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.

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.

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.

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.

Rapidly and continuously frequency-scanning opto-electronic oscillator.

An opto-electronic oscillator (OEO) scheme which operates at "chirp oscillation" mode and generates low-phase-noise, frequency-swept microwave is proposed and experimentally demonstrated. This frequency-swept OEO is achieved by embedding a rapidly frequency-scanning microwave filter in an opto-electronic cavity. The filter has fixed passband while its center frequency scans rapidly and periodically at cavity round-trip time, covering a large frequency range (~GHz). Experimentally, the generated frequency-swept microwave is linear frequency-modulated continuous wave (FMCW) which centers at 7 GHz with 1-GHz bandwidth. Its instantaneous frequency varies linearly from 6.5 GHz to 7.5 GHz, back and forth, in a period of 12.8 µs, resulting in a frequency scanning rate of ~156 MHz/µs. The single-side-band (SSB) noise of the generated FMCW is -104 dBc/Hz at 10 kHz offset frequency, which is much lower than that from a commercial electronic arbitrary waveform generator (E-AWG). Improvement as large as 23 dB is experimentally reported.

Low phase noise microwave extraction from femtosecond laser by frequency conversion pair and IF-domain processing.

Extraction of a microwave component from a low-time-jitter femtosecond pulse train has been attractive for current generation of spectrally pure microwave. In order to avoid the transfer from the optical amplitude noise to microwave phase noise (AM-PM), we propose to down-convert the target component to intermediate frequency (IF) before the opto-electronic conversion. Due to the much lower carrier frequency, the AM-PM is greatly suppressed. The target is then recovered by up-conversion with the same microwave local oscillation (LO). As long as the time delay of the second LO matches that of the IF carrier, the phase noise of the LO shows no impact on the extraction process. The residual noise of the proposed extraction is analyzed in theory, which is also experimentally demonstrated as averagely around -155 dBc/Hz under offset frequency larger than 1 kHz when 10-GHz tone is extracted from a home-made femtosecond fiber laser. Large tunable extraction from 1 GHz to 10 GHz is also reported.

Large-scale coherent Ising machine based on optoelectronic parametric oscillator.

Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.

Optoelectronic parametric oscillator.

Oscillators are one of the key elements in various applications as a signal source to generate periodic oscillations. Among them, an optical parametric oscillator (OPO) is a driven harmonic oscillator based on parametric frequency conversion in an optical cavity, which has been widely investigated as a coherent light source with an extremely wide wavelength tuning range. However, steady oscillation in an OPO is confined by the cavity delay, which leads to difficulty in frequency tuning, and the frequency tuning is discrete with the minimum tuning step determined by the cavity delay. Here, we propose and demonstrate a counterpart of an OPO in the optoelectronic domain, i.e., an optoelectronic parametric oscillator (OEPO) based on parametric frequency conversion in an optoelectronic cavity to generate microwave signals. Owing to the unique energy-transition process in the optoelectronic cavity, the phase evolution in the OEPO is not linear, leading to steady single-mode oscillation or multimode oscillation that is not bounded by the cavity delay. Furthermore, the multimode oscillation in the OEPO is stable and easy to realize owing to the phase control of the parametric frequency-conversion process in the optoelectronic cavity, while stable multimode oscillation is difficult to achieve in conventional oscillators such as an optoelectronic oscillator (OEO) or an OPO due to the mode-hopping and mode-competition effect. The proposed OEPO has great potential in applications such as microwave signal generation, oscillator-based computation, and radio-frequency phase-stable transfer.

Breaking the limitation of mode building time in an optoelectronic oscillator.

An optoelectronic oscillator (OEO) is a microwave photonic system with a positive feedback loop used to create microwave oscillation with ultra-low phase noise thanks to the employment of a high-quality-factor energy storage element, such as a fiber delay line. For many applications, a frequency-tunable microwave signal or waveform, such as a linearly chirped microwave waveform (LCMW), is also needed. Due to the long characteristic time constant required for building up stable oscillation at an oscillation mode, it is impossible to generate an LCMW with a large chirp rate using a conventional frequency-tunable OEO. In this study, we propose and demonstrate a new scheme to generate a large chirp-rate LCMW based on Fourier domain mode locking technique to break the limitation of mode building time in an OEO. An LCMW with a high chirp rate of 0.34 GHz/µs and a large time-bandwidth product of 166,650 is demonstrated.