Virtual-State Model for Analyzing Electro-Optical Modulation in Ring Resonators.

Ring resonators play a crucial role in optical communication and quantum technology applications. However, these devices lack a simple and intuitive theoretical model to describe their electro-optical modulation. When the resonance frequency is rapidly modulated, the filtering and modulation within a ring resonator become physically intertwined, making it difficult to analyze the complex physical processes involved. We address this by proposing an analytical solution for electro-optic ring modulators based on the concept of a "virtual state." This approach equates a lightwave passing through a dynamic ring modulator to one excited to a virtual state by a cumulative phase and then returning to the real state after exiting the static ring. Our model simplifies the independent analysis of the intertwined physical processes, enhancing its versatility in analyzing various incident signals and modulation formats. Experimental results, including resonant and detuning modulation, align with the numerical simulation of our model. Notably, our findings indicate that the dynamic modulation of the ring resonator under detuning driving approximates phase modulation.

High-resolution reconfigurable RF signal spectral processor.

Recent developments in microwave photonic filters (MPFs) offer superior properties for radio frequency (RF) signal processing, such as large instantaneous bandwidth, high resolution and multifunctional shapes. However, it is quite challenging to realize two or more characteristics simultaneously to meet the diverse needs in complex electromagnetic environment. In this paper, we propose a reconfigurable RF signal spectral processor with both large instantaneous bandwidth and high resolution. In the proposed spectral processor, sufficient taps supplied by an optical frequency comb (OFC) offer a large instantaneous bandwidth to process broadband RF signals. Flexible tap coefficients can be obtained by manipulating an optical spectral shaper (OSS), which provides excellent reconfigurability. This tap-by-tap manipulation is realized with a high resolution of hundreds of megahertz, allowing precise shape configuration of the response. In the experiment, we demonstrate a flat-top response with a wide bandwidth of 7.1 GHz. Reconfigurable features such as tunable bandwidth, adjustable center frequency and diverse shapes are also shown. In particular, the measured frequency resolution of 96.5 MHz demonstrates the ability for precise configuration.

Laser frequency noise correction in LFM-based interferometric fiber-optic hydrophone array.

In this paper, we propose a novel time-division multiplexed (TDM) array for a large-scale interferometric fiber-optic hydrophone system, in which we introduce a power-optimized reference probe and effectively reduce the additional white noise while correcting for light source frequency noise. Laser frequency noise usually introduces appreciable phase noise during demodulation of interferometric fiber-optic hydrophones. In the previous means, one would introduce an additional probe isolated from the environment in sensor array, and use it as a reference to calibrate the demodulation results of the other actual sensors. However, while correcting, the reference probe also introduces a large white noise. In our array, the echo of the reference probe is higher than the other sensors, thus solving this problem. The novel array design is applied to our previously proposed fiber-optic hydrophone based on a linear frequency modulated (LFM) light source. Experiments show that the deterioration of phase noise floor caused by additional white noise is improved from at least 3 dB originally to within 1 dB. This paper analyzes the factors that need to be concerned for the successful implementation of correction algorithms in hydrophone systems based on LFM sources. Particular focus is given to the impact of the power optimization of reference probe on the white noise and the corrected phase noise. Our proposal allows a significant relaxation of the demanding linewidth requirement for interferometric hydrophone. It is shown that laser with linewidth of 338.06 MHz can replace that with 1.417 kHz in our new system, while achieves the same demodulation noise floor.

Hybrid-integrated wideband tunable optoelectronic oscillator.

As a photonic-based microwave signal generation method, the optoelectronic oscillator (OEO) has the potential of meeting the increasing demand of practical applications for high frequency, broadband tunability and ultra-low phase noise. However, conventional OEO systems implemented with discrete optoelectronic devices have a bulky size and low reliability, which extremely limits their practical applications. In this paper, a hybrid-integrated wideband tunable OEO with low phase noise is proposed and experimentally demonstrated. The proposed hybrid integrated OEO achieves a high integration level by first integrating a laser chip with a silicon photonic chip, and then connecting the silicon photonic chip with electronic chips through wire-bonding to microstrip lines. A compact fiber ring and an yttrium iron garnet filter are also adopted for high-Q factor and frequency tuning, respectively. The integrated OEO exhibits a low phase noise of -128.04 dBc/Hz @ 10 kHz for an oscillation frequency of 10 GHz. A wideband tuning range from 3 GHz to 18 GHz is also obtained, covering the entire C, X, and Ku bands. Our work demonstrates an effective way to achieve compact high-performance OEO based on hybrid integration, and has great potential in a wide range of applications such as modern radar, wireless communication, and electronic warfare systems.

Broadband linear frequency modulation signal compression based on a spectral Talbot effect.

Broadband linear frequency modulation (LFM) signals with a long duration are widely used in radar and broadband communication systems. The LFM signals are compressed to a Fourier-transform-limited pulse train after matched filtering, which effectively improves the signal-to-noise ratio (SNR) of detection. Quadratic phase response is the key component of matched filtering, which can be achieved by phase filters or dispersion elements. Suffering from the limited resolution of phase filters and complex equivalent large dispersion structures, pulse compression of broadband LFM signals with a long duration remains an open challenge. In this paper, LFM signal compression based on the spectral Talbot effect is proposed and experimentally demonstrated, where ultra-large equivalent dispersion (around 1.7 × 109 ps/nm) is realized by a simple optical filter ring. Experimentally, the LFM signal with a bandwidth of 12 GHz and a duration of 163 µs is compressed into a Fourier-transform-limited pulse train, which improves the SNR by 24 dB. Moreover, the proposed method also measures the delay difference between two LFM signals, ranging from 0 to 110 ns.

Time reversal of broadband microwave signal based on frequency conversion of multiple subbands.

Time reversal of broadband microwave signals based on frequency conversion of multiple subbands is proposed and experimentally demonstrated. The broadband input spectrum is cut into a number of narrowband subbands, and the center frequency of each subband is reassigned by multi-heterodyne measurement. The input spectrum is inversed, while the time reversal of the temporal waveform is also realized. The equivalence between time reversal and the spectral inversion of the proposed system is verified by mathematical derivation and numerical simulation. Meanwhile, spectral inversion and time reversal of a broadband signal with instantaneous bandwidth larger than 2 GHz are experimentally demonstrated. Our solution shows good potential for integration where no dispersion element is employed in the system. Moreover, this solution for an instantaneous bandwidth larger than 2 GHz is competitive in the processing of broadband microwave signals.

Low latency microwave photonic RTFT processing based on bandwidth slicing and equivalent dispersion.

Microwave photonic real-time Fourier transformation (RTFT) processing based on optical dispersion is a promising solution for microwave spectrum analysis. However, it usually brings the drawbacks of limited frequency resolution and large processing latency. Here, we demonstrate a low-latency microwave photonic RTFT processing based on bandwidth slicing and equivalent dispersion. The input RF signal is first divided into different channels with the help of bandwidth slicing technique, and then finely analyzed by the fiber-loop based frequency-to-time mapping. In the proof-of-concept experiment, a 0.44-m fiber-loop offers an equivalent dispersion as high as 6 × 105 ps/nm with a small transmission latency of 50 ns. As a result, we can realize a wide instantaneous bandwidth of 1.35 GHz, a high frequency resolution of approximately 20 MHz, and a high acquisition frame rate of approximately 450 MHz, together with a total latency of less than 200 ns.

Phase-diagram investigation of frustrated 1D and 2D Ising models in OEO-based Ising machine.

Ising machines have emerged as promising solvers for combinatorial optimization problems in recent years. In practice, these problems are often mapped into a frustrated Ising model due to randomness or competing interactions, which reduces the success ratio for finding the optimal solution. In this study, we simulate one-dimensional and two-dimensional frustrated Ising models in an Ising machine based on the optoelectronic oscillator. Our experiment aims to show the relationship between the Fourier mode of the coupling matrix and the spin distribution under frustration. The results prove the validity of the theoretical predictions and provide insights into the behavior of Ising machines in the presence of frustration. We believe it would help to develop a better strategy to improve the performance of Ising machines.

Microwave-photonics iterative nonlinear gain model for optoelectronic oscillators.

The nonlinear dynamic behavior of optoelectronic oscillators (OEOs), which is important for the OEO based applications, is investigated in detail by a Microwave-photonics Iterative Nonlinear Gain (MING) model in this paper. We connect the oscillating processes with the trajectories of an iterated map based on a determined nonlinear mapping relation referred to as open-loop input to output amplitude mapping relation (IOAM). The results show that the envelope dynamic is determined by the slope of IOAM at a special point called fixed point. Linear features dominate the loop if the slope is relatively large, and the nonlinear features emerge and become increasingly significant with the decreasing of the slope. Linear features of homogeneity and monotonicity are gradually lost. Furthermore, OEO is even unstable when the slope is less than a general threshold value of -1. The behavior of OEO loops with the different slope values are discussed by simulations and are experimentally confirmed. Moreover, the proposed model also applies to the OEO with an externally injected microwave signal, the bifurcation phenomena caused by injected signal are experimentally evidenced.

Generation of a coherent distributed RF array with a strong positive correlation.

In this work, we present a coherent distributed radio frequency (RF) array, discover and quantitatively describe the strong positive correlation between reconstructed signals for the first time. Eight replicable parallel receivers are connected to the phase-locked common trunk link via eight optical couplers spaced 1 km apart. The forward and backward signals at each receiver, extracted from two ports of optical couplers, are recovered to RF signals separately and then mixed to achieve upward frequency conversion. The link delay jitter is counteracted by wavelength-tuning of the optical carrier. With the long-term stability of point-to-multipoint fiber-optic RF dissemination effectively improved, the coherent distributed array is generated, and further the relative frequency stability between signals at different receivers is studied. The proposed correlation coefficient at 103 s is ∼0.8 and shows a slight downward trend with the increase of averaging time based on our experimental results.

Dynamic intelligent measurement of multiple chirped signals of different types based on the optical computing STFT and the YOLOv3 neural network.

We propose a simultaneous measurement system for multiple signals of different types which combines the optical computing short-time Fourier transform (STFT) and You Only Look Once (YOLOv3) neural network. Through the system, the analytical expressions of multiple broadband signals of different types can be obtained in real time with high-frequency resolution. Experimentally, the accuracy of the signal type in the detection results can almost reach 100%. Additionally, the parameter measurement errors for the bandwidth (BW), pulse width (PW), center frequency (CF), and time of arrival (TOA) of each linear frequency-modulated (LFM) or quadratic frequency-modulated (QFM) signal are within ±30 MHz, ±20 ns, ±15 MHz, and ±20 ns, respectively. The frequency resolution can reach 60 MHz. Factors affecting the performance of the measurement system, such as the quantity of the signal and the number of the category, are discussed.

Optically magnified dispersion of microwave signals with a wide and flexible tunable range.

Tunable microwave dispersion is highly desired for a wide field of microwave signal processing. However, a conventional microwave dispersive delay line usually suffers from either a small dispersion value or a narrow operation bandwidth. Here, we experimentally demonstrate the optically magnified dispersion of a microwave signal with a wide and flexible tunable range, based on a bandwidth-scaling microwave photonic system. The obtained microwave dispersion can therefore be magnified from the corresponding optical dispersion with a magnification factor that can be continuously tuned from 10,000 to 85,000. Meanwhile, a proof-of-concept experiment that includes both compression and stretching of chirped microwave pulses is reported. Microwave dispersion from 1.34 ns/GHz to 10.92 ns/GHz can be secured by the corresponding magnification of an optical dispersion value of 16 ps/nm.

Broadband radio-frequency signal synthesis by photonic-assisted channelization.

A channelized radio-frequency (RF) signal synthesis scheme is proposed to generate broadband RF signals with reconfigurable waveform, center frequency and instantaneous bandwidth. Based on dual optical frequency combs (OFCs) with different free spectrum ranges (FSRs), multiple narrowband signals are up-converted and synthesized into a broadband signal. Reconfigurable waveforms are generated in the simulation, including a symmetrical triangular linear frequency modulation continuous wave (STLFMCW) signal and a binary phase shift keying (BPSK) signal. In addition, to realize phase stability among channels, dual OFCs are differently modulated through polarization-multiplexing electro-optical modulators (EOMs). An RF signal synthesis experiment shows the relative phase fluctuation among channels is only 1.8°.

Microwave photonic radar system with ultra-flexible frequency-domain tunability.

Both effective detection demand against diversified development of flight targets and remote sensing providing identifiable and fine target information all call for microwave radar system with flexible and ultra-wideband frequency-domain ability to provide more high-resolution and multi-source information. A microwave photonic radar system with theoretically full-band and ultra-wideband working ability is presented and experimentally demonstrated. An optical frequency operation module is employed in the transmitter to break the frequency-domain limitation on the emitted radar signal, while two types of optical mixing structures are switched to provide the ability to receive target echoes at any frequency band. In the experiments, high-SNR optical frequency operation and subsequent waveform generation at each normal radar band, that is from HF to Ka, are carried out. Good linearity and coherence of the generated waveforms are also demonstrated. Then, multi-band system-level detection experiments are completed to show the full-band working ability. Centimeter-scale or even sub-centimeter-scale resolution are realized at different bands, which identifies the proposed system can handle target detection with flexible performance and support acquiring rich target information at different frequency bands in future.

Low spurious optoelectronic oscillator achieved by frequency conversion filtering without deteriorating phase noise.

In order to obtain microwave signals with low spurs and low phase noise, we studied the residual phase noise of the frequency-conversion filtering oscillator and methods to improve its phase noise performance. We first analyze the influence of the dispersion of the intermediate frequency (IF) filter on the residual phase noise in the frequency conversion filtering process. Then, we use an electro-optic modulator to achieve up-conversion in the frequency conversion filtering and extend the intra-cavity delay with an optical fiber after the modulator. This allows the optoelectronic oscillator (OEO) to improve the phase noise performance while having a good suppression of spurs. The spurs suppression ratio of the proposed OEO is 80 dB with a fiber of about 1.6 km in the cavity. The phase noise of the proposed OEO is -130 dBc/Hz at 10 kHz offset from 10 GHz, which is 10 dB lower than our previous work.

Stable downlink frequency transmission from arbitrary injection point with endless and quick phase error correction.

A stable frequency downlink transmission scheme, which delivers the frequency signal back to the central station from an arbitrary injection point along a radio-over-fiber (RoF) loop link, is proposed and demonstrated. The frequency signal at the arbitrary remote point is injected into the RoF loop link in both clockwise and counter-clockwise directions, simultaneously. The phase variation induced by the fiber loop link is obtained in real time with the help of a round-trip assistant frequency signal. The phase error can be exactly cancelled by a series of frequency mixing (i.e., up-conversion and down-conversion) among the signals. In the experiment, a 1.21-GHz frequency signal at an arbitrary remote point is downlink transferred to the central station in a 45-km fiber loop link. The result shows the overlapping Allan deviation (ADEV) of 1.04×10-12 at 0.1 s, 1.3×10-13 at 1 s and 1.1×10-15 at 104 s, respectively. The phase error correction operates entirely at the central station, leaving a simple and robust configuration of the remote site. No active adjusting part is integrated, and the all-passive compensation achieves an endless phase error correction range, as well as quick response to fiber delay changes.

Wide-band RF receiver based on dual-OFC-based photonic channelization and spectrum stitching technique.

A novel wide-band RF receiver based on a dual-OFC-based channelization and spectrum stitching technique is proposed and demonstrated experimentally. In the scheme, a dual-OFC-based channelizer is utilized as the front-end to slice the RF signals into multiple channels. In the back-end, through the channel estimation and spectrum stitching, the received signals can be well reconstructed in the digital domain. A proof-of-concept experiment is performed, in which signals with 3 GHz bandwidths are sliced and reconstructed using the proposed receiver with a normalized mean squared error (NMSE) of 7.9×10-3. The performances of the reconstructed signals on pulse compression are also demonstrated to evaluate the potential of the proposed technique in practical applications.

Broadband lower-IF RF receiver based on microwave photonic mixer and Kramers-Kronig detection.

A broadband lower- intermediate-frequency (IF) radio frequency (RF) receiver with low cost and complexity based on a microwave photonic mixer and Kramers-Kronig (KK) detection is proposed and experimentally demonstrated. The feasibility of the proposed RF receiver is verified by comparing the error vector magnitude (EVM) performance of a down-converted IF signal with and without KK detection. EVM is measured as a function of IF carrier frequency, input local oscillator (LO) power, input RF power, and the coupling ratio between RF and LO paths. With KK detection, EVM can be improved by more than 9.5% when the IF carrier frequency is close to half of the signal bandwidth. This implies that a lower IF frequency can be down-converted with good EVM and that a low-speed photodetector and a low sampling rate analog to digital converter can be used for wideband RF signal reception.

Real-time Fourier transformation based on the bandwidth magnification of RF signals.

We demonstrate a novel real-time Fourier transformation scheme with megahertz-level resolution realized by bandwidth magnification of radio frequency (RF) signals. Before the frequency-to-time mapping, the RF signal is modulated on an optical frequency comb, and then extracted by a Vernier comb filter. As a result, RF components can be separated in the spectrum with a greatly magnified optical bandwidth. Thus, even with limited dispersion provided by an ordinary optical fiber, the frequency-dependent pulses can be distinguished in the time domain. Experimentally, the RF signal with the frequency difference of 60 MHz is separated by around 123 ps in the time domain, equivalent to the dispersion of 1975.5 ps/GHz (2.47×105 ps/nm), while the physical dispersion is 1500 ps/nm. Thus, based on the bandwidth magnification of signals, the dispersion is equivalently amplified by 165 times.

Megahertz-resolution programmable microwave shaper.

A novel microwave shaper is proposed and demonstrated, of which the microwave spectral transfer function could be fully programmable with high resolution. We achieve this by bandwidth-compressed mapping a programmable optical wave-shaper, which has a lower frequency resolution of tens of gigahertz, to a microwave one with resolution of tens of megahertz. This is based on a novel technology of "bandwidth scaling," which employs bandwidth-stretched electronic-to-optical conversion and bandwidth-compressed optical-to-electronic conversion. We demonstrate the high resolution and full reconfigurability experimentally. Furthermore, we show the group delay variation could be greatly enlarged after mapping; this is then verified by the experiment with an enlargement of 194 times. The resolution improvement and group delay magnification significantly distinguish our proposal from previous optics-to-microwave spectrum mapping.