2.1 Principles and designs
The schematic of the proposed FDML OEO system with the size on chip only 9 mm×1 mm is illustrated in Fig. 1 (a), which includes a phase modulator (PM) (ⅱ), a tunable high-quality factor (Q-factor) micro-ring resonator (MRR) (ⅲ), and grating couplers (ⅳ). The detailed working principle of the FDML OEO system is illustrated in Fig. 1 (b) and explained in the following: Light from a continuous wave (CW) laser is coupled into the chip through a gating coupler and routed to the PM, which generates double sidebands with π phase difference. After that, the resonance notch of the tunable MRR filters parts of one sideband of the spectrum while introducing a π phase shift. Then the processed optical signal is routed to a photodetector (PD), which converts the optical signal to the RF signal with a frequency equal to the spacing between the notch and the carrier wave. Finally, the RF signal is amplified by an electric amplifier (EA) before feeding back to the PM to complete the OEO loop. When the overall gain of the opto-electronic loop exceeds the loss, a stable single-mode oscillation would occur (see Note S1, Supporting Information).[46] In the proposed FDML OEO system, the fast-tuning microwave photonic bandpass filter (MBPF) (shown in Fig. 1 (b)) is used for frequency tuning, which is driving by periodic signals with the frequency tuning period or its multiple be synchronized with the round-trip time of the OEO loop. The process produces a quasi-stationary operation, which break the maximum frequency tuning rate limited by the characteristic time constant or mode building time for up oscillation in a new oscillation mode in the cavity, facilitates the generation of high-quality time-frequency signals that meet the needs of future applications (see Note S2, Supporting Information).[26]
The micrograph of PM is shown in Fig. 1 (c). Thanks to the Pockels effect of LN, the bandwidth of the achieved PM meets the requirement by using optimized traveling wave electrodes. The widths of optical waveguide, ground, and signal electrodes are chosen as 1 µm, 100 µm, and 50 µm, respectively. The gap between ground and signal electrodes is designed to be 6 µm (see Note S3, Supporting Information). These parameters are designed to achieve group refractive index matching between light and electricity, while matching the 50 Ω resistor to reduce retroreflection, thereby increasing the electro-optic bandwidth of the PM. Unlike the Mach-Zehnder intensity modulator (MZM), there is no need to consider bias stability control when using PMs in OEO systems, avoiding the requirement for complex thermal modulation or feedback systems, facilitating high volume ultra-compact integration.
The Q-factor of the MRR directly affects the sharpness of the spectral cropping and the free spectra range (FSR) of the MRR determines the range of available spectra, which influence the phase noise and the bandwidth of the signal generated by the OEO, respectively. Therefore, it is imperative to maximize the Q-factor and the FSR of the MRR. Here, we demonstrate a micro-racetrack resonator with compact Euler-curve bends as shown in Fig. 1 (d), which can improve the Q-factor of the MRR while maintain a satisfactory FSR. To reduce the impact of the waveguide sidewalls roughness on the optical transmission loss, we widen the optical waveguide to 4.5µm to support multi-mode transmission while pushing the supported fundamental mode away from the waveguide sidewall, which can vastly improve the Q-factor of the MRR. Simultaneously, the use of Euler-curve bends and 200 µm adiabatic tapers to prevent the excitation of high-order optical modes, thus ensure that only single-mode is present in the MRR. Compared with pure circular bends of the same crosstalk, Euler-curve bends have a shorter length which in turn results in wider FSR.[47] Fig. 1 (e) illustrates a titanium (Ti) micro-heater, which utilizes the thermos-optic effect to tune the wavelength shift and in turn for tuning the frequency of the generated signal.
2.2 Experimental results
Characterization of key devices
In order to facilitate the characterization of the on-chip PM in the OEO, we measured the MZM composed of two PMs with the same parameters. Figure 2 (a) shows the electro-optic S21 response of the modulator. One can see that the 3 dB electro-optic bandwidth is about 78 GHz (from 0.3 GHz), which meets the bandwidth requirement of the desired OEO system.
As the key component in the system, a tunable MRR plays a decisive role in the spectral response of the OEO. The transmission spectrum of the high-Q MRR measured by an high resolution optical spectrum analyzer (OSA, APEX A2687) is presented in Fig. 2 (b), which allowed us to extract 3 dB bandwidth of 12 pm, corresponding to a loaded Q-factor of 1.3×105. The MRR’s Q-factor is affected by the close proximity of the heater electrode and the rough waveguide sidewall which can be further improved in the future. The measured FSR of the MRR is 87 GHz, providing sufficient spectral range for microwave signals generation by the OEO system. Figure 2 (c) shows the spectrum tuning of the MRR by applying different electrical power to the micro-heater. The resonant wavelength of the high-Q MRR redshifts, when the voltage applied to the Ti micro-heater is increased from 0 V to 15 V, exhibiting the desired broadband tunability.
Frequency-tunable MBPF
The performance of the on-chip microwave photonic bandpass filter is evaluated, using the experimental setup shown in Fig. 3. A CW light with a power of 13 dBm generated by an external tunable laser (TL, Santec TSL-570) is sent to the polarization controller (PC, Thorlabs-FPC561) and then routed to the chip. The vector network analyzer (VNA, Keysight N4372E) provides a frequency swept RF signal with a power of -5 dBm to the PM, by using a high-speed microwave GSG probe (T-PLUS 110 GHz). A 50 Ω matched resistor is used to reduce the reflection of microwave signals at the end of the PM. The recovered RF signals from the lightwave component analyzer (LCA, Keysight N4372E) is sent back to the VNA to acquire the frequency response of the integrated MBPF.
In order to verify the frequency tunability, the center frequency of the notch band of the filter can be continuously tuned by applying various power to the micro-heater generated by the multichannel power supply (MPS, GWINSTEK GDP-3303S), as shown in Fig. 4 (a). With the voltage applied to the micro-heater is varied, the center frequency is continuously ranged, while the rejection ratio of the filter does not change with frequency to remain at 10 dB. Figure 4 (b) depicts the stability of the filter’s 3 dB bandwidth with the change in frequency, and multiple measurements result in the filter with a 3 dB bandwidth of approximately 3.1 GHz.
Integrated tunable FDML OEO
The experimental setup for measuring the performance of the FDML OEO is shown in Fig. 5. The optical signal and electrical signal are amplified by an erbium-doped fiber amplifier (EDFA, KEOPSYS CEFA-C-PB-LP-SM-23-MSA1-B201-FA-FA) and an electrical amplifier (EA, SHF S807C) in order to achieve stable single mode oscillations in the experiment. The frequency of the generated signal can be tuned by varying the voltage applied to the micro-heater by an arbitrary waveform function generator (AFG, Tektronix 3102C). In the OEO system, the amplified signal is equally divided into two paths by an electrical coupler (EC). In the one path, the single is guided to the input of the PM to realize the OEO loop. The other path routes the signal to an electrical spectrum analyzer (ESA, Keysight N9030B) for real-time monitoring and analysis of the signals by the OEO.
Frequency tunability of the integrated OEO is demonstrated as shown in Fig. 6 (a), the superimposed spectrums of the generated microwave signal, which shows a wideband frequency range from 3 to 42.5 GHz is obtained, covering S, C, X, Ku, K, and Ka bands. We can also see that the amplitude of the signal is lower at higher frequencies, which can be attributed to the frequency dependent attenuation of the OEO system cables and instrumentations. The tuning range of the OEO is limited by the FSR of the high-Q MRR and the gain provided by the amplifier in the loop. A wider frequency tuning range of more than 60 GHz is possible by using a MRR with a wider FSR and cascade multiple amplifiers to provide ample gain. We also demonstrated the side mode suppression ratio (SMSR) of the microwave signals generated by the OEO as shown in Fig. 6 (b), a satisfactory SMSR of 48 dB is achieved at an oscillation frequency of 8.8 GHz. Figure 6 (c) shows the generated microwave waveform in the time domain, which is measured by high-speed real-time oscilloscope (OSC, Keysight UXR0594AP) with a sampling rate of 256 GSa/s. The inset in Fig. 6 (c) show a real-time capture of a section of the generated waveform.
Figure 6 (d) displays the RF spectrum of the OEO signal at around 23.76 GHz with a span of 20 MHz, and it can be concluded that the separation between two adjacent modes is 4.27 MHz, which is determined by the length of the OEO experimental link (see Note S4, Supporting Information) and also an essential indicator of the formation of the FDML. Figure 6 (e) and (f) show the phase noise with a frequency tuning step of 5 GHz from 15 GHz to 35 GHz and the measured phase noise at a 10 KHz offset frequency of different microwave signal frequencies, respectively. It is clear to see that the phase noise values are maintained around − 93 dBc/Hz at the offset frequency of 10 KHz, which verifies the most important advantage of the OEO to have a stable phase noise with different oscillation frequencies. The phase noise is mainly determined by the Q-factor, which can be further improved by increasing the Q-factor of the MRR. Additionally, according to the Yao-Maleki phase noise model, the use of kilometer-scale fiber-optic coils in the OEO loop can significantly improve the phase noise of the generated RF signal (see Note S5, Supporting Information).[48]
A stable time-frequency signal is generated when the AFG applies a periodic drive signal to control the MBPF to synchronize its frequency tuning period or a multiple thereof with the round-trip time of the OEO loop, which is the key to formation of the FDML OEO. By varying the waveform function of the AFG output voltage, the type of signal generated can be controlled. As shown in Fig. 7, we demonstrate high-quality time-frequency waveform generation based on the FDML OEO with examples of LCMW, quadratic-chirp signal, and triangle waveform. The duration and peak value of the applied voltage function are contingent upon the performance of the AFG, which consequently affects the bandwidth and period of the generated signal.
To intuitively demonstrate the flexibility and reconfigurability of the device, images of various types of signals generated by the FDML OEO measured with real-time OSC are shown in Fig. 8. Designing and varying the output voltage function of the AFG to modify the waveform, center frequency, and the frequency scanning range of the generated signal. Figure 8 (a) shows the generated chirp signals with center frequencies from 12 to 30.5 GHz, which exhibits a favorable linear shape. The fluctuations that appear in the figure are possibly due to the change in the link state during the experiments. The quadratic chirp signals with center frequencies from 14 to 36 GHz are illustrated by Fig. 8 (b). Figure 8 (c) shows the real-time frequency distribution of triangle wave signals, which center frequencies from 4 to 18.5 GHz. The applied periodic voltages could not meet the experimental requirements to obtain satisfactory results limited by the AFG performance. However, this problem can be solved by using an AFG with a longer voltage cycle time and higher peak voltage.