Interferometric sampling oscilloscopes for light waves

Theodor W.Hänsch

(Max Planck Institute for Quantum Optics, Ludwig-Maximilian University, Munich, Germany)

Abstract: With the rapid development of femtosecond laser technology and nonlinear optics at the beginning of this century, optical frequency comb technology has become an important precision frequency measurement technology.It connects the radio and optical frequency realm by inching through the vast frequency gap via the coherent relationship between their separated frequencies and phases, which has a significant application value in the fields of time-keeping and frequency standards, precision spectral metrology and constants measurement in fundamental physics.

Keywords：optical frequency comb；single photon；Nobel prize in physics；precision spectroscopy

Editor’s note: This paper was organized and translated by Professor Yong Ma and Professor Guangyu Wang of Chongqing University of Posts and Telecommunications, based on the academic presentation of Professor Theodor W.Hänsch on the 70th anniversary of Chongqing University of Posts and Telecommunications in October 2020.The paper was revised and authorized by Professor Hänsch for publication in this journal.Since 2015, Chongqing University of Posts and Telecommunications has established extensive academic exchanges and cooperation with the Nobel Prize Laboratory led by Professor Hänsch.

编者按：本文由重庆邮电大学马勇教授、王光宇教授，根据西奥多·W·汉希 于2020 年 10 月重庆邮电大学建校70周年庆典的学术报告整理、翻译，并经汉希教授修订后授权本刊发表。重庆邮电大学从2015年开始和汉希教授领导的诺贝尔奖实验室建立了广泛的学术交流及合作。

Visible light has approximately 500,000 billion oscillations per second.These sampling oscilloscopes create a new type of spectroscopy where the radiation emitted by complex molecules over a broad spectral range can be analyzed.This approach is based on the laser frequency comb, invented 20 years ago[1-6].This tool measures the optical frequencies of hundreds of thousands of terahertz.Further, it provides a phase-coherent link between the optical and radio frequency regions and offers a clockwork mechanism for optical atomic clocks, where the pendulum is formed by atoms or ions oscillating with the frequency of light.

众所周知，可见光每秒钟振荡500 000亿次。光波的高速振荡采样可以实现一种新的光谱分析技术，能够在很宽的光谱范围内对复杂分子的荧光信息进行分析，其核心技术是20年前发明的光频率梳技术[1-6]。光频率梳技术可用于测量频率为104 THz的光学振荡。它提供了光学和射频区域之间的相位相干链接，并基于此技术制造光学原子钟，其“钟摆”由以光频率振荡的原子或离子形成。

A frequency comb is explained in the time domain as follows.Fig.1 shows the spectrum of a laser that emits an ultrashort pulse.A broad spectrum is observed for ultrashort pulse, i.e., the shorter the pulse, the broader the spectrum.If two identical pulses are considered, instead of one, then they interfere and produce fringes in the spectrum.Interestingly, this is comparable to Young’s double-slit experiment, where two slits separated in space produce spatial interference fringes on the screen.Here two laser pulses separated in time produce interference fringes in the spectrum.The separation between two interference maxima precisely equals the inverse time interval between the two pulses.The further apart the two pulses, the closer the fringes become, resembling a comb.Notable, two pulses only can produce a frequency comb; however, with blunt teeth.

Fig.1 Two pulses separated in time and their spectrum

时域分析可以用来阐述光频梳的性质。图1给出了激光器发射的超短脉冲的光谱。超短光脉冲的光谱很宽，且脉冲越短产生的光谱就越宽。在发射2个相同且性质一致的脉冲时，脉冲之间会产生干涉。这种现象类似于杨氏的双缝实验，杨氏实验中，光经过2个在空间上分开的狭缝后会在空间屏幕上产生干涉条纹。2个时间分开的脉冲也会在光谱上产生干涉条纹。2个干涉条纹最大值之间的频率间隔等于脉冲时间间隔的倒数。2个脉冲相距越远，干涉条纹就越相互靠近。光谱干涉条纹的形状类似于常见的梳子。2个时域脉冲就可以产生光频梳，只是其“梳齿”不是很锋利。

Nevertheless, if a whole train of regular pulses, such as produced by a mode-locked femtosecond laser, is used rather than two pulses, then an interference pattern with sharp comb lines can be produced.The longer the interval between pulses, the sharper these lines become.Comb lines as sharp as continuous-wave radiation from a well-stabilized laser can be obtained with precisely controlled timing only.Any small random fluctuations in timing or phase will disrupt the spectrum.

如果使用一整列规则脉冲，如锁模飞秒激光器产生的脉冲，而不是2个脉冲，那么就可以产生具有尖锐梳状线的干涉图案。脉冲间隔时间越长，梳状谱线会越尖锐，在精准时间控制下，其谱线堪比高稳定激光器发出的连续波辐射对应的频谱。在时间或相位上任何小的随机波动都会破坏这种频谱。

This technical challenge can be overcome by different means, including electronic servo-controls, which can produce an octave-spanning comb.However, this was not anticipated by most experts.Although the principle of comb generation is simple, nobody expects these principles to produce an octave-spanning rainbow of colors., This rainbow is not an ordinary rainbow but consists of 100,000 to as many as 1 million sharp comb lines.

时间控制技术可以通过不同的方法来实现，包括可以产生八跨度光频梳的电子伺服控制器。然而，大多数专家并没有预料到，如此简单的光频梳生成原理，可以产生如彩虹似的跨越八度的光频梳，且这种“彩虹”不是普通的彩虹，而是由10万到100万条锋利的光频梳谱线组成。

The spacing between adjacent comb lines precisely equals the repetition frequency of the laser, measured using a cesium atomic clock[7].The entire comb can be slightly shifted using the carrier-envelope offset frequency, which depends on slips of the phase of the pulses.This carrier-envelope offset frequency can be easily measured using an octave-spanning comb.Then, the two radio frequencies act as the absolute optical frequency for each comb line.If the frequency of an unknown laser needs to be measured, an interference signal in the form of a beat node between the unknown and comb lines should be identified.Conversely, one comb line can be taken and locked electronically to a sharp optical transition in some atom or iron; thus, the repetition frequency can be related to the optical frequency.Essentially, an optical atomic clock works on this mechanism.

相邻梳状光谱线之间的频率间距非常精确地等于激光的重复频率，其测量精度不亚于铯原子钟[7]。整个光频梳由于载波包络截止频率产生略微偏移，而载波包络截止频率取决于脉冲相位的斜率。该载波包络截止频率也可以很容易地通过使用倍频八跨度梳进行测量。2个无线电频率用于确定每条梳状线的光频率绝对值。通过测量未知谱线和光频梳的频谱线之间的差频干涉信号来计算待测激光器的频率。另一方面，光频梳谱线可以用于锁定某个原子或离子中非常尖锐的光学跃迁，从而使得激光器的重复频率同该光频率相关，得到一个光学原子钟的“发条”。

This spectroscopic tool has been particularly useful for high resolution and precision spectroscopy of atomic hydrogen[8-9].Atomic hydrogen exhibits a very sharp line corresponding to the 1S-2S transition that can be excited with an ultraviolet laser beam.For this, the frequency of the laser beam that excites the atoms needs to be measured.The accuracy was improved up to 15 decimal digits[10-11].The accuracy of the unit of time, i.e., second, defined in terms of the microwave cesium clock, is nearing the limits of what is possible with that technology.However, much greater precision is can be achieved with optical clocks in future.

这种光谱工具对于氢原子的高分辨率和精密光谱学非常有用[8-9]。氢原子在1S-2S跃迁时有一条非常清晰的能级线，可以通过紫外激光束激发出来，故需要测量激发原子的激光束的频率。同时，我们已经将光频梳的测量精度提高到1015，几乎达到现在已知的根据微波铯钟定义的单位时间—秒的精度极限[10-11]。未来，使用光学时钟可以实现更高的精度。

Why is this important? Because hydrogen is the simplest atom, its energy levels and transition frequencies can be calculated more accurately than other atoms using the sophisticated theory of quantum electrodynamics.

为什么这很重要？因为氢是最简单的原子，相对其他原子，我们可以使用复杂的量子电动力学理论比较准确地计算出氢的能级和跃迁频率。

Furthermore, validation of the theory is equally important.In particular, precision spectroscopy can be used to validate the theory.Based on this theory, fundamental constants, including the Rydberg constant and proton charge radius, which form cornerstones in the system of fundamental constants, can be obtained[12].However, an important question is whether these constants are constant or slowly change with time.For example, consider hydrogen and its antimatter anti-hydrogen.Are they precisely mirror images of each other? Are they precisely the same? Alternatively, is there any difference? Any difference would violate the standard model; thus, precision spectroscopy would allow searching for new physics.Perhaps, this may have been the motivation for the Nobel committee to award the physics Nobel Prize for high-resolution laser spectroscopy, including the frequency comb technique to the author and John L.Hall in 2005.Interestingly, Roy Glauber also received the Nobel Prize in the same year for his pioneering contributions to quantum optics[1-2].

另一方面，如果该理论正确，那么可以通过光频梳技术测量相关物理学基本常数的精确值。特别是构成了物理学基本常数系统基石的里德堡常数和质子电荷半径[12]。这里我们也许会问一个非常重要的问题：这些常数真的是常数还是随着时间慢慢变化？如考虑氢及其对应反物质的反能量，两者是否恰好是彼此的镜像？或者完全相同还是有什么区别？任何差异都会撼动我们的标准模型，因此精密光谱技术提供了探索物理学新知识的机会，也是验证该理论实际效果的重要方法之一。这可能是诺贝尔委员会授予高分辨率激光光谱诺贝尔物理学奖的原因，包括2005年授予作者和约翰·霍尔的频率梳技术。有趣的是，因对量子光学开创性的贡献，2005年诺贝尔物理学奖同时授予了Theodor W.Hänsch，John L.Hall和Roy[1-2]。

Nowadays, frequency combs have become standard tools for frequency metrology.The optical frequencies of complete systems, including lasers and all electronics, can be measured with unprecedented precision.It has become the most precise measurement tool known to man.Even the frequency comb of a smart desktop size can be obtained.The light from a laser of unknown frequency can be sent through a fiber into the frequency comb.Then, the absolute frequency can be read to as many digits as a reference clock will allow.

如今，光频梳已成为频率计量的标准工具。完整的光学频率系统、激光器和所有电子设备，达到前所未有的测量精度。光频梳技术已经成为人类已知的最精确的测量工具，其尺寸甚至可以小至桌面大小。通过将未知频率的激光经过光纤发送到该仪器中就能够获取其绝对频率，精度可以达到参考时钟允许的尽可能多的位数。

Chip-scaled comb generators based on microscopic frequencycombs areemerging.The pioneering work for the chip-scaled comb generators was completed in the Max Planck Institute, by Kippenberg’s group, now a professor at the Swiss Federal Institute of Technology, Lausanne[13].They showed that microscopic ring resonator formed using silica could be used with light from a continuous-wave laser through evanescent wave coupling.In this ring, the intensity can be increased to a high level, so that four wave-mixing and soliton formation can result in a comb of evenly spaced comb lines.

微型光频梳发生器以及芯片级的片上光频梳发生器正在出现。Kippenberg课题组在马克思普朗克研究所完成了一些开创性工作[13]，他本人现在是位于洛桑的洛桑联邦理工学院(EPFL)的教授。通过使用由二氧化硅构成的微型环形谐振器同来自连续激光器的渐逝波耦合实现光耦合进入微型环形谐振器。环中形成的高强度电场促使产生4波混合效应，产生的光孤子可以给予光频梳均匀的频率间隔。

Widespread interests in frequency combs are due to their broad spectrum of applications.Fig.2 shows the evolutionary tree of frequency comb applications.

Fig.2 Evolutionary tree of the applications of frequency combs

更多远远超出了最初想象的应用出现促使光频梳更加引起关注，包括光学频率的高精度测量、光钟的实用化、精密光谱学工具等，其应用演化树如图2。

Frequency combs are used to measure optical frequencies accurately and realize optical clocks.In addition, they serve as a tool for precision spectroscopy.Nowadays, combs are used to compare distant atomic clocks, by time and frequency transfer over large distances.If frequencies can be measured, lengths can also be estimated; thus, frequency combs are also used for length metrology, including light detection and ranging remote sensing.Astronomers employ frequency combs as calibration tools for analyzing large astronomical spectrographs.They search for earth-like planets around distant stars using the radial velocity method(Doppler shifts)as the star and planet orbit around a common center of gravity.Frequency combs are finding new uses in radio frequency photonics.For instance, the most stable microwaves with the lowest phase and timing jitter have been produced using laser frequency combs.

光频梳还可用于比较相距很远的2个原子钟经过远距离信号传输后的时间以及频率。因为能够测量频率，就可以测量长度。因此，光频梳可以作为长度的计量工具，例如LIDAR遥感应用。由于恒星和行星都围绕着一个共同的重心运行，因此天文学家将光频梳作为大型天文光谱图的校准工具，以使用测量径向速度的方法(多普勒频移)搜索遥远恒星周围的类地行星。光频梳在射频光子学中获得了新的用途。例如，在激光频梳的帮助下，产生具有最低相位和时序抖动的最稳定的微波。

Moreover, they have been used in low noise microwaves, communications, radars, and other applications.Frequency combs are essential in attosecond science because they facilitate the control of the phase of the electric field inside the short pulse, making it possible to produce controlled single pulses of high harmonic generation, lasting only tens of attoseconds.

此外，低噪声微波不仅被用在通信中还被用于在雷达或其他方面。光频梳已成为阿秒科学的关键工具，因为有助于控制短脉冲内电场的相位，这种方法可以通过高次谐波产生可控的单个脉冲，该脉冲持续时间仅为几十阿秒。

Concentrating on spectroscopy with frequency combs, Fig.3 shows direct frequency comb spectroscopy[14].

Fig.3 Direct frequency comb spectroscopy

本文主要聚焦于光频梳光谱技术应用的讨论和分析。图3给出了直接频梳光谱测量方法[14]。

In this spectroscopy, the frequency comb is not used as a calibration tool but all the comb lines in the multiplex are used to interrogate broad spectra with high resolution.While conducting these spectroscopic investigations, light from a frequency comb source is sent through an absorbing gas cell using either Fourier transform or grating spectrometers.Upon absorption, the corresponding comb lines attenuate.Notably, by replacing the incoherent light source of a Fourier spectrometer with a comb, a substantial gain in sensitivity and recording speed are achieved.However, resolving the comb lines with a conventional spectrometer remains difficult.Otherwise, the frequencies of these comb lines can be known with the accuracy of an atomic clock.Nevertheless, how high-resolution can be obtained? In this respect, dual-comb spectroscopy is a technique that is comparable to a sampling oscilloscope for optical radiation.If a gong is hit, it reverberates and emits sound waves that can be analyzed using a microphone and an oscilloscope to learn about the different vibrational eigenmodes of this gong.Similarly, molecules can be hit with a short light pulse, resulting in their oscillation and reverberation.If this radiation can be analyzed using an oscilloscope, the dynamics of the molecules can be learned.However, how can this be accomplished? Using two frequency combs.Fig.4 shows a schematic of the approach.

Fig.4 Dual-comb spectrometer

光频梳技术不仅可以作为校准工具，而且可以在很宽的光谱范围内使用所有的梳状谱线，以多路复用方式实现高分辨率的光谱技术。这类光谱分析技术中，光频梳作为光源并通过吸收气室传输到光谱仪，例如傅里叶变换光谱仪或光栅光谱仪。当有吸收时，相应的梳状线会衰减。如果用光频梳代替傅里叶光谱仪的非相干光源，可以大大提升光谱仪的灵敏度和测量速度。传统的光谱仪很难分辨光频梳的谱线。如果可以实现谱线的分辨，那么就可以通过使用一个高精度的原子钟获取这些光频梳的精确频率。那么怎样才能达到高分辨率？在这方面，双频梳光谱技术有其用武之地，可以与用于光辐射的采样示波器相提并论。假设敲击一个锣，其回响及发出的声波可以通过麦克风和示波器进行分析，获取锣的本征振动模式。如果短光脉冲激励一个分子，也会产生振荡和反馈，利用示波器分析其发出的辐射就可以得到很多关于分子动力学的信息。可以使用2个双光频梳实现，如图4。

In this technique, one frequency comb emits a train of regular pulses, which hit the molecules and reverberate them.To investigate that radiation, a second frequency comb with a slightly different repetition frequency is used.Both beams are combined and a single photodetector is used to record the interference in the time domain.This is called asynchronous sampling.Because the repetition frequencies are different, the time interval between combs 1 and 2 pulses shift and change from pulse to pulse.Such that coinciding of two pulses on the detector results in a big burst of interference.On the contrary, if the weak free induction decay is analyzed, a weaker interference signal is obtained, which is ideally the sampling trace of the molecular waveform.Over a sufficiently long time, the interference disappears, as there is no overlap.There is one way of paying attention to a particular aspect of this type of two combs spectroscopy.Consider a repetitive waveform, where the molecules are hit periodically by these pulses, and the free induction decay is greatly simplified.If this periodically repetitive waveform is sampled, a waveform that appears stretched in time is obtained，as shown in Fig.5.

Fig.5 Optical sampling oscilloscope.

一个光频梳发射一串规则脉冲并激励分子，产生反馈。使用重复频率略有不同的第2个光频梳用以研究分子产生的荧光辐射的特性(这里指的是分子产生的荧光辐射)。该过程将2束光束通过合束器合束，并在时域中观察在单个光电探测器上的干涉信号，称为异步采样。由于2个激光器的重复频率不同，梳1脉冲和梳2脉冲之间的时间间隔会随着脉冲而变化。如果2个脉冲在检测器上重合，会出现明显的干涉信号。相反，如果我们测量微弱的自由感应衰减，就会得到一个较弱的干涉信号，实际上是分子的波形采样轨迹。当然，如果测量时间足够长，干涉就会消失，就像没有重叠一样。如果有一个重复的脉冲波形周期性地撞击分子，自由感应衰减会显著减小。但是，如果采用这种周期性重复的波形并对其进行采样，就会得到一个时域上延展的波形。因此，这是采样示波器需要注意的一个方面，如图5。

However, small fluctuations in timing appear magnified, indicating that considerable attention needs to be paid to the stability of the lasers.Similar situations can be considered in the frequency domain.Consider two combs with slightly different comb line spacing.Radio frequency beat notes in megahertz units can be detected between pairs of comb lines, whereas the original optical frequency is measured in terahertz units.Figs.6 and 7 show the dual-comb spectroscopy in both time and frequency domains.

然而，时间微小的波动，就会放大信号，所以需要注意激光器的稳定性。在频域中也要考虑类似的情况:2个梳线间距略有不同的光频梳,通过检测光频梳谱线之间的射频差频信号就会得到一个常规频梳。其中检测到的射频信号以兆赫兹为单位测量，原始光学频率以太赫兹为单位测量。图6和图7显示了时域和频域的双频梳光谱测量技术。

The conversion factor corresponds to the difference in the repetition rates of both lasers divided by the repetition rate.Here is an example of such a signal.Given the instances where the pulses from the two lasers overlap, suppose mode-locked Er-doped fiber lasers operating in the telecommunications band are used.After this burst, smaller signals that need to be magnified are obtained.The free induction decay is clearly seen with the help of the sampling oscilloscope.

转换系数就是2个激光器(激光器1和激光器2)的重复频率之差除以激光器2的重复频率。图7就是此类信号的示例。在2个激光器脉冲重叠的特殊情况下，使用在电信波段中工作的掺铒光纤激光器实现锁模，可以使微弱信号得到放大。目前，利用采样示波器可以清楚地看到自由感应的衰减。图8是通过傅立叶变换后信号的光谱[15]。

Fig.6 Dual-comb spectroscopy in time domain.

Fig.7 Dual-comb spectroscopy in the frequency domain.

Fig.8 depicts the use of a Fourier transformation to obtain a spectrum from this signal[15]for acetylene in the v1+v3 combination band[15].The resolution achieved is 3 GHz only.A similar resolution can be achieved using the traditional Fourier spectrometer.However, this spectrum is recorded in just 42 μs, which is quite remarkable considering that a traditional Fourier spectrometer requires several minutes to produce a spectrum of this quality.This shows one potential advantage of dual-comb spectroscopy.

Fig.8 Fourier transformation of a time-domain interference signal shown in Fig.6. Through transformation, the absorption spectrum of acetylene(C2H2)is obtained

图8描述了使用傅立叶变换可以得到处于v1+v3重叠能级中的乙炔光谱，实现的分辨率是3 GHz[14]。该结果不是特别显著。使用传统的傅里叶光谱仪也可以获得类似的分辨率。但值得注意的是，该频谱仅在42 μs内记录下来，而对于传统的傅立叶光谱仪，至少需要几分钟才能产生这种质量的光谱。因此，这是双光频梳光谱技术的一项潜在优势。

Much faster measurements are possible because no limits exist in the mechanical motion or motion path of the Fourier spectrometer.Besides, the telecommunications band is easier to access.However, it is not the most sought out region in molecular spectroscopy, as most molecules have strong characteristic absorption bands in the molecular fingerprint region of the mid-infrared.Thus, producing frequency combs in the mid-infrared is highly desired.In this respect, several approaches have been adopted over many years and are still being investigated.A readily accessible is to start with near-infrared telecom-type fiber lasers and produce mid-infrared spectra using difference frequency generation.

由于傅里叶光谱仪的机械运动或运动路径没有限制，这使可以更快地进行光谱测量成为可能。此外，电信频段光源的获取相对容易，但是分子光谱学最重要的频谱信息并不是处于这个波段。大多数分子在中红外的分子指纹区具有很强的特征吸收带。因此，在中红外线中产生频率梳是非常理想的。在这方面，多年来已经使用了几种方法，有的方法还在研究中。一种方法是利用近红外、光通信波段光纤激光器通过差频产生中红外光频梳信号。

Recently, this was achieved when frequency combs of approximately 3 μm were produced and used to investigate the spectrum of ethylene.Fig.9 shows the dual-comb absorption spectrum of ethylene near 3 μm[16].

Fig.9 Dual-comb absorption spectrum of ethylene near 3 μm.

我们最近做的工作获得了差不多3 μm波长的光频梳，并且用来观察乙烯的光谱。图9显示了3 μm左右的乙烯双频梳吸收光谱[16]。

Ethylene’s vibrational modes v9 and v11 fall into this spectral region.At first sight, the spectrum looks all black; however, individual comb lines can be resolved.Figs.10 and 11 show the magnified ethylene spectra with reduced frequency range.First, the molecular lines are seen, and then, with further magnification, the comb lines become discernible.The comb line is a fantastic calibration tool because it provides precise frequency.

乙烯的振动模式v9和v11属于该光谱区域。虽然频谱看起来全黑，实际上我们已经解析了单独的梳状线。当我们把曲线的局部放大后就会逐渐看到分子线，如图10。进一步放大时，就会看到梳状线，如图11。梳状线是一个很有效的校准工具，因为它提供了精确的频率。

Although, setting up a laboratory to conduct all the above experiments is expensive, not much power is needed to produce these spectra because the detectors can saturate by intense short pulses.Typically, only a few microwatts of average power will suffice.Furthermore, investigations were performed to explore the lowest intensities where dual-comb spectroscopy can be performed.Through these explorations, the single-photon level was achieved by N.Picque and Hänsch[17].

虽然建立一个实验室来进行上述实验是昂贵的，但产生这些光谱并不需要太多的能量，因为探测器可以被强烈的短脉冲饱和。通常，只有几微瓦的平均功率就足够了。另外，近期我们也在探索双光频梳光谱可以达到的最低强度，通过这些研究，我们实现了单光子能级。相关成果在美国国家科学院院刊PNAS发表[17]。

Fig.10 Zooming into the ethylene spectrum shown in Fig.9 reveals comb lines and molecular absorption lines.

Fig.11 Expanded region of the dual-comb spectrum of ethylene(12C2H4)showing both absorption and dispersion.

To prove the fundamental experiment, two frequency-doubled Er-doped fiber lasers were used and both beams were combined.One beam was sent to a photodetector that detects when both pulses from the two lasers overlap and then triggers a scalar for the detected photons.The other beam probing the sample is attenuated dramatically so that the power is 20 fW or the detection is down to about only one detector click for a thousand pulses.Nevertheless, difficulties are encountered if a photon is imagined to exist before detection.

为了验证基础实验：采用2个掺铒光纤激光器，在分束器上组合两束光束以产生二次谐波信号。一束光被发送到光电检测器，该检测器检测来自2个激光器的2个脉冲何时重叠后，触发另外一个检测光子的检测器。透过样品的另一束光衰减得非常大，最终我们只有低至20 fw或每1 000脉冲只触发了一次探测信号，但它仍然能实现有效探测。但是如果试图在探测器之前检测光子的存在，就会很难。

Otherwise, it opens intriguing prospects for future applications.This technique can still be applied for frequency comb sources in the extreme ultraviolet or soft X-ray regime, where very few photons are produced.Furthermore, it can be used to analyze backscattered light over a long distance through attenuating media.In addition, it is still possible to observe fluorescence signal from an individual molecule or a small nanostructure, although the photon count rate is small.However, what about a future miniaturized chip-scale instrument? Will it be possible to have a gas spectroscopy laboratory on a photonic chip? There is one obstacle to achieving these.

但除此之外(指的基于单个光子探测的双频梳光谱仪是探测效率有待提高这个问题)，未来的应用前景光明而有趣。这种技术可以应用于产生光子很少的极紫外或软x射线的光频梳源；该技术可以通过衰减介质分析远距离的背向散射光，也可能通过来自单个分子或小纳米结构的荧光来观察信号，即使光子计数率非常小仍然可以工作。另外，我们也在未来的小型化、芯片级仪器、基于光子芯片的气体光谱研究方面遇到了一个个的挑战。

These microscopic frequency comb generators have large spacing of the comb lines, wider than the line widths of the molecular lines.Thus, molecular lines can be missed, resulting in a spectrum lacking all the desired information.One approach is to work with different positions of the comb line and generate a set of interleaved spectra.Thus, the molecular information can be retrieved, but not as a multiplex spectrum.

以上展示的这些微型光频梳发生器，其梳线间距往往很大。如果间距比分子线的线宽还要宽就可能会错过分子线进而无法提供所需要的信息。一种解决方法是使用光频梳线的不同位置，并生成一组交错光谱，这样就可以检索分子信息，但它并不是真正的多路光谱。

A comb with line spacing of a gigahertz or less, which corresponds to a round path of 30 cm in the cavity, is typically required.How is it possible to accommodate such a path in a microscopic sub-millimeter-sized chip cavity? This has been recently explored in collaboration with a group of B.Kuyken at the University of Ghent, Belgium[18].This group has designed a chip-based mode-locked laser using a SiO2waveguide on a silicon substrate for several years.This waveguide can be shaped into a spiral, winding the long interferometer path to a small coil.To realize a laser, gain and saturated absorbers are required, which are implemented with III-V semiconductor devices bonded to the silicon waveguide.Then, the pulse reaches the grating reflector and part of it is coupled out.Therefore, a small mode-locked laser is obtained.

我们真正希望的是千兆赫兹或更小的线距梳子。1 GHz对应于腔中30 cm的圆形路径，我们最近也在探索如何在微观亚毫米尺寸的芯片腔中容纳这样长路径的方法。该项工作是同比利时根特大学的B.Kuyken课题组进行的合作[18]，该小组多年来设计基于芯片的锁模激光器。当使用硅波导时，在SiO2衬底上可以将这个波导塑造成螺旋形，这样就可以将长干涉仪路径缠绕到一个小线圈上。为了实现这种激光器，需要一种与硅波导结合的III-V族半导体器件实现的增益和饱和吸收器。如果一切顺利，脉冲到达光栅反射器，部分耦合出去。这样，就得到了一个小型的锁模激光器。

One fundamental question is whether this laser is stable enough to perform dual-comb spectroscopy.The answer lies is in a sample wafer that carries quite a few laser devices.It comprises a laser, a coil, an amplifier, and a saturated absorber.As there are two lasers, whose outputs combine on the beam splitter, a dual-comb spectrometer on a chip may already exist.Unfortunately, two matching lasers could not be achieved.

得到的锁模激光器的主要问题是，该激光器是否足够稳定，可以实现双频梳光谱分析？答案在于一个携带相当多激光设备的样品晶片，它包括激光器、线圈、放大器和饱和吸收器。2个激光器，其输出通过分束器合并，一个芯片上的双梳状光谱仪就可能实现。不幸的是，由于需要2个激光器，但我们无法找到2个匹配的激光器。

To characterize the chip-based mode-locked laser, a different type of experiment was conducted[19].For using only one of these lasers with its pulses as input for spectrometer, its pulses were sent through a gas cell into a detector.The comb lines were produced using a continuous-wave laser and an electro-optic modulator.The first experiment was unsuccessful because on-chip lasers are unstable.However, subsequent trials produced a stable comb.A key point is to take some continuous-wave lasers and incident them into the on-chip mode-locked laser so that one of the comb lines is injection-locked, and, as a consequence, all the comb lines.

为了表征基于芯片的锁模激光器，进行了一个不同类型的实验[19]。采用一个激光器，用于输出光谱仪所需的脉冲，并将脉冲通过气室发送到检测器中。参考光频梳通过连续激光和电光调制器产生梳线。第一个实验因为片上激光器不稳定失败了。随后的试验产生了一个稳定的梳子。关键就是采用一些连续激光并将其注入片上锁模激光器，以便能够锁定光频梳中一根谱线，进而锁定所有梳状谱线。

For instance, beat notes in the radio frequency region over 600 GHz are limited by the span of the electro-optic modulator comb.The on-chip comb is about three times wider and can be further broadened in nonlinear waveguides.However, enough stability has been achieved to resolve individual comb lines.Precise spectroscopy of the carbon monoxide can be achieved by analyzing its absorption line.No systematic distortion is observed for the complete spectrum of carbon monoxide on comparison with the calculated spectrum from the HITRAN database.The contributions from the carbon 13-isotope are easily recognized as a good technique to measure precise isotopic ratios.

例如，超过600 GHz的射频差频信号会受到电光调制器光频梳跨度的限制。片上光频梳大约宽3倍且可以在非线性波导中进一步拓宽，但是已经达到了足够的稳定性可以解析单个梳线。通过分析一氧化碳的吸收线，实验获得了一氧化碳的精确光谱，与HITRAN数据库的光谱进行比较，结果表明有非常好的一致性，没有产生系统失真，且很容易地识别出碳13的痕迹信号。因此，该方法能够有效的测量精确的同位素含量。

Fundamentally, we want to realize a complete spectrometer on a chip and work is ongoing to achieve this.Timeframes are uncertain but it remains an aspiration.An entire wafer with several such spectrometers is feasible.Each spectrometer has two mode-locked lasers and a spiral waveguide for evanescent wave detection of molecular absorptions.The size and power consumption can be reduced enough to integrate into a smartphone or smartphone accessory.Only with a single photodetector, the signal can be processed on the smartphone using the built-in computer.In this way, a small, portable, and inexpensive gas-phase spectrometer is realized.The high resolution can be used in medical diagnostics, pollution monitoring, industrial control, domestic air quality monitoring, and checking the fruit in the market.

从根本上说，我们希望在芯片上实现一个完整的光谱仪，且正在努力进行，以期早日实现这一希望。一个完整晶片包含许多光谱仪单元，每个光谱仪都有2个锁模激光器和一个螺旋波导，用于检测某些分子吸收的倏逝波。因此尺寸和功耗足够小，可以集成到智能手机或智能手机配件中。只需使用一个光电探测器，信号甚至可以通过内置计算机在智能手机上进行处理。这样，就实现了一种小型、便携式、廉价的气相光谱仪。高分辨率可用于医疗诊断、污染监测、工业控制、国内空气质量监测和市场上的水果检测。

The possibilities are immense.Many creative research groups worldwide are likely to have new ideas and surprising novel applications.The molecular spectroscopy described in this paper was conducted at the Max Planck Institute of Quantum Optics, under the supervision of Dr.Nathalie Picque(1)https://www.frequency-comb.eu/index.html.

可能性是无限的，世界各地的许多创意研究小组很可能会有新的想法和令人惊讶的新应用。本文中描述的分子光谱学是在马克斯·普朗克量子光学研究所，在娜塔莉·皮克博士的监督下进行的(2)https://www.frequency-comb.eu/index.html。

Thanks are given to the sponsors, the European Research Council(3)https://erc.europa.eu/, Max Planck Foundation(4)https://www.maxplanckfoundation.org/?lang=en, and Carl Friedrich von Siemens Foundation(5)https://www.siemens-stiftung.org/en/.

最后，感谢科研经费提供单位：欧洲研究委员会(6)https://erc.europa.eu/、Max Planck基金会(7)https://www.maxplanckfoundation.org/?lang=en、Curl Friedrich Von Siemens基金会(8)https://www.siemens-stiftung.org/en/。