Hybrid FDML laser
A hybrid FDML laser is realized based on a fiber ring cavity in which a tunable optical filter is incorporated to perform Fourier-domain mode locking. Figure 1 shows the schematic of the proposed hybrid FDML laser, which has a discrete fiber-based ring cavity incorporating an integrated silicon-based tunable MDR filter having a top-placed metallic micro-heater for thermal tuning. By applying a driving signal with a frequency that is a multiple of the FSR of the ring cavity to the micro-heater on top of the MDR, Fourier-domain mode locking is achieved and a broadband frequency-chirped optical pulse is generated. By controlling the temporal profile of the driving signal, the generated optical pulse is linearly frequency chirped. Specifically, when the driving signal has a parabolic profile, the generated optical pulse is frequency-chirped with linearly increasing frequency, as shown in Fig. 1. Then, the generated linearly frequency-chirped optical pulse is sent to a high-speed PD together with an optical carrier from an LD, to generate an LCMW due to heterodyne beating at the PD. Since the linearly frequency-chirped optical pulse has a broad bandwidth and wide temporal duration, the generated LCMW has an ultra-large TBWP. In addition, when the driving signal applied to the MDR is tuned, the frequency-chirped optical pulse from the FDML laser can be tuned in terms of bandwidth, temporal duration, chirp rate, and center frequency, leading to the generation of a fully tunable LCMW.
In the implementation of the FDML laser, mode selection is realized using a highly frequency-selective and fast frequency-tunable optical filter. The higher the frequency selectivity of the optical filter, the more precise the mode selection. To enable Fourier-domain mode locking, the repetition time of the driving signal applied to the optical filter needs to match the round-trip time of the laser ring cavity29,31,32. In the proposed FDML laser, a specially designed add-drop MDR is employed as the optical filter. The MDR is designed to have an additional slab waveguide to wrap the disk and bus waveguide, to increase the wavelength selectivity and to enhance the optical coupling between the bus waveguide and the disk. Figure 2a gives the perspective view of the MDR. A slab waveguide is added to wrap the disk and the bus waveguide to weaken the disk sidewall roughness, and thus increase the confinement of the optical field33,34. Figure 2b shows the cross-sectional view of the MDR along the dashed line AA’, shown in Fig. 2a. The disk has a radius of 10 μm and the coupling gap between the bus waveguide and the disk is 200 nm. The chip is fabricated with the use of 193 nm lithography fabrication process. Figure 2c shows the image of the chip prototype captured by a microscope camera. Figure 2d shows the measured transmission spectrum at the drop port of the MDR. The first- and second-order whispering gallery modes (WGMs) are effectively excited, in which the first-order WGMs have an FSR of 10.56 nm, and the second-order WGMs have an FSR of 10.76 nm. Figure 2e is a zoom-in view of the WGM1,107, which has a -3-dB bandwidth of 72 pm, corresponding to a Q-factor as large as 2.1 × 104. By applying a driving signal to the micro-heater on top of the MDR, the filter is thermally tuned. Figure 2f shows the wavelength tuning of the MDR. With the increase in the applied electrical power, the WGM1,107 and WGM2,102 are red shifted. For the WGM1,107, the wavelength shift rate is calculated to be 155 pm/mW, and for the WGM2,102, the wavelength shift rate is calculated to be 196 pm/mW. In addition, thanks to the strong thermal-optic effect in silicon, the response time is in the order of tens of microseconds, which is much faster than a conventional tunable optical filter such as liquid crystal based tunable optical filter35, and acoustically tunable optical filter36, a feature that is highly needed for Fourier-domain mode locking.
Frequency-chirped optical pulse generation
First, an experiment is performed to demonstrate the operation of the hybrid FDML laser with the use of the silicon photonic integrated MDR chip. Since the length of the laser cavity is around 9 km, a round-trip time is calculated to be about 44.4 µs. In the experiment, a driving signal with a repetition time of 44.7 µs having a parabolic profile is applied to the micro-heater. The tuning of the driving signal has a resolution of 1 mHz, to precisely tune the repetition time to make it match precisely the cavity round-trip time to ensure a stable operation of the FDML laser. The generated frequency-chirped optical pulse is measured by an optical spectrum analyzer (OSA) (see Supplementary Note 1). Figure 3a shows the temporal profile of the frequency-chirped optical pulse after photodetection at a high-speed PD, which is captured by a real-time oscilloscope. As can be seen, the waveform is periodic with a repetition time of 44.7 µs, which is identical to the repetition time of the driving signal applied to the MDR. Figure 3b shows the optical spectrum of the generated frequency-chirped optical pulse, measured using an OSA. The pulse has a 3-dB bandwidth as large as 0.49 nm. Such a broad bandwidth is of significant benefit to the generation of a wideband LCMW based on heterodyne beating. When the driving signal is tuned, the generated optical pulse is also tuned. Figure 3c–e shows the tuning of the frequency-chirped optical pulse. As can be seen, with the peak-to-peak voltage (Vpp) of the driving signal applied to the micro-heater is increased from 350 to 1040 mV, the bandwidth of the frequency-chirped optical pulse is increased from 0.08 to 0.8 nm. Thanks to the broad bandwidth of the frequency-chirped optical pulse, an ultra-large TBWP is generated when the optical pulse is heterodyne beating with an optical carrier from an LD.
Then, the generated frequency-chirped optical pulse is combined with a CW optical carrier from an LD and beat at a high-speed PD. At the output of the PD, an LCMW is generated. Figure 4a shows the temporal waveform of the generated LCMW when the frequency-chirped optical pulse with a bandwidth of 0.4 nm from the FDML laser is used. Figure 4b and c gives the zoom-in views of the generated LCMWs at different time locations. As can be seen, the instantaneous frequency of the waveform is changing with time, which confirms the effectiveness of the LCMW generation with the use of the FDML laser. Figure 4d presents its spectrogram of the generated LCMW which exhibits a linear chirp profile. As can be seen, the generated LCMW has a time duration of 30 μs and a bandwidth of 50 GHz. From the time-domain waveform and its carrier frequency distribution, the TBWP of the generated LCMW is calculated to be as large as 1.5 × 106. To evaluate the linearity of the generated LCMW, the instantaneous frequency is linearly fitted to an ideal LCMW. An R-square value is calculated which is 0.99763, a very high value confirming that the waveform has good linearity. A slight nonlinearity of the frequency distribution of the generated LCMW that can be observed from Fig. 4d is mainly resulted from the nonlinear response of the MDR to the driving signal, which can be reduced or completely eliminated if the driving signal is pre-distorted to fully compensate for the nonlinearity. Figure 4e shows a compressed pulse by calculating the autocorrelation. The temporal width of the compressed pulse is 25 ps. By comparing the pulse widths of the waveforms in Figs. 4a and e, a pulse compression ratio as large as 1.2 × 106 is obtained. Note that when calculating the autocorrelation, the direct-current (DC) component in the generated LCMW is removed before the calculation. By tuning the Vpp and the parabolic profile of the driving signal applied to the micro-heater, the frequency-chirped optical pulse can be tuned in terms of bandwidth, temporal duration, chirp rate, and repetition rate. When the frequency-chirped optical pulse is combined with an optical carrier and beat at a high-speed PD, a tunable LCMW is generated. Specifically, the parameters of the generated LCMW, in terms of bandwidth, duration time and repetition rate, can be tuned by tuning the driving signal through tuning the Vpp, the temporal duration, and the repetition time, respectively (the time-domain profile of the driving signal can be found in Supplementary Note 2). Figure 5a–d shows the spectrograms of the generated LCMW with different bandwidths while maintaining an identical temporal duration by controlling the Vpp of the driving signal. As can be seen, the bandwidth is increased from 10.2 to 38.1 GHz when the Vpp of the driving signal is increased from 350 to 650 mV. The chirp rate is correspondingly increased from 0.34 to 1.27 GHz/µs. By using a PD with a wider bandwidth, the bandwidth of the generated LCWM could be largely increased, and the chirped rate could also be increased accordingly. The R-square value of the spectrogram in Fig. 5a is relatively smaller than those in Fig. 5b–d which indicates that a lower Vpp will lead to a poorer linearity of the LCMW. Figure 5e–h shows the spectrograms of the generated LCMWs with an identical bandwidth but different temporal durations by controlling the parabolic duration of the driving signal. The duration is increased from 8.5 to 30.0 µs when the parabolic duration of the driving signal is increased from 8.5 to 30.0 µs, and the chirp rate of the generated LCWM is tuned from 1.24 G to 0.37 GHz/µs. The R-square value of the spectrogram of Fig. 5e is relatively smaller than those in Fig. 5f–h, which indicates that a shorter driving duration could lead to poorer linearity of the LCMW. Table 1 summarizes the parameters of the generated LCMWs.
The center frequency of the generated microwave waveform is determined by the frequency difference between the frequency-chirped optical pulse and the CW optical carrier. In our experiment, by changing the wavelength of the CW optical carrier, the center frequency of the generated LCMW is tuned. Figure 6a–d shows the spectrograms of the generated LCMWs with different center frequencies. As can be seen the center frequency is increased from 15.68 to 44.73 GHz when the wavelength of the CW optical carrier is reduced from 1547.89 to 1547.65 nm. If a PD with a wider bandwidth is employed, the center frequency of the generated LCMW can be significantly higher. Since the parabolic driving signal is maintained unchanged, the chirp rates of the LCMWs are maintained unchanged. The R-square values are kept unchanged which indicates the linearity of the LCMWs is maintained without change when tuning the center frequency of the LCMW. Table 2 summarizes the parameters of the generated LCMWs.
The repetition rate of the frequency-chirped optical pulse can be tuned by adjusting the repetition time of the parabolic driving signal. To ensure effective Fourier-domain mode locking, the repetition rate should be controlled to be equal exactly to a multiple of the FSR of the ring cavity. Figure 7a–d shows the spectrograms of the generated LCMWs with different repetition times. In the experiment, the repetition time is reduced from 44.71 to 11.17 µs. To maintain the bandwidth of the LCMW fixed at around 25 GHz, the Vpp of the driving signal is increased from 469 to 1140 mV. The reason that an increased VPP is needed to maintain a fixed bandwidth is because the average electrical power applied to the MDR is decreased when the repetition time of the driving signal is reduced. The shortest repetition time is determined by the highest VPP of the driving signal that will not damage the thermal resistance in the MDR (as shown in Fig. 2c). The R-square value is decreased from 0.99714 to 0.988 when the repetition time is decreased from 44.71 to 11.17 µs, which can be improved by fine tuning the profile of the driving signal to compensate for the nonlinearity. Table 3 summarizes the parameters of the generated LCMWs.
Note that due to the optical carrier from the LD used to perform heterodyne beating is independent from the optical pulse from the FDML, the phase noise of the optical carrier will be translated to the generated LCMW. A potential solution to make the optical carrier from the LD be phase correlated with the optical pulse from the FDML laser is to select one longitudinal mode from the FDML to phase lock the LD, to make the two wavelengths highly coherent. Thus, the phase noise could be significantly reduced37.