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Comparison between the current TO result (blue trace), the previous lowest phase noise TO result (connected orange dots).⁴¹
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Coherent frequency division of high-stability optical sources permits the extraction of microwave signals with ultra-low phase noise, enabling their application to systems with stringent timing precision. To date, the highest performance systems have required tight phase stabilization of laboratory grade optical frequency combs to Fabry–Pérot optic...
Citations
... 一种是通过反馈控制光梳重复频率 frep 来稳定光梳的一条特定谱线到光学参考 [55,56] , 而光 梳载波包络频率 fceo 被锁定到微波频率参考, 因此 frep 可以作为种子源, 通过使用如直接数字合成器(DDS) 的下变频产生时钟频率. 另一种是传递振荡器技术 [57,58] , 即基于合理的混频, 滤波和分频以免疫光梳噪 声的影响, 再通过电学网络可将光频率转换为具有 超高同步性的微波频率. Page 8 of 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 其中∆qi(t)表征激光频率和时钟频率间的同源水平, 该噪声在空间引力波探测科学频段内已被实验证明 是非常小的 [60] , 因此本文分析中将忽略这一项的影 响. 基于式 (19), 式(7-8)所示的六个组合数据流可被 重写为: (20) 从上式可见, 在光梳连接的情况下, 时钟噪声可被等 效地转换为激光频率噪声, 因此只需利用光梳 TDI 算法抑制该等效的激光频率噪声即可 [25,26] . ...
... 相较于 先 抑 制 激 光 频 率 噪 声 后 抑 制 时 钟 噪 声 的 时 钟 比 对 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 [33] , 开展光梳 TDI 实验验证. 传递振荡器的 优点是不需要将光梳锁定在信号激光中, 并且可以 通过设计电学配置来免疫光梳噪声 [57,58] . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 In space-borne gravitational wave detection, each satellite is required to carry an Ultra Stable Oscillator (USO) as a timing reference to drive the Analog-to-Digital Converter (ADC) for digital sampling of signals. High-precision clock timing is crucial for achieving the required sensitivity in gravitational wave detection. ...
... [3][4][5][6] The development of broad and stable combs has led to their integration in various fields, notably playing vital roles in the establishment of ultra-stable frequency references for metrology applications, high-capacity coherent telecommunication, and highprecision spectroscopy. [7][8][9][10] While extensive research efforts have been made to realize various types of optical frequency combs, the development of novel noise characterization techniques has not followed a similar trend. ...
Performing noise characterizations of lasers and optical frequency combs on sampled data offers numerous advantages compared to analog measurement techniques. One of the main advantages is that the measurement setup is greatly simplified. Only a balanced detector followed by an analog-to-digital converter is needed, allowing all the complexity to be moved to the digital domain. Secondly, near-optimal phase estimators are efficiently implementable, providing accurate phase noise estimation in the presence of measurement noise. Finally, joint processing of multiple comb lines is feasible, enabling the computation of the phase noise correlation matrix, which includes all information about the phase noise of the optical frequency comb. This tutorial introduces a framework based on digital signal processing for phase noise characterization of lasers and optical frequency combs. The framework is based on the extended Kalman filter (EKF) and automatic differentiation. The EKF is a near-optimal estimator of the optical phase in the presence of measurement noise, making it very suitable for phase noise measurements. Automatic differentiation is key to efficiently optimizing many parameters entering the EKF framework. More specifically, the combination of EKF and automatic differentiation enables the efficient optimization of phase noise measurement for optical frequency combs with arbitrarily complex noise dynamics that may include many free parameters. We show the framework’s efficacy through simulations and experimental data, showcasing its application across various comb types and in dual-comb measurements, highlighting its accuracy and versatility. Finally, we discuss its capability for digital phase noise compensation, which is highly relevant to free-running dual-comb spectroscopy applications.
... Over the past two decades, the field of optical frequency combs has witnessed significant advancements, leading to the development of various types of frequency combs with distinct characteristics and applications [3][4][5][6] . The development of broad and stable combs has led to their integration in various fields, notably playing vital roles in the establishment of ultra-stable frequency references for metrology applications, high-capacity coherent telecommunication, and high-precision spectroscopy [7][8][9][10] . ...
Performing noise characterizations of lasers and optical frequency combs on sampled and digitized data offers numerous advantages compared to analog measurement techniques. One of the main advantages is that the measurement setup is greatly simplified. Only a balanced detector followed by an analog-to-digital converter is needed, allowing all the complexity to be moved to the digital domain. Secondly, near-optimal phase estimators are efficiently implementable, providing accurate phase noise estimation in the presence of the measurement noise. Finally, joint processing of multiple comb lines is feasible, enabling computation of phase noise correlation matrix, which includes all information about the phase noise of the optical frequency comb. This tutorial introduces a framework based on digital signal processing for phase noise characterization of lasers and optical frequency combs. The framework is based on the extended Kalman filter (EKF) and automatic differentiation. The EKF is a near-optimal estimator of the optical phase in the presence of measurement noise, making it very suitable for phase noise measurements. Automatic differentiation is key to efficiently optimizing many parameters entering the EKF framework. More specifically, the combination of EKF and automatic differentiation enables the efficient optimization of phase noise measurement for optical frequency combs with arbitrarily complex noise dynamics that may include many free parameters. We show the framework's efficacy through simulations and experimental data, showcasing its application across various comb types and in dual-comb measurements, highlighting its accuracy and versatility. Finally, we discuss its capability for digital phase noise compensation, which is highly relevant to free-running dual-comb spectroscopy applications.
... The generation of low-phase-noise microwaves from optics has found great interest and extensive use in applications such as high-performance Doppler radar systems [1], communications [2], low-timing jitter analog-digital conversion [3], and time and frequency metrology [4,5]. Additionally, low-noise microwaves carried by an optical beam are required in vapor cell atomic clocks based on coherent population trapping (CPT) [6] because the phase noise of the microwave field that interrogates the atoms can limit the clock's short-term stability [7]. ...
... Therefore, moving such systems outside metrological labs is a challenge [10,11]. Simpler and compact systems have been proposed [12], relying on the use of a free-running monolithic femtosecond laser [13], or on the transfer oscillator technique [5,14], possibly coupled with soliton-microcombs [15,16]. ...
We characterize the phase noise of a microwave photonic channel, where a 10 GHz signal is carried by an intensity-modulated light beam over a short optical fiber, and detected. Two options are compared: (i) an electro-optic modulator (EOM), and (ii) the direct modulation of the laser current. The 1.55 µm laser and the detector are the same. The effect of experimental parameters is investigated, the main being the microwave power and the laser bias current. The main result is that the upper bound of the phase flicker is − 117 dBrad 2 in the case of the EOM, limited by the background noise of the setup. In contrast, with direct modulation of the laser, the flicker is of − 114 to − 100 dBrad 2 , depending on the laser bias current (50–90 mA), and the highest noise occurs at the lowest bias. Our results are of interest in communications, radar systems, instrumentation, and metrology.
... Moreover, if ultra-stable signals generated using optical clocks, optical frequency combs [9], or ultra-low noise ovencontrolled crystal oscillators are measured, the instrument noise-floor is often a limitation near or far from the carrier. In this case, more advanced techniques such as crosscorrelation or carrier-suppression must be used to overcome the measurement system single-channel performance. ...
In this paper, we present a direct digital measurement system capable of simultaneously measuring phase noise, amplitude noise, and Allan deviation with and without cross-correlation. The residual phase noise of the single-channel system achieves
L
(1 Hz) = −143 dBc/Hz for a 10 MHz input signal and an Allan deviation noise floor of 3.2 × 10
−15
at 1 second averaging time (τ). The system’s performance improves as expected with cross-correlation, resulting in an average-limited residual white noise floor of −185 dBc/Hz after only a few minutes of averaging, an improvement of 30 dB compared to a single-channel system. It also reaches an average limited flicker phase noise floor of
L
(1 Hz) = −160 dBc/Hz within two days, with an Allan deviation of 5 × 10
−16
@ τ = 1 second. To our knowledge, this represents the lowest noise performance ever reported for a digital measurement system. Our solution is based on a pair of high-performance analog-to-digital converters and a single system-on-achip (SoC) with multiple processors and a field programmable gate array (FPGA). The architecture allows for processing all data samples in real-time without dead-time between calculation frames, enabling the fastest averaging possible during cross-correlation.
... L'oscillateur optoélectronique est une hybridation des oscillateurs électroniques micro-ondes avec l'optique, que nous présentons dans la prochaine section. Par ailleurs, il existe plusieurs autres moyens d'utiliser l'optique pour générer des signaux micro-ondes spectralement purs, par exemple la division de fréquence optique [30,31] ou le mélange hétérodyne [32]. ...
La génération de signaux micro-ondes de grande pureté spectrale est un enjeu majeur dans différentes applications telles que les télécommunications et les technologies RADAR. L'oscillateur optoélectronique utilise la fibre optique pour implémenter un retard dans sa boucle de rétroaction, ce qui permet d'atteindre de meilleurs bruits de phase que les synthétiseurs de fréquences électroniques. Dans ce travail de thèse, nous étudions une architecture particulière qui utilise le courant d'alimentation d'un laser comme support de rétroaction. Nous avons ainsi pu obtenir un signal stable et monomode à 10 GHz dont le bruit de phase était de -135 dBc/Hz à 10 kHz de la porteuse. Dans un deuxième temps, nous avons implémenté une compression d'impulsion en tirant parti d'une propagation non-linéaire dans la fibre optique. Nous avons pu générer des impulsions de quelques picosecondes présentant une faible gigue temporelle sans dégrader le bruit de phase. Nous avons modélisé le bruit de phase du système et la propagation non-linéaire dans la fibre. Afin de prendre également en compte la dynamique du laser, nous avons dû mesurer le facteur de Henry. Nous y sommes parvenus en développant une nouvelle technique de mesure qui est simple et reproductible et qui a permis d'atteindre des précisions de 3%.
... 47 Similarly, an ultra-low phase noise microwave can be generated via the transfer oscillator scheme based on the same OFC. 48 No matter which configuration is used, the beating signals between cw lasers and their nearby comb lines with high SNRs are requisite. In order to obtain several beating signals between optical atomic clocks and the comb with an optimized SNR, we employ two PCFs, as shown in Fig. 1(a). ...
Recent advances in optical frequency standards and optical frequency combs (OFCs) have drawn wide attention since by transforming other quantities into frequency metrology, a higher measurement sensitivity or accuracy can be achieved. Among them, the search for dark matter, tests of relativity, and detection of gravitational wave anticipate even more precise frequency ratio measurement of optical signals, which challenges the state-of-the-art optical frequency standards and OFCs. Here, we report an optical frequency divider (OFD) based on a Ti:sapphire mode-locked laser, which can realize ultraprecise optical frequency ratio measurements and optical frequency division to other desired frequencies. The OFD is based on an OFC frequency-stabilized to a hydrogen maser, whose frequency noise in optical frequency division is subtracted via the transfer oscillator scheme. An optically referenced radio frequency time-base is introduced for the fine-tuning of the divisor and the reduction in division noise. Using the OFD, the frequency ratio between the fundamental and its second harmonic of a 1064 nm laser is measured with a fractional uncertainty of 3 × 10−22, nearly five times better than previous results. Meanwhile, we also report the ability to transport between laboratories, the long-term operation, and the multi-channel division of the OFD.
... The parameters of the transfer oscillator is listed in Table 1. In fact, transfer oscillator has been often used in the low-noise microwave generation [19] and the comparison between optical clocks [20]. In this work, we actually do not focus on the absolute stability of the generated microwave. ...
... The microresonator combs [24] with compact device footprints and low power consumption could provide the solution to this problem in future. The technique of the transfer oscillator has been widely used in low-noise microwave generation [5,17,19], the optical frequency synthesizer [3], and the optical clock comparison [20]. Taking into account the practical operation in space and considering the equipment size, weight, and power consumption, our work indicates that the rubidium frequency standard for the frequency comb is sufficient to realize the high-fidelity transfer from optical frequencies to the microwave frequency. ...
In this work, we experimentally perform time delay interferometry by using a transfer oscillator, which is capable of reducing the laser frequency noise and the clock noise simultaneously in the post processing. The iodine frequency reference is coherently downconverted to the microwave frequency using a laser frequency comb. The residual noise of the downconversion network is 5 × 10⁻⁶Hz/Hz1/2 at 0.7 mHz, and 4 × 10⁻⁶Hz/Hz1/2 at 0.1 Hz, indicating high homology between the optical frequency and the microwave frequency. We carry out time delay interferometry with the aid of the electrical delay module, which can introduce large time delays. The results show that the laser frequency noise and the clock noise can be reduced simultaneously by ten and three orders of magnitude, respectively, in the frequency band from 0.1 mHz to 0.1 Hz. The performance of the noise reduction can reach 6 × 10⁻⁸Hz/Hz1/2 at 0.1 mHz, and 7 × 10⁻⁷Hz/Hz1/2 at 1 mHz, meeting the requirements of the space-borne gravitational wave detection. Our work will be able to offer an alternative method for the frequency comb-based time delay interferometry in the future space-borne gravitational wave detectors.
... The purest microwave signals have been achieved by frequency-dividing the optical wave of ultra-narrow linewidth cavity-stabilized lasers to the microwave domain using optical frequency combs [18][19][20]. The best systems offer microwave signals with phase noise levels of −103 and −180 dBrad 2 /Hz at 1 Hz and 100 kHz offset frequencies, respectively [18][19][20][21]. Substantial effort has also been made toward the use of the transfer oscillator technique [21,22], the use of monolithic free-running combs [23], and the development of chip-scale microresonator combs [24,25]. ...
... The best systems offer microwave signals with phase noise levels of −103 and −180 dBrad 2 /Hz at 1 Hz and 100 kHz offset frequencies, respectively [18][19][20][21]. Substantial effort has also been made toward the use of the transfer oscillator technique [21,22], the use of monolithic free-running combs [23], and the development of chip-scale microresonator combs [24,25]. ...
The generation and transfer of ultra-stable microwave signals are of paramount importance in numerous applications spanning from radar systems to communications and metrology. We demonstrate residual phase noise mitigation at 10 GHz of a directly modulated laser system through active control of the laser bias current. The latter is tuned to a finely selected point, where the current-to-phase dependence, measured at several microwave power and frequency values, is maximized. A residual phase noise of − 113 d B r a d 2 / H z at 1 Hz offset frequency from a 10 GHz carrier, with a fractional frequency stability of 1.2 × 10 − 16 at 1 s and below 10 − 19 at 10 5 s , is measured. These performances are compliant with the transfer of the most stable microwave signals available to date, obtained with cryogenic sapphire oscillators or combs locked to cavity-stabilized lasers. This approach is of interest for the distribution of ultra-stable microwave signals in a very simple photonic configuration.
