Esther Baumann’s research while affiliated with University of Colorado Boulder and other places

What is this page?


This page lists works of an author who doesn't have a ResearchGate profile or hasn't added the works to their profile yet. It is automatically generated from public (personal) data to further our legitimate goal of comprehensive and accurate scientific recordkeeping. If you are this author and want this page removed, please let us know.

Publications (8)


Precision optical and microwave synthesis of atomic clock frequencies with optical frequency combs
  • Conference Paper

March 2022

·

22 Reads

Nicholas Nardelli

·

Tara M. Fortier

·

·

[...]

·


Transfer oscillator setup with a 500 MHz repetition rate Er/Yb:glass OFC. Optical pulses from the Er/Yb:glass oscillator are fiber-coupled and amplified by an EDFA before being sent through an HNLF for supercontinuum generation. The spectrum is split in two paths, one for carrier-envelope offset frequency detection and the other for the detection of heterodyne beat signals between the OFC and light from two cavity-stabilized optical references at 1157 and 1070 nm. An optical interleaver multiplies the repetition frequency to 2 GHz, which is detected on an MUTC photodiode whose spectrum near 10 GHz is shown in the bottom-right inset (RBW = 300 kHz). The optical beats, fb1 and fb2, and the M = 20 harmonic (bold red in the inset) of the 2 GHz pulses are sent to two TO circuits along with fceo. Each circuit generates a 10 GHz output, fTO,i, that is derived from one of the two optical references by adding and dividing microwave signals, shown in blue boxes in upper right. Although the two TO electronics boards are identical, except for bandpass filters (BPF), to isolate fbi, the top board in the figure is used to represent the transfer oscillator mathematical operations and the bottom board shows the 2-DDS scheme as well as the approximate RF frequencies at each stage. The following integer constants are used: M = 20, N1 = 518 907, and N2 = 561 211.
Comparison between the current TO result (blue trace), the previous lowest phase noise TO result (connected orange dots).⁴¹
Top: Microwave phase noise characterization setups for the measurements in the plot. Bottom: Phase noise comparison between Mfrep generated by the Er/Yb:glass OFC when unstabilized (blue) and when stabilized to the 1070 nm optical reference (green) and fTO,1 vs fTO,2 when the OFC is unstabilized (orange). The 10 GHz limit (red) is set by the relative phase noise between 1157 and 1070 nm optical references, found by measuring the optical beat with an OFC and scaling to 10 GHz by subtracting 89 dB from the optical phase noise.
Phase noise comparison between fTO,2 derived from the 1070 nm reference (blue) and the total of all calculated noise sources (red). Constituent noise sources are plotted as dashed lines and thin traces.
Demonstration of noise suppression. Transfer oscillator microwave phase noise without added OFC frequency noise (blue) and with added OFC frequency noise (orange). Inset: the optical beat between a cavity stabilized laser and the comb, without and with added noise (blue and orange, respectively). Without added noise, the optical linewidth is 25 kHz, and with added noise, the optical linewidth is 2 MHz.

+1

10 GHz Generation with Ultra-Low Phase Noise via the Transfer Oscillator Technique
  • Article
  • Full-text available

February 2022

·

217 Reads

·

19 Citations

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 optical reference cavities for faithful optical-to-microwave frequency division. This requirement limits the technology to highly controlled laboratory environments. Here, we employ a transfer oscillator technique, which employs digital and RF analog electronics to coherently suppress additive optical frequency comb noise. This relaxes the stabilization requirements and allows for the extraction of multiple independent microwave outputs from a single comb, while at the same time, permitting low-noise microwave generation from combs with higher noise profiles. Using this method, we transferred the phase stability of two high-finesse optical sources at 1157 and 1070 nm to two independent 10 GHz signals using a single frequency comb. We demonstrated absolute phase noise below −106 dBc/Hz at 1 Hz from the carrier with corresponding 1 s fractional frequency instability below 2 × 10−15. Finally, the latter phase noise levels were attainable for comb linewidths broadened up to 2 MHz, demonstrating the potential for out-of-lab use with low SWaP lasers.

Download

10 GHz Generation with Ultra-Low Phase Noise via the Transfer Oscillator Technique

October 2021

·

73 Reads

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-Perot optical reference cavities for faithful optical-to-microwave frequency division. This requirement limits the technology to highly-controlled laboratory environments. Here, we employ a transfer oscillator technique, which employs digital and RF analog electronics to coherently suppress additive optical frequency comb noise. This relaxes the stabilization requirements and allows for the extraction of multiple independent microwave outputs from a single comb, while at the same time, permitting low-noise microwave generation from combs with higher noise profiles. Using this method we transferred the phase stability of two high-Finesse optical sources at 1157 nm and 1070 nm to two independent 10 GHz signals using a single frequency comb. We demonstrated absolute phase noise below -106 dBc/Hz at 1-Hz from carrier with corresponding 1 second fractional frequency instability below 2×10152\times10^{-15}. Finally, the latter phase noise levels were attainable for comb linewidths broadened up to 2 MHz, demonstrating the potential for out-of lab use with low SWaP lasers.





Fig. 1 Frequency comb representations and detection of the offset frequency. a Time and frequency domain representation of an optical frequency comb. The optical output of a mode-locked laser is a periodic train of optical pulses with pulse period, T r , and pulse envelope A(t). In the frequency domain, this pulse train can be expressed as a Fourier series of equidistant optical frequencies, with mode spacing, f r = 1/T r . It is the regular frequency spacing of the modes in the optical spectrum that inspired the analogy to a comb, although the analogy of a frequency ruler better describes the OFCs measurement capability. The frequency of any optical mode, ν N , is characterized by only two degrees of freedom, f r and f 0 , such that ν N = N ⋅ f r + f 0 . The mode spacing, f r , is accessed by directly detecting the amplitude modulation of the optical pulse train using an optical photodetector. This detection results in an electronic pulse train composed of coherently related microwave Fourier harmonics, n ⋅ f r . Note that the optical spectrum contains information about the offset of the harmonic comb from 0 Hz, f 0 , whereas the microwave spectrum only yields harmonics of f r because direct photodetection is not sensitive to the optical carrier. In the yellow shaded inset, we show the relationship between f 0 and the carrier-envelope offset phase, ϕ CEO (t). The evolution in the pulse-to-pulse change in the carrier-envelope phase is given by Δϕ CEO = 2πf 0 /f r . Notably, when f 0 = 0, every optical pulse has an identical carrier-envelope phase. The pulse envelope, A (t), depicted by a blue dashed line is related by the periodic Fourier transform to the spectral envelope. b Offset frequency detection via self-referencing. Frequency depiction of how nonlinear self-comparison can be used to detect f 0 .
Fig. 2 Overview of the development of optical frequency comb sources as function of year. The left axis indicates the mode-spacing of the various sources. To the right of the graph we indicate what mode-spacing range is most suitable for various applications. Milestones in source development, as well as some notable applications, beyond and including some of those listed in section "The offset frequency and measurement of the comb parameters", are indicated at the bottom and top of the graph. Filled markers indicate systems that have accessed f 0 , while empty markers have not. Sources that have become commercial products are circled with a solid outline and comb-based products are circled with a dashed outline and filled in yellow. AOWG -arbitrary optical waveform generation, OFD -optical frequency division, TWOTFT -two-way optical time and frequency transfer, DCS -dual-comb spectroscopy. List of references: 1 21,25,26 : 2 13 : 3 35 : 4 157 : 5 158-160 : 6 161 : 7 33,147 : 8 162 : 9 14 : 10 127 : 11 163 : 12 38 : 13 131 : 14 164 : 15 44 : 16 92 : 17 64 : 18 11 : 19 153 : 20 165 : 21 40 : 22 59 : 23 68 : 24 154 : 25 83 : 26 74 : 27 166 : 28 167 : 29 60 : 30 168 .
Fig. 4 How frequency chains and frequency combs measure an unknown optical frequency. Frequency generators bridge frequency gaps by counting the number of equidistant modes between the last multiplication state of the frequency chain and the optical transition of interest, ν opt . Because the offset frequency of these systems is unknown, f 0 is constrained by locking a single mode of the comb generator to the output stage of the frequency chain. The measurement is limited by the stability of the 133 Cs reference. An optical frequency comb (OFC) eliminates the need for a frequency chain by directly connecting optical frequencies to the microwave domain via access to f 0 . The same optical frequency measured by an OFC is compared to a microwave standard by measuring f r , f 0 and Δf on frequency counters referenced to 133 Cs, that once against limits the measurement stability. Finally, an OFC compares two optical clocks by measuring the difference frequencies, Δf and Δf 2 , with regards to their nearest OFC modes, N and M, respectively. Optical comparisons can be determined via the mode numbers and difference frequencies alone. For this reason, optical comparisons yield amazing precision because microwave reference errors on Δf and Δf 2 are additive to the optical frequency. A 10 −12 fractional error on Δf = 100 MHz, only yields a frequency error of 100 μHz. This error on a 500 THz optical carrier only contributes fractionally at 2 parts in 10 19 . Put differently, using a ruler one can split a centimeter marker by about a factor of 20, while difference frequency measurement can split 1 GHz-spaced OFC optical modes by parts in 10 14 .
20 years of developments in optical frequency comb technology and applications

December 2019

·

2,320 Reads

·

733 Citations

Optical frequency combs were developed nearly two decades ago to support the world’s most precise atomic clocks. Acting as precision optical synthesizers, frequency combs enable the precise transfer of phase and frequency information from a high-stability reference to hundreds of thousands of tones in the optical domain. This versatility, coupled with near-continuous spectroscopic coverage from microwave frequencies to the extreme ultra-violet, has enabled precision measurement capabilities in both fundamental and applied contexts. This review takes a tutorial approach to illustrate how 20 years of source development and technology has facilitated the journey of optical frequency combs from the lab into the field.


20 years of developments in optical frequency comb technology and applications

September 2019

·

214 Reads

Optical frequency combs were developed nearly two decades ago to support the world's most precise atomic clocks. Acting as precision optical synthesizers, frequency combs enable the precise transfer of phase and frequency information from a high-stability reference to hundreds of thousands of tones in the optical domain. This versatility, coupled with near-continuous spectroscopic coverage from the terahertz to the extreme ultra-violet, has enabled precision measurement capabilities in both fundamental and applied contexts. This review takes a tutorial approach to illustrate how 20 years of source development and technology has facilitated the journey of optical frequency combs from the lab into the field.

Citations (3)


... 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] . ...

Reference:

空间引力波探测中的时钟噪声抑制技术研究进展
10 GHz Generation with Ultra-Low Phase Noise via the Transfer Oscillator Technique

... O wing to the widespread applications in both scientific research and industries such as frequency combbased spectroscopy, [1][2][3] laser processing, 4,5) and bio-imaging, 6) high repetition rate fiber lasers have been developed intensively and many breakthroughs have been achieved. Techniques such as active mode-locking, 7) passively harmonic mode-locking, 8,9) dissipative four-wave mixing 10) and mode filtering 11) could achieve a very high repetition rate, however, they exhibit a higher instability in terms of output performance compared to fundamentally passive mode-locking. ...

Author Correction: 20 years of developments in optical frequency comb technology and applications

... In the optical realm, optical parametric coupling has played a major role in quantum engineering endeavors. [11][12][13][14][15][16][17] Optical frequency combs (FCs), 18,19 squeezed laser, 20 and squeezed optical frequency combs 13 have gained recognition as formidable tools for precision metrology and spectroscopy, positioning themselves as strong contenders for quantum processing. [21][22][23][24] The landscape of frequency comb (FC) research has seen a rich tapestry of studies delving into nonlinear processes, unveiling techniques for generating bosonic FCs. ...

20 years of developments in optical frequency comb technology and applications