Carrier-envelope Offset Research Articles

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.

Femtosecond Frequency Combs with Few‐kHz Passive Stability over an Ultrabroadband Spectral Range

AbstractFemtosecond frequency combs are among the most precise measurement tools in existence. They have applications ranging from high‐precision spectroscopy and metrology to time‐domain quantum physics. Maximizing the passive stability of these instruments is essential to achieve their full potential in fundamental science and high‐tech industry. However, the noise mechanisms across the entire operating space of these devices have not been fully characterized. Here the noise properties of fiber‐based frequency combs are studied as a function of intracavity dispersion, pump power, and repetition rate. Distinct minima are discovered in this parameter space where the free‐running linewidth of the carrier‐envelope offset (CEO) frequency fCEO drops below 1 kHz. The individual comb lines are analyzed spread over a wide spectral range producing a complete understanding of the particular contributions to the phase noise and their interplay. Exploiting these findings, combs featuring sharp teeth at specific frequency positions and over the entire spectrum from fCEO to 300 THz are demonstrated. The ultrabroadband stability offered by these compact systems provides a new level of quality for front‐end measurement tasks in both time and frequency domains.

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.

Direct f-3f self-referencing using an integrated silicon-nitride waveguide.

We have achieved the simultaneous generation of a 2.6-octave-wide supercontinuum (SC) spectrum over 400-2500 nm and third-harmonic light solely by a dispersion-controlled silicon-nitride waveguide (SiNW). To increase the visible intensity of the SC light component, we fabricated low-loss 5-mm-long deuterated SiNWs with spot-size converters by low-temperature deposition. We succeeded in measuring the carrier-envelope-offset (CEO) signal with a 34-dB signal-to-noise ratio because this short deuterated SiNW provides a large temporal overlap between the f and 3f components. In addition, we have demonstrated this method of CEO locking at telecommunications wavelengths with f-3f self-referencing generated solely by the SiNW without the use of highly nonlinear fiber and an additional nonlinear crystal. Compared with the method of CEO locking with a highly nonlinear fiber and a standard f-2f self-referencing interferometer, this method is not only simple and compact but also stable.

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.

Simple method for mid-infrared optical frequency comb generation with dynamic offset frequency tuning

We present a simple method for fully stabilized mid-infrared optical frequency comb generation based on single-pass femtosecond optical parametric generation that is seeded by a continuous-wave laser. We have implemented the method in a periodically poled lithium niobate crystal that produces a frequency comb tunable across 3325 nm–4000 nm (2380 cm−1–3030 cm−1). The method generates the mid-infrared (idler) comb with known and stabilized Carrier-Envelope Offset (CEO) frequency without the need to directly detect it. The idler CEO is continuously tunable for almost half of the repetition rate and can be modulated. Together with the high output power (up to 700 mW) and low intensity noise (0.018% integrated in 10 Hz–2 MHz bandwidth), this makes the demonstrated mid-infrared frequency comb promising for many applications such as high-precision molecular spectroscopy, frequency metrology, and high harmonic generation.

Carrier-envelope offset stable, coherently combined ytterbium-doped fiber CPA delivering 1 kW of average power.

We present a carrier-envelope offset (CEO) stable ytterbium-doped fiber chirped-pulse amplification system employing the technology of coherent beam combining and delivering more than 1 kW of average power at a pulse repetition rate of 80 MHz. The CEO stability of the system is 220 mrad rms, characterized out-of-loop with an f-to-2f interferometer in a frequency offset range of 10 Hz to 20 MHz. The high-power amplification system boosts the average power of the CEO stable oscillator by five orders of magnitude while increasing the phase noise by only 100 mrad. No evidence of CEO noise deterioration due to coherent beam combining is found. Low-frequency CEO fluctuations at the chirped-pulse amplifier are suppressed by a "slow loop" feedback. To the best of our knowledge, this is the first demonstration of a coherently combined laser system delivering an outstanding average power and high CEO stability at the same time.

Flexible all-PM NALM Yb:fiber laser design for frequency comb applications: operation regimes and their noise properties

We present a flexible all-polarization-maintaining (PM) mode-locked ytterbium (Yb):fiber laser based on a nonlinear amplifying loop mirror (NALM). In addition to providing detailed design considerations, we discuss the different operation regimes accessible by this versatile laser architecture and experimentally analyze five representative mode-locking states. These five states were obtained in a 78-MHz configuration at different intracavity group delay dispersion (GDD) values ranging from anomalous (-0.035 ps2) to normal (+0.015 ps2). We put a particular focus on the characterization of the intensity noise as well as the free-running linewidth of the carrier-envelope-offset (CEO) frequency as a function of the different operation regimes. We observe that operation points far from the spontaneous emission peak of Yb (∼1030 nm) and close to zero intracavity dispersion can be found, where the influence of pump noise is strongly suppressed. For such an operation point, we show that a CEO linewidth of less than 10-kHz at 1s integration can be obtained without any active stabilization.

Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification.

A simple and compact straight-cavity laser oscillator incorporating a cascaded quadratic nonlinear crystal and a semiconductor saturable absorber mirror (SESAM) can deliver stable femtosecond modelocking at high pulse repetition rates >10 GHz. In this paper, we experimentally investigate the influence of intracavity dispersion, pump brightness, and cavity design on modelocking with high repetition rates, and use the resulting insights to demonstrate a 10.4-GHz straight-cavity SESAM-modelocked Yb:CALGO laser delivering 108-fs pulses with 812 mW of average output power. This result represents a record-level performance for diode-pumped femtosecond oscillators with repetition rates above 10 GHz. Using the oscillator output without any optical amplification, we demonstrate coherent octave-spanning supercontinuum generation (SCG) in a silicon nitride waveguide. Subsequent f-to-2f interferometry with a periodically poled lithium niobate waveguide enables the detection of a strong carrier-envelope offset (CEO) beat note with a 33-dB signal-to-noise ratio.

Carrier-Envelope Offset Frequency Stabilization of a Thin-Disk Laser Oscillator via Depletion Modulation

We present a novel concept for the stabilization of the carrier-envelope offset (CEO) frequency of femtosecond pulse trains from thin-disk laser oscillators by exploiting gain depletion modulation in the active gain region. We shine a small fraction of the laser output power back onto the thin disk allowing the population inversion in the gain medium to be controlled. We employ this technique in our home-built Kerr-lens mode-locked Yb:YAG thin-disk laser and benchmark the performance against the proven technique of pump current modulation for CEO stabilization, showing that the two techniques have equivalent performance. The new method which only requires an additional AOM demonstrates a scalable and cost-effective method for CEO stabilization of high-power laser oscillators.

Ultra-Dense CEO-Stabilized Broadband Optical Frequency Comb Generation Through Simple, Programmable, and Lossless 1000-Fold Frequency-Spacing Division

Ultra-dense broadband optical frequency combs with sub-MHz frequency spacing and stabilized carrier-envelope offset (CEO) are needed for many important applications, including high-accuracy real-time sub-Doppler spectroscopy, precise characterization of photonic devices, and greenhouse gas sounding. However, the generation of such combs remains very challenging because they require mode-locked lasers with impractically long cavities (>few hundred meters). Here we demonstrate a CEO-stabilized optical frequency comb with a programmable sub-MHz frequency spacing, obtained through simple, suitable temporal phase modulation of a 250-MHz input comb. The method preserves the energy, the bandwidth, and the CEO-stabilization of the input comb, achieving a combined (CEO and repetition-rate) integrated phase noise below $\pi /10$ , and a frequency spacing down to 250 kHz over a 5-dB bandwidth of 10 THz, i.e., corresponding to a record high 1000-fold frequency spacing reduction and more than 40 000 000 comb lines. The demonstrated method bridges the gap between presently available high-quality optical frequency combs and a host of demanding and important applications that require CEO-stabilized broadband frequency combs with sub-MHz spacings.

A Femtosecond Pulse Train with a Selectable Carrier–Envelope Offset Phase

A method and a scheme of obtaining a femtosecond pulse train without frequency comb offset and selectable carrier–envelope offset phase are proposed.

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.

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.

Carrier-Envelope Offset Frequency Stabilization of a Fiber Laser by Cross Gain Modulation

We present the first carrier-envelope offset (CEO) frequency stabilization of a fiber laser by cross gain modulation. The Yb-doped fiber laser is mode-locked by nonlinear polarization evolution and emits 32-nm wide dissipative solitons at a repetition rate of 125 MHz with 150 mW of average output power. A continuous wave laser signal at a wavelength of 1025 nm is used as an intracavity power modulator. A low power of only 200 μW of modulator signal is coupled into the fiber laser and amplified in the gain segment. This signal cross modulates the laser gain, achieving 40 times larger modulation bandwidth of the intracavity laser power than with standard pump-current control. A tight CEO lock is demonstrated with 361 mrad of residual integrated phase noise (from 1 Hz to 1 MHz). The method allows easy implementation in many existing fiber laser frequency combs based on various saturable absorbers and fiber configurations.

Frequency Noise Characterization of a 25-GHz Diode-Pumped Mode-Locked Laser With Indirect Carrier-Envelope Offset Noise Assessment

We present a detailed frequency noise characterization of an ultrafast diode-pumped solid-state laser operating at 25-GHz repetition rate. The laser is based on the gain material Er:Yb:glass and operates at a wavelength of 1.55 μm. Using a beating measurement with an ultralow-noise continuous-wave laser in combination with a dedicated electrical scheme, we measured the frequency noise properties of an optical mode of the 25-GHz laser, of its repetition rate and indirectly of its carrier-envelope offset (CEO) signal without detecting the CEO frequency by the standard approach of nonlinear interferometry. We observed a strong anticorrelation between the frequency noise of the indirect CEO signal and of the repetition rate in our laser, leading to optical modes with a linewidth below 300 kHz in the free-running laser (at 100-ms integration time), much narrower than the individual contributions of the carrier envelope offset and repetition rate. We explain this behavior by the presence of a fixed point located close to the optical carrier in the laser spectrum for the dominant noise source.

Carrier-envelope offset frequency stabilization of a gigahertz semiconductor disk laser

Optical frequency combs based on ultrafast lasers have enabled numerous scientific breakthroughs. However, their use for commercial applications is limited by the complexity and cost of femtosecond laser technology. Ultrafast semiconductor lasers might change this issue as they can be mass produced in a cost-efficient way while providing large spectral coverage from a single technology. However, it has not been proven to date if ultrafast semiconductor lasers are suitable for stabilization of their carrier-envelope offset (CEO) frequency. Here we present what we believe to be the first CEO frequency stabilization of an ultrafast semiconductor disk laser (SDL). The optically pumped SDL is passively modelocked by a semiconductor saturable absorber mirror. It operates at a repetition rate of 1.8 GHz and a center wavelength of 1034 nm. The 273 fs pulses of the oscillator are amplified to an average power level of 6 W and temporally compressed down to 120 fs. A coherent octave-spanning supercontinuum spectrum is generated in a photonic crystal fiber. The CEO frequency is detected in a standard f–to–2f interferometer and phase locked to an external reference by feedback applied to the current of the SDL pump diode. This proof-of-principle demonstrates that ultrafast SDLs are suitable for CEO stabilization and constitutes a key step for further developments of this comb technology expected in the coming years.