Interferometric sampling oscilloscopes for light waves

Theodor W.H?nsch

(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.H?nsch on the 70th anniversary of Chongqing University of Posts and Telecommunications in October 2020.The paper was revised and authorized by Professor H?nsch 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 H?nsch.

編者按：本文由重慶郵電大學馬勇教授、王光宇教授，根據(jù)西奧多·W·漢希 于2020 年 10 月重慶郵電大學建校70周年慶典的學術報告整理、翻譯，并經(jīng)漢希教授修訂后授權本刊發(fā)表。重慶郵電大學從2015年開始和漢希教授領導的諾貝爾獎實驗室建立了廣泛的學術交流及合作。

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.

眾所周知，可見光每秒鐘振蕩500 000億次。光波的高速振蕩采樣可以實現(xiàn)一種新的光譜分析技術，能夠在很寬的光譜范圍內(nèi)對復雜分子的熒光信息進行分析，其核心技術是20年前發(fā)明的光頻率梳技術[1-6]。光頻率梳技術可用于測量頻率為104 THz的光學振蕩。它提供了光學和射頻區(qū)域之間的相位相干鏈接，并基于此技術制造光學原子鐘，其“鐘擺”由以光頻率振蕩的原子或離子形成。

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

時域分析可以用來闡述光頻梳的性質(zhì)。圖1給出了激光器發(fā)射的超短脈沖的光譜。超短光脈沖的光譜很寬，且脈沖越短產(chǎn)生的光譜就越寬。在發(fā)射2個相同且性質(zhì)一致的脈沖時，脈沖之間會產(chǎn)生干涉。這種現(xiàn)象類似于楊氏的雙縫實驗，楊氏實驗中，光經(jīng)過2個在空間上分開的狹縫后會在空間屏幕上產(chǎn)生干涉條紋。2個時間分開的脈沖也會在光譜上產(chǎn)生干涉條紋。2個干涉條紋最大值之間的頻率間隔等于脈沖時間間隔的倒數(shù)。2個脈沖相距越遠，干涉條紋就越相互靠近。光譜干涉條紋的形狀類似于常見的梳子。2個時域脈沖就可以產(chǎn)生光頻梳，只是其“梳齒”不是很鋒利。

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.

如果使用一整列規(guī)則脈沖，如鎖模飛秒激光器產(chǎn)生的脈沖，而不是2個脈沖，那么就可以產(chǎn)生具有尖銳梳狀線的干涉圖案。脈沖間隔時間越長，梳狀譜線會越尖銳，在精準時間控制下，其譜線堪比高穩(wěn)定激光器發(fā)出的連續(xù)波輻射對應的頻譜。在時間或相位上任何小的隨機波動都會破壞這種頻譜。

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.

時間控制技術可以通過不同的方法來實現(xiàn)，包括可以產(chǎn)生八跨度光頻梳的電子伺服控制器。然而，大多數(shù)專家并沒有預料到，如此簡單的光頻梳生成原理，可以產(chǎn)生如彩虹似的跨越八度的光頻梳，且這種“彩虹”不是普通的彩虹，而是由10萬到100萬條鋒利的光頻梳譜線組成。

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.

相鄰梳狀光譜線之間的頻率間距非常精確地等于激光的重復頻率，其測量精度不亞于銫原子鐘[7]。整個光頻梳由于載波包絡截止頻率產(chǎn)生略微偏移，而載波包絡截止頻率取決于脈沖相位的斜率。該載波包絡截止頻率也可以很容易地通過使用倍頻八跨度梳進行測量。2個無線電頻率用于確定每條梳狀線的光頻率絕對值。通過測量未知譜線和光頻梳的頻譜線之間的差頻干涉信號來計算待測激光器的頻率。另一方面，光頻梳譜線可以用于鎖定某個原子或離子中非常尖銳的光學躍遷，從而使得激光器的重復頻率同該光頻率相關，得到一個光學原子鐘的“發(fā)條”。

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.

這種光譜工具對于氫原子的高分辨率和精密光譜學非常有用[8-9]。氫原子在1S-2S躍遷時有一條非常清晰的能級線，可以通過紫外激光束激發(fā)出來，故需要測量激發(fā)原子的激光束的頻率。同時，我們已經(jīng)將光頻梳的測量精度提高到1015，幾乎達到現(xiàn)在已知的根據(jù)微波銫鐘定義的單位時間—秒的精度極限[10-11]。未來，使用光學時鐘可以實現(xiàn)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.

為什么這很重要？因為氫是最簡單的原子，相對其他原子，我們可以使用復雜的量子電動力學理論比較準確地計算出氫的能級和躍遷頻率。

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，如果該理論正確，那么可以通過光頻梳技術測量相關物理學基本常數(shù)的精確值。特別是構成了物理學基本常數(shù)系統(tǒng)基石的里德堡常數(shù)和質(zhì)子電荷半徑[12]。這里我們也許會問一個非常重要的問題：這些常數(shù)真的是常數(shù)還是隨著時間慢慢變化？如考慮氫及其對應反物質(zhì)的反能量，兩者是否恰好是彼此的鏡像？或者完全相同還是有什么區(qū)別？任何差異都會撼動我們的標準模型，因此精密光譜技術提供了探索物理學新知識的機會，也是驗證該理論實際效果的重要方法之一。這可能是諾貝爾委員會授予高分辨率激光光譜諾貝爾物理學獎的原因，包括2005年授予作者和約翰·霍爾的頻率梳技術。有趣的是，因?qū)α孔庸鈱W開創(chuàng)性的貢獻，2005年諾貝爾物理學獎同時授予了Theodor W.H?nsch，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，光頻梳已成為頻率計量的標準工具。完整的光學頻率系統(tǒng)、激光器和所有電子設備，達到前所未有的測量精度。光頻梳技術已經(jīng)成為人類已知的最精確的測量工具，其尺寸甚至可以小至桌面大小。通過將未知頻率的激光經(jīng)過光纖發(fā)送到該儀器中就能夠獲取其絕對頻率，精度可以達到參考時鐘允許的盡可能多的位數(shù)。

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.

微型光頻梳發(fā)生器以及芯片級的片上光頻梳發(fā)生器正在出現(xiàn)。Kippenberg課題組在馬克思普朗克研究所完成了一些開創(chuàng)性工作[13]，他本人現(xiàn)在是位于洛桑的洛桑聯(lián)邦理工學院(EPFL)的教授。通過使用由二氧化硅構成的微型環(huán)形諧振器同來自連續(xù)激光器的漸逝波耦合實現(xiàn)光耦合進入微型環(huán)形諧振器。環(huán)中形成的高強度電場促使產(chǎn)生4波混合效應，產(chǎn)生的光孤子可以給予光頻梳均勻的頻率間隔。

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

更多遠遠超出了最初想象的應用出現(xiàn)促使光頻梳更加引起關注，包括光學頻率的高精度測量、光鐘的實用化、精密光譜學工具等，其應用演化樹如圖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.

光頻梳還可用于比較相距很遠的2個原子鐘經(jīng)過遠距離信號傳輸后的時間以及頻率。因為能夠測量頻率，就可以測量長度。因此，光頻梳可以作為長度的計量工具，例如LIDAR遙感應用。由于恒星和行星都圍繞著一個共同的重心運行，因此天文學家將光頻梳作為大型天文光譜圖的校準工具，以使用測量徑向速度的方法(多普勒頻移)搜索遙遠恒星周圍的類地行星。光頻梳在射頻光子學中獲得了新的用途。例如，在激光頻梳的幫助下，產(chǎn)生具有最低相位和時序抖動的最穩(wěn)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，低噪聲微波不僅被用在通信中還被用于在雷達或其他方面。光頻梳已成為阿秒科學的關鍵工具，因為有助于控制短脈沖內(nèi)電場的相位，這種方法可以通過高次諧波產(chǎn)生可控的單個脈沖，該脈沖持續(xù)時間僅為幾十阿秒。

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

Fig.3 Direct frequency comb spectroscopy

本文主要聚焦于光頻梳光譜技術應用的討論和分析。圖3給出了直接頻梳光譜測量方法[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

光頻梳技術不僅可以作為校準工具，而且可以在很寬的光譜范圍內(nèi)使用所有的梳狀譜線，以多路復用方式實現(xiàn)高分辨率的光譜技術。這類光譜分析技術中，光頻梳作為光源并通過吸收氣室傳輸?shù)焦庾V儀，例如傅里葉變換光譜儀或光柵光譜儀。當有吸收時，相應的梳狀線會衰減。如果用光頻梳代替傅里葉光譜儀的非相干光源，可以大大提升光譜儀的靈敏度和測量速度。傳統(tǒng)的光譜儀很難分辨光頻梳的譜線。如果可以實現(xiàn)譜線的分辨，那么就可以通過使用一個高精度的原子鐘獲取這些光頻梳的精確頻率。那么怎樣才能達到高分辨率？在這方面，雙頻梳光譜技術有其用武之地，可以與用于光輻射的采樣示波器相提并論。假設敲擊一個鑼，其回響及發(fā)出的聲波可以通過麥克風和示波器進行分析，獲取鑼的本征振動模式。如果短光脈沖激勵一個分子，也會產(chǎn)生振蕩和反饋，利用示波器分析其發(fā)出的輻射就可以得到很多關于分子動力學的信息?？梢允褂?個雙光頻梳實現(xiàn)，如圖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.

一個光頻梳發(fā)射一串規(guī)則脈沖并激勵分子，產(chǎn)生反饋。使用重復頻率略有不同的第2個光頻梳用以研究分子產(chǎn)生的熒光輻射的特性(這里指的是分子產(chǎn)生的熒光輻射)。該過程將2束光束通過合束器合束，并在時域中觀察在單個光電探測器上的干涉信號，稱為異步采樣。由于2個激光器的重復頻率不同，梳1脈沖和梳2脈沖之間的時間間隔會隨著脈沖而變化。如果2個脈沖在檢測器上重合，會出現(xiàn)明顯的干涉信號。相反，如果我們測量微弱的自由感應衰減，就會得到一個較弱的干涉信號，實際上是分子的波形采樣軌跡。當然，如果測量時間足夠長，干涉就會消失，就像沒有重疊一樣。如果有一個重復的脈沖波形周期性地撞擊分子，自由感應衰減會顯著減小。但是，如果采用這種周期性重復的波形并對其進行采樣，就會得到一個時域上延展的波形。因此，這是采樣示波器需要注意的一個方面，如圖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，時間微小的波動，就會放大信號，所以需要注意激光器的穩(wěn)定性。在頻域中也要考慮類似的情況:2個梳線間距略有不同的光頻梳,通過檢測光頻梳譜線之間的射頻差頻信號就會得到一個常規(guī)頻梳。其中檢測到的射頻信號以兆赫茲為單位測量，原始光學頻率以太赫茲為單位測量。圖6和圖7顯示了時域和頻域的雙頻梳光譜測量技術。

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.

轉(zhuǎn)換系數(shù)就是2個激光器(激光器1和激光器2)的重復頻率之差除以激光器2的重復頻率。圖7就是此類信號的示例。在2個激光器脈沖重疊的特殊情況下，使用在電信波段中工作的摻鉺光纖激光器實現(xiàn)鎖模，可以使微弱信號得到放大。目前，利用采樣示波器可以清楚地看到自由感應的衰減。圖8是通過傅立葉變換后信號的光譜[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

圖8描述了使用傅立葉變換可以得到處于v1+v3重疊能級中的乙炔光譜，實現(xiàn)的分辨率是3 GHz[14]。該結果不是特別顯著。使用傳統(tǒng)的傅里葉光譜儀也可以獲得類似的分辨率。但值得注意的是，該頻譜僅在42 μs內(nèi)記錄下來，而對于傳統(tǒng)的傅立葉光譜儀，至少需要幾分鐘才能產(chǎn)生這種質(zhì)量的光譜。因此，這是雙光頻梳光譜技術的一項潛在優(yōu)勢。

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.

由于傅里葉光譜儀的機械運動或運動路徑?jīng)]有限制，這使可以更快地進行光譜測量成為可能。此外，電信頻段光源的獲取相對容易，但是分子光譜學最重要的頻譜信息并不是處于這個波段。大多數(shù)分子在中紅外的分子指紋區(qū)具有很強的特征吸收帶。因此，在中紅外線中產(chǎn)生頻率梳是非常理想的。在這方面，多年來已經(jīng)使用了幾種方法，有的方法還在研究中。一種方法是利用近紅外、光通信波段光纖激光器通過差頻產(chǎn)生中紅外光頻梳信號。

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.

我們最近做的工作獲得了差不多3 μm波長的光頻梳，并且用來觀察乙烯的光譜。圖9顯示了3 μm左右的乙烯雙頻梳吸收光譜[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.

乙烯的振動模式v9和v11屬于該光譜區(qū)域。雖然頻譜看起來全黑，實際上我們已經(jīng)解析了單獨的梳狀線。當我們把曲線的局部放大后就會逐漸看到分子線，如圖10。進一步放大時，就會看到梳狀線，如圖11。梳狀線是一個很有效的校準工具，因為它提供了精確的頻率。

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 H?nsch[17].

雖然建立一個實驗室來進行上述實驗是昂貴的，但產(chǎn)生這些光譜并不需要太多的能量，因為探測器可以被強烈的短脈沖飽和。通常，只有幾微瓦的平均功率就足夠了。另外，近期我們也在探索雙光頻梳光譜可以達到的最低強度，通過這些研究，我們實現(xiàn)了單光子能級。相關成果在美國國家科學院院刊PNAS發(fā)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.

為了驗證基礎實驗：采用2個摻鉺光纖激光器，在分束器上組合兩束光束以產(chǎn)生二次諧波信號。一束光被發(fā)送到光電檢測器，該檢測器檢測來自2個激光器的2個脈沖何時重疊后，觸發(fā)另外一個檢測光子的檢測器。透過樣品的另一束光衰減得非常大，最終我們只有低至20 fw或每1 000脈沖只觸發(fā)了一次探測信號，但它仍然能實現(xiàn)有效探測。但是如果試圖在探測器之前檢測光子的存在，就會很難。

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(指的基于單個光子探測的雙頻梳光譜儀是探測效率有待提高這個問題)，未來的應用前景光明而有趣。這種技術可以應用于產(chǎn)生光子很少的極紫外或軟x射線的光頻梳源；該技術可以通過衰減介質(zhì)分析遠距離的背向散射光，也可能通過來自單個分子或小納米結構的熒光來觀察信號，即使光子計數(shù)率非常小仍然可以工作。另外，我們也在未來的小型化、芯片級儀器、基于光子芯片的氣體光譜研究方面遇到了一個個的挑戰(zhàn)。

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.

以上展示的這些微型光頻梳發(fā)生器，其梳線間距往往很大。如果間距比分子線的線寬還要寬就可能會錯過分子線進而無法提供所需要的信息。一種解決方法是使用光頻梳線的不同位置，并生成一組交錯光譜，這樣就可以檢索分子信息，但它并不是真正的多路光譜。

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.

我們真正希望的是千兆赫茲或更小的線距梳子。1 GHz對應于腔中30 cm的圓形路徑，我們最近也在探索如何在微觀亞毫米尺寸的芯片腔中容納這樣長路徑的方法。該項工作是同比利時根特大學的B.Kuyken課題組進行的合作[18]，該小組多年來設計基于芯片的鎖模激光器。當使用硅波導時，在SiO2襯底上可以將這個波導塑造成螺旋形，這樣就可以將長干涉儀路徑纏繞到一個小線圈上。為了實現(xiàn)這種激光器，需要一種與硅波導結合的III-V族半導體器件實現(xiàn)的增益和飽和吸收器。如果一切順利，脈沖到達光柵反射器，部分耦合出去。這樣，就得到了一個小型的鎖模激光器。

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.

得到的鎖模激光器的主要問題是，該激光器是否足夠穩(wěn)定，可以實現(xiàn)雙頻梳光譜分析？答案在于一個攜帶相當多激光設備的樣品晶片，它包括激光器、線圈、放大器和飽和吸收器。2個激光器，其輸出通過分束器合并，一個芯片上的雙梳狀光譜儀就可能實現(xiàn)。不幸的是，由于需要2個激光器，但我們無法找到2個匹配的激光器。

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.

為了表征基于芯片的鎖模激光器，進行了一個不同類型的實驗[19]。采用一個激光器，用于輸出光譜儀所需的脈沖，并將脈沖通過氣室發(fā)送到檢測器中。參考光頻梳通過連續(xù)激光和電光調(diào)制器產(chǎn)生梳線。第一個實驗因為片上激光器不穩(wěn)定失敗了。隨后的試驗產(chǎn)生了一個穩(wěn)定的梳子。關鍵就是采用一些連續(xù)激光并將其注入片上鎖模激光器，以便能夠鎖定光頻梳中一根譜線，進而鎖定所有梳狀譜線。

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，超過600 GHz的射頻差頻信號會受到電光調(diào)制器光頻梳跨度的限制。片上光頻梳大約寬3倍且可以在非線性波導中進一步拓寬，但是已經(jīng)達到了足夠的穩(wěn)定性可以解析單個梳線。通過分析一氧化碳的吸收線，實驗獲得了一氧化碳的精確光譜，與HITRAN數(shù)據(jù)庫的光譜進行比較，結果表明有非常好的一致性，沒有產(chǎn)生系統(tǒng)失真，且很容易地識別出碳13的痕跡信號。因此，該方法能夠有效的測量精確的同位素含量。

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.

從根本上說，我們希望在芯片上實現(xiàn)一個完整的光譜儀，且正在努力進行，以期早日實現(xiàn)這一希望。一個完整晶片包含許多光譜儀單元，每個光譜儀都有2個鎖模激光器和一個螺旋波導，用于檢測某些分子吸收的倏逝波。因此尺寸和功耗足夠小，可以集成到智能手機或智能手機配件中。只需使用一個光電探測器，信號甚至可以通過內(nèi)置計算機在智能手機上進行處理。這樣，就實現(xiàn)了一種小型、便攜式、廉價的氣相光譜儀。高分辨率可用于醫(yī)療診斷、污染監(jiān)測、工業(yè)控制、國內(nèi)空氣質(zhì)量監(jiān)測和市場上的水果檢測。

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.

可能性是無限的，世界各地的許多創(chuàng)意研究小組很可能會有新的想法和令人驚訝的新應用。本文中描述的分子光譜學是在馬克斯·普朗克量子光學研究所，在娜塔莉·皮克博士的監(jiān)督下進行的(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，感謝科研經(jīng)費提供單位：歐洲研究委員會(6)https://erc.europa.eu/、Max Planck基金會(7)https://www.maxplanckfoundation.org/?lang=en、Curl Friedrich Von Siemens基金會(8)https://www.siemens-stiftung.org/en/。