Etgar C. Levy

Spurious mode reduction in dual injection-locked optoelectronic oscillators

Optoelectronic oscillators (OEOs) are promising sources of low phase noise radio frequency (RF) signals. However, at X-band frequencies, the long optical fiber delay line required for a high oscillator Q also leads to spurious modes (spurs) spaced too narrowly to be filtered by RF filters. The dual injection-locked OEO (DIL-OEO) has been proposed as a solution to this problem. In this work, we describe in detail the construction of a DIL-OEO. We also present experimental data from our systematic study of injection-locking in DIL-OEOs. With this data, we optimize the DIL-OEO, achieving both low phase noise and low spurs. Finally, we present data demonstrating a 60 dB suppression of the nearest-neighbor spur without increasing the phase noise within 1 kHz of the 10 GHz central oscillating mode.

Modeling optoelectronic oscillators

We have developed a comprehensive simulation model for accurately studying the dynamics in optoelectronic oscillators (OEOs). Although the OEO is characterized by three widely separated time scales, our model requires neither long run times nor a large amount of memory storage. The model generalizes the Yao-Maleki model and includes all of the physical effects in the Yao-Maleki model as well as other physical effects that are needed to calculate important features of the OEO dynamics, such as the impact of the fast response time of the modulator on the phase noise power spectral density, the fluctuations of the OEO output due to the input noise, the cavity mode competition during the OEO start-up, and temporal amplitude oscillations in steady state. We show that the absolute value of the phase noise is 2-3 dB lower than predicted by the Yao-Maleki model. The Yao-Maleki model does not take into account amplitude noise suppression due to the fast time response of the modulator, which accounts for this difference. We show that a single cavity mode oscillates in the OEO at steady state, and this mode is determined by the noise that is present when the OEO is turned on. When the small-signal open-loop gain is higher than 2.31, we show that the OEO amplitude oscillates in steady state. This temporal amplitude oscillation can be suppressed by using a narrow filter. Our simulation model, once extended to include flicker (1/f) noise and different amplifier and modulator designs, will enable its users to accurately design OEOs.

Comprehensive computational model of single- and dual-loop optoelectronic oscillators with experimental verification

We describe a comprehensive computational model for singleloop and dual-loop optoelectronic oscillators (OEOs). The model takes into account the dynamical effects and noise sources that are required to accurately model OEOs. By comparing the computational and experimental results in a single-loop OEO, we determined the amplitudes of the white noise and flicker noise sources. We found that the flicker noise source contains a strong component that linearly depends on the loop length. Therefore, the flicker noise limits the performance of long-cavity OEOs (≧5 km) at low frequencies (f<500 Hz). The model for a single-loop OEO was extended to model the dual-loop injection-locked OEO (DIL-OEO). The model gives the phase-noise, the spur level, and the locking range of each of the coupled loops in the OEO. An excellent agreement between theory and experiment is obtained for the DIL-OEO. Due to its generality and accuracy, the model is important for both designing OEOs and studying the physical effects that limit their performance. We demonstrate theoretically that it is possible to reduce the first spur in the DIL-OEO by more than 20 dB relative to its original performance by changing its parameters. This theoretical result has been experimentally verified.

Experimental and simulation study of dual injection-locked OEOs

We investigate the physics of bidirectional injection-locking in optoelectronic oscillators (OEO). In particular, we identify the effects of injection strength on phase noise and spurious modes for a dual injection-locked OEO. Our experimental data is then used to design a numerical model of a dual injection-locked OEO. This model will be used in the future to optimize the multi-dimensional injection-locking parameters to achieve minimal phase noise and spurious mode levels.

Study of dual-loop optoelectronic oscillators

Dual-loop optoelectronic oscillators are used to obtain high-frequency harmonic signal with a very low phase noise while maintaining very low spurs. However, the fundamental limits of these devices are not known. Therefore, it is essential to develop theoretical models to improve the performance of dual-loop optoelectronic oscillators (OEOs) and in particular the performance of the dual-injection-locked optoelectronic oscillator (DIL-OEO). In this work we use a multi-time scale approach to model dual-loop OEOs. The model enables calculating the phase noise and the spurs level for an arbitrary coupling strength between the two locked OEOs. A good quantitative agreement between theory and experiments is obtained for the DIL-OEO.

Loop-length dependent sources of phase noise in optoelectronic oscillators

Optoelectronic oscillators are a promising source of spectrally pure, easily tunable microwave signals. These oscillators use a low-loss fiber optic delay line as a very high Q resonant cavity. However, length-dependent sources of phase noise prevent the full Q of the resonant cavity from being realized. Here we show evidence that this length-dependent phase noise is in part dependent upon the optical power and laser noise. This dependence is consistent with the conversion of laser noise to phase noise via the Kerr effect.

Non-ideal loop-length-dependence of phase noise in OEOs

We present an experimental study of the phase noise spectrums dependence on the loop length in OEOs. As the loop length increases, the spectrum deviates significantly from the ideal dependence.

Spurious-mode suppression in optoelectronic oscillators

Optoelectronic oscillators (OEOs) are promising low phase noise radio frequency sources. However, the long fiber loops required for a high Oscillator Q also lead to spurious modes (spurs) spaced too narrowly to be filtered by standard electronic devices. As a solution to this problem, the dual injection-locked OEo (DIL-OEO) has been proposed and studied. Previously, we presented experimental data demonstrating spur suppression in the DIL-OEO. We also developed theoretical models enabling us to optimize the DIL-OEO. In this work, we present data demonstrating 60 dB suppression of the nearest-neighbour spur in a high-Q OEO without increasing the phase noise within 1 kHz of the 10 GHz oscillating mode.

An analytical model of the dual-injection-locked opto-electronic oscillator (DIL-OEO)

We derive the equations that govern the phase noise at steady state in two coupled oscillators with delay. This simple model is then applied to the dual-injection-locked opto-electronic oscillator (DIL-OEO). This model is an extension of the Yao-Maleki model from one OEO loop to two, and it is complementary to other work on full simulations and experiments that we have carried out. We use this model to understand the key features of our current experiments and to point to a new regime in which the spurs can potentially be greatly reduced without greatly increasing the phase noise.

Noise distribution in the radio frequency spectrum of optoelectronic oscillators.

We analyze the distribution of the rf spectrum in optoelectronic oscillators due to the finite duration of the spectrum measurement. The distribution of the periodogram or the rf spectrum at a given frequency is calculated using a reduced model and is compared to a comprehensive numerical simulation. The model shows that the rf spectrum at a given frequency fluctuates from measurement to measurement with an exponential distribution.