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Optical Frequency Metrology
Abstract
Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.
... Both benefited each other with their respective technological advancements. In a parallel scientific universe, from 2000, the development of femtosecond lasers or optical frequency comb [4][5][6] has revolutionized the impact of RF-photonics in the field of high precision spectroscopy [7], arbitrary waveform generation [8], highly precise atomic clocks [9], arbitrary RF waveform generation [10] and massively parallel optical communication system [11][12][13][14][15][16][17][18][19][20][21]. An optical frequency comb is an optical range spectrum of multiple evenly spaced optical frequencies. ...
... Nevertheless, the characteristic parameters requirement in optical frequency comb (like frequency of operation, frequency spacing, spectral width, spectral flatness, phase correlation, phase noise, center frequency tunability, frequency spacing tunability etc) depends on its application area [23]. For example, precision optical metrology applications demand high periodicity, dense channel spacing, and a higher number of frequency lines but are not so demanding for center frequency tunability and channel spacing tunability [7]. In contrast to metrology, optical arbitrary waveform generators require high-frequency spacing (>10 GHz), tunable optical frequency and tunable frequency spacing but less demanding for bandwidth and precise stabilization [8]. ...
... A widely spaced and flat optical frequency comb with other required parameters discussed in section 2 can be exploited as a multichannel source for future flexible optical networks. To date, multiple approaches have been proposed to realize a comb-based WDM transmission system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The basic block diagram corresponding to the comb-based WDM transmission system is shown in figure 17. ...
A flexible optical communication network is needed to realize a backbone transport network for 6G communication and further higher generation communication technologies. However, the practical implementation of the higher generation network experiences some serious challenges due to the existing multicarrier generation technology i.e. an array of multiple discrete laser sources (less spectrally efficient, complex, bulkier and costlier). Recently, a multicarrier generation technique using the optical frequency comb has been extensively researched. It can reduce the complexity, cost, and size compared to the existing multicarrier generator. Moreover, it increases the utilization of available spectral efficiency due to its capability to tune the operating frequency and carrier spacing. So, considering these advantages, we reviewed the multiple optical frequency comb generation techniques, categorized as mode-locked laser, microresonator and electro-optic modulator based frequency combs. We identify the salient features of different frequency comb generation techniques by keeping the requirements of a flexible optical network in mind. We also reviewed the drawbacks and possible solutions proposed to improve the characteristics of the optical frequency comb. Further, we reviewed the optical frequency comb expansion techniques to broaden the spectrum of the optical frequency comb, which is the requirement in optical frequency comb suitable for communication applications. At last, we summarize the progress in the practical implementation of the optical frequency comb as a multichannel source in a flexible optical network.
... 几百至几千纳米的超宽谱带的激光 [1][2][3] 。白激光指的是谱带覆盖可见光波段的超 连续激光。超连续激光的产生通常通过将一个窄带入射脉冲聚焦至介质中，使局 部光强足够高，从而激发介质中的多种非线性效应 [4] 。常见的非线性机制包括： 光孤子效应 [5][6] 、 四波混频 [7] 、 克尔效应 [8][9] ， 以及自相位调制 (Self-phase modulation, SPM)等 [10][11][12][13] 。在过去 10 年中，本课题组系统性地发展了基于钛宝石飞秒激光 的白激光技术 [14][15][16][17][18][19][20] 。在这些方案中，白激光由钛宝石飞秒激光器经过多种非线性 效应产生，在获得超宽谱带的同时保留激光的特性，如高强度和相干性。这样的 光源在多个领域具有广阔的应用前景。其中，多通道共聚焦显微镜、白光干涉测 量以及彩色全息三维显示是三大关键潜在应用，值得深入探索。多通道共聚焦显 微镜是一种高精度的彩色显微成像技术，通常需要高强度激光，并能够快速切换 波长 [21] 。相比传统的多种单色激光集成方案，白激光可以更方便地切换波长，并 提供更多的颜色。 白光干涉测量是一种利用宽光谱光源通过干涉进行高精度三维 表面形貌测量的技术 [22] 。与传统的相干性较差的白光，如 LED 或卤素灯相比， 白激光在该方应用中可以显著提高分辨率并增强抗噪能力。此外，彩色全息 [23] 被 认为是三维(Three dimension, 3D)显示技术的"圣杯"，其原理是利用干涉条纹 White light is typically considered incoherent; however, the recently popular supercontinuum laser-also known as white laser-that spans the visible spectrum, features high laser intensity and good coherence, challenging this traditional limitation. The white laser has a wide range of applications, including multi-channel confocal microscopy, color holography, and white light interferometric surface topography. ...
... Analysis scheme of laser characteristics such as spatial coherence of white laser. 3rd-NL) 效应， 例如自相位调制 (Self-phase modulation， SPM) 、 四波混频和受激拉曼散射， 这通常在光子晶体光纤 (Photonic crystal fiber， PCF)[8] 2nd-NL 和 3rd-NL) 效应来产生飞秒白激光[14][15][16][17][18][19][20] 。 通过优化了2nd-NL 和 3rd-NL 效应的单独功能及其协同作用， 最终实现了一种高性能的飞秒白激光 [20] 。 该激光具有高脉冲能量(~1.1 mJ) Basic information of the white laser. (a) Schematic diagram of a homemade femtosecond white laser created by sending an intense Ti: Sapphire femtosecond pulse laser beam through a fused silica-CPPLN 2 nd -NL and 3 rd -NL synergistic nonlinear frequency conversion module. ...
White light is typically considered incoherent; however, the recently popular supercontinuum laser—also known as white laser—that spans the visible spectrum, features high laser intensity and good coherence, challenging this traditional limitation. The white laser has a wide range of applications, including multi-channel confocal microscopy, color holography, and white light interferometric surface topography. Although white lasers have been proposed and developed extensively in terms of technology, specific analyses of their optical wave properties—especially spatial coherence—are still lacking. Since many applications impose certain requirements on the spatial coherence of white light, the lack of research into the spatial coherence of white lasers has, to some extent, limited their practical use.
This paper presents a detailed experimental study and analysis of the wavefront intensity, polarization characteristics, and spatial coherence of a high-intensity, ultra-flat spectrum white laser independently developed by our research group in 2023. The laser was generated by broadening the spectrum of a high-intensity Ti:sapphire femtosecond laser through second- and third-order nonlinear effects.
A bandpass filter was used to extract eight components from the white laser, with central wavelengths ranging from 405 nm to 700 nm and a bandwidth of 10 nm each. By measuring the performance of these eight quasi-monochromatic lasers, the characteristics of the white laser across the visible spectrum can be evaluated.
CCD imaging of the collimated quasi-monochromatic laser spots revealed that their wavefront intensities exhibit a quasi-Gaussian distribution with uniform beam profiles. Polarization measurements using polarizers at various angles showed that the white laser is linearly polarized. A Young's Double-Slit Interferometer (YDSI) was used to measure the interference fringe contrast of the eight quasi-monochromatic beams to assess their spatial coherence. The experimental results showed that the average interference fringe contrast across the visible spectrum was 0.77, with little variation among different wavelengths. This indicates that the white laser has excellent spatial coherence in the visible range.
The eight quasi-monochromatic lasers in the visible spectrum all exhibit quasi-Gaussian wavefront intensity distributions, linear polarization, and high spatial coherence. This indicates that the white laser inherits the excellent properties of the Ti:sapphire laser. All of this data provides valuable guidance for the application of white lasers in areas such as color holography, white light interferometric surface tomography, microscopic imaging, and other fields that require white light with a certain degree of coherence.
... Kerr microresonators [1][2][3][4][5][6][7][8] are optical devices capable of generating wavetrain structures covering a spectral region over an octave [9,10], while operating in a low-noise and phase-stable configuration. These wavetrain structures are particular for they exhibit periodic properties consequent upon the crystallization of almost identical opical pulses that are multiplexed in space and/or time, forming a comb-like wave structure of a well -defined periodicity [11][12][13][14][15]. ...
... This leads to a remainder of order eight instead of five as in the fourth-order Runge-Kutta scheme. Numerical values for the seven variables y[i] (with {y[0], y [1], y [2], y [3], y [4], y [5], y [6]} ≡ [a(τ), b(τ), φ(τ), M(τ), x(τ), y(τ), ∆T(τ)] generated by the sixth-order Runge-Kutta scheme are expressed: ...
Optomechanical microresonators have attracted particular attention in the recent past, due to their possible applications in a broad range of optical metrology contexts. Experimental studies have established that in addition to modifying the microresonator’s refractive index through the so-called thermal-lensing process, the heat stored in the microresonator cavity during roundtrips of the optical field also induces thermal expansion of the cavity, promoting mechanical excitations (phonon modes). In the present study, we examine the emergence of soliton trains in the anomalous dispersion regime of a Kerr optomechanical microresonator subjected to thermal-lensing processes, combined with phonon radiations from thermally-induced expansion of the optomechanical microresonator. The model consists of the Lugiato-Lefever equation with two extra detunings accounting for optomechanical and thermo-optic effects, coupled to the phonon equation and to a two-level equation accounting for the temporal variation of the temprature difference within the microresonator cavity. By solving numerically the model equations using a sixth-order Runge-Kutta algorithm, it is shown that a strong optomechanical coupling can inflict severe impairements on soliton-comb structures in the optomechanical microresonator. Phonon-mode amplitudes emerge to be enhanced with an increase of the optomechanical coupling coefficient, while time variation of the cavity temperature is marked by an exponential rise and saturation in an oscillating regime. Relatively high phonon characteristic frequencies favor optical soliton-crystal patterns as well as regular periodic anharmonic structures for phonon modes.
... Where E n is the n th temporal envelope of the electric field, characterizing the shape and duration of the optical pulse, τ is the period of the pulse, that is the time it takes for one complete cycle of oscillation, e i(ω 0 [t−nT ]) is the pulse oscillation at the carrier wave frequency ω 0 , ω 0 = k 0 c = optical angular frequency of the carrier field, k 0 being the wave vector and c the speed of light in vacuum. ϕ 0 is the initial phase of pulse for n = 0, and ∆ϕ cep is the carrier-envelope phase difference (CEP stands for Carrier Phase Envelope offset), which determines the phase difference between the carrier wave and the envelope at each pulse [115] [114]. ...
... ∂G 2π the transverse mode spacing, ∂G is the Gouy phase shift per round trip. Its magnitude depends on the resonator design [114]. ...
... Optical frequency combs (OFCs), which originate from the precise synergy between laser technologies and nonlinear parametric conversion, are characterized by an equidistant pattern of comb-like spectral lines in the frequency domain. With the support of mode-locked ultrafast lasers [1,2] or Kerr-assisted microresonators [3][4][5], this subject has achieved unprecedented progress and sparked various applications such as optical frequency metrology and synthesis [1,4], optical clocks [6,7] and calibration of astronomical spectrograms [8]. Among all these achievements, it is difficult to simultaneously pursue OFCs with a repetition rate smaller than 1GHz and a structural design for on-chip integration due to the limitations of energy bands and material structures. ...
... Optical frequency combs (OFCs), which originate from the precise synergy between laser technologies and nonlinear parametric conversion, are characterized by an equidistant pattern of comb-like spectral lines in the frequency domain. With the support of mode-locked ultrafast lasers [1,2] or Kerr-assisted microresonators [3][4][5], this subject has achieved unprecedented progress and sparked various applications such as optical frequency metrology and synthesis [1,4], optical clocks [6,7] and calibration of astronomical spectrograms [8]. Among all these achievements, it is difficult to simultaneously pursue OFCs with a repetition rate smaller than 1GHz and a structural design for on-chip integration due to the limitations of energy bands and material structures. ...
Parametric frequency conversion involving phonons is an intriguing physical issue in cavity optomechanics. Here, this phenomenon is exploited to devise multiple frequency combs in a three-mode optomechanical system assisted by a degenerate parametric amplifier (DPA). In the optomechanical model, the configuration of optical-mechanical-mechanical coupled resonators provides a well-established environment containing photon-phonon and phonon-phonon interactions. When the system satisfies the frequency matching of parametric conversion involving photons, both integral and fractional multiples of phonons, we observe that the two interactions contribute respectively to generating optical frequency combs (OFCs) with a tooth spacing of 1GHz and phonon-based frequency combs (PBFCs) of integer- and fraction-order with a tooth spacing of 80MHz/N f (N f is an integer). Since N f can be adjusted by mechanical pumps operating on the mechanical resonators, the repetition rate of the frequency combs is flexibly modulated, thus enabling the pursuit of an ultra-small tooth spacing. More importantly, we report that by increasing the nonlinear gain coefficient of the DPA, the PBFCs can grow explosively, forming dense plateau regions and summing up to hundreds of comb lines. The proposal may be useful in facilitating dual-comb spectroscopy and achieving the ultrahigh resolution of frequency combs.
... Broadband spectral radiation sources across the visible, nearinfrared (IR), and mid-IR have paved the way for a multitude of applications, from multicomponent trace gas analysis and single-shot spectroscopy of molecules to frequency metrology and remote sensing [1]. The widely known techniques for broadband generation are the use of χ (3) Kerr microcavities pumped by mode-locked or continuous-wave (cw) lasers, mode-locked femtosecond laser oscillators, and synchronously pumped ultrafast optical parametric oscillators (OPOs) [2][3][4]. Although these sources have had a remarkable impact on photonics, these techniques rely on sophisticated fabrication facilities or complex and costly femtosecond lasers. ...
... Although these sources have had a remarkable impact on photonics, these techniques rely on sophisticated fabrication facilities or complex and costly femtosecond lasers. Circumventing the need for femtosecond lasers, another approach to achieve broadband radiation is by exploiting large parametric gain bandwidth, cascaded χ (2) non-linearity, or non-collinear phase matching in cw OPOs in a singly resonant oscillator (SRO) configuration [5][6][7]. However, these techniques are limited by specific phase-matching conditions. ...
Controlling cavity dispersion in a continuous-wave (cw) optical parametric oscillator operating in a doubly resonant oscillator (DRO) configuration, pumped by a single-mode laser source, has the potential to yield stable, broadband, multiaxial-mode output generation with flexible spectral coverage. This paper reports, for the first time to the best of our knowledge, the design considerations and theoretical analysis of the role of dispersion compensation on the cavity-mode structure and passive stability in a cw dispersion-compensated DRO (DCDRO) cavity. The study demonstrates that in a cw DCDRO, instabilities, including cluster hops and mode hops, can be eliminated, and spectral tunability can be controlled. A theoretical comparison with the conventional cw DRO (CDRO) emphasizes the unique properties of the analyzed cw DCDRO. The results also indicate that a cw DCDRO at degeneracy can be exploited for optical frequency comb (OFC) generation, offering increased flexibility in frequency comb spacing, practical powers, lower complexity, and lower cost.
... The polarizability measures the change in charge distribution of atoms/molecules when exposed to an external electric field and is important to study due to its wide range of applications. It has applications not only in the molecular science in understanding the intermolecular [30,31] and electron-molecule interactions, [32,33] linear and non-linear optical phenomena, [34,35] various electromagnetic response and collision properties such as refractive index, dielectric constant, energy shift, ion mobility in gas, long-range electron/ion-atom interaction potential etc, [36] and calculation of molecular spectra such as Raman and infrared spectra, [30,37] but also in atomic physics to study parity violations in atoms, [38,39] optical atomic clocks, [40,41] high-harmonic generation and ultra-fast processes, [42 -45] and in the search for the variation in the fundamental constants. [46] In our group, polarizability calculations have been successfully employed to calculate various spectroscopic properties, such as Raman spectra, [47 -52] sum frequency generation, [53] Raman optical activity, [54,55] and electric circular dichroism (ECD) spectra. ...
... Frequency combs, composed of discrete, equally spaced frequencies [1], have contributed to advancements in optical communication [2,3], precision metrology [4,5], spectroscopy [6,7], and atomic clock [8][9][10]. The compact on-chip frequency combs (microcombs) include microresonator-based combs [11][12][13] and electro-optic (EO) combs [14][15][16][17][18]. Microresonator combs relying on Kerr nonlinearity have been successfully demonstrated in silica [11], silicon nitride [19], silicon carbide [20], diamond [21], and lithium niobate (LN) [22]. ...
Frequency combs have revolutionized communication, metrology and spectroscopy. Numerous efforts have been dedicated to developing integrated combs, predominantly relying on Pockels or Kerr mechanisms. In this work, we propose and demonstrate a new type of frequency comb-Floquet cavity frequency comb-that does not rely on intrinsic non-linearity. By periodically modulating the resonance frequency of a cavity, a giant-mode cavity with multiple equally spaced frequency components is created. The pump tone interacts with the pre-modulated cavity, generating the output frequency comb. This approach offers a flexible tuning range and operates in a threshold-less manner, obviating the need to overcome nonlinear initiation thresholds. We implement this on a microwave cavity optomechanical system on-chip. Compared to Kerr optomechanical combs, this approach efficiently generates comb with pump signal far from the cavity's intrinsic frequency, and the power required for detection is reduced by approximately a factor of (), providing a promising platform for frequency comb generation.
... Frequency combs are generated by mode-locked pulse trains in the time domain and manifest as a series of equidistant spectral lines in the frequency domain 1 . The frequency comb offers advantages such as a broad spectrum and high coherence, making it a powerful light source in spectral detection, imaging, and communications [2][3][4][5][6] . ...
Frequency combs show various applications in molecular fingerprinting, imaging, communications, and so on. In the terahertz frequency range, semiconductor-based quantum cascade lasers (QCLs) are ideal platforms for realizing the frequency comb operation. Although self-started frequency comb operation can be obtained in free-running terahertz QCLs due to the four-wave mixing locking effects, resonant/off-resonant microwave injection, phase locking, and femtosecond laser based locking techniques have been widely used to broaden and stabilize terahertz QCL combs. These active locking methods indeed show significant effects on the frequency stabilization of terahertz QCL combs, but they simultaneously have drawbacks, such as introducing large phase noise and requiring complex optical coupling and/or electrical circuits. Here, we demonstrate Farey tree locking of terahertz QCL frequency combs under microwave injection. The frequency competition between the Farey fraction frequency and the cavity round-trip frequency results in the frequency locking of terahertz QCL combs, and the Farey fraction frequencies can be accurately anticipated based on the downward trend of the Farey tree hierarchy. Furthermore, dual-comb experimental results show that the phase noise of the dual-comb spectral lines is significantly reduced by employing the Farey tree locking method. These results pave the way to deploying compact and low phase noise terahertz frequency comb sources.
... Optical frequency combs (OFC) have emerged as a revolutionary tool in the fields of spectroscopy, metrology, and optical clocks [1][2][3]. Owing to its unique spectral structure, an OFC not only enables the precise conversion of optical frequencies to microwaves, but also establishes coherent links between optical frequencies across a wide wavelength range [4,5]. Mode-locked lasers are the most commonly utilized sources generating OFCs with ultra-low noise [6][7][8]. ...
We present a low-noise extraction of individual frequency lines from an optical frequency comb based on fiber Brillouin amplification. The phase and intensity noise properties of this extraction process are comprehensively investigated. The excess phase noise introduced by the extraction process under various conditions is studied in detail and found to be determined by environmental disturbances on the Brillouin gain fiber, which is reduced in our short-fiber, all-polarization-maintaining (PM) scheme. The simplicity and low phase noise characteristics of this approach demonstrate its capability in maintaining the coherence of a frequency comb line with ultra-narrow linewidth. Furthermore, the intensity noise of the extracted comb line is found to be strongly dependent on amplified spontaneous Brillouin scattering, further emphasizing the benefits of the all-PM design. These findings underscore the potential of this comb line extraction technique as a robust low-noise single-frequency laser generator or optical frequency synthesizer required in demanding fields such as cold atomic physics, optical communications, and optical clocks.
... Optical frequency combs generated by mode-locked lasers have revolutionized laser spectroscopy, enabling unprecedented precision [1][2][3][4]. Recognizing their profound importance, the 2005 Nobel Prize in Physics was awarded to John L. Hall and Theodor W. Hänsch 'for their contributions to the development of laser-based precision spectroscopy, including the optical frequency comb technique'. Optical and extreme ultraviolet (XUV) frequency combs have been instrumental in the development of atomic clocks [5,6], the enhancement of attosecond pulse generation [7], and rigorous tests of bound-state * Author to whom any correspondence should be addressed. ...
Highly coherent and powerful light sources capable of generating soft x-ray frequency combs are essential for high precision measurements and rigorous tests of fundamental physics. In this work, we derive the analytical conditions required for the emission of coherent radiation from an electron beam colliding with a laser pulse, modeled as a plane wave. These conditions are applied in a series of numerical simulations, where we show that a soft x-ray frequency comb can be produced if the electrons are regularly-spaced and sufficiently monoenergetic. High quality beams of this kind may be produced in the near future from laser-plasma interactions or linear accelerators. Furthermore, we highlight the advantageous role of employing few-cycle laser pulses in relaxing the stringent monoenergeticity requirements for coherent emission. The conditions derived here can also be used to optimize coherent emission in other frequency ranges, such as the terahertz domain.
... Fiber-optic time-frequency transfer systems have been applied across various fields, such as fundamental physics, geodesy, and metrology [1][2][3][4][5]. Optical fiber, as an excellent transmission medium, has been extensively explored for time-frequency transfer capabilities over the past several decades. ...
In this Letter, we propose a fiber-optic round trip time transfer system tolerant to the received optical signal noise ratio (OSNR) degradation through forward frequency transfer. Typically, OSNR degrades with increased transmission distance and noise accumulation in fiber-optic time transfer systems, affecting the received signal-to-noise ratio (SNR) and system stability. The broad bandwidth of time signals limits the effectiveness of filtering to improve the received SNR. The proposed system overcomes these limitations by incorporating a forward-transmitted frequency (FTF) signal and a phase-locked pulse generator (PLPG), enhancing the received SNR and generating high-precision time pulses with minimal jitter. Theoretical simulations confirm the insensitivity to OSNR degradation of the system in short-term stability. Experiments over laboratory fiber links of 320 km, 640 km, and 960 km demonstrate short-term stabilities below 10 ps, with no significant deterioration despite increased transmission distance and OSNR degradation. Given its superior performance and noise resistance, this system holds significant promise for future ground-based fiber-optic time–frequency systems.
... Optical frequency combs [1] have resulted in significant advances in precise physical metrology including optical frequency [2][3][4] and time [5][6][7]. Their phononic and miniature analog, also known as (micro)mechanical frequency combs (MFCs), have also attracted great attention recently but are nontrivial due to the distinctively different dispersion of phonons. ...
Pure mechanical frequency combs attracted a lot of attention recently due to the intriguing nonlinear dynamics and potential of miniatured precision timekeeping but are currently limited by narrow spectra and missing frequency locking physics. In this Letter, we report the design and experiment of a self-injection locked micromechanical frequency comb that is further intrinsically immune to phase offset. We show that by tuning the pump frequency of a pair of nonlinearly coupled flexural and torsional oscillations, self-injection locking could be achieved via aligning the comb teeth from neighboring harmonic clusters, leading to decade-wide cascading of hundreds of equidistant teeth. Inside the injection locking region, the stability of the comb spacing and the phase noise are significantly improved. Moreover, the phase offset in the temporal signal also disappears because all comb lines are locked as integer multiples of the comb spacing and the first tooth is locked to the d.c. frequency due to the comb origination from harmonics. The observation of self-injection locking and zero phase offset in mechanical frequency combs greatly promotes their value for precision applications.
... Precise time synchronization and frequency dissemination between remote locations underpins various applications, including precision timing [1,2], advanced satellite navigation [3,4], geophysics [5,6], molecular spectroscopy [7], deep space exploration [8][9][10], and integrated sensing and communication [11,12]. With the rapid development of modern quantum frequency standards, the uncertainties of advanced cesium fountains clocks and optical lattice clocks have been continuously improved to the levels of 10 −16 and 10 −19 , respectively [13][14][15]. ...
Accurate and stable long-haul time and frequency distribution plays an important role in advanced scientific and industrial application fields, for instance, large-scale optical clock networks, advanced satellite navigation, very long baseline interferometry, clock-based geodesy, and fundamental physics. Here, we present a parallel transfer of optical reference frequency, radio frequency, and a one pulse per second (1 PPS) signal with timestamp over a single optical carrier by merging optical phase-locking with pseudo-code spread spectrum modulation. The method effectively reduces the crosstalk and non-reciprocity in dense wavelength division multiplexing (DWDM)-based fiber links. Measurement campaign has been conducted over a 120-km fiber link for half a month. Experimental results show that the fractional frequency instability of optical reference frequency transfer reached 7.3 × 10⁻¹⁶ and 4.6 × 10⁻¹⁹ at 1-s and 10⁵-s averaging times, respectively, while the fractional frequency instability of radio frequency transfer reached 7.9 × 10⁻¹³ and 2.9 × 10⁻¹⁹ at 1-s and 10⁵-s averaging times, respectively. The time deviation of 1 PPS signal transfer reached 0.02 ps at an average time of 10⁵-s. This approach also shows a potential in free-space simultaneous time and frequency transfer to establish satellite-to-ground and inter-satellite optical time and frequency transfer networks.
... Another less explored application of OMOs is the generation of optical frequency combs (OFCs). Nowadays, extensive research is being conducted on OFCs due to their crucial role in various applications such as optical metrology, precision spectroscopy, optical clocks, and rf photonics [34][35][36]. So far, researchers have successfully utilized electro-optic (EO) modulation or intrinsic parametric nonlinearities of materials (such as Kerr media), commonly exhibiting high repetition rates, to demonstrate the integrated optical microcombs [36][37][38][39][40]. On the other hand, OFCs with low repetition rates (typically below 1 GHz) are better suited for other applications, such as high-resolution spectroscopy [41,42], mode-locked lasers with ultranarrow spectral widths [43], integrated pulse sources for quantum optics [44], and lownoise microwave frequency comb generations [45,46]. ...
Cavity optomechanical oscillations (OMOs) have been extensively studied for their rich physics and various practical applications. However, due to the highly nonlinear nature of the dynamical process, the exact sideband structure of an optomechanically oscillating optical cavity field remains unknown, although it is essential to a comprehensive understanding and accurate manipulation of such systems. Here, we establish a correspondence between the Bloch-band structure and the coupled sideband dynamics of OMOs, thus providing a theoretical framework for unveiling the detailed structure of cavity optical modes in terms of their resemblance to the well-known Wannier-Stark states and ladders. Surprisingly, the locations of these ladders are irrelevant to pump frequency or power but only depend on the resonant frequency of the optical mode and mechanical-mode frequency. By an energy transfer picture, we build up a connection between the highly nonlinear OMOs and a Bloch-band structure that can be solved linearly. Quantitatively, this picture uncovers the underlying mechanism of the optimization of the pump detuning and optical decay rate, as well as the determination of the minimum input pump power, for sustaining a cavity OMO.
Published by the American Physical Society 2025
... The kinematics and dynamics of the QHO are governed by the frequency parameter, whose determination is essential to characterize the system properly. Indeed, accurate frequency estimation is relevant for several fields, including metrology [1][2][3][4][5][6] and quantum sensing [7][8][9], spectroscopy [10][11][12], and precision timekeeping [13]. Additionally, frequency estimation finds application in quantum communication and computation [14,15]. ...
The frequency of a quantum harmonic oscillator cannot be determined through static measurement strategies on a prepared state, as the eigenstates of the system are independent of its frequency. Therefore, dynamic procedures must be employed, involving measurements taken after the system has evolved and encoded the frequency information. This paper explores the precision achievable in a protocol where a known detuning suddenly shifts the oscillator's frequency, which then reverts to its original value after a specific time interval. Our results demonstrate that the squeezing induced by this frequency jump can effectively enhance the encoding of frequency information, significantly improving the quantum signal-to-noise ratio (QSNR) compared to standard free evolution at the same resource (energy and time) cost. The QSNR exhibits minimal dependence on the actual frequency and increases with both the magnitude of the detuning and the overall duration of the protocol. Furthermore, incorporating multiple frequency jumps into the protocol could further enhance precision, particularly for lower frequency values.
... Usually, they are derived from femtosecond pulsed lasers and their frequency components are described by ν m = mf rep + f ceo , where f rep and f ceo are the laser's pulse repetition rate and carrier-envelope-offset frequency, and m ∈ N 0 is the comb line index. While the initial comb spectra are often limited in span by the laser gain medium, nonlinear spectral broadening through self-phase modulation (SPM) in optical fibers [3] has enabled octave spanning spectra [4], which are now routinely used to implement self-referencing i.e., detection of f ceo as a beating between harmonics of the comb [5][6][7][8]. Complementing silica fibers and specialty fibers [9], as powerful nonlinear platforms waveguides have enabled access not only to SPM, but additional second order nonlinear processes such as sum and difference frequency generation (SFG/DFG) [10]. Especially in nanophotonic waveguides [11], effects beyond SPM have enabled ultrabroadband spectra and power efficient implementation of f ceo beatnote detection [12][13][14][15][16][17][18][19][20][21][22][23][24], holding potential for optical spectroscopy and efficient phase coherent links from infrared to ultraviolet wavelengths. ...
Optical frequency combs and their spectra of evenly spaced discrete laser lines are essential to modern time and frequency metrology. Recent advances in integrated photonic waveguides enable efficient nonlinear broadening of an initially narrowband frequency comb to multi-octave bandwidth. Here, we study the nonlinear dynamics in the generation of such ultra-broadband spectra where different harmonics of the comb can overlap. We show that a set of interleaved combs with different offset frequencies extending across the entire spectrum can emerge, which transform into a single evenly spaced ultra-broadband frequency comb when the initial comb is offset-free.
... frequency estimation plays a central role in various fields such as quantum communication [1,2], quantum sensing [3][4][5], and quantum computation [6]. Its importance extends to key applications in metrology [7][8][9][10][11][12][13][14], spectroscopy [15][16][17], and precision timekeeping [18]. Quantum sensors, probes that exploit quantum phenomena, have been demonstrated to surpass the precision limits achievable by classical sensors in frequency estimation [3, 5, 7-9, 19, 20]. ...
Frequency estimation, a cornerstone of basic and applied sciences, has been significantly enhanced by quantum sensing strategies. Despite breakthroughs in quantum-enhanced frequency estimation, key challenges remain: static probes limit flexibility, and the interplay between resource efficiency, sensing precision, and potential enhancements from nonlinear probes remains not fully understood. In this work, we show that dynamically encoding an unknown frequency in a nonlinear quantum electromagnetic field can significantly improve frequency estimation. To provide a fair comparison of resources, we define the energy cost as the figure of merit for our sensing strategy. We further show that specific higher-order nonlinear processes lead to nonlinear-enhanced frequency estimation. This enhancement results from quantum scrambling, where local quantum information spreads across a larger portion of the Hilbert space. We quantify this effect using the Wigner-Yanase skew information, which measures the degree of noncommutativity in the Hamiltonian structure. Our work sheds light on the connection between Wigner-Yanase skew information and quantum sensing, providing a direct method to optimize nonlinear quantum probes.
... For detection of the CEO frequency a supercontinuum-generating optical fiber that broadens the comb to an octave-spanning spectrum via strong optical non-linearities is used [5,6]. The octave-spanning spectrum and second harmonic generation make it possible to produce a beat note between comb mode number 2n on the shorter wavelength side of the spectrum and the frequency doubled mode number n on the longer wavelength side of the spectrum by means of an f-to-2f interferometer, cancelling out the second term on the right-hand-side of Eq. (1) and giving access to the value of f CEO , hence the "self-referenced" denomination. ...
Airborne and spaceborne integral-path differential absorption (IPDA) lidar has the potential to deliver column measurements of the major greenhouse gases influenced by human activity with the high accuracy that is required to significantly reduce the uncertainties in our estimations of surface fluxes of methane and carbon dioxide by inverse modelling. A prerequisite is the highly accurate knowledge of the emitted wavelengths, especially for carbon dioxide in the 1.6-µm region, where a long-term optical frequency knowledge accuracy of the online channel down to a few tens of kHz is required. Deutsches Zentrum für Luft- und Raumfahrt’s airborne IPDA lidar for simultaneous measurements of carbon dioxide at 1.57 µm and methane at 1.64 µm, CHARM-F, uses a specifically developed frequency reference unit based on optimized wavelength modulation spectroscopy which can reach the required accuracy in a stabilized laboratory environment, but whose in-flight performance in the more challenging aircraft environment could not be independently validated. In the frame of the Carbon Dioxide and Methane Mission (CoMet) field campaigns in 2018 and 2022, CoMet 1.0 and CoMet 2.0 Arctic, respectively, a cooperation with Menlo Systems GmbH made it possible to bring a prototype of a new generation of portable and rugged self-referenced frequency combs (SRFCs) on board the German research aircraft HALO. This airborne frequency comb served as an independent frequency reference to characterize the performance of the carbon dioxide channel of CHARM-F’s frequency reference system in flight. We report here on the frequency stability measurements carried out during the CoMet 2.0 Arctic campaign and demonstrate the potential of such portable SRFCs as next-generation frequency references for atmospheric lidars.
... Optics-based data acquisition methods are indispensable in many applications, including communications, metrology, spectroscopy, sensing, imaging and astrophysics. They enable information to be extracted from signals on the intensity, frequency, phase or polarization of optical waveforms [1][2][3][4] . Ultra-short pulses are capable of high-speed data acquisition, meaning they can provide vast data quantities that are crucial for artificial intelligence, machine learning and other digital technologies requiring large datasets. ...
... The ultra-broad bandwidth and the fast frequency change (chirp) along the short pulse are important for Photonics Radars 22,23 . The optical and the RF spectrum of the phase pulses contain a very dense frequency comb (FC), which is locked to the injected frequency, and therefore it can be used for various measurements based on frequency combs, such as high-resolution spectroscopy 24 , which also often requires a very long time measurements. TL oscillators also offer a simple and accurate solution for applications that require synchronization between clocks or measurement systems, which are located in different sites, such as in Bistatic Radars, optical or electronic coherent receivers, and distributed processing. ...
We demonstrate a novel injection-locking effect in oscillators, which is obtained in both the time and frequency domains. The “temporal-locked” oscillator generates an ultra-low phase noise continuous-wave (CW) signal, accompanied by an ordered train of short phase pulses with precise timing, where both signals are phase-locked to an external sinusoidal source. Remarkably, even when the cavity delay drifts, the period of the temporal-locked pulses remains constant. Furthermore, the instantaneous phase and the timing of the minimum and maximum amplitudes within part of the pulse remain approximately constant. These unexpected results stem from the nonlinear effect of strong injection on the waveform of the phase pulses. In particular, this effect leads to the self-adaptation of the instantaneous frequency to delay variations, thereby preserving the periodicity of the pulses. We theoretically show that a simple and general setup can accurately model the pulse propagation within the cavity. We experimentally demonstrate the effect in an optoelectronic oscillator (OEO). The pulse timing inherits the stability of the external CW source. The combination of an ultra-low phase noise CW signal with precisely timed pulses is important for various applications that require accurate measurements in both the time and frequency domains.
... In the two decades since the introduction of the OFC, entirely new scientific and technology have been opened in the field of dimensional metrology [13]. The periodic trains of ultrashort pulses exhibit the characteristic of being able to be traced back to a length reference, thus serving as the starting points for measuring absolute distance. ...
High-precision and multi-degree-of-freedom geometric measurement holds significant importance in feature detection for large-scale equipment manufacturing. The measurement process demands the qualities of absoluteness, simultaneity, and traceability, especially in the face of attitude compensation, target monitoring, and the construction of length references. The measurement range of commonly used high-precision optical interferometry is constrained by the wavelength of light and the size of diffraction grating, thus limiting its applicability to long distances. The optical frequency comb (OFC), with an ultra-short pulse characteristic of a periodic sequence, can be traced back to a length reference so that specific points can be determined for long-distance measurements. When integrating OFC with optical interferometry, it enables the achievement of absolute high precision distance measurements. It is essential to address the design issue which demands simultaneous multi-group distance measurements to achieve multiple-degree-of-freedom expansion. In this study, we presented a technique for three-degree-of-freedom (DOF) simultaneous measurements based on dispersive interferometry using an optical frequency comb by improving the optical structure. To solve the nonlinear problem of frequency sampling in dispersive spectrum broadening, two non-even Fourier transform algorithms are improved as a method of phase calculation. By incorporating phase ω information into the non-uniform fast Fourier transform (NUFFT) method, we achieved effective calculation of non-uniform discrete Fourier transform (NUDFT). At the same time, it can reduce the mitigate mutual interference during the extraction of multiple sets of interference peaks. The experimental findings indicate that when compared with an autocollimator, there is a consistent agreement within 3 arcsec for angles up to 1000 arcsec. This absolute measurement scheme is almost not affected by time and other factors, which provides potential for angle information monitoring.
... Microcombs benefit from the dual balance of dispersion, nonlinearities, and gain and loss [1]. To date, research on microcombs has shown great potential in spectroscopy [2][3][4][5], communications [6], and medical bioimaging [7,8]. However, the extension of microcombs into the visible wavelength range has been hindered by the strong normal dispersion of most dielectric materials in this band. ...
We propose a reliable and simple approach for dispersion engineering in lithium niobate microring resonators (MRRs). With strong coupling-induced mode hybridization and inverse design method, we overcome the large normal dispersion and achieve broadband frequency comb coverage near 525 nm. We adopt a neural network method in the inverse design, which outperforms the traditional forward design based on manual trial-and-error and intuitive judgment. Our numerical results demonstrate the possibility of generating a visible Kerr soliton microcomb with a bandwidth of 214.4 nm in a single MRR, which holds significant potential for applications in bioimaging and on-chip atomic clocks.
... Over the past decades the generation of combs with broad frequency spectrum has become the subject of intensive research, mainly due to the fact that such broad bandwidth frequency combs have revolutionized the precision and accuracy with which different optical transition frequencies can be measured, a discovery that was awarded with the Nobel prize in physics and has promising applications to optical communications [32], broadband gas sensing [45], spectroscopy [7,37], and frequency metrology [48], to name but a few. The generation of broadband frequency combs in high-quality microresonators has sparked significant interest [10,13], mainly due to the potential of chip-scale implementation, which facilitates the integration of frequency comb technology into applications outside the laboratory. ...
Kerr frequency combs are optical signals consisting of a multitude of equally spaced excited modes in frequency space. They are generated by converting a continuous-wave pump laser within an optical microresonator. It has been observed that the interplay of Kerr nonlinearity and dispersion in the microresonator can lead to a stable optical signal consisting of a periodic sequence of highly localized ultra-short pulses, resulting in broad frequency spectrum. The discovery that stable broadband frequency combs can be generated in microresonators has unlocked a wide range of promising applications, particularly in optical communications, spectroscopy and frequency metrology. In its simplest form, the physics in the microresonator is modeled by the Lugiato-Lefever equation, a damped nonlinear Schr\"odinger equation with forcing. In this paper we demonstrate that the Lugiato-Lefever equation indeed supports arbitrarily broad Kerr frequency combs by proving the existence and stability of periodic solutions consisting of any number of well-separated, strongly localized and highly nonlinear pulses on a single periodicity interval. We realize these periodic multiple pulse solutions as concatenations of individual bright cavity solitons by phrasing the problem as a reversible dynamical system and employing results from homoclinic bifurcation theory. The spatial dynamics formulation enables us to harness general results, based on Evans-function techniques and Lin's method, to rigorously establish diffusive spectral stability. This, in turn, yields nonlinear stability of the periodic multipulse solutions against localized and subharmonic perturbations.
Lasers with high spectral coherence are in high demand for applications requiring high precision. Single frequency (SF) and ultrafast lasers represent two types of highly coherent light sources, each with distinct time‐frequency characteristics. The advent of novel technologies based on electro‐optics and nonlinear optics has bridged the gap between these two types of lasers, enabling coherent conversion between them. This review examines several technologies that enable coherent conversion between SF and ultrafast lasers. The generation of ultrafast pulses by modulation of an SF laser, covering both electro‐optic modulation (EOM) and optic‐optic modulation (OOM) is discussed. With respect to Kerr soliton generation by SF laser‐induced parametric frequency conversion, schemes with and without resonator structure are compared and discussed. The extraction of a single comb line from an ultrafast laser using stimulated Brillouin scattering is also presented. The advent of new technologies using all‐polarization‐maintaining fiber structures has made fiber Brillouin amplification a practical and robust solution for single comb line extraction. These coherent lasers with customizable time and frequency characteristics are poised to become essential building blocks in future photonic technologies.
Dual‐comb spectrometer based on quantum cascade lasers (QCLs) is gaining fast development and revolutionizing the precision measurement with high‐frequency and temporal resolutions. In these measurements, high‐bandwidth photodetectors are normally used for signal acquisition and processing, which complicates the measurement system. QCL is well‐known for its picosecond gain‐recovery time with an intrinsic bandwidth of tens of GHz. In this work, a compact self‐detecting dual‐comb spectroscopy (DCS) is demonstrated based on dispersion‐engineered, high‐speed packaged QCLs under coherent injection locking. The laser source is designed and fabricated into a hybrid‐monolithic‐integrated waveguide and epi‐down packaged on a wideband‐designed submount to fully explore the high‐speed feature up to fourth‐order harmonic state with a cutoff frequency of 40 GHz. The effective radio frequency (RF) injection locking diminishes the issue of optical feedback and enables high‐bandwidth self‐detection based on QCLs. Clear and stable multiheterodyne signal corresponding to a spectral range of 68 cm⁻¹ and narrow comb tooth linewidth of ≈10 kHz is observed without using external detector or numerical process. The demonstrated broadband, high‐power, self‐detecting mid‐infrared QCL DCS has a great potential for future applications of molecular sensing and spectroscopy.
Accurately measuring spatial angles in large-scale metrological scenarios holds critical significance for applications in geodesy and industrial large-scale metrology, which long-term face challenges due to the increase of non-linearity and the massive unknown disturbances coupled into the large-scale dimensions. Directly building a physical mapping from an optical frequency comb (OFC) to spatial angels can overcome the above fundamental issues, but has never been achieved. Here, we propose a full closed-loop laser scanning angle measurement system by introducing a rotary optical frequency comb technology. In the system, the rotary laser pulses segment the spatial angles based on the repetition frequency locked on the atomic clock, which guarantee the traceability between the atomic clock and spatial angles. Moreover, the consecutive pulses’ intervals received by the detector can be seemed as a feedback signal to adjust the rotary speed of the turntable. Two validation experiments demonstrate that the proposed technology effectively compensates for disturbances caused by temperature variations and the resultant angle can maintain a high precision by counting the pulse numbers of an optical frequency comb. This technology offers enhanced precision and traceability, thereby advancing large-scale metrology for applications in geodesy and industrial settings.
We propose and demonstrate a tunable femtosecond electro-optic optical frequency comb by shaping a continuous-wave seed laser in an all-fiber configuration. The seed laser, operating at 1.5 μm, is first cascade-phase-modulated and subsequently de-chirped to generate low-contrast pulses of approximately 8 ps at a repetition rate of 5.95 GHz. These pulses are then refined into clean, high-quality picosecond pulses using a Mamyshev regenerator. The generated source is further amplified using an erbium–ytterbium-doped fiber amplifier operating in a highly nonlinear regime, yielding output pulses compressed to around 470 fs. Tunable continuously across a 5.7~6 GHz range with a 1 MHz resolution, the picosecond pulses undergo nonlinear propagation in the final amplification stage, leading to output pulses that can be further compressed to a few hundred femtoseconds. By using a tunable bandpass filter, the center wavelength and spectral bandwidth can be flexibly tuned. This system eliminates the need for mode-locked cavities, simplifying conventional ultrafast electro-optic combs by relying solely on phase modulation, while delivering femtosecond pulses at multiple-gigahertz repetition rates.
We demonstrate a quantum walk comb in synthetic frequency space formed by externally modulating a semiconductor optical amplifier operating in the telecommunication wavelength range in a unidirectional ring cavity. The ultrafast gain saturation dynamics of the gain medium and its operation at high current injections is responsible for the stabilization of the comb in a broad frequency modulated state. Our device produces a nearly flat broadband comb with a tunable repetition frequency reaching a bandwidth of 1.8THz at the fundamental repetition rate of 1GHz while remaining fully locked to the RF drive. Comb operation at harmonics of the repetition rate up to 14.1GHz is also demonstrated. This approach paves the way for next-generation optical frequency comb devices with potential applications in precision ranging and high-speed communications.
Laser-based light detection and ranging technology, a vital tool for fast long-range distance measurement, plays an essential role across both scientific and industrial fields. The conventional dual-comb ranging method is a critical player in this field with high precision. However, the Nyquist sampling theorem results in a trade-off between the measurement speed and precision, and the non-ambiguity range (NAR) is also limited by the comb cycle, which hinders the further advancement of the technology. To address these issues, dual-chirped-comb interferometry has emerged as an innovative technique that eliminates the measurement speed limitation and extends the NAR for real-time ranging. With the utilization of dual-comb and dispersive time-stretch techniques (or dispersive Fourier transform), the inherent constraint imposed by the Nyquist sampling theorem is considerably alleviated, facilitating a transient distance measurement. This paper introduces the principle of dual-chirped-comb interferometry and discusses the critical factors for achieving absolute distance measurement. The advancement in speed, in comparison to the conventional dual-comb ranging method, has also been emphasized. In addition, some remarkable works and results are presented to visualize the system’s performance. Finally, this paper provides a perspective on potential future improvements and applications, such as in acoustic sensing, and explores the outlook for this emerging technology in the conclusion part.
As photonic technologies grow in multidimensional aspects, integrated photonics holds a unique position and continuously presents enormous possibilities for research communities. Applications include data centers, environmental monitoring, medical diagnosis, and highly compact communication components, with further possibilities continuously growing. Herein, we review state-of-the-art integrated photonic on-chip sensors that operate in the visible to mid-infrared wavelength region on various material platforms. Among the different materials, architectures, and technologies leading the way for on-chip sensors, we discuss the optical sensing principles that are commonly applied to biochemical and gas sensing. Our focus is on passive optical waveguides, including dispersion-engineered metamaterial-based structures, which are essential for enhancing the interaction between light and analytes in chip-scale sensors. We harness a diverse array of cutting-edge sensing technologies, heralding a revolutionary on-chip sensing paradigm. Our arsenal includes refractive-index-based sensing, plasmonics, and spectroscopy, which forge an unparalleled foundation for innovation and precision. Furthermore, we include a brief discussion of recent trends and computational concepts, incorporating Artificial Intelligence & Machine Learning (AI/ML) and deep learning approaches over the past few years to improve the qualitative and quantitative analysis of sensor measurements.
One area in which quantum-based technology is already having a significant impact is in the area of metrology and sensing. Metrology is the science of high-precision measurement. As discussed in the following sections, quantum superposition, entanglement, and squeezing allow unprecedented resolution and sensitivity in a broad range of measurements. These improvements are in part due to the reduction of disruptive effects such as turbulence and dispersion and in part due to the more rapid phase oscillations of entangled states. Applications that are discussed include sensing of gravitational fields, quantum gyroscopes, magnetoencephalography, and atomic clocks.
We present electric dipole polarizability calculations employing atomic‐orbitals based linear response theory within the Kohn‐Sham Density Functional Theory (KS‐DFT) framework, considering both non‐periodic and periodic boundary conditions. We adopt the optimization scheme introduced by T. Helgaker et al. in Chemical Physics Letters 327, 397 (2000) for the single‐electron atomic‐orbitals density matrix. We conduct a compara‐ tive analysis between the static polarizability computed using atomic orbitals‐based and previously implemented molecular orbitals‐based methods. In our calculations involving periodic boundary conditions, we implement polarizability calculation using velocity representation of the electric dipole operator in atomic orbitals‐based algorithm, subsequently comparing the results with those computed using the Berry‐phase formulation and ve‐ locity representation in molecular orbitals‐based algorithm. We investigate 10 small and large molecules in the gas phase, analyze liquid‐phase systems with up to 256 water molecules, and the solid‐state structures of anatase TiO2 and bulk WO3. All polarizability results obtained from the AO‐based solver exhibit good agreement with MO‐based results. From our example calculations, we find that the AO‐based solver exhibits better computa‐ tional scaling and less memory demand than the MO‐based solvers, which makes it better suited for very large systems.
This study introduces a waveguide design capable of generating supercontinuum spectrum and frequency combs within the mid-infrared range. The proposed structure consists of an As2Se3 core and cladding layers of MgF2 and SiO2, exhibiting two zero-dispersion wavelengths at 2100 nm and 2850 nm. Theoretical modeling and numerical simulations demonstrate the generation of a supercontinuum spanning a wavelength range of 4500 nm, from 1000 to 5500 nm, at a − 30 dB level, as well as frequency combs featuring up to 44 comb lines with a flatness of 15 dBm. The supercontinuum was generated in the maximum range of 30 dB using a 1 kW input pulse and 1 and 4 mm long waveguides. The generated frequency combs cover the wavelength range of 2073.1–2159.8 nm, making them suitable for applications such as gas sensing, industrial process monitoring, and medical diagnostics. The proposed waveguide design offers advantages over existing methods in terms of the number of comb lines, flatness, and effective area while operating in the mid-infrared region.
The advent of Beyond 5G (emerging 6G) technologies represents a significant step forward in telecommunications, offering unprecedented data speeds and connectivity. These advances enable a wide range of applications, from enhanced mobile broadband and the Internet of Things to ultra-reliable low-latency communication and the tactical Internet. Thus, having accurate and dependable time synchronization is of utmost importance and plays a critical role in ensuring that all processes function smoothly and effectively. However, existing standards, such as the precision time protocol, are unreliable due to jitters, datagram losses, and complexity. Increasing the synchronization error from the ideal tens of nanoseconds to hundreds of microseconds is unacceptable in future-generation networks. This work provides a novel way to establish ultraprecise synchronization, which is critical for the growth of converged optical communication networks and the 6G era. We investigate quantum non-linear synchronization (QNS), which explores the interaction between the non-linear dynamics of atomic systems and dissipation to establish a stable limit-cycle state. In this process, atoms confined within optical resonators are subjected to potential fields, and their spatial motion is synchronized by achieving a stable, phase-locked configuration. By introducing photons into the optical resonators and precisely managing the dissipation effects, it is possible to synchronize multiple optical resonators (referred to as nodes), even in systems with more than three interconnected resonators containing non-linear atoms. To transcend the synchronization signal from the optical setup to communication networks, we propose a distinct mechanism that utilizes the exceptional precision of QNS in the optical lattice setup and frequency down-conversion using frequency combs. In addition, it is combined with electronic components such as analog-to-digital converters and field-programmable gate arrays (FPGAs) to create synchronized digital signals that are understandable to communication networks. Our method transforms optical pulses into precisely timed electrical signals that can be analyzed and used in sophisticated network systems. We demonstrated that QNS and dissipation can synchronize a tri-node clock network to the highest precision of thulium atom-based optical lattice clocks. Our work also highlights the practicality of these applications through MATLAB simulations, bridging theoretical principles and real-world solutions with current technology. In our simulations, we utilized an optical signal with a frequency of 263 THz, downconverted to a lower microwave frequency of 100 GHz to achieve subnanosecond-level synchronized signals. The down-converted signal was subjected to white noise and subsequently digitized. The digital signal was then simulated by sampling rate of GHz or GSa/s (gigasample per second) and limiting the resolution to bits. Finally, high-frequency noise was removed by implementing low-pass filtration using FPGAs. This study takes an essential step toward meeting the rising demands for rapid and efficient data transfer in the ever-evolving digital communications landscape, enabling faster and more reliable connectivity for future communication networks and the quantum Internet.
Automatic mode-locking techniques, the integration of intelligent technologies with nonlinear optics offers the promise of on-demand intelligent control, potentially overcoming the inherent limitations of traditional ultrafast pulse generation that have predominantly suffered from the instability and suboptimality of open-loop manual tuning. The advancements in intelligent algorithm-driven automatic mode-locking techniques primarily are explored in this review, which also revisits the fundamental principles of nonlinear optical absorption, and examines the evolution and categorization of conventional mode-locking techniques. The convergence of ultrafast pulse nonlinear interactions with intelligent technologies has intricately expanded the scope of ultrafast photonics, unveiling considerable potential for innovation and catalyzing new waves of research breakthroughs in ultrafast photonics and nonlinear optics characters.
Ultrafast optical frequency combs allow for both high spectral and temporal resolution in molecular spectroscopy and have become a powerful tool in many areas of chemistry and physics. Ultrafast lasers and frequency combs generated from ultrafast mode-locked lasers often need to be converted to other wavelengths. Commonly used wavelength conversions are optical parametric oscillators, which require an external optical cavity, and supercontinuum generation combined with optical parametric amplifiers. Whether commercial or home-built, these systems are complex and costly. Here, we investigate an alternative, simple, and easy-to-implement approach to tunable frequency comb ultrafast lasers enabled by new continuous-wave laser technology. Sum-frequency generation between an Nd:YAG continuous-wave laser and a Yb:fiber femtosecond frequency comb in a beta-barium borate (BBO) crystal is explored. The resulting sum-frequency beam is a pulsed frequency comb with the same repetition rate as the Yb:fiber source. SNLO simulation software is used to simulate the results and provide benchmarks for designing future systems to achieve wavelength conversion and tunability in otherwise difficult-to-reach spectral regions.
We have performed a pure optical frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, R∞ = 109737.31568516(84)cm-1 (relative uncertainty of 7.7×10-12) and for the 1S and 2S Lamb shifts L1S = 8172.837(22)MHz and L2S-2P = 1057.8446(29)MHz [respectively, L1S = 8183.966(22)MHz, and L2S-2P = 1059.2337(29)MHz for deuterium]. These are now the most accurate values available.
Spectra extending from 600 to 1200 nm have been generated from a Kerr-lens mode-locked Ti:sapphire laser producing 5-fs pulses. Specially designed double-chirped mirror pairs provide broadband controlled dispersion, and a second intracavity focus in a glass plate provides additional spectral broadening. These spectra are to our knowledge the broadest ever generated directly from a laser oscillator.
We have measured the absolute frequency of the hydrogen 1S{endash}2S two-photon resonance with an accuracy of 3.4 parts in 10{sup 13} by comparing it with the 28th harmonic of a methane-stabilized 3.39 {mu}m He-Ne laser. A frequency mismatch of 2.1 THz at the 7th harmonic is bridged with a phase-locked chain of five optical frequency interval dividers. From the measured frequency f{sub 1S{endash}2S}=2466061413187.34(84) kHz and published data of other authors we derive precise new values of the Rydberg constant, R{sub {infinity}}=10973731.568639(91) m{sup {minus}1} and of the Lamb shift of the 1S ground state, L{sub 1S}=8172.876(29) MHz. These are now the most accurate values available. {copyright} {ital 1997} {ital The American Physical Society}
This work examines the current status of research on optical frequency standards based upon single trapped ions. Methods for
the containment and laser cooling of such single-ion samples are briefly discussed. Detection of ultra-narrow reference transitions
via the observation of quantum jumps is outlined, together with the progress in the development of laser sources to provide
cooling, detection and probing for such standards. A brief discussion on methods employed to date on stabilization to single-ion
transition resonances is given, together with a summary of some of the principal sources for systematic shifts in such systems.
Progress in the investigation of Ba+, Sr+, Ca+, Hg+, Yb+, and In+ single-ion reference transitions is given. The work concludes with an overview of the progress in the measurement of single-ion
referenced optical frequency relative to the Cs realization of the SI second and other reference standards.
Summary form only given. The key feature of the microstructured fibre is the large index step between core (silica) and cladding (mostly air). This permits confinement in a very small core and hence (a) high intensity for a given power (or pulse energy), and (b) zero or anomalous dispersion at the pump wavelength, despite the strong normal dispersion of bulk silica. The disadvantage is the need for the special fibre with its tiny core. Having obtained fibre (perhaps at some expense), the user finds input coupling problematic and sensitive to mechanical instabilities, with high intensities that can degrade the endfaces. A large index step is also found in conventional telecoms fibre tapered (heated and stretched) to a narrow uniform waist ∼2 μm in diameter and several cm long. Tapering need not increase the loss by more than 0.1 dB. As a waveguide, the waist is like the core of the microstructured fibre - a thread of glass surrounded by air - and we found that such a structure similarly broadened fs pulses from a Ti:sapphire laser to a two-octave supercontinuum. The output was in the fundamental mode even where the fibre itself was multimode.
The shortest pulses periodically emitted directly from a mode-locked Ti:sapphire laser are approaching the two-optical-cycle range. In this region, the phase of the optical carrier with respect to the pulse envelope becomes important in nonlinear optical processes such as high-harmonic generation. Because there are no locking mechanisms between envelope and carrier inside a laser, their relative phase offset experiences random fluctuations. Here, we propose several novel methods to measure and to stabilize this carrier-envelope offset (CEO) phase with sub-femtosecond uncertainty. The stabilization methods are an important prerequisite for attosecond pulse generation schemes. Short and highly periodic pulses of a two-cycle laser correspond to an extremely wide frequency comb of equally spaced lines, which can be used for absolute frequency measurements. Using the proposed phase-measurement methods, it will be possible to phase-coherently link any unknown optical frequency within the comb spectrum to a primary microwave standard. Experimental studies using a sub-6-fs Ti:sapphire laser suggesting the feasibility of carrier-envelope phase control are presented.
We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools
of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal
cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which we used to perform
absolute optical frequency measurements that were directly referenced to a stable microwave clock.
The 88Sr+ frequency standard is one of several promising optical quantum oscillators that have the potential to surpass the accuracy and stability of the best atomic clocks. In this article we review the present state of our 88Sr+ frequency standard, and the changes planned to improve on it.
An optical frequency chain referenced to a Cs atomic clock has been used to measure directly the frequency of the electric quadrupole allowed 5s(2)S(1/2) - 4d(2)D(5/2) transition at 445 TI-Iz in a single, trapped, and laser cooled Sr-88(+) ion. A transition frequency, f(S-D) = 444779044095.4 kHz with an estimated standard uncertainty of 0.2 kHz has been determined. Intrinsic offsets of the probed ion transition in the current experiment are calculated to be at the 10(-15) level. [S0031-9007(99)08942-5].
Using an iodine-stabilized He-Ne laser as a transfer oscillator, we compare absolute measurements of the optical frequency from a traditional frequency synthesis chain based on harmonic generation and from the frequency division technique of an ultrawide bandwidth femtosecond frequency comb. The agreement between these two measurements, both linked to the Cs standard, is 220+/-770 Hz, yielding a measurement accuracy of 1.6x10(-12). We report 473 612 353 604.8+/-1.2 kHz as a preliminary updated value of the absolute frequency of the " f" component for the He-Ne laser international standard at 633 nm.
We have performed a pure optical frequency measurement of the 2S-12D
two-photon transitions in atomic hydrogen and deuterium. From a complete
analysis taking into account this result and all other precise
measurements (by ourselves and other authors), we deduce optimized
values for the Rydberg constant, R∞ = 109 737.315 685
1684 cm-1 (relative uncertainty of
7.7×10-12) and for the 1S and 2S Lamb shifts
L1S = 8172.83722 MHz and L2S-2P =
1057.844629 MHz [respectively, L1S = 8183.96622 MHz,
and L2S-2P = 1059.233729 MHz for deuterium]. These are
now the most accurate values available.
Absolute frequency measurements of a transportable optical frequency standard based on a He-Ne/CH4 laser at lambda = 3.39 mum stabilized on the central 7-6 component of the hyperfine structure of the F2(2) methane absorption line were made. For the first time, two different phase-coherent frequency chains based on the femtosecond comb technology and a transportable cesium fountain clock were used in the experiment.
We explore and demonstrate the feasibility of an optical-frequency-to-radio-frequency division method that is based on visible or near-infrared laser oscillators only. Comparing harmonic and sum frequencies, we generate the arithmetic average of two visible frequencies. Cascading n stages provides difference-frequency division by 2 ⁿ . For a demonstration we have phase locked the second harmonic and the sum frequency of two independent diode lasers.
We demonstrate a great simplification in the long-standing problem of measuring optical frequencies in terms of the cesium primary standard. An air-silica microstructure optical fiber broadens the frequency comb of a femtosecond laser to span the optical octave from 1064 to 532 nm, enabling us to measure the 282 THz frequency of an iodine-stabilized Nd:YAG laser directly in terms of the microwave frequency that controls the comb spacing. Additional measurements of established optical frequencies at 633 and 778 nm using the same femtosecond comb confirm the accepted uncertainties for these standards.
We describe the results of a search for time variability of the fine structure constant alpha using absorption systems in the spectra of distant quasars. Three large optical data sets and two 21 cm and mm absorption systems provide four independent samples, spanning approximately 23% to 87% of the age of the universe. Each sample yields a smaller alpha in the past and the optical sample shows a 4 sigma deviation: Delta alpha/alpha = -0.72+/-0.18 x 10(-5) over the redshift range 0.5<z<3.5. We find no systematic effects which can explain our results. The only potentially significant systematic effects push Delta alpha/alpha towards positive values; i.e., our results would become more significant were we to correct for them.
Two octave-spanning optical-frequency combs (750-MHz comb spacing) are phase locked to a common continuous-wave laser diode. The measured instability of the heterodyne beat between the two combs demonstrates that the intrinsic fractional frequency noise of a comb is ≤ 6.3 × 10 - 16 in 1 s of averaging across the ∼ 300 ‐ THz bandwidth. Furthermore, the average frequencies of the elements of the two combs are found to agree within an uncertainty of 4 × 10 - 17 across the entire octave. We demonstrate the possibility of transfering the stability and accuracy of the best current optical standards to ∼ 500,000 individual oscillators across the visible and near-infrared spectrum.
We demonstrate experimentally for what is to our knowledge the first time that air–silica microstructure optical fibers can exhibit anomalous dispersion at visible wavelengths. We exploit this feature to generate an optical continuum 550 THz in width, extending from the violet to the infrared, by propagating pulses of 100-fs duration and kilowatt peak powers through a microstructure fiber near the zero-dispersion wavelength.
The absolute frequency of the In + 5 s 2 S 1 0 – 5 s 5 p P 3 0 clock transition at 237 nm was measured with an accuracy of 1.8 parts in 10 13 . Using a phase-coherent frequency chain, we compared the S 1 0 – P 3 0 transition with a methane-stabilized He–Ne laser at 3.39 µ m , which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the He–Ne standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In + clock transition was found to be 1 267 402 452 899.92 (0.23) kHz, the accuracy being limited by the uncertainty of the He–Ne laser reference. This result represents an improvement in accuracy of more than 2 orders of magnitude over previous measurements of the line and now stands as what is to our knowledge the most accurate measurement of an optical transition in a single ion.s
We have performed a pure optical frequency measurement of the 2S-12D two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, R∞ = 109 737.315 685 16(84) cm-1 (relative uncertainty of 7.7 × 10-12) and for the 1S and 2S Lamb shifts L1S = 8172.837(22) MHz and L2S-2P = 1057.8446(29) MHz [respectively, L1S = 8183.966(22) MHz, and L2S-2P = 1059.2337(29) MHz for deuterium]. These are now the most accurate values available.
This paper reports absolute frequency measurements of trapped ion and HeNe/I2 systems using the NPL femtosecond comb. Two transition frequencies in laser-cooled single trapped ions have been measured: the 88Sr+ 5s 2S1/2 - 4d 2D5/2 electric quadrupole transition at 674 nm and the 171Yb+ 4f146s 2S1/2 (F = 0) - 4f136s2 2F7/2 (F = 3) electric octupole transition at 467 nm. In addition, the frequency of the helium-neon laser NPL-S stabilised to four hyperfine components of the 127I2 11-5 R(127) line at 633 nm has been measured.
Using an atom interferometer method based on adiabatic transfer between atomic states, we measure the recoil velocity of cesium due to the coherent scattering of a photon. The value of h/MCs is used to obtain a preliminary new value for the fine structure constant. The current experimental uncertainty in alpha is 7.4 ppb.
© 2003 Optical Society of America
We have demonstrated the feasibility of Doppler-free two-photon spectroscopy with a train of picosecond standing-wave light pulses from a synchronously pumped mode-locked cw dye laser. The actively controlled mode spectrum provides a means for accurate measurements of large frequency intervals. From a multipulse spectrum of the sodium 3s-4d transition we have determined a new value of the 4d fine-structure splitting, 1028±0.4 MHz.
Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years, nding widespread use in basic scienti c studies, communications, and navigation. However, with its higher operating frequency, an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced to the 1.064-petahertz transition of a single trapped,Hg, ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional frequency instability of 7 3 10, is measured in 1 second of averaging a value substantially better than that of the world s best microwave atomic clocks.
In this paper, we address two aspects of this general problem. First, we discuss the problem of frequency standards in the optical spectrum. analogue in the microwave region of the spectrum is the cesium beam frequency standard.) If one or a few of these reference frequencies can be accurately calibrated (perhaps by a frequency synthesis chain1) then it may be possible to compare optical spectra to these standards. precision that might be achieved, we discuss only optical standards based on stored ions. Second, we discuss the problem of frequency comparison of unknown frequencies to the standards. to generation of wideband frequency "combs". (An
The hydrogen atom continues to hold fascinating challenges for spectroscopists. As the simplest of the stable atoms it has long permitted unique confrontations between basic theory and experiment. Very large further improvements in spectral resolution and accuracy appear feasible with the help of emerging new methods for stabilizing and measuring optical frequencies, together with advanced laser techniques for preparing, slowing, and manipulating atoms. Such prospects make more accurate quantum electrodynamic computations of hydrogen levels highly desirable. If theory is correct, measurements and comparisons of transition frequencies in hydrogen will yield precise new values of fundamental constants, in particular the Rydberg constant, the electron mass, and the charge radius of the proton. It would be much more exciting, of course, if we found out that theory fails at some level of scrutiny.
We have used a single laser femtosecond optical frequency synthesizer together with a widely tunable Nd:YAG laser to measure
the absolute frequency of several absorption lines in molecular iodine around 532nm. The use of two different repetition
frequencies allows us to determine the number of modes used for the frequency measurement unambiguously. The lines also provide
data for the determination of improved ro-vibrational constants of the iodine molecule.
The synchronization of atomic quantum transitions with natural Raman oscillations by ultrashort light pulses has been investigated. This phenomenon may be observed if the duration of the perturbation pulse is less than the period of oscillations of the forbidden atomic transitions. The accuracy of the direct measurements of the quantum transition times for trapped particles can be of the same order as the ratio of the two-photon transition frequency to the homogeneous line width.
We have demonstrated the feasibility of Doppler-free polarization spectroscopy with a train of ultrashort pulses from a synchronously
pumped mode-locked dye laser. The sensitivity of the method is compared with saturation spectroscopy with a single-mode laser.
We have investigated the detailed operation of a frequency modulated dye laser (FML). The FML consists of a standing wave Rh6G dye laser with an intracavity transverse ADP phase modulator which is driven at a frequency close to the cavity mode spacing. An ideal FML output consists of a laser beam which is constant in amplitude but sinusoidally varying in frequency. This provides a source of many laser modes which are equally spaced by the modulation frequency. Several dye laser configurations have been investigated. Measurements of the mode intensities, total power, amplitude modulation and rf beat amplitudes have been made as a function of the rf driving frequency of the phase modulator. The FM laser obtained has been frequency stabilised by locking it to a reference interferometer and also by frequency offset locking it to a single-frequency dye laser.
We have used the comb of optical frequencies emitted by a mode-locked laser as a ruler to measure frequency differences of
up to 45.2 THz between two laser signals. We have shown that the modes are distributed uniformly in frequency space within
the experimental limit of 3.0 parts in 1017, and that the mode separation equals the pulse repetition rate within an experimental limit of 6.0 parts in 1016. We have used this comb to bridge a frequency mismatch of 18.4 THz for an absolute optical frequency measurement of the cesium
D
1 line at 335 THz (895 nm) by comparison with the fourth harmonic of a methane-stabilized He-Ne Laser at 88.4THz (3.39 m).
Bridging a frequency gap of 45.2THz, we could demonstrate for the first time a new type of frequency chain that is based on
the measurement of frequency differences between laser harmonics. With this type of apparatus we have also measured the absolute
frequency of the hydrogen 1S 2S transition at 2466 THz (121 nm) in a direct comparison with the output signal from a commercial cesium atomic clock.
The current status and prospects of optical frequency standards based on neutral atomic and molecular absorbers are reviewed.
Special attention is given to an optical frequency standard based on cold Ca atoms which are interrogated with a pulsed excitation
scheme leading to resolved line structures with a quality factor Q τ; 1012. The optical frequency was measured by comparison with PTB’s primary clock to be νCa = 455 986 240 494.13 kHz with a total relative uncertainty of 2.5 × 10−13. After a recent recommendation of the International Committee of Weights and Measures (CIPM), this frequency standard now
represents one of the most accurate realizations of the length unit.
The frequencies of three lasers stabilized to molecular absorptions were measured with an infrared‐frequency synthesis chain extending upwards from the cesium frequency standard. The measured values are 29.442 483 315 (25) THz for the 10.18‐μm R(30) transition in CO 2 , 32.134 266 891 (24) THz for the 9.33‐μm R(10) transition in CO 2 , and 88.376 181 627 (50) THz for the 3.39‐μm P(7) transition in CH 4 . The frequency of methane, when multiplied by the measured wavelength reported in the following letter, yields 299 792 456.2(1.1) m/sec for the speed of light.
A frequency comparison and an absolute frequency measurement of iodine stabilized frequency-doubled Nd:YAG lasers at 532 nm has been performed at the Max-Planck-Institute for Quantum Optics. Two independent I2-stabilized laser systems, one assembled at the Institute of Laser Physics, Novosibirsk, Russia, the other at the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany were investigated. Using a phase-coherent frequency chain, the absolute frequency of the I2-stabilized lasers has been compared to a CH4-stabilized He–Ne laser at 3.39 μm which has been calibrated against an atomic cesium fountain clock. A new value for the R(56)32-0:a10 component, recommended by the Comit International des Poids et Mesures for the realization of the meter [Metrologia 30 (1993/1994) 523; Metrologia 36 (1999) 211], has been obtained with reduced uncertainty. Improved absolute frequency values of the R(56)32-0 and P(54)32-0 iodine absorption lines together with the hyperfine line separations are presented.
We have stabilized the modes of a comb of optical frequencies emitted by a mode-locked femtosecond-laser and used it as a ruler to measure differences of up to 45.2 THz between laser frequencies in a new type of frequency chain. Directly converting optical to radio frequencies, we have used it for an absolute frequency measurement of the 1S–2S transition in the hydrogen atom. Here, an intuitive model of the comb's properties is given and essential techniques for its stabilization and efficient detection of beat signals are presented.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A critical examination of dispersion theory indicates that a measurement of the refractive index of atomic hydrogen is important for the theory of matter. Such an experiment is fully described and discussed. The result is that [...]. Incidentally it is found that a partial pressure of half a millimeter of atomic hydrogen can be had in a discharge tube while the discharge is on. Thermal conditions in such tubes are discussed and investigated. The experimental result is at first sight not in support of the new quantum mechanics which requires [...]. However, by assuming that [...] is connected with volume, in the kinetic theory sense it turns out that the expectation from the theory is effectively [...]. This leads support to the physical reality of the quantity [...] and leads to a prediction of an increase in refractivity at very low pressures for almost any gas. Pictures are given of the normal hydrogen atom and also its excited states and of the configuration under the action of a light waves
Submitted to the Department of Physics. Copyright by the author. Thesis (Ph. D.)--Stanford University, 2002.
The results of a test of general relativity with use of a hydrogen-maser frequency standard in a spacecraft launched nearly vertically upward to 10,000 km are reported. The agreement of the observed relativistic frequency shift with prediction is at the 70 x 10 to the -6th level.
We have determined the frequency of the - intercombination transition of atomic stored in a magneto-optical trap to be \nu with an estimated standard uncertainty of (\delta\nu\nu{}<{10}^{-{}12}) using a phase-coherent optical frequency chain from the Cs atomic clock to the visible. This allows the realization of the SI-unit meter according to its definition by visible radiation with 25-fold reduced uncertainty compared to previous measurements.
We have used the frequency comb generated by a femtosecond mode-locked laser and broadened to more than an optical octave in a photonic crystal fiber to realize a frequency chain that links a 10 MHz radio frequency reference phase-coherently in one step to the optical region. By comparison with a similar frequency chain we set an upper limit for the uncertainty of this new approach to 5. 1x10(-16). This opens the door for measurement and synthesis of virtually any optical frequency and is ready to revolutionize frequency metrology.
Using a coherent nonlinear optical technique, slipping of the carrier through the envelope of 6-fs light wave packets emitted from a mode-locked-oscillator/pulse-compressor system has been measured, permitting the generation of intense, few-cycle light with precisely reproducible electric and magnetic fields. These pulses open the way to controlling the evolution of strong-field interactions on the time scale of the light oscillation cycle and are indispensable to reproducible attosecond x-ray pulse generation.
We report on an absolute frequency measurement of the hydrogen 1S-2S two-photon transition in a cold atomic beam with an accuracy of 1.8 parts in 10(14). Our experimental result of 2 466 061 413 187 103(46) Hz has been obtained by phase coherent comparison of the hydrogen transition frequency with an atomic cesium fountain clock. Both frequencies are linked with a comb of laser frequencies emitted by a mode locked laser.
We demonstrate a versatile new technique that provides a phase coherent link between optical frequencies and the radio frequency domain. The regularly spaced comb of modes of a mode-locked femtosecond laser is used as a precise ruler to measure a large frequency gap between two different multiples (harmonics or subharmonics) of a laser frequency. In this way, we have determined a new value of the hydrogen 1S-2S two-photon resonance, f(1S-2S) = 2 466 061 413 187.29(37) kHz, representing now the most accurate measurement of an optical frequency.
Single soft-x-ray pulses of ∼90–electron volt (eV) photon energy are produced by high-order harmonic generation with 7-femtosecond
(fs), 770-nanometer (1.6 eV) laser pulses and are characterized by photoionizing krypton in the presence of the driver laser
pulse. By detecting photoelectrons ejected perpendicularly to the laser polarization, broadening of the photoelectron spectrum
due to absorption and emission of laser photons is suppressed, permitting the observation of a laser-induced downshift of
the energy spectrum with sub-laser-cycle resolution in a cross correlation measurement. We measure isolated x-ray pulses of
1.8 (+0.7/−1.2) fs in duration, which are shorter than the oscillation cycle of the driving laser light (2.6 fs). Our techniques
for generation and measurement offer sub-femtosecond resolution over a wide range of x-ray wavelengths, paving the way to
experimental attosecond science. Tracing atomic processes evolving faster than the exciting light field is within reach.
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. 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 these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).
Microwave atomic clocks have been the de facto standards for precision time and frequency metrology over the past 50 years,
finding widespread use in basic scientific studies, communications, and navigation. However, with its higher operating frequency,
an atomic clock based on an optical transition can be much more stable. We demonstrate an all-optical atomic clock referenced
to the 1.064-petahertz transition of a single trapped199Hg+ ion. A clockwork based on a mode-locked femtosecond laser provides output pulses at a 1-gigahertz rate that are phase-coherently
locked to the optical frequency. By comparison to a laser-cooled calcium optical standard, an upper limit for the fractional
frequency instability of 7 × 10−15 is measured in 1 second of averaging—a value substantially better than that of the world's best microwave atomic clocks.
Currently, the shortest laser pulses that can be generated in the visible spectrum consist of fewer than two optical cycles (measured at the full-width at half-maximum of the pulse's envelope). The time variation of the electric field in such a pulse depends on the phase of the carrier frequency with respect to the envelope-the absolute phase. Because intense laser-matter interactions generally depend on the electric field of the pulse, the absolute phase is important for a number of nonlinear processes. But clear evidence of absolute-phase effects has yet to be detected experimentally, largely because of the difficulty of stabilizing the absolute phase in powerful laser pulses. Here we use a technique that does not require phase stabilization to demonstrate experimentally the influence of the absolute phase of a short laser pulse on the emission of photoelectrons. Atoms are ionized by a short laser pulse, and the photoelectrons are recorded with two opposing detectors in a plane perpendicular to the laser beam. We detect an anticorrelation in the shot-to-shot analysis of the electron yield.