Carrier-envelope Offset Frequency Research Articles

An Yb-fiber frequency comb phase-locked to microwave standard and optical reference**Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDA1502040404 and XDB21010400) and the National Natural Science Foundation of China (Grant Nos. 91850209 and 11774234).

We present a fully stabilized Yb-fiber frequency comb locked to a microwave standard and an optical reference separately. The carrier-envelope offset frequency is generated by a standard f –2f interferometer with 40 dB signal-to-noise ratio. The offset frequency and the repetition rate are stabilized simultaneously to the radio frequency reference for more than 30 hours, and the fractional Allan deviation of the comb is the same as the microwave standard of 10−12 at 1 s. Alternatively, the comb is locked to an ultra-stable optical reference at 972 nm using an intracavity electro-optic modulator, exhibiting a residual integrated phase noise of 458 mrad (1 Hz–10 MHz) and an in-loop tracking stability of 1.77 × 10−18 at 1 s, which is significantly raised by six orders comparing to the case locked to the microwave frequency standard.

Middle-IR frequency comb based on Cr:ZnS laser.

We report, to the best of our knowledge, the first fully referenced Cr:ZnS optical frequency comb. The comb features few cycle output pulses with 3.25 W average power at 80 MHz repetition rate, spectrum spanning 60 THz in the middle-IR range 1.79-2.86 µm, and a small footprint (0.1 m2), The spectral components used for the measurement of the comb's carrier envelope offset frequency were obtained directly inside the polycrystalline Cr:ZnS laser medium via intrinsic nonlinear interferometry. Using this scheme we stabilized the offset frequency of the comb with the residual phase noise of 75 mrads.

Versatile digital approach to laser frequency comb stabilization

We demonstrate the use of a flexible digital servo system for the optical stabilization of both the repetition rate and carrier-envelope offset frequency of a laser frequency comb. The servo system is based entirely on a low-cost field programmable gate array, simple electronic components, and existing open-source software. Utilizing both slow and fast feedback actuators of a commercial mode-locked laser frequency comb, we maintain cycle-slip free locking of optically-derived beatnotes over a 30 hour period and measure residual phase noise at or below ~0.1 rad, corresponding to <100 attosecond timing jitter on the optical phase locks. This stability is sufficient for high-precision frequency comb applications and indicates comparable performance to existing frequency control systems. The modularity of this system allows for it to be easily adapted to suit the servo actuators of a wide variety of laser frequency combs and continuous-wave lasers, reducing cost and complexity barriers, and enabling digital phase control in a wide range of settings.

Ultrastable Laser System for Spectroscopy of the 1.14 μm Inner-Shell Clock Transition in Tm and Its Absolute Frequency Measurement

We characterize a 1.14 μm ultrastable semiconductor laser system for precision spectroscopy of Tm inner-shell clock transition using a frequency comb. We stabilize both the repetition and the carrierenvelope offset frequencies of a commercial Ti : sapphire femtosecond laser to a passive hydrogen maser using a home-built f-2f interferometer. By measuring the absolute frequency of the 1.14 μm laser stabilized to a high-finesse ULE cavity, we determine the zero-expansion temperature point of the cavity and the rate of linear drift of the the cavity resonance frequency due to “aging” of the ULE glass. We achieve less than 10 Hz frequency instability of the laser within 1,000 s after the linear drift compensation. We also measured the absolute frequency of the 1.14 μm transition in Tm to be 262 954 938 269 213(30) Hz.

XUV Sources Based on Intra-Oscillator High Harmonic Generation With Thin-Disk Lasers: Current Status and Prospects

Ultrafast thin-disk laser (TDL) oscillators provide higher intracavity pulse energy, average power, and peak power levels than any other femtosecond laser oscillator technology. They are suitable for driving extreme nonlinear interactions directly inside the laser oscillator. High harmonic generation (HHG) driven inside ultrafast TDL oscillators is a very recent approach for the generation of coherent extreme ultraviolet (XUV) light at multi-megahertz repetition rates. In this paper, we review the current state of the development, discuss the technological potential, and give an outlook toward the future developments. We compare the current performance to established technologies and evaluate possible limitations. We discuss future improvements, such as reduction of the driving pulse duration and increase of the intracavity peak power, efficient extraction of the XUV light from the cavity, and carrier-envelope offset frequency stabilization of the generated XUV light. Due to the power scalability of the TDL concept and the possibility to operate in a spectrally broadened regime with pulse durations below the gain bandwidth limitation, intra-oscillator HHG with TDLs has a high potential for powerful table-top multi-megahertz coherent XUV light sources for science and applications.

Multi-octave visible to long-wave IR femtosecond continuum generated in Cr:ZnS-GaSe tandem.

We report a technique for generation of broad and coherent femtosecond (fs) continua that span several octaves from visible to long-wave IR parts of the spectrum (0.4-18 µm). The approach is based on simultaneous amplification of few-cycle pulses at 2.5 µm central wavelength at 80 MHz repetition rate, and augmentation of their spectrum via three-wave mixing in a tandem arrangement of polycrystalline Cr:ZnS and single crystal GaSe. The obtained average power levels include several mW in the 0.4-0.8 µm visible, 0.23 W in the 0.8-2 µm near-IR, up to 4 W in the 2-3 µm IR, and about 17 mW in the 3-18 µm long-wave IR bands, respectively. High brightness and mutual coherence of all parts of the continuum was confirmed by direct detections of the carrier envelope offset frequency of the master oscillator.

Coherent two-octave-spanning supercontinuum generation in lithium-niobate waveguides

We demonstrate coherent supercontinuum generation (SCG) in a monolithically integrated lithium-niobate waveguide, under the presence of second- and third-order nonlinear effects. We achieve more than two octaves of optical bandwidth in a 0.5-cm-long waveguide with 100-picojoule-level pulses. Dispersion engineering of the waveguide allows for spectral overlap between the SCG and the second harmonic, which enables direct detection of the carrier-envelope offset frequency fCEO using a single waveguide. We measure the fCEO of our femtosecond pump source with a 30-dB signal-to-noise ratio.

High-coherence ultra-broadband bidirectional dual-comb fiber laser.

Dual-comb spectroscopy has emerged as an attractive spectroscopic tool for high-speed, high-resolution, and high-sensitivity broadband spectroscopy. It exhibits certain advantages when compared to the conventional Fourier-transform spectroscopy. However, the high cost of the conventional system, which is based on two mode-locked lasers and a complex servo system with a common single-frequency laser, limits the applicability of the dual-comb spectroscopy system. In this study, we overcame this problem with a bidirectional dual-comb fiber laser that generates two high-coherence ultra-broadband frequency combs with slightly different repetition rates (frep). The two direct outputs from the single-laser cavity displayed broad spectra of > 50 nm; moreover, an excessively small difference in the repetition rate (< 1.5 Hz) was achieved with high relative stability, owing to passive common-mode noise cancellation. With this slight difference in the repetition rate, the applicable optical spectral bandwidth in dual-comb spectroscopy could attain ~479 THz (~3,888 nm). In addition, we successfully generated high-coherence ultra-broadband frequency combs via nonlinear spectral broadening and detected high signal-to-noise-ratio carrier-envelope offset frequency (fCEO) beat signals using the self-referencing technique. We also demonstrated the high relative stability between the two fCEO beat signals and tunability. To our knowledge, this is the first demonstration of fCEO detection and frequency measurement using a self-referencing technique for a dual-comb fiber laser. The developed high-coherence ultra-broadband dual-comb fiber laser with capability of fCEO detection is likely to be a highly effective tool in practical, high-sensitivity, ultra-broadband applications.

Control of Kerr-microresonator optical frequency comb by a dual-parallel Mach-Zehnder interferometer

A technique to integrate key functions of a Kerr-microresonator optical frequency comb into one device, i.e., a dual-parallel Mach-Zehnder interferometer (DP-MZI), is proposed. In the technique, a DP-MZI enables the control of carrier envelope offset frequency (fceo), as well as repetition frequency (frep), in addition to generating a stable dissipative Kerr soliton. In experiments, influences on fceo and frep by pump frequency and power modulation via a DP-MZI are investigated, followed by a demonstration of long-term full stabilization of a microresonator soliton comb to a fiber-based optical frequency comb. As another example demonstration, timing jitter of a microresonator soliton comb is significantly suppressed by referencing to a fiber through a two-wavelength delayed self-heterodyne interferometer (TWDI).

Octave-spanning Cr:ZnS femtosecond laser with intrinsic nonlinear interferometry

We report a few-cycle, super-octave, polycrystalline Cr:ZnS laser system with 4 W power at 78 MHz repetition rate, where all of the necessary optical signals for the measurement of the carrier–envelope offset frequency are generated intrinsically.

Carrier‐Envelope‐Offset Frequency Stable 100 W‐Level Femtosecond Thin‐Disk Oscillator

AbstractIn this paper, the carrier‐envelope‐offset (CEO) frequency stabilization of a Kerr‐lens mode‐locked femtosecond oscillator with average power 105 W is presented. Intra‐cavity Kerr lensing is realized in a quartz crystal that simultaneously serves as an acousto‐optic loss modulator. This novel method results in a CEO frequency stable laser with high average power and a residual in‐loop phase noise below 90 mrad. Furthermore, an all‐solid‐state bulk broadening stage is presented. The compressed, CEO frequency‐stabilized output has a peak power exceeding 67 MW at a pulse duration of 40 fs and a repetition rate of 15.6 MHz. The intra‐cavity peak power of the CEO frequency‐stabilized oscillator is around 200 MW. These results pave the way toward compact, transportable all‐solid‐state drivers with high repetition rates for deep UV and XUV frequency combs and other nonlinear processes.

Carrier-envelope offset frequency stabilization of a thin-disk laser oscillator operating in the strongly self-phase modulation broadened regime.

We demonstrate the carrier-envelope offset (CEO) frequency stabilization of a Kerr lens mode-locked Yb:Lu2O3 thin-disk laser oscillator operating in the strongly self-phase modulation (SPM) broadened regime. This novel approach allows overcoming the intrinsic gain bandwidth limit and is suited to support frequency combs from sub-100-fs pulse trains with very high output power. In this work, strong intra-oscillator SPM in the Kerr medium enables the optical spectrum of the oscillating pulse to exceed the bandwidth of the gain material Yb:Lu2O3 by a factor of two. This results in the direct generation of 50-fs pulses without the need for external pulse compression. The oscillator delivers an average power of 4.4 W at a repetition rate of 61MHz. We investigated the cavity dynamics in this regime by characterizing the transfer function of the laser output power for pump power modulation, both in continuous-wave and mode-locked operations. The cavity dynamics in mode-locked operation limit the CEO modulation bandwidth to ~10 kHz. This value is sufficient to achieve a tight phase-lock of the CEO beat via active feedback to the pump current and yields a residual in-loop integrated CEO phase noise of 197 mrad integrated from 1 Hz to 1 MHz.

Frequency Comb Stabilization of Ultrafast Lasers by Opto-Optical Modulation of Semiconductors

In this paper, we review the current state and discuss new developments in opto-optical modulation (OOM) of semiconductor elements for frequency comb self-referenced stabilization of ultrafast lasers. This method has been successfully used for carrier-envelope offset (CEO) frequency stabilization of diode-pumped solid-state lasers operating in 1-μm and 1.5-μm regimes, providing high feedback bandwidth and resulting in low noise performance. We compare the achieved results for Er- and Yb-based laser materials and in different regimes of repetition rates up to 1 GHz. In addition, we present the first semiconductor OOM for CEO stabilization in an ultrafast fiber laser. Moreover, we discuss requirements and design guidelines for OOM chips. In most demonstrations, semiconductor saturable absorber mirrors have been used for OOM, which in parallel were also responsible for pulse formation. By separating the OOM functionality from the pulse formation, we expect that it will enable low-noise CEO stabilization in other types of ultrafast lasers, such as, for example, high-power Kerr-lens mode-locked thin disk lasers.

A phase-stable dual-comb interferometer

Laser frequency combs emit a spectrum with hundreds of thousands of evenly spaced phase-coherent narrow lines. A comb-enabled instrument, the dual-comb interferometer, exploits interference between two frequency combs and attracts considerable interest in precision spectroscopy and sensing, distance metrology, tomography, telecommunications, etc. Mutual coherence between the two combs over the measurement time is a pre-requisite to interferometry, although it is instrumentally challenging. At best, the mutual coherence reaches about 1 s. Computer-based phase-correction techniques, which often lead to artifacts and worsened precision, must be implemented for longer averaging times. Here with feed-forward relative stabilization of the carrier-envelope offset frequencies, we experimentally realize a mutual coherence over times approaching 2000 s, more than three orders of magnitude longer than that of state-of-the-art dual-comb systems. An illustration is given with near-infrared Fourier transform molecular spectroscopy with two combs of slightly different repetition frequencies. Our technique without phase correction can be implemented with any frequency comb generator including microresonators or semiconductor lasers.

Downsampling of optical frequency combs

We demonstrate repetition-rate downsampling of optical frequency combs by way of pulse gating. This results in a frequency comb with reduced repetition rate and increased pulse energy, which enables efficient spectral broadening and f-2f interferometry. To explore the technique, we downsample a 250 MHz repetition-rate comb to 25 MHz and detect the carrier–envelope offset frequency of the downsampled pulse train. We investigate the effects of pulse gating on the noise properties of the pulse train and the limitations of the technique by characterizing the phase-noise spectrum of the downsampled comb and deliberately imposing timing jitter on the pulse gate. We show that, up to an expected reduction modulo the new repetition rate, downsampling neither shifts nor introduces noise to the carrier–envelope offset frequency of the comb above the level of several microhertz. Additionally, we discuss the effect of downsampling on the spectrum of intensity fluctuations of the optical pulse train. Finally, we discuss some practical considerations relevant for the application of the technique to frequency combs with repetition rates in the 10 GHz range and higher.

Octave-spanning optical frequency comb based on a laser-diode pumped Kerr-lens mode-locked Yb:KYW laser for optical frequency measurement.

We developed an optical frequency comb based on a Yb:KYW laser. Soft-aperture Kerr-lens mode-locking at the cavity transverse-mode degeneration enabled us to generate 360mW from a 750mW pump laser diode. This resulted in spectral broadening over one octave using just a photonic crystal fiber. We achieved a free-running linewidth of 15kHz in the carrier-envelope offset frequency by optimizing the cavity group delay dispersion, crystal position, and pump laser power, which led to a residual phase noise of 0.51rad during phase-locking. We measured the frequency drift of a cavity-stabilized laser for a clock transition in Yb171+.

Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis.

We report accurate phase stabilization of an interlocking pair of Kerr-microresonator frequency combs. The two combs, one based on silicon nitride and one on silica, feature nearly harmonic repetition frequencies and can be generated with one laser. The silicon-nitride comb supports an ultrafast-laser regime with three-optical-cycle, 1-picosecond-period soliton pulses and a total dispersive-wave-enhanced bandwidth of 170THz, while providing a stable phase-link between optical and microwave frequencies. We demonstrate nanofabrication control of the silicon-nitride comb's carrier-envelope offset frequency and spectral profile. The phase-locked combs coherently reproduce their clock with a fractional precision of <6×10-13/τ, a behavior we verified through 2h of measurement to reach <3×10-16. Our work establishes Kerr combs as a viable technology for applications like optical-atomic timekeeping and optical synchronization.

Phase-stabilized 100\xa0mW frequency comb near 10\xa0\u03bcm

Long-wavelength mid-infrared (MIR) frequency combs with high power and flexible tunability are highly desired for molecular spectroscopy, including investigation of large molecules such as C60. We present a high power, phase-stabilized frequency comb near 10 μm, generated by a synchronously pumped, singly resonant optical parametric oscillator (OPO) based on AgGaSe2. The OPO can be continuously tuned from 8.4 to 9.5 μm, with a maximum average idler power of 100 mW at the center wavelength of 8.5 μm. Both the repetition rate (frep) and the carrier-envelope offset frequency (fceo) of the idler wave are phase-locked to microwave signals referenced to a Cs clock. We describe the detailed design and construction of the frequency comb, and discuss potential applications for precise and sensitive direct frequency comb spectroscopy.

Carrier-envelope offset frequency stabilization of a 100 fs-scale Ti:sapphire mode-locked laser for quantum frequency comb generation

The carrier-envelope offset (CEO) frequency stabilization of a Ti:sapphire mode-locked laser with a Fourier-transform-limited pulse width of 100 fs-scale has been successfully realized. With the home-built f-2f interferometer, the CEO beat signal has been measured with a signal-to-noise ratio (SNR) as high as 40 dB under a resolution bandwidth of 100 kHz, which means that the coherence of the octave-spanning supercontinuum (SC) is well retained, although the evaluated pulse soliton order (N ≈ 23) completely violate the previous theoretical limitation that N should be smaller than 16. Furthermore, a stabilized CEO frequency is achieved with residual phase noise suppressed to 660 mrad (integrated from 1 Hz to 100 kHz) and an Allan deviation relative to the optical carrier of 7.6 × 10−18 at 1 s integration time. This realization constructs a solid foundation for further generation of quantum frequency comb needed for ultra-sensitive optical timing measurement applications.

Computation of the timing jitter, phase jitter, and linewidth of a similariton laser

We perform what we believe is the first computational study of phase jitter and comb linewidths in a nonsolitonic fiber laser with large changes in the pulse on each round trip. For fiber lasers operating in or near the similariton regime, we investigate how the pulse parameters and noise performance depend on the system parameters. Across a large dispersion range, the dechirped pulse width, timing jitter, phase jitter, and comb linewidths are smaller when the gain in the optical amplifier is larger. Over a narrow range of negative dispersion values near zero, the timing jitter and comb linewidths are smaller with a wider optical filter. However, with the wider optical filter, the pulse width increases significantly, and the noise performance deteriorates rapidly as the dispersion increases above zero. These trends are in general agreement with experimental studies of timing jitter and the linewidth of the carrier-envelope offset frequency in Yb-fiber lasers and are consistent with the Namiki–Haus theory of timing jitter in a stretched-pulse laser.