Coherent optical phase transfer over a 32-km fiber with 1 s instability at 10{-17}

The phase coherence of an ultrastable optical frequency reference is fully maintained over actively stabilized fiber networks of lengths exceeding 30 km. For a 7-km link installed in an urban environment, the transfer instability is 6 x 10{-18} at 1 s. The excess phase noise of 0.15 rad, integrated from 8 mHz to 25 MHz, yields a total timing jitter of 0.085 fs. A 32-km link achieves similar performance. Using frequency combs at each end of the coherent-transfer fiber link, a heterodyne beat between two independent ultrastable lasers, separated by 3.5 km and 163 THz, achieves a 1-Hz linewidth.     

Timing jitter reduction over 20-km urban fiber by compensating harmonic phase difference of locked femtosecond comb

A novel timing jitter reduction system over a round trip 20-km urban fiber link is reported. The phase difference of the ninth harmonic of a high-repetition-rate mode-locked laser between the local and the returned signals is obtained. Based on the phase difference, the system uses an optical delay line （ODL） to compensate the optical fiber link. The root-mean-square （RMS） timing jitter is reduced from 50 to 8.9 ps in 80 min.     

Synchronization of mode-locked femtosecond lasers through a fiber link

Two mode-locked femtosecond fiber lasers, connected via a 7 km fiber link, are synchronized to an rms timing jitter of 19 fs, observed over the entire Nyquist bandwidth (half of the 93 MHz repetition frequency). This result is achieved in two steps. First, active cancellation of the fiber-transmission noise reduces timing jitter caused by path length fluctuations to a record level of 16 fs. Second, using a wide bandwidth interactivity actuator, the slave laser is synchronized to the incoming stable pulse train from the reference laser to within 10 fs. These results are confirmed by an optical cross-correlation measurement performed independently of the feedback loop operated in the microwave domain.     

High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser

We demonstrate the transfer of an ultrastable microwave frequency by transmitting a 30-nm-wide optical frequency comb from a mode-locked laser over 86?km of installed optical fiber. The pulse train is returned to the transmitter via the same fiber for compensation of environmentally induced optical path length changes. The fractional transfer stability measured at the remote end reaches 4×10(-17) after 1600?s, corresponding to a timing jitter of 64?fs.     

Attosecond-resolution timing jitter characterization of free-running mode-locked lasers

Timing jitter characterization of optical pulse trains from free-running mode-locked lasers with attosecond resolution is demonstrated using balanced optical cross correlation in the timing detector and the timing delay configurations. In the timing detector configuration, the balanced cross correlation between two mode-locked lasers synchronized by a low-bandwidth phase-locked loop is used to measure the timing jitter spectral density outside the locking bandwidth. In addition, the timing delay configuration using a 325 m long timing-stabilized fiber link enables the characterization of timing jitter faster than the delay time. The limitation set by shot noise in this configuration is 2.2 x 10(-8) fs(2)/Hz corresponding to 470 as in 10 MHz bandwidth.     

Investigations on Timing Jitter by Chirp Selection of External Modulator in Return-to-Zero Optical Soliton Pulse Transmission at 10 Gb/s

Abstract

We investigate the chirp selection of externally modulated return-to-zero soliton pulse at 10 Gb/s for fiber optical communication system for the reduction in timing jitter. The chirp range (?5 to +5), as well as the effect of the post compensation, have been examined up to ten regenerated fiber spans in the link. Here, it is shown that the chirp value of the external modulator should be set to either 0 or ?1 to reduce timing jitter. Moreover, for more number of spans, it will be better to adopt other chirp values.     

Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link

We have explored the performance of two “dark fibers” of a commercial telecommunication fiber link for a remote comparison of optical clocks. The two fibers, linking the Leibniz University of Hanover (LUH) with the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, are connected in Hanover to form a total fiber length of 146 km. At PTB the performance of an optical frequency standard operating at 456 THz was imprinted to a cw transfer laser at 194 THz, and its frequency was transmitted over the fiber. In order to detect and compensate phase noise related to the optical fiber link we have built a low-noise optical fiber interferometer and investigated noise sources that affect the overall performance of the optical link. The frequency stability at the remote end has been measured using the clock laser of PTB’s Yb⁺ frequency standard operating at 344 THz. We show that the frequency of a frequency-stabilized fiber laser can be transmitted over a total fiber length of 146 km with a relative frequency uncertainty below 1×10⁻¹⁹, and short term frequency instability given by the fractional Allan deviation of σ _y (τ)=3.3×10⁻¹⁵/(τ/s).     

Subfemtosecond synchronization of microwave oscillators with mode-locked Er-fiber lasers

We synchronize an 8.06 GHz microwave signal from a voltage-controlled oscillator with an optical pulse train from a 77.5 MHz mode-locked Er-fiber laser using a fiber-based optical-microwave phase detector. The residual phase noise between the optical pulse train and the synchronized microwave signal is -133 dBc/Hz (-154 dBc/Hz) at 1 Hz (5 kHz) offset frequency, which results in 838 as integrated rms timing jitter [1 Hz-1 MHz]. The long-term residual phase drift is 847 as (rms) measured over 2 h, which reaches 4×10(-19) fractional frequency instability at 1800 s averaging time. This method has a potential to provide both subfemtosecond-level short-term phase noise and long-term phase stability in microwave extraction from mode-locked fiber lasers.     

Sub-100-as timing jitter optical pulse trains from mode-locked Er-fiber lasers

We demonstrate sub-100-as timing jitter optical pulse trains generated from free-running, 77.6 MHz repetition-rate, mode-locked Er-fiber lasers. At -0.002(±0.001) ps2 net cavity dispersion, the rms timing jitter is 70 as (224 as) integrated from 10 kHz (1 kHz) to 38.8 MHz offset frequency, when measured by a 24 as resolution balanced optical cross correlator. To our knowledge, this result corresponds to the lowest rms timing jitter measured from any mode-locked fiber lasers so far. The measured result also agrees fairly well with the Namiki-Haus analytic model of quantum-limited timing jitter in stretched-pulse fiber lasers.     

Measurement of pulse width and amplitude jitter noises of gigahertz optical pulse trains by time-domain demodulation

We propose a technique for measuring both pulse width and amplitude jitter noises of high-repetition-rate optical pulse trains and the cross correlation between these noises as well. The technique is based on time-domain amplitude demodulation of three harmonic components of the detected pulse train. We applied this technique to characterize noises of a gigahertz optical pulse train generated by an actively mode-locked Er-doped fiber laser. Correlation between pulse width jitter and pulse amplitude jitter was observed at low frequencies in this laser. Unlike relaxation oscillation noise, low-frequency noise is free from pulse energy jitter. Owing to its ability to measure pulse width jitter in addition to amplitude and phase jitters, this technique is of great interest for characterizing noises of a wide variety of optical pulse train sources.     

Remote transfer of a high-stability and ultralow-jitter timing signal

Transfer of a high-stability and ultralow-jitter timing signal through a fiber network via a mode-locked fiber laser is demonstrated. With active cancellation of the fiber-transmission noise, the fractional instability for transfer of a radio-frequency signal through a 6.9- (4.5-) km round-trip installed (laboratory-based) fiber network is below 9(7) x 10(-15) tau(-1/2) for an averaging time tau > or = 1 s, limited by the noise floor of the frequency-counting system. The noise cancellation reduces the rms timing jitter, integrated over a bandwidth from 1 Hz to 100 kHz, to 37 (20) fs for the installed (laboratory-based) fiber network, representing what is to our knowledge the lowest reported jitter for transfer of a timing signal over kilometer-scale distances using an installed (laboratory-based) optical-fiber network.     

Effects of precompensation and postcompensation on timing jitter in dispersion-managed systems

We present an analytic theory of timing jitter in dispersion-managed light-wave systems that is based on the moment method and the assumption of a chirped Gaussian pulse. We apply the theory to a soliton system and show that 50% postcompensation of the accumulated dispersion can reduce the jitter by a factor of 2. We also apply the theory to a low-power light-wave system employing the return-to-zero format and find that timing jitter can be minimized along the fiber link for an optimal choice of precompensation and postcompensation.     

Attosecond‐precision ultrafast photonics

We review our recent progress toward attosecond‐precision ultrafast photonics based on ultra‐low timing jitter optical pulse trains from mode‐locked lasers. In femtosecond mode‐locked lasers, the concentration of a large number of photons in an extremely short pulse duration enables the scaling of timing jitter into the attosecond regime. To characterize such jitter levels, we developed new attosecond‐resolution measurement techniques and show that standard fiber lasers can achieve sub‐fs high‐frequency jitter. By leveraging the ultra‐low jitter of free‐running mode‐locked lasers, we pursued high‐precision optical‐optical and optical‐microwave synchronization techniques. Optical signals spanning 1.5 octaves were synthesized by attosecond‐precision timing and phase synchronization of two independent mode‐locked lasers. High‐stability microwave signals were also synthesized from mode‐locked lasers with drift‐free sub‐10‐fs precision. We further demonstrated the attosecond‐precision distribution of optical pulse trains to remote locations via timing‐stabilized fiber links. Finally, the application of optical pulse trains for high‐resolution sampling and analog‐to‐digital conversion is discussed.     

Generation of 10-GHz ultra-short pulses with low time jitter in an actively mode-locked fiber laser

We have experimentally achieved the 8.3-ps ultra-short pulse at 10 GHz repetition rate with the time jitter as low as 590 fs in an actively mode-locked fiber ring laser. The ring-cavity laser is mode-locked by a semiconductor optical amplifier based on cross-gain modulation. The external CW source is modulated with radio frequency signal by an amplitude modulator as the external optical pulses and, then, injected into the fiber ring cavity to achieve active mode locking. Further investigating the laser output characteristics, it indicates that the linewidth of employed CW source affects properties of the generated ultra-short pulse, such as phase noise and time jitter. Ultra-short pulse at high repetition rate with low time jitter can be generated by the optimization of CW laser source.     

Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator

We independently phase lock the repetition rates of two femtosecond lasers at their approximately 456, 000th harmonic to a common optical oscillator. The timing jitter of each individual laser relative to the optical reference is only 0.45 fs in a 100-Hz bandwidth. Our method takes advantage of the tremendous leverage that is possible when stability is transferred from the optical to the microwave domain. The low timing jitter is commensurate with the independently measured fractional frequency instability in the repetition rates of < or = 2.3 x 10(-15) in 1-s averaging time, limited by the measurement system. The microwave signals at 1 GHz that are extracted by photodetection of the pulse trains have a 10-times-greater instability, confirming the presence of excess noise in the photodetection.     

Long-distance frequency dissemination with a resolution of 10(-17)

We use a new technique to disseminate microwave reference signals along ordinary optical fiber. The fractional frequency resolution of a link of 86 km in length is 10(-17) for a one day integration time, a resolution higher than the stability of the best microwave or optical clocks. We use the link to compare the microwave reference and a CO2/OsO4 frequency standard that stabilizes a femtosecond laser frequency comb. This demonstrates a resolution of 3 x 10(-14) at 1 s. An upper value of the instability introduced by the femtosecond laser-based synthesizer is estimated as 1 x 10(-14) at 1 s.     

Photonic generation of arbitrary waveforms based on incoherent wavelength-to-time mapping

We demonstrate experimentally a radio frequency arbitrary waveform generator using the incoherent wavelengthto-time mapping technique.The system is implemented by amplitude modulation of a broadband optical resource whose spectrum is reshaped by a programmable optical pulse shaper and transmitted over a single mode fiber link.The shape of the generated waveform is controlled by the optical pulse shaper,and the fiber link introduces a certain group velocity delay to implement wavelength-to-time mapping.Assisted by the flexible optical pulse shaper,we obtain different shapes of optical waveforms,such as rectangle,triangle,and sawtooth waveforms.Furthermore,we also demonstrate ultra-wideband generation,such as Gaussian monocycle,doublet,and triplet waveforms,using the incoherent technique.     

Characterization of ROF signal based on cascaded optical carrier suppression modulation technique

The paper experimentally demonstrated the optical frequency quadrupling microwave signal generation, a 4 GHz radio frequency (RF) signals up-conversion to 16 GHz in a radio over fiber (ROF) link, using twice optical carrier suppression modulation. The RF signal was mixed with 1.25 Gbps NRZ-OOK data firstly and then modulated by two cascaded single-electrode optical intensity modulators. The obtained 1.25 Gbps/16 GHz ROF signal was transmitted and characterized in the optical fiber link. At BER of 10^?9, low power penalty of 1.0 and 1.4 dB were obtained over a fiber link with a transmission distance of 25 and 50 km.     

Common-mode-free frequency comparison of lasers with relative frequency stability at the millihertz level

We report on a frequency comparison of frequency-stabilized lasers located in remote laboratories resting on different foundations. By locating the lasers in this way correlated frequency excursions of the lasers are suppressed to a high degree. The beat signal between them shows a linewidth at the hertz level for averaging times of 1 s. The optical link is established by a 100 m single-mode optical fiber where the frequency noise induced by the fiber is reduced to the level of a few tens of millihertz. One laser is stabilized onto a Fabry-Perot resonator with a long-term precision of 25 mHz (fractional frequency instability, sigma(y) = 1.2 x 10(-16)), the highest lock fidelity obtained so far to our knowledge.     

Precise frequency transfer through a fiber network by use of 1.5-microm mode-locked sources

We report the precise transfer of radio-frequency signals by use of the pulse repetition frequency of mode-locked laser sources at 1.5 microm transmitting through a fiber network. The passive transfer instability through a 6.9-km fiber is below 3 x 10(-14) at 1 s, which is comparable with the optical carrier-frequency transfer of a narrow-linewidth cw laser. The instability of the measurement system is below 7 x 10(-15) at 1 s. It is noted that the pulsed mode of operation offers almost an order-of-magnitude improvement in stability at 1 s over that with a sinusoidal amplitude modulation on an optical carrier.