Accurate measurement of large optical frequency differences with a mode-locked laser

Time/frequency-domain characterization of a mid-IR DFG frequency comb via two-photon and heterodyne detection

Mid-infrared frequency combs are nowadays well-appreciated sources for spectroscopy and frequency metrology. Here, a comprehensive approach for characterizing a difference-frequency-generated mid-infrared frequency comb (DFG-comb) both in the time and in the frequency domain is presented. An autocorrelation scheme exploiting mid-infrared two-photon detection is used for characterizing the pulse width and to verify the optimal compression of the generated pulses reaching a pulse duration (FWHM) as low as 196 fs. A second scheme based on mid-infrared heterodyne detection employing two independent narrow-linewidth quantum cascade lasers (QCLs) is used for frequency-narrowing the modes of the DFG-comb down to 9.4 kHz on a 5-ms timescale.

Rapid, high-sensitivity detection of biomolecules using dual-comb biosensing

Rapid, sensitive detection of biomolecules is important for biosensing of infectious pathogens as well as biomarkers and pollutants. For example, biosensing of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is still strongly required for the fight against coronavirus disease 2019 (COVID-19) pandemic. Here, we aim to achieve the rapid and sensitive detection of SARS-CoV-2 nucleocapsid protein antigen by enhancing the performance of optical biosensing based on optical frequency combs (OFC). The virus-concentration-dependent optical spectrum shift produced by antigen-antibody interactions is transformed into a photonic radio-frequency (RF) shift by a frequency conversion between the optical and RF regions in the OFC, facilitating rapid and sensitive detection with well-established electrical frequency measurements. Furthermore, active-dummy temperature-drift compensation with a dual-comb configuration enables the very small change in the virus-concentration-dependent signal to be extracted from the large, variable background signal caused by temperature disturbance. The achieved performance of dual-comb biosensing will greatly enhance the applicability of biosensors to viruses, biomarkers, environmental hormones, and so on.

Carrier conversion from terahertz wave to dual-wavelength near-infrared light for photonic terahertz detection in wireless communication

THz waves are promising wireless carriers for next-generation wireless communications, where a seamless connection from wireless to optical communication is required. In this study, we demonstrate carrier conversion from THz waves to dual-wavelength NIR light injection-locking to an optical frequency comb using asynchronous nonpolarimetric electro-optic downconversion with an electro-optic polymer modulator. THz wave in the W band was detected as a stable photonic RF beat signal of 1 GHz with a signal-to-noise ratio of 20 dB via the proposed THz-to-NIR carrier conversion. In addition, the results imply the potential of the photonic detection of THz waves for wireless-to-optical seamless communication.

Below-threshold harmonic generation in gas-jets for Th-229 nuclear spectroscopy

The generation of below-threshold harmonics in gas-jets constitutes a promising path towards optical frequency combs in the vacuum ultra-violet (VUV) spectral range. Of particular interest is the 150 nm range, which can be exploited to probe the nuclear isomeric transition of the Thorium-229 isotope. Using widely available high-power, high-repetition-rate Ytterbium-based laser sources, VUV frequency combs can be generated through the process of below-threshold harmonic generation, in particular 7^th harmonic generation of 1030 nm. Knowledge about the achievable efficiencies of the harmonic generation process is crucial for the development of suitable VUV sources. In this work, we measure the total output pulse energies and conversion efficiencies of below-threshold harmonics in gas-jets in a phase-mismatched generation scheme using Argon and Krypton as nonlinear media. Using a 220 fs, 1030 nm source, we reach a maximum conversion efficiency of 1.1 × 10^-5 for the 7^th harmonic (147 nm) and 0.78 × 10^-4 for the 5^th harmonic (206 nm). In addition, we characterize the 3^rd harmonic of a 178 fs, 515 nm source with a maximum efficiency of 0.3%.

Control of Frequency Combs with Passive Resonators

Tailored optical frequency combs are generated by nesting passive etalons within mode-locked oscillators. In this work, the oscillator generates a comb of 6.8 GHz with 106 MHz side-bands. This tailored comb results from the self-synchronized locking of two cavities with precision optical frequency tuning. In this manuscript, it is demonstrated that these combs can be precisely predicted utilizing a temporal ABCD matrix method and precise comb frequency tuning by scanning over the D1 transition line of 87Rb and observing the fluorescence.

Phase Nanoscopy with Correlated Frequency Combs

This study addresses any sensor based on measuring a physical quantity through the phase of a probing beam. This includes sensing of rotation, acceleration, index change, displacement, fields… While most phase measurements are made by detecting an amplitude change in interfering beams, we detect instead a phase change through a relative frequency shift of two correlated frequency combs. This paper explores the limit sensitivity that this method can achieve, when the combs are generated in an Optical Parametric Oscillator (OPO), pumped synchronously by a train of femtosecond pulses separated by half the OPO cavity round-trip time. It is shown that a phase difference as small as 0.4 nanoradians can be resolved between the two pulses circulating in the cavity. This phase difference is one order of magnitude better than the previous record. The root-mean-square deviation of the measured phase over measuring time is close to the standard quantum limit (phase-photon number uncertainty product of 0.66). Innovations that made such improved performances possible include a more stable OPO cavity design; a stabilization system with a novel purely electronic locking of the OPO cavity length relative to that of the pump laser; a shorter pump laser cavity; and a square pulse generator for driving a 0.5 mm pathlength lithium niobate phase modulator. Future data acquisition improvements are suggested that will bring the phase sensitivity exactly to the standard quantum limit, and beyond the quantum limit by squeezing.

Evolution of the frequency-comb structure and coherence from a Keldysh multiphoton into a tunneling regime

We present a theoretical study of the characteristics of the frequency-comb structure and coherence via high-order harmonic generation (HHG) driven by the laser pulse trains when the ionization process is pushed from Keldysh multiphoton into tunneling regime. HHG is obtained by solving accurately the time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. We find that the nested comb structures are formed from each harmonic order in the Keldysh multiphoton ionization regime. But it is severely suppressed or even disappeared in the Keldysh tunneling ionization regime. It implies that the temporal coherence of the emitted frequency comb modes is very sensitive to the Keldysh ionization regime. To understand the evolution of frequency-comb structure and coherence, we perform the calculation of the time-dependent ionization probability and the spectral phase of frequency-comb HHG. We find that the frequency-comb HHG driven by the laser pulse trains in the Keldysh multiphoton regime has a good coherence because the ionization probability of the atom driven by each laser pulse is stable, leading to a phase-coherent frequency-comb structure rather than those cases in the Keldysh tunneling regime with high laser intensity. Our results shed light on current interest and significance to the experimental realization of controllable and frequency-comb vacuum-ultraviolet light sources.

Intracavity Measurement Sensitivity Enhancement without Runaway Noise

A method to increase the sensitivity of an intracavity differential phase measurement that is not made irrelevant by a larger increase of noise is explored. By introducing a phase velocity feedback by way of a resonant dispersive element in an active sensor in which two ultrashort pulses circulate, it is shown that the measurement sensitivity is elevated without significantly increasing the Petermann excess noise factor. This enhancement technique has considerable implications for any optical phase based measurement; from gyroscopes and accelerometers to magnetometers and optical index measurements. Here we describe the enhancement method in the context of past dispersion enhancement studies including the recent work surrounding non-Hermitian quantum mechanics, justify the method with a theoretical framework (including numerical simulations), and propose practical applications.

Tunable dual-comb spectrometer for mid-infrared trace gas analysis from 3 to 4.7 µm

Dual-frequency comb spectroscopy has emerged as a disruptive technique for measuring wide-spanning spectra with high resolution, yielding a particularly powerful technique for sensitive multi-component gas analysis. We present a spectrometer based on two electro-optical combs with subsequent conversion to the mid-infrared via tunable difference frequency generation, operating in the range from 3 to 4.7 µm. The repetition rate of the combs can be tuned from 250 to 500 MHz. For 500 MHz, the number of detected comb modes is 440 with a signal-to-noise ratio exceeding 10⁵ in 1 s. The conversion preserves the coherence of the combs within 3 s measurement time. Concentration measurements of 5 ppm methane at 3.3 µm, 100 ppm nitrous oxide at 3.9 µm and a mixture of 15 ppm carbon monoxide and 5% carbon dioxide at 4.5 µm are demonstrated with a noise-equivalent absorption coefficient of 6.4(3) x 10^-6 cm^-1 Hz^-1/2.

Compression-coding-based surface measurement using a digital micromirror device and heterodyne interferometry of an optical frequency comb

We propose a compression-coding-based surface measurement method that combines single-pixel imaging and heterodyne interference using an optical frequency comb. The real and imaginary parts of the heterodyne interference signals are used to obtain the depth information rapidly. By optimizing the ordering of the Hadamard measurement basis, we reconstruct a three-step sample with heights of approximately 10, 20, and 30 µm without an iterative operation in 6 ms, with a precision of 5 nm. Compared with the uncompressed measurement, the sampling times reduced to 20%, and the measurement time reduced by five times without measurement accuracy loss. The proposed method is effective for rapid measurements, particularly for objects with a simple surface topography.

Rotation Active Sensors Based on Ultrafast Fibre Lasers

Gyroscopes merit an undeniable role in inertial navigation systems, geodesy and seismology. By employing the optical Sagnac effect, ring laser gyroscopes provide exceptionally accurate measurements of even ultraslow angular velocity with a resolution up to 10-11 rad/s. With the recent advancement of ultrafast fibre lasers and, particularly, enabling effective bidirectional generation, their applications have been expanded to the areas of dual-comb spectroscopy and gyroscopy. Exceptional compactness, maintenance-free operation and rather low cost make ultrafast fibre lasers attractive for sensing applications. Remarkably, laser gyroscope operation in the ultrashort pulse generation regime presents a promising approach for eliminating sensing limitations caused by the synchronisation of counter-propagating channels, the most critical of which is frequency lock-in. In this work, we overview the fundamentals of gyroscopic sensing and ultrafast fibre lasers to bridge the gap between tools development and their real-world applications. This article provides a historical outline, highlights the most recent advancements and discusses perspectives for the expanding field of ultrafast fibre laser gyroscopes. We acknowledge the bottlenecks and deficiencies of the presented ultrafast laser gyroscope concepts due to intrinsic physical effects or currently available measurement methodology. Finally, the current work outlines solutions for further ultrafast laser technology development to translate to future commercial gyroscopes.

Computationally image-corrected dual-comb microscopy with a free-running single-cavity dual-comb fiber laser

Dual-comb microscopy (DCM), an interesting imaging modality based on the optical-frequency-comb (OFC) mode and image pixel one-to-one correspondence, benefits from scan-less full-field imaging and simultaneous confocal amplitude and phase imaging. However, the two fully frequency-stabilized OFC sources requirement hampers DCM practicality due to the complexity and costs. Here, a bidirectional single-cavity dual-comb fiber laser (SCDCFL) is adopted as a DCM low-complexity OFC source. Although the residual timing jitter in the SCDCFL blurs the image of a static object acquired by DCM, computational image correction significantly suppresses the image blur. Nanometer-order step surface profilometry with a 14.0 nm uncertainty highlights the computationally image-corrected DCM effectiveness. We further discuss a possibility to expand the computational image correction to a dynamic object and demonstrate its preliminary experiment. The proposed method enhances the DCM generality and practicality due to low-complexity OFC source.

Full-field fluorescence lifetime dual-comb microscopy using spectral mapping and frequency multiplexing of dual-comb optical beats

Fluorescence lifetime imaging microscopy (FLIM) is a powerful tool for quantitative fluorescence imaging because fluorescence lifetime is independent of concentration of fluorescent molecules or excitation/detection efficiency and is robust to photobleaching. However, since most FLIMs are based on point-to-point measurements, mechanical scanning of a focal spot is needed for forming an image, which hampers rapid imaging. Here, we demonstrate scan-less full-field FLIM based on a one-to-one correspondence between two-dimensional (2D) image pixels and frequency-multiplexed radio frequency (RF) signals. A vast number of dual-comb optical beats between dual optical frequency combs are effectively adopted for 2D spectral mapping and high-density frequency multiplexing in the RF region. Bimodal images of fluorescence amplitude and lifetime are obtained with high quantitativeness from amplitude and phase spectra of fluorescence RF comb modes without the need for mechanical scanning. The parallelized FLIM will be useful for rapid quantitative fluorescence imaging in life science.

Long-term hybrid stabilization of the carrier-envelope phase

Controlling the carrier envelope phase (CEP) in mode-locked lasers over practically long timescales is crucial for real-world applications in ultrafast optics and precision metrology. We present a hybrid solution that combines a feed-forward technique to stabilize the phase offset in fast timescales and a feedback technique that addresses slowly varying sources of interference and locking bandwidth limitations associated with gain media with long upper-state lifetimes. We experimentally realize the hybrid stabilization system in an Er:Yb:glass mode-locked laser and demonstrate 75 hours of stabilization with integrated phase noise of 14 mrad (1 Hz to 3 MHz), corresponding to around 11 as of carrier to envelope jitter. Additionally, we examine the impact of environmental factors, such as humidity and pressure, on the long-term stability and performance of the system.

Dynamic characterization of polarization property in liquid-crystal-on-silicon spatial light modulator using dual-comb spectroscopic polarimetry

Spectroscopic polarimetry (SP) is a powerful tool for characterization of thin film, polarization optics, semiconductor, and others. However, mechanical polarization modulation of broadband light hampers its application for dynamic monitoring of a sample. In this article, we demonstrate the dynamic SP with features of polarization-modulation-free polarimetry and spectrometer-free spectroscopy benefiting from dual-comb spectroscopy (DCS) using a pair of optical frequency combs (OFCs). DCS enables the direct determination of polarization without the need for polarization modulation by using mode-resolved OFC spectra of amplitude and phase for two orthogonally linear-polarized lights while securing rapid, high-precision, broadband spectroscopy without the need for spectrometer. Effectiveness of the proposed system is highlighted by visualizing the hysteresis property of dynamic response in a liquid-crystal-on-silicon spatial light modulator at a sampling rate of 105 Hz.

Optical Angle Sensor Technology Based on the Optical Frequency Comb Laser

A mode-locked femtosecond laser, which is often referred to as the optical frequency comb, has increasing applications in various industrial fields, including production engineering, in the last two decades. Many efforts have been made so far to apply the mode-locked femtosecond laser to the absolute distance measurement. In recent years, a mode-locked femtosecond laser has increasing application in angle measurement, where the unique characteristics of the mode-locked femtosecond laser such as the stable optical frequencies, equally-spaced modes in frequency domain, and the ultra-short pulse trains with a high peak power are utilized to achieve precision and stable angle measurement. In this review article, some of the optical angle sensor techniques based on the mode-locked femtosecond laser are introduced. First, the angle scale comb, which can be generated by combining the dispersive characteristic of a scale grating and the discretized modes in a mode-locked femtosecond laser, is introduced. Some of the mode-locked femtosecond laser autocollimators, which have been realized by combining the concept of the angle scale comb with the laser autocollimation, are also explained. Angle measurement techniques based on the absolute distance measurements, lateral chromatic aberration, and second harmonic generation (SHG) are also introduced.

Optical image amplification in dual-comb microscopy

Dual-comb microscopy (DCM), based on a combination of dual-comb spectroscopy (DCS) with two-dimensional spectral encoding (2D-SE), is a promising method for scan-less confocal laser microscopy giving an amplitude and phase image contrast with the confocality. However, signal loss in a 2D-SE optical system hampers increase in image acquisition rate due to decreased signal-to-noise ratio. In this article, we demonstrated optical image amplification in DCM with an erbium-doped fiber amplifier (EDFA). Combined use of the image-encoded DCS interferogram and the EDFA benefits from not only the batch amplification of amplitude and phase images but also significant rejection of amplified spontaneous emission (ASE) background. Effectiveness of the optical-image-amplified DCM is highlighted in the single-shot quantitative nanometer-order surface topography and the real-time movie of polystyrene beads dynamics under water convection. The proposed method will be a powerful tool for real-time observation of surface topography and fast dynamic phenomena.

Refractive index sensing with temperature compensation by a multimode-interference fiber-based optical frequency comb sensing cavity

We proposed a refractive index (RI) sensing method with temperature compensation by using an optical frequency comb (OFC) sensing cavity including a multimode-interference (MMI) fiber, namely, the MMI-OFC sensing cavity. The MMI-OFC sensing cavity enables simultaneous measurement of material-dependent RI and sample temperature by decoding from the comb spacing frequency shift and the wavelength shift of the OFC. We realized the simultaneous and continuous measurement of RI-related concentration of a liquid sample and its temperature with precisions of 1.6 × 10^-4 RIU and 0.08 °C. The proposed method would be a useful means for the various applications based on RI sensing.

Refractive-index-sensing optical comb based on photonic radio-frequency conversion with intracavity multi-mode interference fiber sensor

Optical frequency combs (OFCs) have attracted attention as optical frequency rulers due to their tooth-like discrete spectra together with their inherent mode-locking nature and phase-locking control to a frequency standard. Based on this concept, their applications until now have been demonstrated in the fields of optical frequency metrology. However, if the utility of OFCs can be further expanded beyond their application by exploiting new aspects of OFCs, this will lead to new developments in optical metrology and instrumentation. Here, we report a fiber sensing application of OFCs based on a coherent link between the optical and radio frequencies, enabling high-precision refractive index measurement based on frequency measurement in radio-frequency (RF) region. Our technique encodes a refractive index change of a liquid sample into a repetition frequency of OFC by a combination of an intracavity multi-mode-interference fiber sensor and wavelength dispersion of a cavity fiber. Then, the change in refractive index is read out by measuring the repetition frequency in RF region based on a frequency standard. Use of an OFC as a photonic RF converter will lead to the development of new applications in high-precision fiber sensing with the help of functional fiber sensors and precise RF measurement.

Multi-branch fiber comb with relative frequency uncertainty at 10-20 using fiber noise difference cancellation

In multi-branch combs, the comb outputs from the branches suffer from different fiber noises, which often limit the uncertainty of the combs referring a highly-stable optical frequency. To overcome this limitation, we introduced fiber noise difference cancellation to multi-branch fiber combs. We detected and phase-locked the beat notes between the branch outputs and a common 1542 nm continuous wave laser. A piezo-electric transducer-based fiber stretcher was installed in each branch except for the branch used as the cancellation reference. We fabricated two quasi-identical combs with this mechanism and confirmed the relative frequency uncertainty by comparing them. The cancellation improved the frequency uncertainty to a low level of 10^-20 at a 100000-s averaging time.

Extending chip-based Kerr-comb to visible spectrum by dispersive wave engineering

Anomalous group velocity dispersion is a key parameter for generating bright solitons, and thus wideband Kerr frequency combs. Extension of the frequency combs spectrum to visible wavelengths has been a major challenge because of the strong normal dispersion of conventional photonic materials at these wavelengths. In this paper, we numerically demonstrate a wideband frequency comb extending from near-infrared to visible wavelengths (∼1200 nm to 650 nm). The proposed frequency comb micro-resonator takes advantage of a wideband blue-shifted anomalous dispersion, achieved in an optimized over-etched silicon nitride waveguide and strong power transfer to shorter wavelengths through radiative dispersive waves, achieved by modulating the dispersion in a coupled resonator architecture. We show the possibility of obtaining a close to visible dispersive Cherenkov radiation peak that is only 10 dB below the overall comb peak and can be tuned by adjusting the coupling structure in the coupled resonator architecture.

Linear and nonlinear frequency- and time-domain spectroscopy with multiple frequency combs

Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical frequency combs has opened up new avenues to metrology and spectroscopy. The ability to generate a series of frequency spikes with precisely controlled separation permits a fast, highly accurate sampling of the material response. Recently, pairs of frequency combs with slightly different repetition rates have been utilized to down-convert material susceptibilities from the optical to microwave regime where they can be recorded in real time. We show how this one-dimensional dual comb technique can be extended to multiple dimensions by using several combs. We demonstrate how nonlinear susceptibilities can be quickly acquired using this technique. In a second class of techniques, sequences of ultrafast mode locked laser pulses are used to recover pathways of interactions contributing to nonlinear susceptibilities by using a photo-acoustic modulation varying along the sequences. We show that these techniques can be viewed as a time-domain analog of the multiple frequency comb scheme.

Scan-less hyperspectral dual-comb single-pixel-imaging in both amplitude and phase

We have developed a hyperspectral imaging scheme that involves a combination of dual-comb spectroscopy and Hadamard-transform-based single-pixel imaging. The scheme enables us to obtain 12,000 hyperspectral images of amplitude and phase at a spatial resolution of 46 µm without mechanical scanning. The spectral resolution given by the data point interval in the frequency domain is 20 MHz and the comb mode interval is 100 MHz over a spectral range of 1.2 THz centered at 191.5 THz. As an initial demonstration of our scheme, we obtained spectroscopic images of a standard test chart through an etalon plate. The thickness of an absorptive chromium-coated layer on a float-glass substrate was determined to be 70 nm from the hyperspectral phase images in the near-infrared wavelength region.

Comparison of symmetric and asymmetric double quantum well extended-cavity diode lasers for broadband passive mode-locking at 780 nm

We present a compact, mode-locked diode laser system designed to emit a frequency comb in the wavelength range around 780 nm. We compare the mode-locking performance of symmetric and asymmetric double quantum well ridge-waveguide diode laser chips in an extended-cavity diode laser configuration. By reverse biasing a short section of the diode laser chip, passive mode-locking at 3.4 GHz is achieved. Employing an asymmetric double quantum well allows for generation of a mode-locked optical spectrum spanning more than 15 nm (full width at -20  dB) while the symmetric double quantum well device only provides a bandwidth of ∼2.7  nm (full width at -20  dB). Analysis of the RF noise characteristics of the pulse repetition rate shows an RF linewidth of about 7 kHz (full width at half-maximum) and of at most 530 Hz (full width at half-maximum) for the asymmetric and symmetric double quantum well devices, respectively. Investigation of the frequency noise power spectral density at the pulse repetition rate shows a white noise floor of approximately 2100  Hz²/Hz and of at most 170  Hz²/Hz for the diode laser employing the asymmetric and symmetric double quantum well structures, respectively. The pulse width is less than 10 ps for both devices.

Impact of resonant dispersion on the sensitivity of intracavity phase interferometry and laser gyros

Intracavity phase interferometry is a phase sensing technique using mode-locked lasers in which two intracavity pulses circulate. The beat frequency between the two output frequency combs is proportional to a phase shift to be measured. A laser gyro is a particular implementation of this device. The demonstrated sensitivity of 10^-8 of these devices could be manipulated by applying a giant dispersion to each tooth of the comb. It is shown that the resonant dispersion of a Fabry-Perot inserted in the cavity couples to the modes of the frequency comb, resulting in a large change in phase response.

High-power ultrafast Yb:fiber laser frequency combs using commercially available components and basic fiber tools

We present a detailed description of the design, construction, and performance of high-power ultrafast Yb:fiber laser frequency combs in operation in our laboratory. We discuss two such laser systems: an 87 MHz, 9 W, 85 fs laser operating at 1060 nm and an 87 MHz, 80 W, 155 fs laser operating at 1035 nm. Both are constructed using low-cost, commercially available components, and can be assembled using only basic tools for cleaving and splicing single-mode fibers. We describe practical methods for achieving and characterizing low-noise single-pulse operation and long-term stability from Yb:fiber oscillators based on nonlinear polarization evolution. Stabilization of the combs using a variety of transducers, including a new method for tuning the carrier-envelope offset frequency, is discussed. High average power is achieved through chirped-pulse amplification in simple fiber amplifiers based on double-clad photonic crystal fibers. We describe the use of these combs in several applications, including ultrasensitive femtosecond time-resolved spectroscopy and cavity-enhanced high-order harmonic generation.

Frequency comb metrology with an optical parametric oscillator

We report on the first demonstration of absolute frequency comb metrology with an optical parametric oscillator (OPO) frequency comb. The synchronously-pumped OPO operated in the 1.5-µm spectral region and was referenced to an H-maser atomic clock. Using different techniques, we thoroughly characterized the frequency noise power spectral density (PSD) of the repetition rate f_rep, of the carrier-envelope offset frequency f_CEO, and of an optical comb line νN. The comb mode optical linewidth at 1557 nm was determined to be ~70 kHz for an observation time of 1 s from the measured frequency noise PSD, and was limited by the stability of the microwave frequency standard available for the stabilization of the comb repetition rate. We achieved a tight lock of the carrier envelope offset frequency with only ~300 mrad residual integrated phase noise, which makes its contribution to the optical linewidth negligible. The OPO comb was used to measure the absolute optical frequency of a near-infrared laser whose second-harmonic component was locked to the F = 2→3 transition of the ⁸⁷Rb D2 line at 780 nm, leading to a measured transition frequency of ν_Rb = 384,228,115,346 ± 16 kHz. We performed the same measurement with a commercial fiber-laser comb operating in the 1.5-µm region. Both the OPO comb and the commercial fiber comb achieved similar performance. The measurement accuracy was limited by interferometric noise in the fibered setup of the Rb-stabilized laser.

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing the free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrödinger equation model. These results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.

Solitons are nonlinear waves that exist in diverse forms of matter. Here, Husko et al. use near-field measurements to observe the spatio-temporal evolution of optical pulses in a nanophotonic semiconductor waveguide, demonstrating that nonlinear photo-carrier generation can induce fission of solitons.

Self-induced transparency and coherent population trapping of ⁸⁷Rb vapor in a mode-locked laser

Simultaneous self-induced transparency and a dark line resonance are observed inside a mode-locked laser. The circulating pulse, tuned to the 795-nm optical resonance of rubidium, has sufficient intensity to create at each passage a population inversion-return to ground state, typical of self-induced transparency. A drop in fluorescence (dark line resonance), is observed as the repetition rate is tuned to a submultiple of the hyperfine ground-state splitting.

Carrier-envelope phase drift measurement of picosecond pulses by an all-linear-optical means

Carrier-envelope phase (CEP) drift of a pulse train of 2 ps pulses has been measured by a multiple beam interferometer. The round trip time of the interferometer is slightly mistuned from the pulse sequence, leading to spectral interference fringes. We extract the pulse-to-pulse CEP drift from the position of the spectral interference pattern. The length of the interferometer has been actively stabilized to ±10  nm, which sets the ultimate limit on the accuracy of the measurement to 78 mrad, while the CEP-drift (rms) noise of the measurement was 127 mrad (at 800 nm).

Precision spectroscopy using a partially stabilized frequency comb

We present a simple method for precision spectroscopy using an optical frequency comb. One mode of a 1 GHz repetition rate mode-locked Ti:sapphire laser is offset-locked to an Rb-stabilized diode laser. This partially stabilized frequency comb stays locked, unattended, for hours at a time. Using the measured offset frequency and repetition rate, we calculate the frequency of each comb mode with absolute uncertainty of about 10 kHz in a 10 s measurement window. We demonstrate the capabilities and limitations of this approach with measurements in Rb, Cs, and Ca.

High-coherence mid-infrared frequency comb

We report on the generation of a frequency comb around 4330 nm with an unprecedented coherence of the single teeth. Generating the comb within a Ti:sapphire laser cavity by a difference-frequency process and using a phase-lock scheme based on direct digital synthesis, we achieve a tooth linewidth of 2.0 kHz in a 1-s timescale (750 Hz in 20 ms). The generated per-tooth power of 1 μW ranks this comb among the best ever realized in the mid-infrared in terms of power spectral density.

Ultrabroadband supercontinuum generation in a CMOS-compatible platform

We demonstrate supercontinuum generation spanning 1.6 octaves in silicon nitride waveguides. Using a 4.3 cm-long waveguide, with an effective nonlinearity of γ=1.2 W(-1) m(-1), we generate a spectrum extending from 665 nm to 2025 nm (at -30 dB) with 160 pJ pulses. Our results offer potential for a robust, integrated, and low-cost supercontinuum source for applications including frequency metrology, optical coherence tomography, confocal microscopy, and optical communications.

Roughness of organ pipe sound due to frequency comb

In the sound spectrum of flue organ pipes in addition to the usual harmonic partials, sometimes a series of equidistant but not harmonic lines can be found. This phenomenon has been observed in the recorded sound of pipes from different pipe ranks. The second set of spectral lines is similar to "frequency combs" used in optics for accurate measurement of optical frequencies. Analysis of measured sound spectra with and without frequency comb and simulations are presented and discussed in the paper. The appearance of frequency combs in the sound spectrum is explained by a model that assumes the presence of a mouth tone in addition to the pipe sound. Mouth tone bursts are generated when the oscillating air jet passes the upper lip. The burst repetition frequency is locked to the fundamental frequency of the pipe and the bursts are coherent with a pulse-to-pulse phase shift. The phase shift explains the observed frequency offset of the frequency comb to the harmonic frequencies. The simulations also show that weak and fluctuating mouth tones cannot generate frequency comb due to a lack of coherence.

Demonstration of an optical frequency synthesizer with zero carrier-envelope-offset frequency stabilized by the direct locking method

We developed an optical frequency synthesizer (OFS) with the carrier-envelope-offset frequency locked to 0 Hz achieved using the "direct locking method." This method differs from a conventional phaselock method in that the interference signal from a self-referencing f-2f interferometer is directly fed back to the carrier-envelope-phase control of a femtosecond laser in the time domain. A comparison of the optical frequency of the new OFS to that of a conventional OFS stabilized by a phase-lock method showed that the frequency comb of the new OFS was not different to that of the conventional OFS within an uncertainty of 5.68x10(-16). As a practical application of this OFS, we measured the absolute frequency of an acetylene-stabilized diode laser serving as an optical frequency standard in optical communications.

Asynchronous encrypted information transmission with sub-6 fs laser system at 2.12 GHz repetition rate

The asynchronous transmission (encoding and decoding) of 64-bit information using binary spectral phase shaping is demonstrated. The accurate introduction and retrieval of the binary information is possible by using multiphoton intrapulse interference phase scan (MIIPS) to measure and correct the spectral phase distortions of the laser and the transmission media. Experimental demonstration is achieved using a sub-6 fs Ti:Sapphire laser with 2.12-GHz repetition rate and an adaptive phase control system.

Passion for precision

Optical frequency combs from mode-locked femtosecond lasers have revolutionized the art of counting the frequency of light. They can link optical and microwave frequencies in a single step, and they provide the long missing clockwork for optical atomic clocks. By extending the limits of time and frequency metrology, they enable new tests of fundamental physics laws. Precise comparisons of optical resonance frequencies of atomic hydrogen and other atoms with the microwave frequency of a cesium atomic clock are establishing sensitive limits for possible slow variations of fundamental constants. Optical high harmonic generation is extending frequency comb techniques into the extreme ultraviolet, opening a new spectral territory to precision laser spectroscopy. Frequency comb techniques are also providing a key to attosecond science by offering control of the electric field of ultrafast laser pulses. In our laboratories at Stanford and Garching, the development of new instruments and techniques for precision laser spectroscopy has long been motivated by the goal of ever higher resolution and measurement accuracy in optical spectroscopy of the simple hydrogen atom which permits unique confrontations between experiment and fundamental theory. This lecture recounts these adventures and the evolution of laser frequency comb techniques from my personal perspective.

Terahertz frequency standard based on three-photon coherent population trapping

A scheme for a terahertz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10(-14) at 1 s can be reached with a precision limited by power broadening to 10(-11) in the less favorable case. The referenced terahertz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.

Noise properties of microwave signals synthesized with femtosecond lasers

We discuss various aspects of high resolution measurements of phase fluctuations at microwave frequencies. This includes methods to achieve thermal noise limited sensitivity, along with the improved immunity to oscillator amplitude noise. A few prototype measurement systems were developed to measure phase fluctuations of microwave signals extracted from the optical pulse trains generated by femtosecond lasers. This enabled first reliable measurements of the excess phase noise associated with optical-to-microwave frequency division. The spectral density of the excess phase noise was found to be -140 dBc/Hz at 100 Hz offset from the 10 GHz carrier which was almost 40 dB better than that of a high quality microwave synthesizer.

Frequency-comb-referenced two-wavelength source for absolute distance measurement

We propose a new tunable laser source concept for multiple-wavelength interferometry, offering an unprecedented large choice of synthetic wavelengths with a relative uncertainty better than 10(-11) in vacuum. Two lasers are frequency stabilized over a wide range of frequency intervals defined by the frequency comb generated by a mode-locked fiber laser. In addition, we present experimental results demonstrating the generation of a 90 mum synthetic wavelength calibrated with an accuracy better than 0.2 parts in 10(6). With this synthetic wavelength we can resolve one optical wavelength, which opens the way to absolute distance measurement with nanometer accuracy.

Efficient 1 GHz Ti:sapphire laser with improved broadband continuum in the infrared

We demonstrate a 1 GHz prismless femtosecond Ti:sapphire ring laser that emits 890 mW for 7.6 W of pump power over a continuum extending from 585 to 1200 nm at -20 dB below the maximum. A broadband continuum is obtained with the net cavity group delay dispersion having -50 to 100 fs2 oscillations from 700 to 900 nm. Further broadening is obtained by use of a slightly convex cavity mirror that increases self-phase modulation. Approximately 17% (75%) of the intracavity (output) power is generated in single pass through the crystal, outside the cavity bandwidth, and concentrated in the low-gain IR from 960 to 1200 nm.

Study of the excess noise associated with demodulation of ultra-short infrared pulses

The demodulation of ultra-short light pulses with photodetectors is accompanied by excess phase noise at the pulse repetition rate and harmonics in the spectrum of the photocurrent. The major contribution to this noise is power fluctuations of the detected pulse train that, if not compensated for, can seriously limit the stability of frequency transfer from optical to microwave domain. By making use of an infrared femtosecond laser, we measured the spectral density of the excess phase noise, as well as power-to-phase conversion for different types of InGaAs photodetectors. Noise measurements were performed with a novel type of dual-channel readout system using a fiber coupled beam splitter. Strong suppression of the excess phase noise was observed in both channels of the measurement system when the average power of the femtosecond pulse train was stabilized. The results of this study are important for the development of low-noise microwave sources derived from optical "clocks" and optical frequency synthesis.