Carrier-envelope Offset Frequency Research Articles

Powerful 1-µm 1-GHz optical frequency comb.

A self-referenced optical frequency comb is presented based on Kerr-lens mode-locking of ytterbium-doped CALGO. The robust source delivers 3.5 W average power in 44 fs-long pulses at 1 GHz repetition rate. The residual root-mean-square timing jitter of the emitted pulse-train is 146 fs and the residual integrated phase noise of the carrier-envelope offset frequency is 107 mrad, both in a span from 1 Hz to 10 MHz. After stabilization, 2.7 W average power remains for direct application. This work represents the first multi-mode pumped Kerr-lens mode-locked optical frequency comb at gigahertz-level repetition rate.

Kerr-induced synchronization of a cavity soliton to an optical reference.

The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3-6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC7 to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier-envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.

Sideband injection locking in microresonator frequency combs

Frequency combs from continuous-wave-driven Kerr-nonlinear microresonators have evolved into a key photonic technology with applications from optical communication to precision spectroscopy. Essential to many of these applications is the control of the comb’s defining parameters, i.e., carrier-envelope offset frequency and repetition rate. An elegant and all-optical approach to controlling both degrees of freedom is the suitable injection of a secondary continuous-wave laser into the resonator onto which one of the comb lines locks. Here, we experimentally study such sideband injection locking in microresonator soliton combs across a wide optical bandwidth and derive analytic scaling laws for the locking range and repetition rate control. As an application example, we demonstrate optical frequency division and repetition rate phase-noise reduction to three orders of magnitude below the noise of a free-running system. The presented results can guide the design of sideband injection-locked, parametrically generated frequency combs with opportunities for low-noise microwave generation, compact optical clocks with simplified locking schemes, and, more generally, all-optically stabilized frequency combs from Kerr-nonlinear resonators.

Ultrafast mode-locked laser in nanophotonic lithium niobate.

Mode-locked lasers (MLLs) generate ultrashort pulses with peak powers substantially exceeding their average powers. However, integrated MLLs that drive ultrafast nanophotonic circuits have remained elusive because of their typically low peak powers, lack of controllability, and challenges when integrating with nanophotonic platforms. In this work, we demonstrate an electrically pumped actively MLL in nanophotonic lithium niobate based on its hybrid integration with a III-V semiconductor optical amplifier. Our MLL generates [Formula: see text]4.8-ps optical pulses around 1065 nm at a repetition rate of ∼10 GHz, with energies exceeding 2.6 pJ and peak powers beyond 0.5 W. The repetition rate and the carrier-envelope offset frequency of the output can be controlled in a wide range by using the driving frequency and the pump current, providing a route for fully stabilized on-chip frequency combs.

Frequency comb with a spectral range of 0.4-5.2 µm based on a compact all-fiber laser and LiNbO3 waveguide.

This Letter presents a 0.4-5.2-µm frequency comb from a compact laser. We designed an integrated fiber device for a figure-9 laser and constructed an all-fiber laser system. The spectrum of the fiber laser was scaled to the broadband region using a chirped periodically poled lithium niobate waveguide. To use this system for gas sensing, a mid-infrared comb with a spectral range of 2.5-5.2 µm and average power of 2.1 mW was divided using an optical filter. The optical part was packaged in a 305 mm × 225 mm × 62 mm box. The comb was stabilized by locking the repetition rate and carrier-envelope offset frequency of the seed source. The system provided an ultrabroadband spectral range from 0.4 to 5.2 µm, which could be applied to spectroscopy, frequency metrology, and optical synthesizers.

A reference-free dual-comb spectroscopy calibrated by passive devices

Dual-comb spectroscopy has enabled new approaches for optical precision measurements. Although Doppler-limited resolution can be achieved over long-time scales across a large bandwidth, the development of dual-comb spectroscopy is hindered by strict demands for light source stability. Typically, expensive and complex self-reference systems are required to lock the carrier-envelope offset frequency (fceo) of the laser. Additionally, simply locking the repetition frequency (frep) to a radio frequency reference source still results in residual relative timing jitter between light sources. Here we extracted the relative fceo fluctuation between the frep-locked lasers from the high-precision passive notch filtering characteristics of the phase-shifted fiber Bragg grating and then eliminated it through online phase calibration. By introducing a passive broadband Fabry–Perot cavity with excellent thermal wavelength stability, we subsequently corrected residual relative timing jitter with online wavelength calibration, and the standard deviation of the relative wavelength drift was reduced to less than 0.4 pm within the full operating range. The spectral profile can also be extracted and removed by the Fabry–Perot cavity through intensity calibration. By calibrating these three dimensions, we built a reference-free post-calibration dual-comb spectroscopy and used this powerful tool to measure the Fabry–Perot cavity resonance peaks, the notch filtering narrow band of phase-shifted fiber Bragg gratings, and the absorption characteristics of hydrogen cyanide gas. The system achieves a spectral resolution of 0.8 pm over a bandwidth of more than 100 nm. This low-cost and convenient scheme provides new ideas for the application of dual-comb spectroscopy systems.

Carrier-envelope offset frequency measurement by means of an external optical resonator

A general-purpose method based on the implementation of the asymmetric Pound–Drever–Hall (PDH) technique is proposed to measure the carrier-envelope offset (CEO) frequency of a mode-locked laser using an external optical cavity. By analyzing the synchronously demodulated signal of the spectrally filtered cavity reflection when the optical resonator is locked to the mode-locked laser, a discriminating signal depending on the relative frequency offset between the mode-locked and optical cavity comb-like spectra is obtained. For a given geometry and group delay dispersion (GDD) of the cavity parameters (i.e., a known cavity mode offset), this signal can be used to retrieve the laser CEO. This approach turns out to be advantageous in terms of setup complexity with respect to other well-known techniques that rely on non-linear frequency generation, such as f–2f interferometers. In addition, this method can be used to precisely determine the laser–cavity spectral coupling, which is an important topic in cavity-enhanced spectroscopy and non-linear optics applications. After the theoretical description of the generalized asymmetric PDH signal, an experimental validation of the proposed method is reported using an Er-doped fiber frequency comb source centered at 1,550 nm, with a repetition rate of 250 MHz, locked to a linear optical cavity with a 1 GHz free spectral range. The theoretical effect of the GDD is confirmed experimentally using different cavity configurations. Moreover, the comparison with the CEO frequency values measured using an f–2f interferometer demonstrates the feasibility of the proposed method.

Vernier microcombs for high-frequency carrier envelope offset and repetition rate detection

Recent developments in Kerr microcombs may pave the way to a future with fully stabilized ultralow size, weight, and power consumption (SWaP) frequency combs. Nevertheless, Kerr microcombs are still hindered by a bandwidth/repetition rate trade-off. That is, the octave bandwidth needed for self-referencing is typically realized only with ∼THz repetition rates beyond the range of standard commercial photodetectors. The carrier envelope offset frequency is often likewise too high for detection. Dual-comb techniques for the measurement of THz repetition rates have made exciting progress, but the fCEO detection problem remains largely unaddressed. In this work, utilizing a Vernier dual-comb configuration, we demonstrate simultaneous detection of the electronically divided repetition rate and fCEO carrier envelope offset frequency of an octave-spanning microcomb. This, in turn, could help usher optical atomic clocks, low-noise microwave generators, and optical frequency synthesizers into various real-world applications.

Relative phase locking of a terahertz laser system configured with a frequency comb and a single-mode laser

Stable operation is one of the most important requirements for a laser source for high-precision applications. Many efforts have been made to improve the stability of lasers by employing various techniques, e.g., electrical and/or optical injection and phase locking. However, these techniques normally involve complex experimental facilities. Therefore, an easy implementation of the stability evaluation of a laser is still challenging, especially for lasers emitting in the terahertz (THz) frequency range because the broadband photodetectors and mature locking techniques are limited. In this work, we propose a simple method, i.e., relative phase locking, to quickly evaluate the stability of THz lasers without a need of a THz local oscillator. The THz laser system consists of a THz quantum cascade laser (QCL) frequency comb and a single-mode QCL. Using the single-mode laser as a fast detector, heterodyne signals resulting from the beating between the single-mode laser and the comb laser are obtained. One of the heterodyne beating signals is selected and sent to a phase-locked loop (PLL) for implementing the relative phase locking. Two kinds of locks are performed by feeding the output error signal of the PLL, either to the comb laser or to the single-mode laser. By analyzing the current change and the corresponding frequency change of the PLL-controlled QCL in each phase-locking condition, we, in principle, are able to experimentally compare the stability of the emission frequency of the single-mode QCL (fs) and the carrier envelope offset frequency (fCEO) of the QCL comb. The experimental results reveal that the QCL comb with the repetition frequency injection locked demonstrates much higher stability than the single-mode laser. The work provides a simple heterodyne scheme for understanding the stability of THz lasers, which paves the way for the further locking of the lasers and their high-precision applications in the THz frequency range.

A low phase noise high power Er-fiber frequency comb synchronized to the hydrogen maser clock by harmonic phase locking

We demonstrate a low phase noise all polarization-maintaining (PM) Er-fiber optical frequency comb (OFC) with low phase noise, which is synchronized to the hydrogen maser clock (HMC) using the 18th harmonic of the repetition rate for tight phase locking. The instability of the locked carrier envelope offset frequency is 1.24 × 10−18@1 s, the phase noise of the OFC is −96 dBc/Hz at 1 Hz offset, and the corresponding RMS timing jitter of the repetition rate is 62 fs (1 Hz–1 MHz). The residual frequency instability of the repetition rate (200 MHz) is 1.46 × 10−14@1 s, and the residual phase noise of the OFC normalized to 10 MHz is −138 dBc/Hz at 1 Hz offset and declines to about −160 dBc/Hz at the far-end, much lower than that of the HMC (−122 dBc/Hz at 1 Hz and −156 dBc/Hz at the far-end).

Versatile tuning of Kerr soliton microcombs in crystalline microresonators

Microresonator-based optical frequency combs emitted from high-quality-factor microresonators, also known as microcombs, have opened up new horizons to areas of optical frequency comb technology including frequency metrology, precision sensing, and optical communication. To extend the capability of microcombs for such applications, large and reliable tunability is of critical importance. Here, we show broad spectral tuning of Kerr soliton microcombs in a thermally controlled crystalline microresonator with pump-detuning stabilization. The fundamental elements composing frequency combs, namely the center frequency, repetition frequency, and carrier-envelope offset frequency, are spectrally tuned by up to −48.8 GHz, −5.85 MHz, and −386 MHz, respectively, leveraging thermal effects in ultrahigh-Q crystalline magnesium fluoride resonators. We further demonstrate a 3.4-fold enhancement of soliton comb power resulting from thermal expansion with a temperature change of only 28 K by employing quantitative analyses of the fiber-to-resonator coupling efficiency.

Low frequency-to-intensity noise conversion in a pulsed laser cavity locking by exploiting carrier envelope offset

We report on the dependence of the frequency-to-intensity noise conversion in the locking of an ultrafast laser against a high-finesse optical enhancement resonator from the carrier envelope offset frequency. By a proper combination of the cavity finesse and laser carrier envelope offset frequency, it is possible to optimize the signal-to-noise ratio of the laser intensity trapped into the optical resonator. In this paper, we describe the effect of the laser-enhancement cavity coupling on the intracavity power relative noise, and we demonstrate both theoretically and experimentally its reduction.

Frequency combs with multiple offsets in THz-rate microresonators.

Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the breather combs into a sequence of sub-combs with different carrier-envelope offset frequencies. The large detuning breathers have a high frequency of oscillations associated with the perturbation extending across the whole microresonator. The small detuning breathers create oscillations localised on the soliton core and can undergo the period-doubling bifurcation, which triggers a sequence of intense sub-combs.

Collinear opto-optical loss modulation for carrier-envelope offset stabilization of a fiber frequency comb.

Opto-optical loss modulation (OOM) for stabilization of the carrier-envelope offset (CEO) frequency of a femtosecond all-fiber laser is performed using a collinear geometry. Amplitude-modulated 1064 nm light is fiber coupled into an end-pumped semiconductor saturable absorber mirror (SESAM)-mode-locked all-polarization-maintaining erbium fiber femtosecond laser, where it optically modulates the loss of the SESAM resulting in modulation of the CEO frequency. A noise rejection bandwidth of 150 kHz is achieved when OOM and optical gain modulation are combined in a hybrid analog/digital loop. Collinear OOM provides a simple, all-fiber, high-bandwidth method for improving the CEO frequency stability of SESAM mode-locked fiber lasers.

Method of adjusting carrier-envelope offset frequency based on electro-optic-crystal Mach-Zehnder interferometer

Electro-optic-modulator (EOM) based Mach-Zehnder (M-Z) interferometer is a novel method of controlling the carrier envelope offset frequency (<i>f</i><sub>0</sub>). It is achieved by adjusting the envelop of the pulse, while keeping the carrier frequency unchanged. In this paper, the polarization control device involved in this method is simulated, and the influences caused by the deviation of the optical axis of the wave plate on the polarization direction and the degree of output laser are analyzed. An optical axis calibration method is proposed to reduce the influence caused by the deviation of optical axis of wave plate. The effects of pump current and EOM based M-Z interferometer on <i>f</i><sub>0</sub> and the beat note (<i>f</i><sub>b</sub>) between the comb and the laser are compared with each other. The experimental results show that the effect of changing the pump current on <i>f</i><sub>b</sub> is 7 MHz, when the <i>f</i><sub>0</sub> adjustment quantity is 9 MHz. Under the same <i>f</i><sub>0</sub> adjustment quantity, the influence of EOM based M-Z interferometer on<i> f</i><sub>b</sub> is 0.2 MHz, which is only 1/35 of the influence of pump current. Therefore, it is verified that EOM based M-Z interferometer can effectively reduce the interference to <i>f</i><sub>b</sub>. It provides a technical means to narrow the line width of optical comb by using <i>f</i><sub>b</sub> to lock repetition rate (<i>f</i><sub>r</sub>) .

Experimental realization and characterization of a two–color dual–comb system for practical large–scale absolute distance measurements

In this paper, a two–color dual–comb system has been realized and characterized for the specific applications of the practical large–scale absolute distance measurements, especially for the investigations of asynchronous optical sampling (ASOPS) with a slight difference of repetition rates. The fundamental 1550 nm wavelength is emitting from the Er–fiber femtosecond frequency combs with a repetition rate of around 200 MHz and carrier-envelope offset frequency of 20 MHz, and the other wavelength of 775 nm is generated by the second harmonic generation crystals. The optical characteristics are investigated in detail, and the stability of frequency parameters are also evaluated for long–term time. The preliminary experimental results of ASOPS show that this two-color dual-comb system has the potential to be applied for further diversified research.

Two-photon dual-comb LiDAR.

The interferometric signals produced in conventional dual-comb laser ranging require femtosecond lasers with long-term carrier-envelope offset frequency stability, and are limited to an upper sampling rate by radio-frequency aliasing considerations. By using cross-polarized dual combs and two-photon detection, we demonstrate carrier-phase-insensitive cross-correlations at sampling rates of up to 12× the conventional dual-comb aliasing limit, recording these in a digitizer-based acquisition system to implement ranging with sub-100 nm precision. We then extend this concept to show how the high data burden of conventional dual-comb acquisition can be eliminated by using a simple microcontroller as a ns-precision stopwatch to record the time intervals separating the two-photon cross-correlation pulses, providing real-time and continuous LiDAR-like distance metrology capable of sub-100 nm precision and dynamic acquisition for unlimited periods.

Carrier-envelope offset frequency dynamics of a 10-GHz modelocked laser based on cascaded quadratic nonlinearities.

Cascaded quadratic nonlinearities from phase-mismatched second-harmonic generation build the foundation for robust soliton modelocking in straight-cavity laser configurations by providing a tunable and self-defocusing nonlinearity. The frequency dependence of the loss-related part of the corresponding nonlinear response function causes a power-dependent self-frequency shift (SFS). In this paper, we develop a simple analytical model for the SFS-induced changes on the carrier-envelope offset frequency (fCEO) and experimentally investigate the static and dynamic fCEO dependence on pump power. We find good agreement with the measured dependence of fCEO on laser output power, showing a broad fCEO tuning capability from zero up to the pulse repetition rate. Moreover, we stabilize the relative intensity noise to the -157dBc/Hz level leading to a tenfold reduction in fCEO-linewidth.

Aluminum nitride nanophotonics for beyond-octave soliton microcomb generation and self-referencing

Frequency microcombs, alternative to mode-locked laser and fiber combs, enable miniature rulers of light for applications including precision metrology, molecular fingerprinting and exoplanet discoveries. To enable frequency ruling functions, microcombs must be stabilized by locking their carrier-envelope offset frequency. So far, the microcomb stabilization remains compounded by the elaborate optics external to the chip, thus evading its scaling benefit. To address this challenge, here we demonstrate a nanophotonic chip solution based on aluminum nitride thin films, which simultaneously offer optical Kerr nonlinearity for generating octave soliton combs and quadratic nonlinearity for enabling heterodyne detection of the offset frequency. The agile dispersion control of crystalline aluminum nitride photonics permits high-fidelity generation of solitons with features including 1.5-octave spectral span, dual dispersive waves, and sub-terahertz repetition rates down to 220 gigahertz. These attractive characteristics, aided by on-chip phase-matched aluminum nitride waveguides, allow the full determination of the offset frequency. Our proof-of-principle demonstration represents an important milestone towards fully integrated self-locked microcombs for portable optical atomic clocks and frequency synthesizers.

Comparison of two low-noise CEO frequency stabilization methods for an all-PM Yb:fiber NALM oscillator

We present a comparison of two low-noise carrier-envelope offset (CEO) frequency stabilization methods studied using an ytterbium (Yb) fiber laser oscillator based on a nonlinear amplifying loop mirror. We first investigate the phase locking performance achieved with cross-gain modulation (XGM) via injection of an auxiliary low-power continuous-wave (CW) laser into the fiber gain medium. Amplification of the injected CW laser light cross-modulates the gain of the oscillator, resulting in an intra-cavity power modulation, thus providing control of the CEO frequency. The XGM method is then compared with the conventional pump-current modulation scheme. Both stabilization methods provide similar locking performances with sub-200-mrad of integrated residual carrier-envelope-phase (CEP) noise (10 Hz to 1 MHz), suitable for high-resolution comb spectroscopy applications.