We report what we believe to be the lowest phase noise optical-to-microwave frequency division using fiber-based femtosecond optical frequency combs: a residual phase noise of -120dBc/Hz at 1 Hz offset from a 11.55GHz carrier frequency. We furthermore report a detailed investigation into the fundamental noise sources which afflicts the division process itself. Two frequency combs with quasi-identical configurations are referenced to a common ultrastable cavity laser source. To identify each of the limiting effects we implement an ultra-low noise carrier-suppression measurement system, which circumvents the detection and amplification noise of more conventional techniques. This technique now allows the suppression of these unwanted sources of noise to very low levels. In the Fourier frequency range of ~200 Hz to 100 kHz, a fed-forward technique based on a voltage-controlled phase shifter delivers a further noise reduction of 10 dB. For lower Fourier frequencies, optical power stabilization is implemented in order to reduce the relative intensity noise which causes unwanted phase noise through power to phase conversion in the detector. We implement and compare two possible control schemes based on an acousto-optical modulator and comb pump current. We also present wideband measurements on the relative intensity noise of the fiber comb.
We have developed a single-shot imaging technique that can capture ultrafast events occurring on femtosecond to picosecond time scales. The technique is based on an optical pump-probe method, in which multiple time-delayed femtosecond pulses simultaneously probe a pump-excited sample. Here we use two sets of 2-by-2 mirror arrays for spatial/temporal division and routing of multiple probe pulses. This single-shot scheme is successfully applied to capture femtosecond ionization fronts propagating at the speed of light in air, as well as laser-induced ablation of solid targets.
Optical frequency combs are laser sources which are capable of generating discrete, equal-spaced and highly coherent comb modes. Optical frequency comb technique provides a significant bridge to transfer the stability between optical frequency and radio frequency. The advances of this technology greatly promote the development of precision spectroscopy, optical time/frequency transfer, optical frequency division, long-distance transfer of time/frequency references and high-precision distance measurement. Benefiting from the wide spectral outputs, femtosecond lasers have become the best choice …
The generation of a laser filament through clouds produces a shockwave which displaces the small water droplets from the air to create a quasi-transparent channel through which, information can be transmitted. We present a robust method that utilizes the channel for free-space optical communication using structured light beams coupled with a femtosecond filament. Vortex beams based on their spatial profiles and non-diffractive characteristics are perfectly suited to propagate around the filament. We have also developed a 4-bit communication channel using these structured light beam. We introdu…
Optical frequency division of an ultrastable laser to the microwave frequency range by an optical frequency comb has allowed the generation of microwave signals with unprecedently high spectral purity and stability. However, the generated microwave signal will suffer from a very low power level if no external optical frequency comb repetition rate multiplication device is used. This paper reports theoretical and experimental studies on the beneficial use of the Vernier effect together with the spectral selective filtering in a double directional coupler add-drop optical fibre ring resonator to…
We combine a tunable continuous-wave optical parametric oscillator and a femtosecond Ti:Sapphire laser frequency comb to provide a phase-coherent bridge between the visible and mid-infrared spectral ranges. As a first demonstration of this new technique we perform a direct frequency comparison between an iodine stabilized Nd:YAG laser at 1064 nm and an infrared methane optical frequency standard at $3.39 μ$m.
Ultrahigh-resolution optical strain sensors provide powerful tools in various scientific and engineering fields, ranging from long-baseline interferometers to civil and aerospace industries. Here we demonstrate an ultrahigh-resolution fibre strain sensing method by directly detecting the time-of-flight (TOF) change of the optical pulse train generated from a free-running passively mode-locked laser (MLL) frequency comb. We achieved a local strain resolution of 18 pε/Hz1/2 and 1.9 pε/Hz1/2 at 1 Hz and 3 kHz, respectively, with largedynamic range of >154 dB at 3 kHz. For remote-point sensing at …
This study proposes and demonstrates a versatile method for near and mid-infrared optical frequency comb generation using multi-seeded femtosecond optical parametric generation. The method allows one to divide the repetition rate by an arbitrarily large integer factor, freely tune the offset frequency, and adjust the common phase offset of the comb modes. Since all possible degrees of freedom are adjustable, the proposed method manifests itself as versatile optical frequency synthesis.
Platform motion poses significant challenges to high-precision optical time and frequency transfer. We give a detailed description of these challenges and their solutions in comb-based optical two-way time and frequency transfer (O-TWTFT). Specifically, we discuss the breakdown in reciprocity due to relativity and due to asynchronous sampling, the impact of optical and electrical dispersion, and velocity-dependent transceiver calibration. We present a detailed derivation of the equations governing comb-based O-TWTFT in the presence of motion. We describe the implementation of real-time signal …
We study femtosecond laser comb driven sustained and coherent spin wave (SW) generation in permalloy (Py) films over a thickness range of $d =$ 40--100 nm. A simple rapid demagnetization model describes the dependence of the observed SW intensity on laser power for all film thicknesses. In the thicker films we observe laser comb excited perpendicular standing spin waves up to third order and to 18 multiples of the 1 GHz laser repetition rate. Our results demonstrate the versatility of femtosecond combs as contact-less SW point sources over a wide range of film thickness and type of SW modes.
We report on a high-power mid-infrared frequency comb source based on a femtosecond Er:fiber oscillator with a stabilized repetition rate at 250 MHz. The mid-infrared frequency comb is produced through difference frequency generation in a periodically poled MgO-doped lithium niobate crystal. The output power is about 120 mW with a pulse duration of about 80 fs, and spectrum coverage from 2.9 to 3.6 um. The coherence properties of the produced high-power broadband mid-infrared frequency comb are maintained, which was verified by heterodyne measurements. As the first application, the spectrum of…
We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intra-cavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for frep and fceo, producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f - 2f interferometer and phase locked to an ultra-stable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz - 1 MHz) respectively. Alternatively, the comb was l…
Results are presented from a series of comparisons between two independent femtosecond frequency comb systems at NPL, which were carried out in order to assess their systematic uncertainty. Simultaneous measurements with the two systems demonstrate agreement at the level of 5 x $10^{-18}$ when measuring an optical frequency against a common microwave reference. When simultaneously measuring the ratio of two optical frequencies, agreement at the 3 x $10^{-21}$ level is observed. The results represent the highest reported level of agreement to date between Ti:sapphire and Er-doped femtosecond co…
Dual terahertz (THz) comb spectroscopy is a promising methods for high accuracy, high resolution, and broadband THz spectroscopy because the mode-resolved THz comb spectrum possesses both characteristics of broadband THz radiation and narrow-linewidth continuous-wave THz radiation and all frequency mode of THz comb can be phase-locked to a microwave frequency standard. However, requirement of stabilized dual femtosecond lasers has often hindered wide use of this method. In this article, we demonstrated the adaptive sampling, dual THz comb spectroscopy, enabling use of free-running dual femtose…
We report a mode-locked Ti:sapphire femtosecond laser with 5GHz repetition rate. Spectral broadening of the 24 fs pulses in a microstructured fiber yields an octave-spanning spectrum and permits self-referencing and active stabilization of the emitted femtosecond laser frequency comb (FLFC). The individual modes of the 5GHz FLFC are resolved with a high-resolution spectrometer based on a virtually imaged phased array (VIPA) spectral disperser. Isolation of single comb elements at a microwatt average power level is demonstrated. The combination of the high-power, frequency-stabilized 5GHz laser…
When a photo-diode is illuminated by a pulse train from a femtosecond laser, it generates microwaves components at the harmonics of the repetition rate within its bandwidth. The phase of these components (relative to the optical pulse train) is known to be dependent on the optical energy per pulse. We present an experimental study of this dependence in InGaAs pin photo-diodes illuminated with ultra-short pulses generated by an Erbium-doped fiber based femtosecond laser. The energy to phase dependence is measured over a large range of impinging pulse energies near and above saturation for two t…
Dual-comb spectroscopy is a rapidly developing technique enabling ultraprecise broadband optical diagnostics of atoms and molecules. This powerful tool typically requires two phase-locked femtosecond lasers, yet it has been shown that it can be realized without any stabilization if the combs are generated from a single laser cavity. Still, unavoidable intrinsic relative phase-fluctuations always set a limit on the precision of any spectroscopic measurements, hitherto limiting the applicability of bulk dual-comb lasers for mode-resolved studies. Here, we demonstrate a versatile concept for low-…
Dual-comb spectroscopy is a promising method for precise optical spectrum analysis with fast data acquisition speed. However, its implementation and applications are often hindered by the complexity of optical comb systems. Here, as a compact and robust system, femtosecond imbalanced time-stretch spectroscopy (FITSS) with simple optical layout is proposed and demonstrated. The time-stretch interferometry from one femtosecond laser builds a mapping from the optical frequency domain to the radio frequency regime. In experiment, the absorption line of a hydrogen cyanide cell is encoded in the pro…
Development of ultrashort pulse sources has had an immense impact on condensed-matter physics, biomedical imaging, high-field physics, frequency metrology, telecommunications, nonlinear optics, and molecular spectroscopy. Although numerous advancements of such sources have been made, it remains a challenge to create a highly compact, robust platform capable of producing femtosecond pulses over a wide range of wavelengths, durations, and repetition rates. Recent observations of frequency comb generation via cascaded parametric oscillation in microresonators11 suggest a path for achieving this g…
Future optical clock networks will require free-space optical time-frequency transfer between flying clocks. However, simple one-way or standard two-way time transfer between flying clocks will completely break down because of the time-of-flight variations and Doppler shifts associated with the strongly time-varying optical link distances. Here, we demonstrate an advanced, comb-based optical two-way time-frequency transfer that can successfully synchronize the optical timescales at two sites connected via a time-varying turbulent air path. The link between the two sites is established using ei…
External passive femtosecond enhancement cavities (fsECs) are widely used to increase the efficiency of non-linear conversion processes like high harmonic generation (HHG) at high repetition rates. Their performance is often limited by beam ellipticity, caused by oblique incidence on spherical focusing mirrors. We introduce a novel three-dimensionally folded variant of the typical planar bow-tie resonator geometry that guarantees circular beam profiles, maintains linear polarization, and allows for a significantly tighter focus as well as a larger beam cross-section on the cavity mirrors. The …
We report on the combined action of a cw diode laser and a train of ultrashort pulses when each of them drives one step of the 5S-5P-5D two-photon transition in rubidium vapor. The fluorescence from the 6P_{3/2} state is detected for a fixed repetition rate of the femtosecond laser while the cw-laser frequency is scanned over the rubidium D_{2} lines. This scheme allows for a velocity selective spectroscopy in a large spectral range including the 5D_{3/2} and 5D_{5/2} states. The results are well described in a simplified frequency domain picture, considering the interaction of each velocity g…
We present a new Randomized Multiple Independent Comb Shaping (RandoMICS) algorithm based on phase-only tailored transmission for ultrashort laser pulse replication. The benefit of this method is satellite-free generation of programmable laser pulse sequences. The result is achieved by creating a transmission function as a stochastic comb of disjoint segments of optical frequency continuum with numerically optimized segment width distribution. The algorithm is realized by generating a regular aperiodic comb and random permutations of its elements. Experimental demonstration is performed with a…
Inspired by the ever-increasing demand for higher data transmission rates and the tremendous attention toward all-optical signal processing based on miniaturized nanophotonics, in this paper, for the first time, we investigate the integrable design of coherent ultrashort light pulse code-division multiple-access (CDMA) technique, also known as femtosecond CDMA, using all-dielectric metasurfaces (MSs). In this technique, the data bits are firstly modulated using ultrashort femtosecond optical pulses generated by mode-locked lasers, and then by employing a unique phase metamask for each data str…
For the growing demand of frequency combs in mid-infrared (mid-IR), known as the "molecular fingerprint" region of the spectrum [1], down conversion of near-IR frequency combs through half- harmonic generation offers numerous benefits including high conversion efficiency and intrinsic phase and frequency locking to the near-IR pump [2]. Hence cascaded half-harmonic generation promises a simple path towards extending the wavelength coverage of stable frequency combs. Here, we report a two-octave down-conversion of a frequency comb around 1 μm through cascaded half-harmonic generation with ~64% …
We review the current state of tabletop extreme ultraviolet (XUV) sources based on high harmonic generation (HHG) in femtosecond enhancement cavities (fsEC). Recent developments have enabled generation of high photon flux (1014 photons/sec) in the XUV, at high repetition rates (>50 MHz) and spanning the spectral region from 40 nm - 120 nm. This level of performance has enabled precision spectroscopy with XUV frequency combs and promises further applications in XUV spectroscopic and photoemission studies. We discuss the theory of operation and experimental details of the fsEC and XUV generation…
We report on the realization of a solid-state-based vacuum ultraviolet frequency comb, using multi-harmonic generation in an external enhancement cavity. Optical conversions in such arrangements were so-far reported only using gaseous media. We present a theory that allows selecting the most suited solid generation medium for specific target harmonics by adapting the bandgap of the material. Consequently, we experimentally use a thin AlN film grown on a sapphire substrate to realize a compact frequency comb multi-harmonic source in the DUV/VUV spectral range. Extending our earlier VUV source […
Within a synchronously pumped optical parametric oscillator (SPOPO), the inherent synchronism between the pump and the resonating signal is the magic to partly transfer the coherence property of the pump to the signal. In our demonstration, Vernier effect is observed within a femtosecond SPOPO by simply detuning the FSR of the cavity, generating signal pulses at tunable repetition rate from several GHz to 1 THz with a maximum 22.58 nm full width half maximum (FWHM) bandwidth supporting 160 fs pulses covering the C- and L-bands of the telecom wavelength region. This technique offers a simple me…
Generation of high-repetition-rate, femtosecond, soliton pulse trains through dual-wavelength pumping of a dispersion-decreasing fiber is studied numerically. The achievable shortest pulse width is found to be limited by third-order dispersion that has a significant effect on the pulse-compression dynamics. The output wavelength is red shifted because of intrapulse Raman scattering and depends heavily on third-order dispersion, whose positive values lead to the most red shifted solitons (>25% of the input pump center wavelength). The proposed scheme allows the generation of ultrashort pulse tr…
Dual-comb spectroscopy is extended to the visible spectral range with a set-up based on two frequency-doubled femtosecond ytterbium-doped fiber lasers. The dense rovibronic spectrum of iodine around 19240 cm-1 is recorded within 12 ms at Doppler-limited resolution with a simple scheme that only uses free-running femtosecond lasers.
We have measured the frequency of the $6s^2S_{1/2} - 5d^2D_{3/2}$ electric-quadrupole transition of $^{171}$Yb$^+$ with a relative uncertainty of $1\times 10^{-14}$, $ν_{Yb}$ = 688 358 979 309 312 Hz $\pm$ 6 Hz. A femtosecond frequency comb generator was used to phase-coherently link the optical frequency derived from a single trapped ion to a cesium fountain controlled hydrogen maser. This measurement is one of the most accurate measurements of optical frequencies ever reported, and it represents a contribution to the development of optical clocks based on an $^{171}$Yb$^+$ ion standard.
Irradiation of intense ultrafast laser pulses in glasses can lead to formation of nanogratings whose periods are significantly smaller than the incident irradiation wavelength. The mechanism of the exotic phenomenon is still under debate. Here, we access the snapshots of morphologies in the laser affected regions in a porous glass which reveal the evolution of the formation of nanogratings with increasing number of laser pulses. Combined with further theoretical analyses, our observation provides important clues which suggest that excitation of standing plasma waves at the interfaces between a…
We report a detailed study on soliton steering dynamics in a parity-time-symmetric directional coupler in the femtosecond domain, which requires incorporation of higher-order perturbative effects such as third-order and fourth-order dispersions, self-steepening, and intrapulse Raman scattering. With a high gain/loss, the combination of all these effects is found to stabilize the soliton pulse evolution in the coupler from the chaotic behavior of unperturbed evolution. This work demonstrates that efficient soliton steering can be achieved at very low critical power and a relatively higher gain/…
We present a general and highly efficient scheme for performing narrow-band Raman transitions between molecular vibrational levels using a coherent train of weak pump-dump pairs of shaped ultrashort pulses. The use of weak pulses permits an analytic description within the framework of coherent control in the perturbative regime, while coherent accumulation of many pulse pairs enables near unity transfer efficiency with a high spectral selectivity, thus forming a powerful combination of pump-dump control schemes and the precision of the frequency comb. The concept is presented analytically and …
We report the synthesis and measurement of an ultra-precise and extremely stable optical frequency in the telecommunications window around 1543 nm. Using a fibre-based femtosecond frequency comb we have phase-stabilised a fibre laser at 194 THz to an optical frequency standard at 344 THz, thus transferring the properties of the optical frequency standard to another spectral region. Relative to the optical frequency standard, the synthesised frequency at 194 THz is determined to within 1 mHz and its fractional frequency instability is measured to be less than 2*10^{-15} at 1 s, reaching 5*10^{-…
Frequency combs with mode spacing in the range of 10 to 20 gigahertz (GHz) are critical for increasingly important applications such as astronomical spectrograph calibration, high-speed dual-comb spectroscopy, and low-noise microwave generation. While electro-optic modulators and microresonators can provide narrowband comb sources at this repetition rate, a significant remaining challenge is a means to produce pulses with sufficient peak power to initiate nonlinear supercontinuum generation spanning hundreds of terahertz (THz) as required for self-referencing in these applications. Here, we pr…
The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg^+ and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be f_Hg=1 064 721 609 899 143(10) Hz and f_Ca=455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg^+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of …
Supercontinuum (SC) generation via femtosecond (fs) pumping in all-normal-dispersion (ANDi) fiber is predicted to offer completely coherent broadening mechanisms, potentially allowing for substantially reduced noise levels in comparison to those obtained when operating in the anomalous dispersion regime. However, previous studies of SC noise typically treat only the quantum noise, typically in the form of one-photon-per-mode noise, and do not consider other technical noise contributions, such as the stability of the pump laser, which become important when the broadening mechanism itself is coh…
The frequency of the Calcium ^3P_1--^1S_0 intercombination line at 657 nm is phase-coherently measured in terms of the output of a primary cesium frequency standard using an optical frequency comb generator comprising a sub-10 fs Kerr-lens mode-locked Ti:Sapphire laser and an external microstructure fiber for self-phase-modulation. The measured frequency of ν_Ca = 455 986 240 494 276 Hz agrees within its relative uncertainty of 4 10^-13 with the values previously measured with a conceptually different harmonic frequency chain and with the value recommended for the realization of the SI unit of…
SNAP microresonators, which are fabricated by nanoscale effective radius variation (ERV) of the optical fiber with sub-angstrom precision, can be potentially used as miniature classical and quantum signal processors, frequency comb generators, as well as ultraprecise microfluidic and environmental optical sensors. Many of these applications require the introduction of nanoscale ERV with a large contrast α which is defined as the maximum shift of the fiber cutoff wavelength introduced per unit length of the fiber axis. The previously developed fabrication methods of SNAP structures, which used …
A fully integrated dispersion-managed femtosecond mode-locked laser
Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Institute of Electrical and Micro Engineering, Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院电气与微工程学院）；EDWATEC SA（EDWATEC公司）；Helmholtz-Zentrum Dresden-Rossendorf (HZDR)（德累斯顿-罗森多夫亥姆霍兹中心）
We report on the first demonstration of nonlinear dual-frequency-comb spectroscopy. In multi-heterodyne femtosecond Raman-induced Kerr-effect spectroscopy, the Raman gain resulting from the coherent excitation of molecular vibrations by a spectrally-narrow pump is imprinted onto the femtosecond laser frequency comb probe spectrum. The birefringence signal induced by the nonlinear interaction of these beams and the sample is heterodyned against a frequency comb local oscillator with a repetition frequency slightly different from that of the comb probe. Such time-domain interference provides mul…
Pump-probe experiments combining pulses from a X-ray FEL and an optical femtosecond laser are very attractive for sub-picosecond time-resolved studies. Since the synchronization between the two independent light sources to an accuracy of 100 fs is not yet solved, it is proposed to derive both femtosecond radiation pulses from the same electron bunch but from two insertion devices. This eliminates the need for synchronization and developing a tunable high power femtosecond quantum laser. In the proposed scheme a GW-level soft X-ray pulse is naturally synchronized with a GW-level optical pulse, …
We perform femtosecond frequency comb vernier spectroscopy in the near infrared with a femtosecond Er doped fiber laser, a scanning high-finesse cavity and an InGaAs camera. By utilizing the properties of a frequency comb and a scanning high-finesse cavity such spectroscopy provides broad spectral bandwidth, high spectral resolution, and high detection sensitivity on a short time scale. We achieved an absorption sensitivity of ~8E-8 cm-1Hz-1/2 corresponding to a detection limit of ~70 ppbv for acetylene, with a resolution of ~1.1 GHz in single images taken in 0.5 seconds and covering a frequen…
Integrated femtosecond pulse and frequency comb sources are critical components for a wide range of applications. The leading approaches for on-chip pulse generation rely on mode locking inside microresonator with either third-order nonlinearity or with semiconductor gain. These approaches, however, are limited in noise performance, wavelength tunability and repetition rates. Alternatively, sub-picosecond pulses can be synthesized without mode-locking, by modulating a continuous-wave (CW) single-frequency laser using a cascade of electro-optic (EO) modulators. This method is particularly attra…
Femtosecond point-projection microscopy (fs-PPM) is an electron microscopy technique that possesses a combination of high spatio-temporal resolution and sensitivity to local electric fields. This allows it to visualize ultrafast charge carrier dynamics in complex nanomaterials. We benchmark the capability of the fs-PPM technique by imaging the ultrafast dynamics of charge carriers produced by multiphoton ionization of silver nanowires. The space-charge driven motion of photoelectrons is followed on \mbox{sub-100}\,nm length scales, while the dynamics are captured on 30-100 fs time scales. The …
Helical gratings (HGs) have an achievement of flexible mode conversion for fibre guided orbital angular momentum (OAM) modes. Sampled reflection HGs can realise the generation and conversion of OAM mode with comb spectra. They can be used to simultaneously filter wavelengths and convert modes, and thus may be applied to the hybrid multiplexing technology with wavelength division multiplexing and mode division multiplexing.
Optical communication systems are able to send the information from one user to another in light beams that travel through the free space or optical fibers, therefore how to send larger amounts of information in smaller periods of time is a long term concern, one promising way is to use multiplexing of photon's different degrees of freedoms to parallel handle the large amounts of information in multiple channels independently. In this work, by combining the wavelength and time division multiplexing technologies, we prepare a multifrequency mode time bin entangled photon pair source at differen…
We report a simple and compact design of a dispersion compensated mode-locked Yb:fiber oscillator based on a nonlinear amplifying loop mirror (NALM). The fully polarization maintaining (PM) fiber integrated laser features a chirped fiber Bragg grating (CFBG) for dispersion compensation and a fiber integrated compact non-reciprocal phase bias device, which is alignment-free. The main design parameters were determined by numerically simulating the pulse evolution in the oscillator and by analyzing their impact on the laser performance. Experimentally, we achieved an 88 fs compressed pulse durati…
In-line Dispersion Control of Femtosecond Laser Pulses by Multilayer Huygens' Metasurfaces
Friedrich-Schiller-University Jena（耶拿弗里德里希·席勒大学）；Australian National University（澳大利亚国立大学）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所）
Hybrid Femtosecond Laser and Ion-Implantation Processing for Controlled, Deep, High-Efficiency Ablation in Fused Silica
Instituto de Optica Daza de Valdes (IO), CSIC（西班牙科学研究中心光学研究所）；HiLASE Centre, FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所 HiLASE 中心）；Universidad Autónoma de Madrid（马德里自治大学）；Centro de Microanálisis de Materiales (CMAM), Universidad Autónoma de Madrid（马德里自治大学材料微分析中心）；FZU - Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）
