High-power low-noise 2-GHz femtosecond laser oscillator at 2.4 µm

Diode-pumped gigahertz modelocked Cr:ZnS laser at 2.36 µm

Gigahertz modelocked lasers operating in the crucial 2-3 µm spectral range are highly sought after for numerous applications. However, they currently rely on bulky and expensive fiber amplifiers for pumping. This paper presents the first, to our knowledge, diode-pumped gigahertz modelocked laser operating at 2.36 µm, utilizing Cr:ZnS as the gain medium and an InGaSb SESAM as the saturable absorber. The modelocked laser emits 199 fs pulses with an average power of 268 mW at a record high 1.06 GHz repetition rate for diode laser pumping, achieving a peak power exceeding 1 kW. The laser exhibits excellent long-term and short-term stability with an integrated relative intensity noise of 0.09% in the frequency interval of 10 Hz-10 MHz. The demonstrated cost-effective, compact yet sufficiently powerful, low-noise, high-repetition-rate femtosecond laser in the short-wave infrared range is a promising source for rapid molecular spectroscopy and efficient nonlinear conversion applications.

UltraStat: Ultrafast Spectroscopy beyond the Fourier Limit Using Bayesian Inference

The discrete Fourier transform (dFT) plays a central role in many ultrafast experiments, allowing the recovery of spectroscopic observables from time-domain measurements. In resonant experiments when population relaxation and coherence components of the signal coexist, the dFT is usually preceded by multiexponential fitting to remove the large population term. However, this procedure results in errors in both the recovered decay rates and the line shapes of the coherence spectral components. While other methods such as linear prediction singular value decomposition fit both terms simultaneously, they are limited to specific models that may not represent the true signal. These methods do not allow for systematic noise analysis or error estimation and require a priori knowledge of the signal rank. Here, we describe a general approach to parameter estimation in ultrafast spectroscopy─UltraStat─grounded in Bayesian analysis without the limitations set by Fourier theory. Using simulated, but realistic data, we demonstrate in a statistical sense how UltraStat provides accurate parameter estimation in the presence of many experimental constraints: noise, signal truncation, limited photon budget, and nonuniform sampling. UltraStat provides superior resolution compared to the dFT, up to an order of magnitude in cases where the line shapes are well-approximated. In these cases, we establish that primarily noise, not sampling, limits spectral resolution. Moreover, we show that subsampling may reduce the number of acquired points by 90% compared to the Nyquist-Shannon criteria. UltraStat greatly improves parameter estimation by providing statistically bound spectral and dynamics analysis, pushing the limits of ultrafast science.

SESAM-assisted Kerr-lens mode-locked Cr:ZnS laser

Mode-locking in Cr:ZnS/Se lasers typically rely on Kerr-lensing (KLM) or a semiconductor saturable absorber mirror (SESAM). The former allows generation of shorter pulses, but, unlike the latter, does not support self-starting mode-locking. Here, we combine the advantages of these two techniques and demonstrate the SESAM-assisted KLM Cr:ZnS laser. Our self-starting oscillator generates up to 1 W of average power with 54 fs pulses at a central wavelength of 2360 nm. We identify a general limitation for further pulse shortening in SESAM mode-locked Cr:ZnS/Se lasers, which is related to the finite operation bandwidth of the semiconductor absorbers. In our experiment, we fully exploit the potential of commercially available GaSb SESAMs and fill their entire reflection bands. Furthermore, we compare the performance of a SESAM-assisted KLM laser with a pure KLM oscillator producing broadband, yet not self-starting, 33 fs pulses with 780 mW power. We also show that the choice of saturable absorbers has a negligible impact on the laser intensity noise, which is exceptionally low with sub-0.005% integrated noise.

High-power, gigahertz repetition frequency self-mode-locked Ho:GdVO4 laser resonantly pumped by a Tm-doped fiber laser

A self-mode-locked Ho:GdVO4 laser with the GHz pulse repetition frequency oscillation near 2.06 µm was demonstrated for the first time to our knowledge. The output performances of the self-mode-locked Ho:GdVO4 laser were investigated for a few output coupler transmittances at the pulse repetition frequency of 1.89 GHz. At the incident pump power of 8.12 W, the maximum average output power was as high as 2.28 W, corresponding to the slope efficiency and optical-to-optical efficiency of 36.3% and 28.1%, respectively. This is the maximum average output for the 2 µm self-mode-locked solid-state laser with a GHz pulse repetition frequency. This work provides a new way for generating an efficient and a high-power ultrafast pulse laser with a GHz repetition frequency in the 2 µm wave band.

GHz repetition rate, sub-100-fs Ho:CALGO laser at 2.1 µm with watt-level average power

We report on a GHz fundamental repetition rate Kerr-lens mode-locked Ho:CALGO laser emitting at 2.1 µm. The laser employs a ring cavity to increase the fundamental repetition rate to 1.179 GHz and can be made to oscillate in both directions stably with nearly identical performance: for the counterclockwise oscillation, it generates 93-fs pulses at 1.68 W of average power, whereas 92 fs and 1.69 W were measured for the clockwise operation. Our current results represent the highest average power from a 2-µm GHz oscillator and, to our knowledge, the first sub-100-fs pulse duration from a Ho-based oscillator.

Parameter estimation in ultrafast spectroscopy using probability theory

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data.

Low-noise, 2-W average power, 112-fs Kerr-lens mode-locked Ho:CALGO laser at 2.1 µm

We report on an in-band pumped soft-aperture Kerr-lens mode-locked Ho³⁺-doped CaGdAlO₄ (Ho:CALGO) bulk laser at 2.1 µm, generating 2 W of average power with 112 fs pulses at 91-MHz repetition rate. To the best of our knowledge, this is the highest average power from a 100-fs class mode-locked laser based on a Tm³⁺ or Ho³⁺ doped bulk material. We show that the laser has excellent noise properties, with an integrated relative intensity noise of 0.02% and a timing jitter of 950 fs (rms phase noise 0.543 mrad) in the integration interval from 10 Hz to 10 MHz of offset frequency. The demonstrated combination of high average power, short pulses, and low noise makes this an outstanding laser source for many applications at 2.1 µm.

Single-cavity dual-modelocked 2.36-µm laser

We present the first dual-modelocked femtosecond oscillator operating beyond 2 µm wavelength. This new class of laser is based on a Cr:ZnS gain medium, an InGaSb SESAM for modelocking, and a two-surface reflective device for spatial duplexing of the two modelocked pulse trains (combs). The laser operates at 2.36 µm, and for each comb, we have achieved a FWHM spectral bandwidth of 30 nm, an average power of over 200 mW, and a pulse duration close to 200 fs. The nominal repetition rate is 242 MHz with a sufficiently large repetition rate difference of 4.17 kHz. We also found that the laser is able to produce stable modelocked pulses over a wide range of output powers. This result represents a significant step towards realizing dual-comb applications directly above 2 µm using a single free-running laser.

Directly diode-pumped femtosecond Cr:ZnS amplifier with ultra-low intensity noise

Diode-pumped Cr:ZnS oscillators have emerged as precursors for single-cycle infrared pulse generation with excellent noise performance. Here we demonstrate a Cr:ZnS amplifier with direct diode-pumping to boost the output of an ultrafast Cr:ZnS oscillator with minimum added intensity noise. Seeded with a 0.66-W pulse train at 50-MHz repetition rate and 2.4 µm center wavelength, the amplifier provides over 2.2 W of 35-fs pulses. Due to the low-noise performance of the laser pump diodes in the relevant frequency range, the amplifier output achieves a root mean square (RMS) intensity noise level of only 0.03% in the 10 Hz-1 MHz frequency range and a long-term power stability of 0.13% RMS over one hour. The diode-pumped amplifier reported here is a promising driving source for nonlinear compression to the single- or sub-cycle regime, as well as for the generation of bright, multi-octave-spanning mid-infrared pulses for ultra-sensitive vibrational spectroscopy.

Multi-gigahertz femtosecond pulses from linear and nonlinear propagation of a phase-modulated laser

We propose and demonstrate a non-mode-locking approach to generating multi-gigahertz repetition rate, femtosecond pulses in burst mode by shaping a continuous-wave (CW) seed laser in an all-fiber configuration. The seed laser at 1030 nm is first phase modulated and de-chirped to low-contrast, ∼2 ps pulses at a 17.5 GHz repetition rate, then carved to bursts at a 60 kHz repetition rate, and finally shaped to <2 ps clean pulses by a Mamyshev regenerator. This prepared high-quality picosecond source is further used to seed an Yb-doped fiber amplifier operating in the highly nonlinear regime, delivering output pulses at 23 nJ/pulse and $20\,\mathrm{\mu}$J/burst, compressible to ∼100 fs level. The system eliminates the need for mode-locked cavities and simplifies conventional ultrafast electro-optic combs to using only one phase modulator, while providing femtosecond pulses at multiple gigahertz repetition rate, enhanced pulse energy in burst mode and the potential of further power/energy scaling.