State-of-the-art RF signal generation from optical frequency division

Improved demodulated phase signal resolution for carrier signals with small modulation index by clipping and synchronous sampling for heterodyne interferometers

Digitization of phase-modulated carrier signals with a commercially available analog-to-digital converter (ADC) is a common task in many communication and sensor applications. ADCs deliver phase-modulated digital carrier signals, which are numerically demodulated in order to extract the relevant information. However, the limited dynamic ranges of available ADCs limit the carrier-to-noise ratio of carrier signals after digitization. Correspondingly, the resolution of the demodulated digital signal is degraded. We demonstrate a sampling method with a simple demodulation scheme for phase-modulated signals with a small modulation index. Our new scheme overcomes the limitation due to digital noise defined by the ADC. Through simulations and experiments, we provide evidence that our method can improve the resolution of the demodulated digital signal significantly, when the carrier-to-noise ratio of phase-modulated signals is limited by digital noise. We employ our sampling and demodulation scheme to solve the problem of a possible degradation of measurement resolution after digital demodulation in heterodyne interferometers measuring small vibration amplitudes.

The photodetection of ultrashort optical pulse trains for low noise microwave signal generation

Electrical signals derived from optical sources have achieved record-low levels of phase noise, and have demonstrated the highest frequency stability yet achieved in the microwave domain. Attaining such ultrastable phase and frequency performance requires high-fidelity optical-to-electrical conversion, typically performed via a high-speed photodiode. This paper reviews characteristics of the direct photodetection of optical pulses for the intent of generating high power, low phase noise microwave signals from optical sources. The two most popular types of photodiode detectors used for low noise microwave generation are discussed in terms of electrical pulse characteristics, achievable microwave power, and photodetector nonlinearities. Noise sources inherent to photodetection, such as shot noise, flicker noise, and photocarrier scattering are reviewed, and their impact on microwave phase fidelity is discussed. General guidelines for attaining the lowest noise possible from photodetection that balances power saturation, optical amplification, and amplitude-to-phase conversion, are also presented.

Sub 23 μHz instantaneous linewidth and frequency stability measurements of the beat note from an offset phase locked single frequency heterodyned Nd:YAG laser system

We report, what is to the best of our knowledge, the narrowest instantaneous linewidth measurement of the beat frequency between two phase locked heterodyned 1.319 μm Nd:YAG lasers. At both 65 kHz and 31.7 GHz beat frequencies, we measured the instantaneous 3 dB linewidth of the optically-generated microwave tones to be < 22.8 μHz, limited only by the minimum instrument resolution. Allan deviation measurements indicate that the laser system follows a 5 MHz quartz reference oscillator to stability levels of σy (1s) = 8.4 × 10^-12. At 10.24 GHz, the laser system follows a sapphire loaded cavity oscillator to stability levels of σy (1s) = 1.6 × 10^-11. For these measurements, the optical beat note closely follows the linewidth and stability of the driving microwave frequency reference.

Self-stabilization of an optical frequency comb using a short-path-length interferometer

We stabilized the repetition rate of an optical frequency comb using a self-referenced phase-locked loop. The phase-locked loop generated its error signal with a fiber-optic delay-line interferometer that had a path-length difference of 8 m. We used the stabilized repetition rate to generate a 10 GHz signal with a single-sideband phase noise that was limited by environmental noise to -120  dBc/Hz at an offset frequency of 1 kHz. Modeling results indicate that thermoconductive noise sets a fundamental phase noise limit for an 8 m interferometer of -152  dBc/Hz at a 1 kHz offset frequency. The short length of the interferometer indicates that it could be realized as a photonic integrated circuit, which may lead to a chip-scale stabilized optical frequency comb with an ultralow-phase-noise repetition rate.

Tight real-time synchronization of a microwave clock to an optical clock across a turbulent air path

The ability to distribute the precise time and frequency from an optical clock to remote platforms could enable future precise navigation and sensing systems. Here we demonstrate tight, real-time synchronization of a remote microwave clock to a master optical clock over a turbulent 4-km open air path via optical two-way time-frequency transfer. Once synchronized, the 10-GHz frequency signals generated at each site agree to 10^-14 at one second and below 10^-17 at 1000 seconds. In addition, the two clock times are synchronized to ±13 fs over an 8-hour period. The ability to phase-synchronize 10-GHz signals across platforms supports future distributed coherent sensing, while the ability to time-synchronize multiple microwave-based clocks to a high-performance master optical clock supports future precision navigation/timing systems.

Frequency comb generation in superconducting resonators

We have generated frequency combs spanning 0.5 to 20 GHz in superconducting λ/2 resonators at T=3  K. Thin films of niobium-titanium nitride enabled this development due to their low loss, high nonlinearity, low frequency dispersion, and high critical temperature. The combs nucleate as sidebands around multiples of the pump frequency. Selection rules for the allowed frequency emission are calculated using perturbation theory, and the measured spectrum is shown to agree with the theory. Sideband spacing is measured to be accurate to 1 part in 10(8). The sidebands coalesce into a continuous comb structure observed to cover at least several frequency octaves.

A low phase noise microwave frequency synthesis for a high-performance cesium vapor cell atomic clock

We report the development, absolute phase noise, and residual phase noise characterization of a 9.192 GHz microwave frequency synthesis chain devoted to be used as a local oscillator in a high-performance cesium vapor cell atomic clock based on coherent population trapping (CPT). It is based on frequency multiplication of an ultra-low phase noise 100 MHz oven-controlled quartz crystal oscillator using a nonlinear transmission line-based chain. Absolute phase noise performances of the 9.192 GHz output signal are measured to be -42, -100, -117 dB rad(2)/Hz and -129 dB rad(2)/Hz at 1 Hz, 100 Hz, 1 kHz, and 10 kHz offset frequencies, respectively. Compared to current results obtained in a state-of-the-art CPT-based frequency standard developed at LNE-SYRTE, this represents an improvement of 8 dB and 10 dB at f = 166 Hz and f = 10 kHz, respectively. With such performances, the expected Dick effect contribution to the atomic clock short term frequency stability is reported at a level of 6.2 × 10(-14) at 1 s integration time, that is a factor 3 higher than the atomic clock shot noise limit. Main limitations are pointed out.