Enrico Rubiola

Photonic-delay technique for phase-noise measurement of microwave oscillators

A photonic-delay line is used as a frequency discriminator for measurement of the phase noise - hence the short-term frequency stability - of microwave oscillators. The scheme is suitable for electronic and photonic oscillators, including the optoelectronic oscillator, mode lock lasers, and other types of rf and microwave pulsed optical sources. The approach is inherently suitable for a wide range of frequency without reconfiguration, which is important for the measurement of tunable oscillators. It is also insensitive to a moderate frequency drift without the need for phase locking.

Contribution of Laser Frequency and Power Fluctuations to the Microwave Phase Noise of Optoelectronic Oscillators

An opto-electronic oscillator is a microwave oscillator in which the resonator is replaced with an optical fiber delay-line carrying an intensity-modulated laser beam. We consider the frequency and power fluctuations of a standard DFB telecom laser, and we investigate their effect on the phase noise of microwaves generated with opto-electronic oscillators. We propose a theoretical study showing how these two laser fluctuations are converted into phase noise in the output microwave. This theory predicts that the power noise should have a minor contribution to microwave phase noise, while the wavelength fluctuations should strongly contribute to phase noise via the chromatic dispersion of the few kilometers long optical fiber delay line. We have experimentally confirmed the validity of this theory by measuring the relative intensity noise and the optical frequency noise of a semiconductor laser, which has later been used for microwave generation. We show that the use of a zero-dispersion fiber delay-line can lead to a 10 dB improvement of the phase noise performance, relatively to the case were a standard single mode fiber is used.

Determination of Phase Noise Spectra in Optoelectronic Microwave Oscillators: A Langevin Approach

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case of optoelectronic oscillators where the microwave is a limit-cycle originated from a bifurcation induced by nonlinearity and time-delay. This Langevin approach based on stochastic calculus is also successfully confronted with experimental measurements.

Phase noise of whispering gallery photonic hyper-parametric microwave oscillators

We report on the experimental study of phase noise properties of a high frequency photonic microwave oscillator based on four wave mixing in calcium fluoride whispering gallery mode resonators. Specifically, the oscillator generates approximately 8.5 GHz signals with -120 dBc/Hz at 100 kHz from the carrier. The floor of the phase noise is limited by the shot noise of the signal received at the photodetector. We argue that the performance of the oscillator can be significantly improved if one uses extremely high finesse resonators, increases the input optical power, supersaturates the oscillator, and suppresses the residual stimulated Raman scattering in the resonator. We also disclose a method of extremely sensitive measurement of the integral dispersion of millimeter scale dielectric resonators.

Advanced interferometric phase and amplitude noise measurements

The measurement of the close-to-the-carrier noise of two-port radio frequency and microwave devices is a relevant issue in time and frequency metrology and in some fields of electronics, physics, and optics. While phase noise is the main concern, amplitude noise is often of interest. Presently the highest sensitivity is achieved with the interferometric method, that consists of the amplification and synchronous detection of the noise sidebands after suppressing the carrier by vector subtraction of an equal signal. A substantial progress in understanding the flicker noise mechanism of the interferometer results in new schemes that improve by 20–30 dB the sensitivity at low Fourier frequencies. These schemes, based on two or three nested interferometers and vector detection of noise, also feature closed-loop carrier suppression control, simplified calibration, and intrinsically high immunity to mechanical vibrations. This article provides the complete theory and detailed design criteria, and reports on the ...

On the 1/f frequency noise in ultra-stable quartz oscillators

The frequency flicker of an oscillator, which appears as a 1/f3 line in the phase noise spectral density, and as a floor on the Allan deviation plot, originates from two basic phenomena, namely, (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.

Phase noise in the regenerative frequency dividers

The authors report on a theoretical analysis of the phase noise in regenerative dividers, and provide design rules for the best spectral unity. The spectral purity is, in fact, the reason why regenerative dividers may be preferred to simpler schemes whenever that characteristic is a fundamental requirement. This class of dividers is suitable for high frequencies, out of reach to other techniques. The nucleus of the theory is the description of the mixer, driven by coherent signals, in terms of differential phase gain, so as to relate noise at the divider output to the noise generated inside the divider itself. After introducing a model of the mixer and some related measurement techniques, it is shown that the most favorable noise condition for the divider is reached by tuning it off the maximum output amplitude. Methods for approximating this condition are then outlined. The experiments prove the feasibility of the proposed approach, and reported results show a phase noise reduction of 10 dB with respect to the maximum amplitude condition. >

Dual photonic-delay line cross correlation method for phase noise measurement

We describe the application of a cross-correlation method with dual photonic delay-line for homodyne phase noise measurement of low-noise microwave oscillators. This method combines a delay-line discriminator and cross correlation with the use of a low-loss kilometer-long photonic delay. By using a 4.5 km optical fiber as a photonic delay, we demonstrated a measurement noise floor of -158 dBc/Hz at 10 kHz offset without a reference oscillator.

ELISA: A cryocooled 10 GHz oscillator with 10−15 frequency stability

This article reports the design, the breadboarding, and the validation of an ultrastable cryogenic sapphire oscillator operated in an autonomous cryocooler. The objective of this project was to demonstrate the feasibility of a frequency stability of 3x10(-15) between 1 and 1000 s for the European Space Agency deep space stations. This represents the lowest fractional frequency instability ever achieved with cryocoolers. The preliminary results presented in this paper validate the design we adopted for the sapphire resonator, the cold source, and the oscillator loop.

Flicker noise in high-speed p-i-n photodiodes

The microwave signal at the output of a photodiode that detects a modulated optical beam contains the phase noise /spl alpha/(t) and amplitude noise /spl alpha/(t) of the detector. Beside the white noise, which is well understood, the spectral densities S/sub /spl psi//(f) and S/sub /spl alpha//(f) show flicker noise proportional to 1/f. We report on the measurement of the phase and amplitude noise of high-speed p-i-n photodiodes. The main result is that the flicker coefficient of the samples is /spl sim/10/sup -12/ rad/sup 2//Hz (-120 dBrad/sup 2//Hz) for phase noise, and /spl sim/10/sup -12/ Hz/sup -1/ (-120 dB) for amplitude noise. These values could be observed only after solving a number of experimental problems and in a protected environment. By contrast, in ordinary conditions, insufficient electromagnetic interference isolation, and also insufficient mechanical isolation, are responsible for additional noise to be taken in. This suggests that if package and electromagnetic compatibility are revisited, applications can take the full benefit from the surprisingly low noise of the p-i-n photodiodes.