the second set of measured datas for a scan rate of 50 Hz. It is clear that for the lower scan rate the cavity gets the greater shift which means the higher temperature of the cavity. Figure 6(b) shows that as the scan rate increase, the measurement results for different pump powers present the same decreasing trend.
Similar thermo-optical dynamics is observed on other resonance wavelengths, regardless of their polarizations and mode orders. One example is evident in a resonance wavelength nearby, (e.g., resonance wavelength B at 1548.98 nm), indicated on Fig. 3(a), which also exhibits the fast thermo-optical effect and the slow heat dissipation process when the pump scans across the microsphere resonator. These observations indicate the universal feature of the thermo-optical dynamics in microsphere resonators.
In conclusion, we have performed real-time observations of the thermo-optical dynamics in silica microsphere resonators based on the dispersive time stretch technique. By introducing the pump-probe technology and mapping the resonance wavelength to the time domain, we provide a more straight-forward way to observe the thermo-optical effect induced resonance wavelength shift, whose duration is at the millisecond timescale. The drift amount of the resonance wavelength can be obtained from the temporal spectra by measuring the time shift of the temporal resonance wavelength. The thermo-optical dynamics was dominated by the power and scanning rate of the pump laser. Simulated results from the theoretical model considering both the fast thermo-optical effect and the slow heat dissipation process of the microsphere resonator agree well with the experimental results. We believe that this ultrafast spectroscopy technique could become an alternative approach for studying the thermo-optical dynamics in WGM microresonators with huge applications in sensing, metrology, and coherent light generation.
National Natural Science Foundation of China (11774110, 61505060, 61631166003, 61675081, 61735006, 61927817, 91850115); State Key Laboratory of Information Photonics and Optical Communications (IPOC2019A012); Fundamental Research Funds for the Central Universities (2019kfyRCPY092, 2019kfyXKJC036).
The authors declare no conflicts of interest.
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