Injection-locked Optoelectronic Oscillator Research Articles

A Practicable Optoelectronic Oscillator with Ultra-Low Phase Noise

In this paper, an optoelectronic oscillator (OEO) with ultra-low phase noise and high stability based on the injection-locked and phase-locked loop is proposed. In theory, the injection-locked frequency range of the injection signal is studied based on the phase dynamics equation, and the phase noise performance of the injection-locked OEO is analyzed. The role of the phase-locked loop on the frequency stability of the OEO is analyzed based on the phase-locked loop transfer function. In addition, this paper builds an injection-locked OEO based on a phase-locked loop. The injection-locked signal is the high-frequency output of the multiplication crystal oscillator (MCO). At the same time, this MCO synchronously outputs a low-frequency signal, which is used as the reference signal of the phase-locked loop. The experimental results show that the proposed OEO output frequency is 10 GHz, and the phase noise is −89.25 dBc/Hz@100 Hz, −121.71 dBc/Hz@1 kHz, and −145.39 dBc/Hz@10 kHz; the side-mode suppression ratio is 80 dB; the frequency stability is 2.06 × 10−11@1 s, 9.03 × 10−11@10 s, 1.03 × 10−10@100 s, and 3.03 × 10−10@1000 s. Consistent with the theoretical analysis results, the solution takes into account the frequency stability, side-mode suppression ratio, and phase noise performance. The simple structure is more advantageous in practical applications.

Study on the performance of injection-locked single-loop optoelectronic oscillators in presence of additive white Gaussian noise

Abstract This paper presents a detailed study on the synchronization characteristics of a single-loop optoelectronic oscillator (OEO) under the influence of radiofrequency (RF) signal, which is contaminated with additive white Gaussian noise (AWGN). The influence of the AWGN on the performance of the injection-locked optoelectronic oscillator (IL-OEO) is investigated in terms of the probability of losing lock, average beat frequency, and frequency of skipping cycles. Fokker–Planck technique is utilized to derive the expression for the probability density function (PDF) of the phase difference between the injection RF signal and the OEO output signal. The probability of losing lock on the two sides of the IL-OEO oscillation frequency and the frequency of skipping cycles are calculated in terms of the signal-to-noise ratio (SNR). An expression for the phase noise spectrum of the IL-OEO is also presented. The analytical model predicts the phase noise of the IL-OEO at very low offset frequencies with the accuracy rate of 75 %, in the presence of AWGN. Experimental verifications are carried out to prove the validity of the proposed analytical model.

Time-domain convolution model for studying oscillation dynamics in an injection-locked optoelectronic oscillator.

A time-domain convolution model is proposed to study the oscillation dynamics in the injection-locked optoelectronic oscillator (OEO). The model has the ability to calculate multiple characteristics of the oscillation signal, such as the spectrum and the phase noise. Based on the model, the injection locking, the frequency pulling and the asymmetrical spectrum generation phenomena are numerically simulated in success. The simulation results fit in with the experimental results, indicating that the proposed model accurately describes the oscillation dynamics in the injection-locked OEO. In addition, the building-up process of the oscillation signal in the OEO is simulated. Alternating appearance of the sidebands on both sides of the primary oscillation mode is observed for the first time in the asymmetrical spectrum generation. This model is a powerful tool to study the oscillation dynamics in the injection-locked OEO.

An All-Optical Ka-Band Microwave Long-Distance Dissemination System Based on an Optoelectronic Oscillator

We proposed an all-optical Ka-band microwave long-distance dissemination system based on an optoelectronic oscillator (OEO). In this system, a single tone with high spectrum purity and low phase noise is excited by an injection-locked OEO, and distributed to the remote site through the fiber loop of the OEO at the same time. The second harmonic of the reference signal modulates the round-tripping optical signal at the local site, which achieves the phase conjugator at the optical domain. At the remote end, the phase-conjugated signal is photomixed with the OEO signal to eliminated the phase offset. The proposed scheme improves the phase noise of the high frequency signal received at the remote site and reduces the photoelectric conversion loss. We demonstrated the transmissions of a 36 GHz frequency-quadrupled RF signal along a 6 km optical fiber loop, and the frequency stability is 1.069 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−14</sup> /1 s and 3.3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−16</sup> /1000 s. The single-sideband (SSB) phase noise of the received signal at the remote site is up to −130 dBc/Hz at 10 kHz offset frequency.

Injection-locked optoelectronic oscillator with high side-mode suppression ratio and low phase noise based on frequency-conversion delay matching

An injection-locked optoelectronic oscillator (OEO) based on frequency-conversion delay matching is proposed and experimentally demonstrated. There are two branches in the proposed OEO, where one branch is used to maintain the oscillation in the cavity, and the other one based on frequency conversion is used to generate a pure frequency-converted injection signal. Owing to the frequency-conversion-based injection locking effect, the side-mode suppression ratio of the proposed OEO can be greatly improved. In addition, the phase noise deterioration induced by the externally-injected signal can be effectively eliminated when the time delays of the two branches are well matched. In the experiment, a pure single-tone microwave signal at 9.99998 GHz is generated, whose side-mode suppression ratio and phase noise are measured to be 74.4 dB and −130 dBc/Hz@10 kHz, respectively.

Self-Injection-Locked Optoelectronic Oscillator Based on Frequency Conversion Filtering

The multi-mode noise is an important issue for the optoelectronic oscillator (OEO) in generating a spectrally pure microwave. Especially in oscillators with low phase noise, increasing the cavity length to improve the phase noise performance will make the mode interval smaller, which is more likely to cause multi-mode noise. Here, we proposed a low phase noise and high side-mode suppression ratio self-injection-locked OEO based on frequency conversion filtering. We theoretically and experimentally studied the influence of the phase noise of the external microwave source on the proposed OEO and, as a comparison, the conventional injection-locked OEO. The results show that, compared with the traditional injection-locked OEO, the proposed OEO is less sensitive to the phase noise of the external microwave source. Under the same experimental conditions, the proposed OEO achieved the same side-mode suppression ratio and the phase noise is reduced by 30 dB at 10 kHz offset from the 10-GHz carrier compared with the conventional injection-locked OEO.

Study of the phase noise spectrum in RF injection-locked single-loop optoelectronic oscillators

Study of the phase noise spectrum in RF injection-locked single-loop optoelectronic oscillators

Power Spectral Density of Injection-Locked Optoelectronic Oscillators: Effects of Phase Noise

Injecting a spectrally pure oscillator signal into a noisy optoelectronic oscillator (OEO) can result in a drastic reduction of the phase noise; however, a unified explanation of this effect may be obscured by implementation-specific models. We show based on an analytically tractable theory that the power spectral density <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S_f(\omega)$</tex-math></inline-formula> of an ideal injection-locked (IL) oscillator signal is composed of a narrow Lorentzian peak at the center frequency lying on top of a broader roughly Lorentzian pedestal using an Ornstein-Uhlenbeck model obtained from the Adler equation in the weak-noise limit. The injected signal imposes its phase on the IL oscillator providing a restoring force for the phase, leading to this fundamentally different behavior of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S_f(\omega)$</tex-math></inline-formula> compared with a self-sustaining oscillator. Our treatment is shown to be grounded in the physics-based approach for IL OEOs of A. F. Talla, R. Martinenghi, G. R. Goune Chengui, J. H. Talla Mbé, K. Saleh, A. Coillet, G. Lin, P. Woufo, and Y. K. Chembo, “Analysis of phase-locking in narrow-band optoelectronic oscillators with intermediate frequency,” <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>I</b></i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EEE J. Quantum Electron.</i> , vol. 51, 5000108, 2015.

Analysis of the suppression of spurious frequencies by the blocking effect in an injection-locked optoelectronic oscillator.

The blocking effect causing the suppression of spurious frequencies in an injection-locked optoelectronic oscillator (IL-OEO) is studied in this paper. The blocking effect analysis in nonlinear systems is carried out using the Volterra series and is experimentally measured in a microwave amplifier. The blocking effect in the nonlinear system helps in analyzing the suppression of spurious frequencies in an IL-OEO. Under injection locking, the spurious frequencies in the IL-OEO are significantly suppressed, and the spurs are further suppressed when the power of the reference signal is increased.

Injection locking and pulling phenomena in an optoelectronic oscillator.

Injection locking and pulling characteristics of a long-loop optoelectronic oscillator (OEO) that has a large number of closely-spaced longitudinal modes are theoretically analyzed and experimentally evaluated. A differential phase equation that relates the phase difference between the OEO and the injected microwave signal to its instantaneous beat angular frequency is derived in the time domain. Based on the differential phase equation, both the locking and pulling characteristics of an injection-locked OEO are studied, and the phase noise performance is analyzed. It is found that the locking and pulling performance depends upon three parameters, the initial frequency difference between the frequency of the signal generated by the free-running OEO and frequency of the injected microwave signal, the voltage ratio between the signal generated by the free-running OEO and the injected microwave signal, and the Q factor of the free-running OEO. The phase noise performance depends upon the locking range, the phase noise performance of the free-running OEO as well as that of the injected microwave signal. The analysis is validated experimentally. Excellent agreement is found between the theoretical analysis and the experimental demonstration.

On the Transient Behavior of Single-Loop Optoelectronic Oscillators Under RF Injection-Locking

A study on the transient behavior of a single-loop optoelectronic oscillator (OEO) under a single sinusoidal radio frequency (RF) signal injection is presented. Considering only the phase perturbation imposed by the external RF signal, the phase-dynamic equation is solved to analyze the frequency settling behavior of the loop. A closed form expression for the required time of an OEO under RF injection-locking, reaching the steady state condition, is derived in terms of the initial phase difference, beat frequency and injection signal strength. The phase modulated signal, which is responsible for the perturbation of the free running oscillation, is expanded in a Fourier series and the expression for the output RF spectrum of the injection pulled OEO is derived. The injection-pulling dynamics approach is used to describe the phase noise of the OEO and also, the influence of the phase settling time constant on the phase noise of the injection-locked OEO is studied. The experimental results corroborating the theoretical findings are given.

A Theoretical and Experimental Study of Injection-Locking and Injection-Pulling for Optoelectronic Oscillators Under Radio Frequency Signal Injection

This article presents a detailed study of injection-locking characteristics of a single-loop optoelectronic oscillator (OEO) under strong radio frequency (RF) signal injection. We provide formulas for the steady-state phase-angle after locking, and the locking time for a higher level of a locking signal, considering only the phase perturbation. We also provide a compact expression for the main spectrum components of the pulled OEO in terms of the beat frequency, which is useful to evaluate and quantify the injection-pulling effects in the OEO. The experimental results provide partial support to the conclusion of the analysis. The analytical and experimental results are presented in design curves, which can be used to determine the required properties of an injection-locked OEO for a specific performance of the oscillator.

Study of injection-locking and injection-pulling in injection-locked optoelectronic oscillator under radio frequency signal injection

We present a detailed study of injection-locking (IL) and injection-pulling behavior of an IL single-loop optoelectronic oscillator (OEO) when injected by radio frequency (RF) signal. From the locking equation, the expression for the output spectrum of the IL-OEO under RF injection is derived in the time domain, to evaluate the spurious performance of the system. The frequency response of the spurious outputs due to RF injection signal is investigated in terms of the injection transfer function. Also, a dual-loop model of the IL-OEO is developed to study the phase noise performance of the system with a cofrequency RF injection signal. Also, the effect of Gaussian minimum shift keying signal interference on the IL-OEO output spectrum is investigated. An analytical expression for the side-mode attenuation is presented to describe the influence of IL on the side-modes of free-running OEO. The experimental results corroborating the theoretical findings are given.

Injection-Locked Millimeter Wave Frequency Divider Utilizing Optoelectronic Oscillator Based Optical Frequency Comb

We propose and experimentally demonstrate a photonic millimeter-wave frequency divider based on a super-harmonic injection-locked optoelectronic oscillator (OEO) and an optical frequency comb. The optical frequency comb generator is incorporated into an OEO loop to create broadband comb lines with low noise. By injecting a millimeter-wave with frequency around N times of the fundamental oscillating frequency f0 of the OEO, the injection signal can be down-converted to an intermediate frequency (IF) signal close to the oscillating frequency of the OEO. The free running OEO is synchronized with the IF signal via an injection locking mechanism. Consequently, it forms an injection-locked frequency divider as the frequency ratio between the injection signal and OEO's output signal is precisely equal to N. We carry out an experiment to divide the 45 GHz signal into 7.5 GHz and the experimental results agree well with the theoretical analysis. By changing the frequency of the injection signal, division ratio from 2 to 5 is also demonstrated on one setup. Due to the broadband spectra of the optical comb and low phase noise characteristics of the OEO, it is potential to realize very large division ratio and low phase noise for multiple input frequencies mf 0 .

Ultralow Phase Noise Optoelectronic Oscillator and Its Application to a Frequency Synthesizer

We propose a novel injection-locked OptoElectronic Oscillator (OEO) with ultralow phase noise based on two cascaded phase modulators, which is further applied to construct a frequency synthesizer. Thanks to the phase modulation, the output optical spectrum expands and the optical power keeps constant while passing through the optical fiber, which dramatically reduces the intensity noise induced by the nonlinear effects of the optical fiber. A dual-output MZI together with a balanced optical detector realizes the phase modulation to intensity modulation conversion and improves the signal to noise ratio of the OEO. The output frequency of the proposed OEO is 9.9999914 GHz with its sidemode suppression ratio larger than 85 dB, and the phase noise reaches –153.1 dBc/Hz at 10 kHz frequency offset which is 38.7 dB lower than that of Keysight E8257D. Moreover, a broadband, high performance frequency synthesizer is established based on the proposed OEO. Combining the DDS and PLL technologies, the proposed frequency synthesizer can cover 5.9～12.9 GHz range. The phase noise is around –130 dBc/Hz@10 kHz, the spur suppression ratio is better than 65 dB, and the frequency hopping time is less than 1.48 μs.

An injection-locked OEO based frequency doubler independent of electrical doubler phase noise deteriorating rule

We propose an injection-locked optoelectronic oscillator (OEO) based wide-band frequency doubler, which is free from phase noise deterioration in electrical doubler, by using a dual-parallel Mach–Zehnder modulator (DPMZM). Through adjusting the optical phase shifts in different arms of the DPMZM, the doubling signal oscillates in the OEO loop while the fundamental signal takes on phase modulation over the light and vanishes at photo-detector (PD) output. By controlling power of fundamental signal the restriction of phase-noise deterioration rule in electrical doubler is totally canceled. Experimental results show that the doubler output has a better phase noise value of, for example, −117 dBc/Hz @ 10 kHz at 6 GHz with an improvement more than 17 dB and 23 dB compared with that of fundamental input and electrical doubler, respectively. Besides, the stability of this doubler output can reach to 1.5×10−14 at 1000 s averaging time. The frequency range of doubling signal is limited by the bandwidth of electrical amplifier in OEO loop.

Frequency domain approach to the steady state and stability analysis of dual injection-locked optoelectronic oscillators.

A frequency domain algorithm is proposed for deriving all of the possible steady state modes of dual injection-locked optoelectronic oscillators (DIL-OEOs), corresponding to the detailed system parameters, such as the fiber lengths, small signal open loop gains, radio frequency filters' bandwidths, phase shifting values, and injection parameters. It is shown that some or all of the modes computed by the new approach may be unstable; these are just mathematical solutions of the steady state equations. Therefore, it is necessary to check the stability of these modes. A stability analysis approach is proposed, which is based on simulating the slowly varying time domain dynamic governing the perturbation variables. The steady state and stability analysis approaches enable one to predict the required injection parameters for having a reliable steady state injection-locked mode in the DIL-OEO system. The new method requires a much smaller runtime compared to the corresponding time domain methods. In addition, it avoids many simplifying assumptions of the corresponding frequency domain approaches presented in the literature. The validities of the steady state and stability analysis methods are verified by comparing their results with full time domain integrations and with other predictions regarding the required injection parameters for phase locking, as presented in the literature.

Frequency domain computation of steady state modes of optoelectronic oscillators with stability analysis.

A frequency domain approach for computing all of the steady state modes of single-loop optoelectronic oscillators (OEOs) corresponding to the exact parameter values, especially the fiber length, is presented. Computing these modes is useful in analyzing their effects on the phase noise performance as well as in designing single-mode OEOs. This computation is also useful in analyzing injection-locked OEO systems where the locking state depends on the values of oscillation frequencies and power levels of the steady state modes of the OEOs involved. The proposed steady state computation approach requires a much smaller amount of run-time compared to time domain methods; however, its results have to be checked for stability. Two stability analysis schemes, one based on the frequency domain Nyquist stability analysis and the other based on solving a slowly varying perturbation system in the time domain, are presented. The validities of these schemes are verified by comparing their results with each other, with full time domain integrations, and with previously published results. It is shown that the modes of a single-loop OEO computed by the presented approach are either stable or unstable, which justifies the need to use the proposed stability analysis schemes. Simulations show that the unstable modes ultimately converge to the dominant mode, i.e., the one with the largest small-signal loop gain. The effect of exciting any mode on the phase noise is also investigated through simulations.

Improving the performance of the injection-locked optoelectronic oscillator by using an extra feedback loop

We describe and demonstrate a practical method for improving the performance of an injection-locked optoelectronic oscillator (IL OEO). An improved IL theory model, which helps to set the optimal locking range and reduce the phase noise of the OEO, is proposed. The IL OEO with an extra feedback loop exhibits good long-term operating stability and can produce a 10 GHz output signal with 80 dB side-mode suppression ratio and better than ±0.0005 ppm frequency drift within 12 h. The presented results can be used to guide the design of high-quality OEOs.

Frequency domain phase noise analysis of dual injection-locked optoelectronic oscillators.

Dual injection-locked optoelectronic oscillators (DIL-OEOs) have been introduced as a means to achieve very low-noise microwave oscillations while avoiding the large spurious peaks that occur in the phase noise of the conventional single-loop OEOs. In these systems, two OEOs are inter-injection locked to each other. The OEO with the longer optical fiber delay line is called the master OEO, and the other is called the slave OEO. Here, a frequency domain approach for simulating the phase noise spectrum of each of the OEOs in a DIL-OEO system and based on the conversion matrix approach is presented. The validity of the new approach is verified by comparing its results with previously published data in the literature. In the new approach, first, in each of the master or slave OEOs, the power spectral densities (PSDs) of two white and 1/f noise sources are optimized such that the resulting simulated phase noise of any of the master or slave OEOs in the free-running state matches the measured phase noise of that OEO. After that, the proposed approach is able to simulate the phase noise PSD of both OEOs at the injection-locked state. Because of the short run-time requirements, especially compared to previously proposed time domain approaches, the new approach is suitable for optimizing the power injection ratios (PIRs), and potentially other circuit parameters, in order to achieve good performance regarding the phase noise in each of the OEOs. Through various numerical simulations, the optimum PIRs for achieving good phase noise performance are presented and discussed; they are in agreement with the previously published results. This further verifies the applicability of the new approach. Moreover, some other interesting results regarding the spur levels are also presented.