Arbitrary and absolute length measurement based on femtosecond optical frequency comb

We report a novel measurement method, referred to as the multiple pulse train interference (MPTI)-based method, to measure the refractive index of air using a femtosecond optical frequency comb. The temperature change around the region of interest is recorded based on the interference of multiple pulse trains, and this change is reflected as the distance between MPTI fringes via the use of the conventional Fourier transformation method. The proposed method is demonstrated using a sealed 600-mm cell containing a given volume of water. The results of this preliminary experiment reveal the potential of the MPTI method towards obtaining a high-accuracy evaluation of the refractive index of air.

Absolute distance measurement based on spectral interferometry using femtosecond optical frequency comb

We demonstrate the measurement of an arbitrary absolute distance with a mode-resolved frequency comb laser. By resolving the frequency comb modes individually with a virtually imaged phase array (VIPA), thousands of lasers modes are available that can be exploited for massively parallel homodyne interferometry. With this method a non-ambiguity range of 15 cm is obtained, allowing for non-incremental distance measurement in an interferometric scheme.

As a bridge connecting microwave frequency and optical frequency, femtosecond laser has important significance in optical frequency measurement. Compared with the traditional Ti-sapphire femtosecond optical frequency comb, with the advantages of compact structure, strong anti-interference ability and low cost, the fiber femtosecond optical frequency comb has a wider application prospect. An experiment of spectrum broadening in a highly nonlinear photonic crystal fiber pumped by an Er-fiber mode-locked femtosecond laser is studied in this paper. Based on optical amplification and frequency doubling, the central wavelength of the output spectrum is 780nm and the average power is 232mW. With the femtosecond pulses coupled into two different photonic crystal fibers, the coverage of visible spectrum is up to 500nm-960nm. The spectral shape and width can be optimized by changing the polarization state for satisfying the requirments of different optical frequencies measurement.

The improved frequency-stability and the very broad frequency-band of femtosecond mode-locked optical frequency comb (FOFC) have led to new applications in several precision metrology application areas such as high-precision optical frequency metrology, spectroscopy, and distance measurements. We have analyzed the temporal coherence function of the FOFC. As a result, it has been understood that the temporal coherence peaks exist during the time which is equal to the repetition interval in the traveling direction of the FOFC. In order to make the best use of the temporal coherence characteristic of an FOFC, we propose an FOFC-based multiplex Michelson interferometer that can use as a distant estimation. The present technique is expected to be useful for high-precision measurement of distances for not only science purposes but also industry requirements.

The fibrograph is an optical instrument employing photovoltaic cells for scanning samples of parallel fibres and tracing a type of length- frequency curve. The theory is developed for a sample of parallel fibres in which the fibres are positioned at random. The geometrical interpreta tion of the resulting curve, or fibrogram, indicates simple length and area measurements that give various average lengths and statistical quantities, such as standard deviation and coefficient of variation. Experimental fibrograms are compared with the equivalent data derived from absolute length measurements, using a projection method. The waviness and taper of the fibres, along with other minor factors, cause the fibrogram to be too short. When the length coördinates are increased 19%, the fibrogram is equivalent to the curve obtained from absolute measurements. The instrument makes possible the rapid measurement of fibre length and fibre-length uniformity of raw fibre samples.

We report on a theoretical study of implementation of a single femtosecond optical frequency comb to perform an efficient transfer of Feshbach molecules to the ground electronic and rovibrational state. A standard optical frequency comb is considered with zero offset frequency and a sinusoidally phase modulated frequency comb, having modulation frequency in the IR region. A stepwise population transfer to the ultracold molecular state is observed, with a negligible population of the excited state in the case of the sinusoidally modulated frequency comb.

Traceability of length measurements to the international system of units (SI) can be realized by using optical interferometry making use of well-known frequencies of monochromatic light sources mentioned in the Mise en Pratique for the realization of the metre. At some national metrology institutes, such as Physikalisch-Technische Bundesanstalt (PTB) in Germany, the absolute length of prismatic bodies (e.g. gauge blocks) is realized by so-called gauge-block interference comparators. At PTB, a number of such imaging phase-stepping interference comparators exist, including specialized vacuum interference comparators, each equipped with three highly stabilized laser light sources. The length of a material measure is expressed as a multiple of each wavelength. The large number of integer interference orders can be extracted by the method of exact fractions in which the coincidence of the lengths resulting from the different wavelengths is utilized as a criterion. The unambiguous extraction of the integer interference orders is an essential prerequisite for correct length measurements. This paper critically discusses coincidence criteria and their validity for three modes of absolute length measurements: 1) measurements under vacuum in which the wavelengths can be identified with the vacuum wavelengths, 2) measurements under air in which the air refractive index is obtained from environmental parameters using an empirical equation, and 3) measurements under air in which the air refractive index is obtained interferometrically by utilizing a vacuum cell placed along the measurement pathway. For case 3), which corresponds to PTB’s Kösters-Comparator for long gauge blocks, the unambiguous determination of integer interference orders related to the air refractive index could be improved by about a factor of ten when an ‘overall dispersion value,’ suggested in this paper, is used as coincidence criterion.

Optical frequency standards based on single trapped ions or ensembles of neutral atoms have recently demonstrated stability and accuracy superior to that of the current generation of microwave primary frequency standards, with significant potential for further improvements. When combined with femtosecond optical frequency combs, these standards can be operated as optical clocks generating a direct microwave output signal, raising the possibility of a future redefinition of the second. In this introductory review, the principles of operation, current state-of-the-art performance and applications of optical frequency standards and clocks are described and the further developments that are likely to occur over the next few years are considered.

Length is one of the fundamental physical quantities and its precise measurement is very important for science and technology. Laser-based distance metrology technique is a powerful tool, which is widely applied in geodetic monitoring, environmental monitoring and precision measurement engineering including in space applications. Since the invention of the optical frequency comb (OFC) at the beginning of this century, it has been used as a versatile tool for many applications, such as frequency metrology, spectroscopy, etc. OFC has played an important role in distance metrology enabling the developed techniques to achieve high accuracy in long distance measurement. In the time domain, OFC is a pulse train, which can measure distance with time of flight method or correlation detection method. In the frequency domain, spectrum of OFC consists of a series of discrete lines with equal frequency difference. Methods of dispersive interferometry, multi-heterodyne interferometry, and multi-wavelength interferometry are the techniques proposed and demonstrated in spectral domain distance metrology. Though distance metrology techniques based on OFC have been developed for tens of years, there are still challenges that need to be overcome. In most applications the measurements are completed in the air, where the results are influenced by refractive index of air. As the OFC is a multi-wavelength laser source, refractive index of air is difficult to determine. The other challenge is complexity and high cost of measurement system. Until now, to my knowledge, there is no commercial rangefinder which is based on OFC. The large size, complex configuration and high price are the bottlenecks restricting OFC’s entrance into industrial applications.

<sec>In this paper, we demonstrate an optical frequency comb (OFC) based on an erbium-doped-fiber femtosecond laser, for the measurement of cavity ring-down spectroscopy (CRDS) with wavelengths of 1064, 1083, 1240, 1380, 1500, 1600, 1750 and 2100 nm. We adopt a multi-branch structure to produce high power at the specific wavelengths to meet the requirement for application in the spectral measurement. The OFC is developed by using a mode-locked fiber ring laser based on the nonlinear amplifying loop mirror mechanism. The laser is self-starting by introducing a nonreciprocal phase bias in the cavity and insensitive to the environmental perturbation. Using the chirped pulse amplification and highly nonlinear fibers, the broad spectra at the specific wavelengths are obtained. By optimizing the parameters of the pulses, the power of per mode at each target wavelength is greater than 300 nW.</sec><sec>The<i> </i><i>f</i><sub>rep</sub> is obtained by detecting the output of the femtosecond laser directly, while the<i> </i><i>f</i><sub>ceo</sub> is detected by <i>f</i>-2<i>f</i> interference. The signal-to-noise ratio of the<i> </i><i>f</i><sub>ceo</sub> is about 35 dB with a 300-kHz resolution bandwidth. By controlling the intra-cavity electro-optic modulator and piezoactuator , the <i>f</i><sub>rep</sub> is stabilized with high bandwidth and large range (about megahertz bandwidth and 3 kHz range). The <i>f</i><sub>ceo</sub> is stabilized by using feedback to the pump current of the femtosecond laser dynamically. The in-loop frequency instability degree of the <i>f</i><sub>ceo</sub>, evaluated by the Allan deviation, is approximately 4.95 × 10<sup>–18</sup>/<i>τ</i><sup>1/2</sup> at 1 s and integrates down to 10<sup>–20</sup> level after 2000 s, while that of the <i>f</i><sub>rep</sub> is well below 5.85 × 10<sup>–13</sup>/<i>τ</i>. The all polarization-maintaining erbium fiber-based femtosecond optical frequency comb with multi-application branches we demonstrate in this paper is efficient and reliable for many other applications including optical frequency metrology and optical atomic clocks.</sec>

Thermal radiative emission from a hot surface to a cold surface plays an important role in many applications, including energy conversion, thermal management, lithography, data storage and thermal microscopy. Recent studies on bulk materials have confirmed long-standing theoretical predictions indicating that when the gap between the surfaces is reduced to tens of nanometres, well below the peak wavelength of the blackbody emission spectrum, the radiative heat flux increases by orders of magnitude. However, despite recent attempts, whether such enhancements can be obtained in nanoscale dielectric films thinner than the penetration depth of thermal radiation, as suggested by theory, remains experimentally unknown. Here, using an experimental platform that comprises a heat-flow calorimeter with a resolution of about 100 pW (ref. 7), we experimentally demonstrate a dramatic increase in near-field radiative heat transfer, comparable to that obtained between bulk materials, even for very thin dielectric films (50-100 nm) when the spatial separation between the hot and cold surfaces is comparable to the film thickness. We explain these results by analysing the spectral characteristics and mode shapes of surface phonon polaritons, which dominate near-field radiative heat transport in polar dielectric thin films.

Cycle bases in graphs characterization, algorithms, complexity, and applications

Knowledge graphs play an important role in many applications, such as link prediction and question answering. Translating embedding for knowledge graphs is done with the aim of encoding structured information on entities and their rich relations in a low-dimensional embedding space. TransE is one of the most important methods in translation-based models, and uses translation invariance to implement translating embedding for knowledge graphs. In this line of work, translating embedding models represent the relation as a translation from the head entity to the tail entity and have achieved impressive results. Currently, the TransE model is only developed on single-node machines. Unfortunately, the computing and storage capacities of a single machine can easily reach their limits as knowledge graphs become larger and more complex, which limits the application scope of TransE. In order to solve this problem, we propose a distributed TransE method, known as DTransE, which can utilize distributed computing resources to calculate knowledge graph embeddings. However, building a distributed TransE is complicated and involves challenges of knowledge graph partitioning and computation. To solve these challenges, we provide a high-quality edge partitioning algorithm for the power-law graph by considering the high-degree and low-degree vertices with adaptive weights, which can balance the workload. By using the unactivated Gather-Apply-Scatter model on TransE, the processes periodically exchange messages in a loop. The irregular data distribution among the processes is also optimized to further accelerate communication. As far as we know, this is the first work on a distributed TransE method. We use link prediction to evaluate the DTransE in a distributed environment. Experiments show that, compared to the original TransE method, our proposed DTransE is, on average, 24.5 times faster with a minimum loss of accuracy; compared to the state-of-the-art parallel TransE implementation, DTransE is two times faster on average.

Micrometre- and nanometre-sized particles play important roles in many applications, including catalysis, optics, biosensing and data storage. Organic particles are usually prepared through polymerization of suitable monomers or precipitation methods. In the case of inorganic materials, particle fabrication tends to involve the reduction of a metal salt, or the controlled mixing of salt solutions supplying a metal cation and an elemental anion (for example, S2-, Se2-, O2-), respectively; in some instances, these methods even afford direct control over the shape of the particles produced. Another class of materials are metal-organic coordination polymers, which are based on metal ions coordinated by polydentate organic ligands and explored for potential use in catalysis, gas storage, nonlinear optics and molecular recognition and separations. In a subset of these materials, the use of organometallic complexes as ligands (so-called metalloligands) provides an additional level of tailorability, but these materials have so far not yet been fashioned into nano- or microparticles. Here we show that simple addition of an initiation solvent to a precursor solution of metal ions and metalloligands results in the spontaneous and fully reversible formation of a new class of metal-metalloligand particles. We observe initial formation of particles with diameters of a few hundred nanometres, which then coalesce and anneal into uniform and smooth microparticles. The ease with which these particles can be fabricated, and the ability to tailor their chemical and physical properties through the choice of metal and organic ligand used, should facilitate investigations of their scope for practical applications.