Simultaneous frequency transfer and time synchronization over a 430 km fiber backbone network using a cascaded system

Based on dense wavelength-division multiplexing technology, frequency transfer and time synchronization are simultaneously realized over a compensated cascaded fiber link of 430 km, which is a part of the Beijing–Shanghai optical fiber backbone network. The entire cascaded system consists of two stages with fiber links of 280 and 150 km, respectively. To keep high symmetry and low noise, specific bi-directional erbium-doped fiber amplifiers are used to compensate the large optical attenuation of each fiber link. When the compensation servo is active in every stage, the cascaded system achieves the stability of 1.94 × 10-13 at 1 s and 1.34 × 10-16at104 s, for frequency transfer. It is also verified that the actual results of the cascaded system are in good agreement with the theoretical ones calculated from error theory. Simultaneously, after calibration of each stage, time synchronization is also realized. The final accuracy of the whole system is within 94 ps.     

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.     

High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link

To significantly improve the frequency references used in radio-astronomy and the precision measurements in atomic physics, we provide frequency dissemination through a 642-km coherent optical fiber link. On the frequency transfer, we obtained a frequency instability of \(3\times 10^{-19}\) at 1,000 s in terms of Allan deviation on a 5-mHz measurement bandwidth, and an accuracy of \(5\times 10^{-19}\) . The ultimate link performance has been evaluated by doubling the link to 1,284 km, demonstrating a new characterization technique based on the double round trip on a single fiber. This method is an alternative to previously demonstrated techniques for link characterization. In particular, the use of a single fiber may be beneficial to long hauls realizations in view of a continental fiber network for frequency and time metrology, as it avoids the doubling of the amplifiers, with a subsequent reduction in costs and maintenance. A detailed analysis of the results is presented, regarding the phase noise, the cycle-slips detection and removal and the instability evaluation. The observed noise power spectrum is seldom found in the literature; hence, the expression of the Allan deviation is theoretically derived and the results confirm the expectations.     

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.     

Rayleigh scattering optical frequency correlation in a single-mode optical fiber

The bichromatic optical frequency correlation function for Rayleigh backscattering from a pulse of laser light propagating along a single-mode optical fiber has been calculated and measured. It is shown that the optical correlation frequency, Dnu(c) , is equal to the reciprocal of pulse width T(w) . These results are important for the development of wavelength diversity techniques for the reduction of coherent Rayleigh noise in distributed Rayleigh backscattering single-mode optical fiber sensors.     

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).     

Microwave frequency transfer over a 112-km urban fiber link based on electronic phase compensation

We demonstrate the transmission of a microwave frequency signal at 10 GHz over a 112-km urban fiber link based on a novel simple-architecture electronic phase compensation system. The key element of the system is the low noise frequency divider by 4 to differentiate the frequency of the forward signal from that of the backward one, thus suppressing the effect of Brillouin backscattering and parasitic reflection along the link. In terms of overlapping Allan deviation,the frequency transfer instability of 4.2 × 10~(-15) at 1-s integration time and 1.6 × 10~(-18) at one-day integration time was achieved. In addition, its sensitivity to the polarization mode dispersion in fiber is analyzed by comparing the results with and without laser polarization scrambling. Generally, with simplicity and robustness, the system can offer great potentials in constructing cascaded frequency transfer system and facilitate the building of fiber-based microwave transfer network.     

Transmission of an optical frequency through a 3 km long optical fiber

A 3 km long optical fiber is used to connect two laboratories in Paris. We present the metrological properties of this optical link to transfer an optical frequency standard at 778 nm and we show that the frequency shift introduced by the fiber is only of few Hz. Received: 23 October 1997 / Accepted: 18 November 1997     

Accuracy of optical frequency comb generation in optical fiber

We evaluated the accuracy of an optical frequency comb in optical fibers by measuring the frequency shift after a sideband from an electro-optic modulator had passed through the fiber. We found that a frequency drift of a few hertz was due largely to a variation in the ambient temperature that corresponded to an increase in the square root of the Allan variance to 0.66 Hz.     

Distributed fiber sensing system with wide frequency response and accurate location

A distributed fiber sensing system merging Mach–Zehnder interferometer and phase-sensitive optical time domain reflectometer (Φ-OTDR) is demonstrated for vibration measurement, which requires wide frequency response and accurate location. Two narrow line-width lasers with delicately different wavelengths are used to constitute the interferometer and reflectometer respectively. A narrow band Fiber Bragg Grating is responsible for separating the two wavelengths. In addition, heterodyne detection is applied to maintain the signal to noise rate of the locating signal. Experiment results show that the novel system has a wide frequency from 1 Hz to 50 MHz, limited by the sample frequency of data acquisition card, and a spatial resolution of 20 m, according to 200 ns pulse width, along 2.5 km fiber link.     

Optical-to-microwave frequency chain utilizing a two-laser-based optical parametric oscillator network

A method for building an optical-to-microwave frequency chain and for measuring optical frequencies relative to the cesium primary frequency standard is described. Based on optical frequency division via parametric oscillators, the concept is to generate two known ratios (1/2 and 4/9) of an optical calibration frequencyf ₁ whose frequency difference is measured relative to the cesium clock. The (1/2) ratio is obtained by either a 2:1 frequency division off ₁ or second-harmonic generation of (l/2)f ₁. The (4/9) ratio off ₁ can be generated with a 3:1 frequency divider driven by a second laser atf ₂ that is chosen to be near (2/3)f ₁, which in turn is obtained with af ₁-pumped 3:1 frequency divider. A set of auxiliary Optical Parametric Oscillators (OPOs) with outputs centered at (1/2)f ₁ is used to facilitate the difference-frequency measurement between the two ratios. A practical configuration utilizing a YAG and a Ti: Al₂O₃ laser and its application to a number of precision measurements of interest are presented.     

Use of copper-coated fiber as a tunable optical time-delay line in precise timing systems

In this paper we present a novel, time-delay approach using a copper-coated fiber. Piezo optical-fiber stretchers and temperature-controlled fiber spools are normally used for a conventional time-delay lines. A copper-coated fiber preserves the performance of a standard single-mode optical fiber, while at the same time acting as an electrical wire, which can be effectively heated by applying an electrical current. As a result of the significant temperature change, the signal (group) delay can be properly adjusted and controlled. Compared to piezo optical-fiber stretchers and temperature-controlled fiber spools, much shorter lengths of fiber are required and a faster response time can be achieved. This paper also proposes a simple, lumped thermal model and thus a copper-coated fiber can be included in the heat-transfer and response-time calculations of a realistic system that involves surrounding elements (e.g., heatsinks).     

Sensitive and accurate dual-wavelength UV-VIS polarization detector for optical remote sensing of tropospheric aerosols

An UV-VIS polarization lidar has been designed and specified for monitoring aerosols in the troposphere, showing the ability to precisely address low particle depolarization ratios, in the range of a few percent. Non-spherical particle backscattering coefficients as low as 5×10^?8 m^?1?sr^?1 have been measured and the particle depolarization ratio detection limit is 0.6 %. This achievement is based on a well-designed detector with laser-specified optical components (polarizers, dichroic beamsplitters) summarized in a synthetic detector transfer matrix. Hence, systematic biases are drastically minimized. The detector matrix being diagonal, robust polarization calibration has been achieved under real atmospheric conditions. This UV-VIS polarization detector measures particle depolarization ratios over two orders of magnitude, from 0.6 up to 40 %, which is new, especially in the UV where molecular scattering is strong. Hence, a calibrated UV-VIS polarization-resolved time-altitude map is proposed for urban and free tropospheric aerosols up to altitude of 4 kilometers, which is also new. These sensitive and accurate UV-VIS polarization-resolved measurements enhance the spatial and time evolution of non-spherical tropospheric particles, even in urban polluted areas. This study shows the capability of polarization-resolved laser UV-VIS spectroscopy to specifically address the light backscattering by spherical and non-spherical tropospheric aerosols.     

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.     

A two-way optical interconnection network using a single mode fiber array

We present a dynamic free space interconnection network for single mode fibers. The architecture consists of a two-way imaging geometry involving only one single mode fiber array. Input and output fibers belong to the same fiber array. Programmable and fixed diffractive optical elements are used for beam steering and wavefront correction. We show that the network ensures favorable conditions for launching and allows for a high interconnection volume with minimal insertion losses at 2.5 Gb/s. The architecture is also adapted to the use of binary electrically addressed spatial light modulators.     

Quantum noise limits on frequency and timing for optical pulses in a linear high-gain amplifier

Frequency and timing noise added in a linear optical amplifier of gain G grows as (G-1)/G. Provided that the pulse is initially in a coherent state, the output frequency and timing noise cannot exceed twice the input value. It is also shown that, in a transmission line with zero net gain and loss, the frequency and timing noise added in the lossy medium is equal to or larger than the noise added in the amplifier.     

Simultaneous Cartesian coordinate display of defocused optical transfer functions

We show that by using a binary spatial filter and a square-law detector we can display all the defocused optical transfer functions (OTF's) in a given study in a single picture. The resulting unique picture has as its horizontal coordinates the spatial frequency and as its vertical coordinates the amount of defocus. The gray-level variations are proportional to the modulus of the OTF, that is, the modulation transfer function. Numerical simulations are included.     

Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber

Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.