Photonic Generation of Chirp-Rate-Tunable Microwave Waveforms Using Temporal Cavity Solitons with Agile Repetition Rate

Wen-Hao Xiong(熊文豪), Chuan-Fei Yao(姚传飞), Ping-Xue Li(李平雪)$^{\hyperlink{s}{*}}$,\\ Fei-Yu Zhu(朱飞宇), and Ruo-Nan Lei(雷若楠)

doi:10.1088/0256-307X/40/6/064201

⇦Chinese Physics Letters, 2023, Vol. 40, No. 6, Article code 064201⇨ Photonic Generation of Chirp-Rate-Tunable Microwave Waveforms Using Temporal Cavity Solitons with Agile Repetition Rate Wen-Hao Xiong (熊文豪), Chuan-Fei Yao (姚传飞), Ping-Xue Li (李平雪)*, Fei-Yu Zhu (朱飞宇), and Ruo-Nan Lei (雷若楠) Affiliations Institute of Ultrashort Pulsed Laser and Application, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, China Received 31 January 2023; accepted manuscript online 21 April 2023; published online 1 June 2023 ^*Corresponding author. Email: pxli@bjut.edu.cn Citation Text: Xiong W H, Yao C F, Li P X et al. 2023 Chin. Phys. Lett. 40 064201 Abstract Chirp-rate-tunable microwave waveforms (CTMWs) with dynamically tunable parameters are of basic interest to many practical applications. Recently, photonic generation of microwave signals has made their bandwidths wider and more convenient for optical fiber transmission. An all-optical method for generation of multiband CTMWs is proposed and demonstrated on all-fiber architecture, relying on dual temporal cavity solitons with agile repetition rate. In the experiment, the triangular optical chirp microwave waveforms with bandwidth above 0.45 GHz (ranging from 1.45 GHz to 1.9 GHz) are obtained, and the chirp rate reaches 0.9 GHz/ms. The reconfigurability is also demonstrated by adjusting the control signal. This all-optical approach provides a technical basis for compact, multi-band reconfigurable microwave photonics transmission and reception systems.

DOI:10.1088/0256-307X/40/6/064201 © 2023 Chinese Physics Society Article Text Chirp-rate-tunable microwave waveforms (CTMWs) are broadband waveforms whose instantaneous frequency exhibits definite temporal variations,[1] which are of great significance for applications in such as laser radar systems,[2] three-dimensional imaging,[3,4] and chirped-pulse Fourier transform microwave spectroscopy.[5] In order to meet the application requirements, the microwave waveforms with readily changeable parameters are essential. Currently, there are two techniques that can be used to achieve the above characteristics of CTMWs. On the one hand, the optoelectronic oscillator (OEO) approach,[6,7] which uses a high-$Q$ microwave oscillator in a feedback loop to produce high-frequency microwave signals with extremely low phase noise, is now one of the main methods for optically generating CTMWs. On the other hand, the multi-heterodyne approach based on electro-optical dual optical frequency combs,[8-10] which facilitates the production of high-quality multiband CTMWs by beating two optical waves in a photodetector (PD), is the other crucial photonic technique for producing microwave signals. Even though both the schemes exhibit good performance, there are still a few unfavorable conditions to limit practicality. Generally, the electrical components and electro-optical modulators remain essential, making the above-mentioned two schemes always opto-electronic hybrid systems. Therefore, combination of each functional unit requires multiple photoelectric/electrical-optical conversions, resulting in unnecessary conversion losses and difficulty in miniaturization. However, all-optical generation of CTMWs, which rely on upshifting the microwave carrier into the optical domain, offers an appealing alternative to the opto-electronic hybrid scheme. For the all-photonic generation of chirped microwaves, all-optical Kerr soliton combs are indispensable building blocks. Recently, the dissipative Kerr soliton technique has become particularly popular due to the distinguished advantages of high coherence and spectral purity (noise).[11-13] Liu et al. first reported the all-photonic microwave generation in the X-band ($\sim$ $10$ GHz) and the K-band ($\sim$ $20$ GHz) using Kerr soliton micro combs.[13] The phase noise performance of the soliton-based microwave carriers was only limited by the pump lasers without additional electrical noise sources. Similarly, Anton et al. recently demonstrated the all-optical generation of multi-band chirped microwave via the dual chirped soliton microcomb technique and successfully realized parallel ranging.[14] A frequency-modulated continuous-wave pump laser's optical chirp achieves homogenous coverage in the optical domain because each comb line inherits the frequency modulation of the pump laser through the dissipative four-wave mixing (FWM) processes. However, the sophistication of the system was further increased by the requirement to constantly fine-tune the micro-cavity comb's cavity resonance and pump frequency.[15,16] Meanwhile, the temporal cavity solitons (TCSs) in a fiber cavity, which were likewise capable of realizing the generation of chirped microwaves, were demonstrated repeatedly by optical comb formation.[17-19] Typically, both the pumping frequency and the cavity resonance are prone to be regulated in the fiber cavity. Furthermore, the repetition rate of TCSs based on fiber cavity could be directly and quickly tuned all-optically in a wide range, which would be the basis of the generation of microwave chirp.[18] The relevant application research for TCSs based on fiber cavities, however, has not yet been put into practice. Therefore, to exploit the potential of the all-fiber system fully, developing a new all-optical microwave generation system by using TCSs and approaching the performance of microcavity soliton combs is still worth exploring. In this Letter, we demonstrate the all-fiber method to generate CTMWs, which was realized by dual-chirped TCSs with agile repetition rate. The proposed scheme could generate wide CTMWs in real time, without electro-optical modulation conversion or complex drive circuit devices. Dual TCSs with slightly different repetition rate were continually generated based on the dissipative FWM processes into two multi-wavelength Brillouin fiber laser cavities. Fast frequency sweeping of the extracavity pump laser was specifically used to implement the rapid tuning of soliton comb line spacing, where each comb line inherits the frequency modulation of the pump laser. By optically channelizing the mixed OFCs, the CTMWs in different bands can be obtained in different channels. As a result, the chirp from the optical field is transmitted to the chirp of the electric field at once. To the best of our knowledge, this is the first time to report TCSs with repetition rate agile for reconfigurable microwave waveforms generating. Experimental Details. Figure 1(a) shows the schematic diagram of the experimental setup consisting of (I) dual-TCSs generation part and (II) heterodyne detection part. To comprehend the formation of the TCSs, Figs. 1(b) and 1(c) depict the dynamic evolutions of cascaded-FWM frequency combs in spectral and time domains, respectively. As shown in Fig. 1(a), one pump laser for the reference frequency of the dual comb was provided by a distributed feedback fiber laser (DFB-FL1) characterized by a linewidth of 50 kHz and an emission wavelength of 1550 nm. Both comb sources had the same architecture except for slightly different repetition rates. The DFB-FL1 output was split, and then individually combined with another pump laser (DFB-FL2 or DFB-FL3), amplified by an erbium-doped fiber amplifier (EDFA), and injected into two equal parts for the generation of dual TCSs. For each single comb, it consisted of two pump lasers, a multi-wavelength laser generator and a Brillouin laser cavity.

Fig. 1. (a) Schematic diagram of the experimental setup. DFB-FL1&DFB-FL2&DFB-FL3: distributed feedback fiber laser; OC: optical couple; EDFA: erbium-doped fiber amplifier; HNLF: highly nonlinear fiber. Dynamic evolutions of cascaded-FWM frequency combs in spectral domain (b) and time domain (c).

For a multi-wavelength-laser generator, the amplified dual pump lasers were injected into a 200-m-long dispersion-flat HNLF to generate multi-wavelength lasers based on FWM processes, which were used as the comb seed. The amplified multi-wavelength lasers were launched into the following ring cavity by terminal 1 of an optical circulator for generating multiple-wavelength Brillouin lasers inside the cavity, which were employed as the pumping beam for temporal cavity soliton generation. Each Brillouin ring cavity laser was composed by connecting ports 2 and 3 of the optical circulator through a 400-m-long dispersion-flat HNLF, an optical isolator, and a 10 dB OC. The HNLF employed in our experiments had a nonlinear coefficient of 10 W$^{-1}\cdot$km$^{-1}$, attenuation below 1.2 dB/km, and a dispersion coefficient of 0.389 ps$\cdot$nm$^{-1}\cdot$km$^{-1}$ @1550 nm. The output wavelengths of DFB-FL3 not only have a thermal tuning range of 0.8 nm, but also possess fast linear tuning via the built-in PZT module. In dual comb beating and microwave generation part, optical spectrum after each ring cavity was split and combined, then optically channelized by programmable optical filter (Finisar 4000A). After filtering, the heterodyne signal was obtained by a photodiode module (Newport BB-818-51F) and amplified to $\sim$ $18$ dBm by high power RF amplifiers (Ixblue DR-AN-20-MO). The electrical spectrum was measured with an electrical spectrum analyzer (Aligent: N9320B-ATO-72979), and the generated microwave waveform was recorded by a real-time oscilloscope (Lecroy SDA 820Zi-B) with a sampling rate of 40 GSa/s. The optical spectrum was measured by an optical spectrum analyzer (Yokogawa AQ6370D). Experimental Results and Discussion. The DFB-FL1 and DFB-FL3 were initially turned on to examine the single-comb performance. The wavelength spacing $f$ between the two pump lasers was precisely set to be 1.6 nm (separated by 200 GHz). Then, the generated multiple-wavelength cw lasers were amplified to 650 mW, and launched into the multiple Brillouin laser cavity. The pump laser only completed one turn when the optical circulator and the optical isolator were placed inside the Brillouin laser cavity, which also suppressed the higher-order ($\ge$ 2) Brillouin lasers.[19] Furthermore, the cavity feedback takes responsibility for phase noise and relative intensity noise restraint of the pump laser, thus resulting in a narrower spectral linewidth Brillouin laser in cavity.[20] The average output power of the cavity was 52 mW. The newly generated comb lines were observed to emerge from the dual-pumping frequency as a cascade of sidebands with a precise spacing of $f$, as pump power increased. The development of TCSs in the passive nonlinear optical cavity resulted from the parametric gain compensating for the resonant cavity losses. The multiple-wavelength Brillouin laser provided an effective pump beam for the emergence of a high-quality soliton pulse train because of its narrower linewidth, phase locking, and higher peak power.

Fig. 2. Output characteristics of the temporal cavity soliton in frequency separation of 200 GHz. (a) Optical spectrum, (b) typical autocorrelation traces, (c) the delayed self-heterodyne beating radio-frequency spectra of the Brillouin laser, and (d) the measured frequency sweeping range of our laser under different driving voltages.

The formation of TCSs always relies on a double balance of dispersion and nonlinearity as well as (parametric) gain and cavity loss. The comb lines are generated via cascaded FWM process and undergo a self-organization process that leads to the emergence of a soliton pulse train.[18] Figure 2 illustrates the output characteristics of the TCSs based on intracavity dissipative FWM process. As shown in Fig. 2(a), the optical spectrum of the one-pulse state spans more than 100 nm with low noise and smooth spectral envelopes without spectral gaps. The red curve shows the spectral sech$^{2}$-shape envelope. The time-frequency features of the Brillouin laser were passed on to newly generated comb lines, which have a clearly defined line structure and a low signal noise basis. The radiation near 1500 nm is the dispersive wave, induced by the temporal perturbation of higher-order dispersion. The corresponding autocorrelation trace is shown in Fig. 2(b). The temporal field envelope exhibited a sech$^{2}$ shape, which has a full width at half maximum (FWHM) of 680 fs. The autocorrelation trace shows a train of pulses well separated by the cavity round-trip time of 5 ps, which corresponds to the frequency interval of 200 GHz. The dip of cw background on both sides of the pulse is a representative feature of TCSs, which presented stable soliton pulses superimposed on a cw background. The newly formed ultra-short pulses propagated without distortion in the cavity, emphasizing the intracavity pulses' soliton properties. These results imply that we have successfully realized the output of single TCSs inside the Brillouin laser cavity. Figure 2(c) depicts the beat electrical spectra of the Brillouin laser measured by the delayed self-heterodyne method. Amplitude of frequency domain profile (purple curve) is fit to a Gaussian function (red curve) to estimate the linewidth, due to the significant $1/f$ frequency noise of single-frequency fiber laser.[21] The measured FWHM is 70 kHz, and the corresponding real linewidth is 49.5 kHz. Surprisingly, the base-order stimulated Brillouin laser's (first-order comb line) narrow linewidth indicates that it possesses good monochromaticity and coherence. The wavelength linear sweeping range of the pump laser measured by the wavelength meter is also shown in Fig. 2(d). As can be seen, the fast-tunning range of wavelength would certainly improve with the growth of amplitude of driving voltage. Such a frequency excursion of the central wavelength performs fine linearity. Its linear frequency fast sweep range is about 3.55 GHz when $\sim$ $30$ V direct current is loaded on the PZT module, and fits a tuning efficiency of 117 MHz/V. The fast tunable repetition rate of TCSs relies on the fast wavelength scanning of the pumped laser. Next, we further investigated the generation of TCSs with tunable high-repetition rate. The electrical control signal was not applied and the central wavelength of the DFB-FL3 was adjusted via a built-in temperature control module. By varying the frequency interval of the two external pump lasers, the repetition rate of the TCSs could be directly altered from GHz to THz. Obviously, the repetition rate difference of the dual TCSs was also continuously adjustable in a wide range. The intracavity multiple Brillouin lasers were spontaneously placed in the resonant region of the fiber cavity in the technique described above, because the frequency interval of the pump beams is always an integral multiple of the free spectral range of the cavity. Neither the pumping frequency nor the cavity resonance was not necessary to be tuned in fiber cavity. As shown in Figs. 3(a)–3(d), we representatively summarize the output spectra of the TCSs at the repetition rates of 100, 125, 158, and 242 GHz, respectively. The optical spectrum all have a typical sech$^{2}$ shape. One can also refer to our previous work for the mechanism of generation and more details of TCSs.[22]

Fig. 3. Output temporal cavity soliton spectrum in frequency separation of (a) 100 GHz, (b) 125 GHz, (c) 158 GHz, and (d) 242 GHz. The red curves indicate the sech$^{2}$ fitting for the envelope of the spectrum profile.

Generally, the principle of the photonic microwave generation employing TCSs with agile repetition rate relies on coherent transfer of a wide-band optical field to an equivalent electrical-domain signal. Moreover, we demonstrated the generation of CTMWs via all-fiber dual-chirped TCSs. The system ran in the following three steps. First, the dual TCSs with a slight repetition rate difference were realized, where the slow tuning was decided by the temperature-controlling module of the pump laser. Second, the set temperature was maintained constant, and fast frequency sweeping of the pump laser was achieved by loading different-format control signals on the PZT module where each comb line inherited the pump laser frequency modulation. Finally, the CTMWs were attained by optically channelizing and beating. In particular, the fixed difference in repetition rate of dual TCSs achieved by thermal tuning determines the central frequency of microwave waveforms, and the rapid frequency sweeping range of the pump laser ultimately controls the bandwidth of signals. To achieve this, we performed fast frequency-modulation of the DFB-FL3 by altering the voltage applied to the PZT integrated into the ultra-short fiber line resonator. In practice, the control signal is typically designed as a triangle waveform to produce the linearly chirped microwave waveforms.[23] By applying the triangular ramp voltage to the PZT, we transduced the cavity resonance shift induced by the PZT to the triangular laser frequency change. Thus, the chirp from the optical field was transferred to the electric field at once. The difference in dual-TCSs repetition rate and the pump laser's sweeping frequency variation were consistently correlated positively in the variation trend. The measured spectrum of dual OFCs is shown in Part I of the Supplementary Material. Then, a 1-kHz control signal $S(t)$, which has a triangular profile and an amplitude of $\sim$ $10$ V (positive bias of 10 V), was applied to the PZT, where the maximum load voltage of PZT could be 150 V. The waveform of the electrical control signal is shown in Fig. 4(a). Figure 4(b) shows the electrical spectrum of the generated triangular linear-chirp microwave signal, in which the outer band signal-to-noise ratio reaches 50 dB. The additional phase noise was introduced into the system through an arbitrary waveform generator and wavelength-swept laser during frequency modulation, degrading the signal-to-noise ratio.[24] As illustrated in Fig. 4(c), the chirped waveforms with a temporal period of 1 ms were detected at the PD's output. Figure 4(d) shows the recovered instantaneous frequency of the waveforms based on a short-time Fourier transform, where triangular chirped microwave waveforms are realized and the linearity is fine. The tuning range of the instantaneous frequency is roughly 0.45 GHz and rises from 1.45 GHz to 1.9 GHz, as shown in Fig. 4(d), and it fits a chirp rate of 0.9 GHz/ms. Due to the PZT module's narrower response bandwidth, there is local hysteresis at the rising edge of the triangle wave.

Fig. 4. (a) The measured control signal, (b) the electrical spectrum with a 0.45-GHz span, (c) measured temporal waveform, (d) the recovered instantaneous frequency (the dashed curve is a linear fitting curve).

Fig. 5. The instantaneous frequencies of the generated sawtooth chirp microwave waveforms with different repetition rates (the dashed curve is a linear fitting curve).

The unique advantages of arbitrary line spacing and fast repetition rate tuning allow for the generation CTMWs in the dual-TCSs system. The mentioned system possesses the advantages of all-fiber capabilities without electro-optical modulation conversion. Subsequently, the CTMWs with sawtooth modulation were demonstrated by regulating the pattern of control signals. The temporal period of the input control signals affects the repetition rate of CTMWs. An arbitrary waveform generator was used to create sawtooth ramp signals with ramping frequencies between 200 Hz and 1 kHz, which were then amplified to 10 V and caused over 1 GHz laser frequency excursion. As depicted in Fig. 5, we demonstrate the three different ramping frequencies of the produced laser frequency spectrograms. At 200 Hz and 300 Hz modulation frequency, the instantaneous frequency increases linearly, where the dashed line is a linear fitting curve. According to the result provided in Fig. 5(c), the measured chirp rate is 210 MHz/ms. The measured results of multiband CTMWs are shown in Part II of the Supplementary Material. Additionally, the bandwidth, frequency chirping linearity, and other parameters of the CTMWs are slightly inferior to the currently reported works,[25,26] which was mainly limited by the low response bandwidth of the PZT module used in our experiments and the absence of a high-voltage amplifier. The bandwidth and frequency chirping linearity of CTMWs based on dual-chirped TCSs still need to be further improved in future. The chirped microwave generation technique based on the dual TCSs with agile repetition rate continues to have outstanding reconfigurability, meaning that the CTMWs' bandwidth, central frequency, repetition rate, envelope, and duration may all be easily adjusted to fit various application requirements. In conclusion, we have proposed an all-optical CTMWs generation scheme without optical–electrical conversion or any complex drive circuit devices. The proposed system can produce high-quality photonic microwave signals, and it is simple to modify the CTMWs' bandwidth, central frequency, envelope, and repetition rate. The tunability is realized by changing operation wavelength, which combines coarse tuning via temperature and fast tuning based on an integrated low-voltage PZT module. The CTMWs transmitter based on the all-optical mechanism provides a potential solution for the application requirements of multi-band and bandwidth microwave signal transmission and reception in multi-band radar systems. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61675009 and 61325021), and the Key Program of Beijing Municipal Natural Science Foundation (Grant No. KZ201910005006). References Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronicsPhotonics for Radars Operating on Multiple Coherent BandsElectronic-Photonic Integrated Circuit for 3D MicroimagingFrequency-Modulated Continuous-Wave LIDAR and 3D Imaging by Using Linear Frequency Modulation Based on Injection LockingSegmented chirped-pulse Fourier transform submillimeter spectroscopy for broadband gas analysisRecent advances in optoelectronic oscillatorsThe optoelectronic oscillatorOptical frequency comb technology for ultra-broadband radio-frequency photonicsFrequency-agile dual-comb spectroscopyPhotonic Generation and Wireless Transmission of Linearly/Nonlinearly Continuously Tunable Chirped Millimeter-Wave Waveforms With High Time-Bandwidth Product at W-BandDissipative Kerr solitons in optical microresonatorsTemporal solitons in optical microresonatorsPhotonic microwave generation in the X- and K-band using integrated soliton microcombsMassively parallel coherent laser ranging using a soliton microcombTemporal solitons in microresonators driven by optical pulsesTemporal cavity solitons in one-dimensional Kerr media as bits in an all-optical bufferTemporal soliton and optical frequency comb generation in a Brillouin laser cavityMulti-frequency radiation of dissipative solitons in optical fiber cavitiesOptical frequency combs generated by four-wave mixing in a dual wavelength Brillouin laser cavityLaser line shape and spectral density of frequency noiseTemporal Cavity Solitons With Tunable High-Repetition-Rate Generation in a Brillouin Pulse Laser CavityLow-noise frequency-agile photonic integrated lasers for coherent rangingPhotonic chirped radio-frequency generator with ultra-fast sweeping rate and ultra-wide sweeping rangeLinearly chirped microwave waveform generation with large time-bandwidth product by optically injected semiconductor laserPhotonic Generation of Linearly Chirped Microwave Waveforms With Tunable Parameters

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