Spurious mode reduction in dual injection-locked optoelectronic oscillators

Dual-loop diode-tuned Fourier domain harmonically mode-locked opto-electronic oscillator with over 50 dB side-mode spur reduction

We propose and demonstrate a dual-loop harmonic Fourier domain mode-locked optoelectronic oscillator (FDML-OEO) for drastically reducing the side-mode spurs. The frequency domain mode-locking is achieved by synchronizing the scanning period of the filter to an integer fraction of the round trip times of the two loops with a self-made low cost diode-tuned RF filter. We found, for the first time to the best of authors' knowledge, that the frequency scanning bandwidth (FSBW) of the mode-locked output is strongly affected by the length mismatch between the two fiber loops. By using the phase noise of FDML OEO's delayed self-heterodyne signal as a performance indicator, we found experimentally that both the locking bandwidth and the FSBW of the device are inversely proportional to the length mis-match of the two loops. Finally, with dual-loop fiber lengths of 2041m and 2449.2m, including 2039m common fiber loop, we successfully obtained linearly chirped microwave signals around 9GHz with a phase noise of -127dBc/Hz at 10kHz offset from the 9GHz carrier, a FSBW of 0.4GHz, and a chirp rate of 200THz/s at 500.38 kHz repetition rate. More impressively, the side-mode spur ratio of the linear frequency modulated (LFM) signal is reduced to less than -83dB, the lowest ever achieved for a FDML OEO to the best of authors' knowledge, which is more than 50dB improvement over that achieved with a single loop FDML OEO reported previously.

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.

Spurious Tone Reduction and Signal Stabilization of Optoelectronic Oscillators by Low-Frequency RF Signal Modulation

In this study, the oscillation signal stabilization and spurious tone suppression of a directly modulated optoelectronic oscillator (DM-OEO) are simultaneously achieved by modulating a laser with a low-frequency radio frequency (RF) signal. The laser in the DM-OEO is modulated by a rectangular wave with a period inversely proportional to the frequency interval of the spurious tones and a duty cycle of 50%. The optical sidebands of the rectangular wave-modulated laser pulled the optical gain of the spurious tones of the DM-OEO, resulting in a spurious tone suppression and time stabilization in the DM-OEO signal. We achieve a 15 GHz DM-OEO with a 40.14 dB side-mode suppression ratio (SMSR) and 2.55 dB improvement in the oscillation power stability compared to that without RF modulation.

Frequency-domain analysis of dual-loop optoelectronic oscillators

Optoelectronic oscillators (OEOs) are hybrid systems consisting of optical and radio-frequency (RF) parts that are used to produce ultralow phase noise RF oscillations. Dual-loop OEOs can overcome some problems incorporated with single-loop OEOs such as the mode-hopping phenomenon and the large spurious peaks in the phase noise. Therefore, they are usually considered the practical implementation of many OEOs. Here, a frequency-domain steady-state and phase noise analysis approach of these systems is presented, based on the conversion matrix approach. Compared with the existing time-domain analysis approaches, it requires much smaller run times. Compared with the other frequency-domain modeling approaches, such as the linear-time-invariant phase transmission models, it can take all noise-transferring phenomena between various sidebands and all amplitude-noise to phase-noise conversions and vice versa into account. Therefore, it can be regarded as a comprehensive analysis approach to dual-loop OEOs. The validity of the new approach is verified by comparing its results with those of the previously published formulations in the literature.

Nonlinear dynamics in an optoelectronic feedback delay oscillator with piecewise linear transfer functions from the laser diode and photodiode

We investigate the nonlinear dynamics of a recent architecture of an optoelectronic oscillator, where the emitting laser and the receiving diode are connected in a head-to-tail configuration via an optical fiber delay line. The resulting nonlinear transfer function is a piecewise linear profile, and its interplay with the delay leads to many complex behaviors such as relaxation oscillations and deterministic chaos. This system belongs to a recent class of optoelectronic oscillators where the nonlinearity does not originate from the sinusoidal transfer function of an imbalanced interferometer, and, in particular, it is a simple optoelectronic oscillator configuration that is capable of displaying a chaotic behavior. The results of the analytic study are confirmed by numerical simulations and experimental measurements.

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.

A normal form method for the determination of oscillations characteristics near the primary Hopf bifurcation in bandpass optoelectronic oscillators: Theory and experiment

We propose a framework for the analysis of the integro-differential delay Ikeda equations ruling the dynamics of bandpass optoelectronic oscillators (OEOs). Our framework is based on the normal form reduction of OEOs and helps in the determination of the amplitude and the frequency of the primary Hopf limit-cycles as a function of the time delay and other parameters. The study is carried for both the negative and the positive slopes of the sinusoidal transfer function, and our analytical results are confirmed by the numerical and experimental data.

Tunable low-drift spurious-free optoelectronic oscillator based on injection locking and time delay compensation

A finely tunable low-drift spurious-free single-loop optoelectronic oscillator (OEO) incorporating injection locking and time delay compensation is proposed and experimentally demonstrated. In the proposed OEO, one mode of a single-loop OEO is injection locked by a tunable electronic oscillator resulting in single-mode oscillation. A time delay compensation system is used to compensate the OEO's loop length change caused by environmental changes, such as temperature and strain. Tuning of the oscillation frequency is realized by controlling the injection frequency and absolute loop length of the single-loop OEO. In the experiments, when the ambient temperature varies between 22°C and 31°C within 1000 s, an output signal at the frequency of 10.664 GHz with a frequency drift better than -0.1  ppb and side-mode suppression ratio greater than 78 dB has been realized. Also, the OEO can be tuned with a precise frequency step of 10 Hz.

High spectral purity electromagnetically induced transparency-based microwave optoelectronic oscillator with a quasi-cylindrical microcavity

High spectral purity microwave oscillators are widely exploited in science and military areas including communication, radar, and navigation. Here, we theoretically analyze and experimentally observe the application of tunable electromagnetically induced transparency (EIT) effect generated within a single quasi-cylindrical microresonator (QCMR) to a high spectral purity microwave optoelectronic oscillator (OEO). Stable single-frequency microwave oscillation with phase noise of -123 dBc/Hz at 10 kHz offset from ~5 GHz carrier and -135 dBc/Hz at 100 kHz offset is demonstrated without using any narrow-band RF filters. Moreover, we evaluate the impact of laser-mode locking state, quality factor as well as spectral lineshapes of the EIT resonance, laser coupling efficiency, and three configurations of optical energy storage elements on the spectral purity of the oscillator, so as to improve its phase noise and stability performances. Extending the concept of EIT to a microwave generator opens a promising avenue towards compact low-phase-noise oscillator systems for emerging mass applications.

Stable and Low-Spurs Optoelectronic Oscillators: A Review

An optoelectronic oscillator (OEO) is an optoelectronic hybrid oscillator which utilizes ultra-low loss fiber as an electro-magnetic energy storage element, overcoming the limits of traditional microwave oscillators in phase noise performance. Due to their ability to generate ultra-low phase noise microwave signal, optoelectronic oscillators have attracted considerable attentions and are becoming one of the most promising and powerful microwave signal sources. In this paper, we briefly introduce the operation principle and discuss current research on frequency stability and spurious suppression of optoelectronic oscillators.

Filtering effect of SiO2 optical waveguide ring resonator applied to optoelectronic oscillator

Single-mode oscillation is crucial to the practicality of optoelectronic oscillator (OEO). Due to the limited by bandwidth and precision of radio frequency (RF) filters, it is difficult to be achieved for the OEO based on the long fiber-optic delay line. So instead of the long fiber-optic delay line, SiO₂ optical waveguide ring resonator (OWRR) with high-Q and mode selection is first presented to be applied to OEO. The OEOs based on the minimum loop and SiO₂ OWRR are constructed. The oscillation characteristics of the minimum loop OEO and the transmission characteristics of the SiO₂ OWRR are simulated by MATLAB, respectively. The filtering effect of the SiO₂ OWRR applied to the OEO is verified theoretically by comparing these simulation results. Subsequently, the contrastive experiments of the above two OEOs on oscillation modes are carried out. The oscillation mode spacing of 40.32 MHz and 2.137 GHz are obtained. These results show that the SiO₂ OWRR can function as an excellent 'filter' in the minimum loop of the OEO. Moreover, the side mode suppression ratio and the phase noise of the OEO have been improved. Our experimental results demonstrate that the OEO adopting SiO₂ OWRR is feasible to achieve the single-mode oscillation and obtain better performance microwave signals.

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.

Hybrid radio-intermediate-frequency oscillator with photonic-delay-matched frequency conversion pair

A low-phase-noise, single-loop radio-frequency (RF) oscillator is proposed and experimentally demonstrated where part of the oscillation is in intermediate-frequency (IF) domain by a pair of frequency conversions. Single-mode operation is achieved by IF filtering. The key design is the matched photonic delay between the two conversions, by which the large phase noise of the common external RF local oscillation (LO) shows no impact on the RF carrier passing through the conversion pair and the low-phase-noise oscillation is guaranteed. The phase-noise performance of the delay-matched conversion pair plus IF filtering is theoretically and experimentally studied. With the proposed scheme, we achieve 120 dBc/Hz phase noise at 10-kHz offset from 10-GHz carrier frequency through a 1-μs loop cavity.

Phase noise performance comparison between optoelectronic oscillators based on optical delay lines and whispering gallery mode resonators

We investigate the phase noise performance of optoelectronic oscillators when the optical energy storage elements are in the following three configurations: a high-Q whispering gallery mode resonator, an optical delay-line and a combination of both elements. The stability properties of these various optical elements are first characterized, and then systematically compared in the optical and in the microwave frequency domains. Subsequently, the spectral purity of the oscillator is theoretically and experimentally examined for each case. When the resonator is used as both delay and filtering element inside the delay-line based oscillator, the generated spurious modes are highly rejected. A spur rejection by more than 53 dB has been demonstrated for the first-neighboring spur.

Optoelectronic oscillator for a measurement of acoustic velocity in acousto-optic device

We report a novel means of measuring the acoustic velocity based on a well-known acousto-optic interaction. With an acousto-optic modulator (AOM), we construct an optoelectronic oscillator (OEO) that can measure the acoustic velocity in the AOM directly. The free spectral range between the modes is a function of the total loop length of the OEO, which is mainly dependent on the propagation time of the acoustic wave through the AOM. By changing the propagation time, we measured the acoustic velocity from the variation of the free spectral range. The results are reported and compared with earlier results. This method is insensitive to the variation of the optical phase shift. In addition, the high frequency-stability and microwave spectral purity of the OEO allow reliable and precise measurements.

Theoretical investigation of the capture effect in intensity-modulation direct-detection microwave photonic links

We introduce the capture effect concept in microwave photonic links (MWPLs) for the first time to our knowledge. The capture effect or the small-signal suppression is the change in the amplitude ratio of the two signals between input and output of the intensity-modulation direct-detection (IMDD) MWPLs. An analytical explanation of the performance of external IMDD MWPLs due to the effects of nonlinearity combined with sum of several input sinusoidal signals is given. We have investigated the suppression of a weaker signal in these links. General analytic expression for the small-signal suppression is derived using a nonlinear analytical approach. We show that the small-signal suppression is quite dependent on the input back-off, the power ratio of input signals, and on the number of input sinusoidal signals. The theoretical maximum possible signal suppression was found to be 6 dB. This analytical asymptotic value is verified by numerical results. We show the influence of the capture effect of the nonlinear MWPL on the optoelectronic oscillator operation that is verified by experimental data in the literature that has already been published.

An optically tunable wideband optoelectronic oscillator based on a bandpass microwave photonic filter

An optoelectronic oscillator (OEO) with wideband frequency tunability and stable output based on a bandpass microwave photonic filter (MPF) has been proposed and experimentally demonstrated. Realized by cascading a finite impulse response (FIR) filter and an infinite impulse response (IIR) filter together, the tunable bandpass MPF successfully replaces the narrowband electrical bandpass filter in a conventional single-loop OEO and serves as the oscillating frequency selector. The FIR filter is based on a tunable multi-wavelength laser and dispersion compensation fiber (DCF) while the IIR filter is simply based on an optical loop. Utilizing a long length of DCF as the dispersion medium for the FIR filter also provides a long delay line for the OEO feedback cavity and as a result, optical tuning over a wide frequency range can be achieved without sacrificing the quality of the generated signal. By tuning the wavelength spacing of the multi-wavelength laser, the oscillation frequency can be tuned from 6.88 GHz to 12.79 GHz with an average step-size of 0.128 GHz. The maximum frequency drift of the generated 10 GHz signal is observed to be 1.923 kHz over 1 hour and its phase noise reaches the -112 dBc/Hz limit of our measuring equipment at 10 kHz offset frequency.

Impact of fiber delay fluctuation on reference injection-locked optoelectronic oscillators

We demonstrate that the phase shift of a reference injection-locked optoelectronic oscillator (OEO) varies as the change of its fiber delay over a long period of time. The dynamic variation of the fiber delay is monitored using an injected probe signal and is compared with the phase shift. With actively stabilized fiber delays according to the monitored data, the long-term frequency stability of the reference injection-locked OEO is evaluated.

Amplifier-free slab-coupled optical waveguide optoelectronic oscillator systems

We demonstrate a free-running 3-GHz slab-coupled optical waveguide (SCOW) optoelectronic oscillator (OEO) with low phase-noise (<-120 dBc/Hz at 1-kHz offset) and ultra-low sidemode spurs. These sidemodes are indistinguishable from noise on a spectrum analyzer measurement (>88 dB down from carrier). The SCOW-OEO uses high-power low-noise SCOW components in a single-loop cavity employing 1.5-km delay. The noise properties of our SCOW external-cavity laser (SCOWECL) and SCOW photodiode (SCOWPD) are characterized and shown to be suitable for generation of high spectral purity microwave tones. Through comparisons made with SCOW-OEO topologies employing amplification, we observe the sidemode levels to be degraded by any amplifiers (optical or RF) introduced within the OEO cavity.

Enhancing long-term stability of the optoelectronic oscillator with a probe-injected fiber delay monitoring mechanism

Optoelectronic oscillators (OEOs), based on optical fiber loops to act as a high-Q cavity, are capable of generating stable radio-frequencies (RF). The long-term frequency stability of the OEO is then limited by the cavity variation that is mainly induced by temperature sensitivity of the optical fiber. In order to actively stabilize the OEO cavity, we employ the technique of RF transfer over optical fibers. We propose and experimentally demonstrate a dual-loop-OEO scheme to enhance the long-term stability with an injected probe signal to monitor the phase variation in the fiber loops. The experimental results show that the resulting spread-spectrum signal is useful in monitoring the fiber delay without observable interference. The relationships between the measured frequency and the monitored delay are theoretically and numerically discussed. We also estimate the long-term stability of the proposed OEO scheme with the cavity phase correction. The corrected result shows the long-term frequency stability of the proposed OEO is within 8.4×10(-8) at one day.