General framework for ultrafast nonlinear photonics: unifying single and multi-envelope treatments [Invited].

Numerical modeling of ultrashort pulse propagation is important for designing and understanding the underlying dynamical processes in devices that take advantage of highly nonlinear interactions in dispersion-engineered optical waveguides. Once the spectral bandwidth reaches an octave or more, multiple types of nonlinear polarization terms can drive individual optical frequencies. This issue is particularly prominent in χ(2) devices where all harmonics of the input pulse are generated and there can be extensive spectral overlap between them. Single-envelope approaches to pulse propagation have been developed to address these complexities; this has led to a significant mismatch between the strategies used to analyze moderate-bandwidth devices (usually involving multi-envelope models) and those used to analyze octave-spanning devices (usually involving models with one envelope per waveguide mode). Here we unify the different strategies by developing a common framework, applicable to any optical bandwidth, that allows for a side-by-side comparison between single- and multi-envelope models. We include both χ(2) and χ(3) interactions in these models, with emphasis on χ(2) interactions. We show a detailed example based on recent supercontinuum generation experiments in a thin-film LiNbO3 on sapphire quasi-phase-matching waveguide. Our simulations of this device show good agreement between single- and multi-envelope models in terms of the frequency comb properties of the electric field, even for multi-octave-spanning spectra. Building on this finding, we explore how the multi-envelope approach can be used to develop reduced models that help build physical insights about new ultrafast photonics devices enabled by modern dispersion-engineered waveguides, and discuss practical considerations for the choice of such models. More broadly, we give guidelines on the pros and cons of the different modeling strategies in the context of device design, numerical efficiency, and accuracy of the simulations.

Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser: erratum.

This erratum corrects a typographical error in equation (8) of our published paper [Opt. Express31, 7103 (2023)10.1364/OE.479356]. All the calculations used the correct equation, so all the results and conclusions remain unchanged.

Coherently averaged dual-comb spectroscopy with a low-noise and high-power free-running gigahertz dual-comb laser.

We present a new type of dual optical frequency comb source capable of scaling applications to high measurement speeds while combining high average power, ultra-low noise operation, and a compact setup. Our approach is based on a diode-pumped solid-state laser cavity which includes an intracavity biprism operated at Brewster angle to generate two spatially-separated modes with highly correlated properties. The 15-cm-long cavity uses an Yb:CALGO crystal and a semiconductor saturable absorber mirror as an end mirror to generate more than 3 W average power per comb, below 80 fs pulse duration, a repetition rate of 1.03 GHz, and a continuously tunable repetition rate difference up to 27 kHz. We carefully investigate the coherence properties of the dual-comb by a series of heterodyne measurements, revealing several important features: (1) ultra-low jitter on the uncorrelated part of the timing noise; (2) the radio frequency comb lines of the interferograms are fully resolved in free-running operation; (3) we validate that through a simple measurement of the interferograms we can determine the fluctuations of the phase of all the radio frequency comb lines; (4) this phase information is used in a post-processing routine to perform coherently averaged dual-comb spectroscopy of acetylene (C2H2) over long timescales. Our results represent a powerful and general approach to dual-comb applications by combining low noise and high power operation directly from a highly compact laser oscillator.

Efficient pump-probe sampling with a single-cavity dual-comb laser: Application in ultrafast photoacoustics.

Ultrafast pump-probe measurements are used to characterize various samples, such as biological cells, bulk, and thin-film structures. However, typical implementations of the pump-probe apparatus are either slow or complex and costly hindering wide deployment. Here we combine a single-cavity dual-comb laser with a simple experimental setup to obtain pump-probe measurements with ultra-high sensitivity, fast acquisition, and high timing precision over long optical delay scan ranges of 12.5 ns that would correspond to a mechanical delay of about 3.75 m. We employ digital signal balancing to obtain shot-noise-limited detection compatible with pump-probe microscopy deployment. Here we demonstrate ultrafast photoacoustics for thin-film sample characterization. We measured a tungsten layer thickness of (700 ± 4) Å with shot-noise-limited detection. Such single-cavity dual-comb lasers can be used for any pump-probe measurements and are especially well-suited for ultrafast photoacoustic studies such as involving ultrasonic echoes, Brillouin oscillations, surface acoustic waves and thermal dynamics.

Dual-comb optical parametric oscillator in the mid-infrared based on a single free-running cavity.

We demonstrate a free-running single-cavity dual-comb optical parametric oscillator (OPO) pumped by a single-cavity dual-comb solid-state laser. The OPO ring cavity contains a single periodically-poled MgO-doped LiNbO3 (PPLN) crystal. Each idler beam has more than 245-mW average power at 3550 nm and 3579 nm center wavelengths (bandwidth 130 nm). The signal beams are simultaneously outcoupled with more than 220 mW per beam at 1499 nm and 1496 nm center wavelength. The nominal repetition rate is 80 MHz, while the repetition rate difference is tunable and set to 34 Hz. To evaluate the feasibility of using this type of source for dual-comb applications, we characterize the noise and coherence properties of the OPO signal beams. We find ultra-low relative intensity noise (RIN) below -158 dBc/Hz at offset frequencies above 1 MHz. A heterodyne beat note measurement with a continuous wave (cw) laser is performed to determine the linewidth of a radio-frequency (RF) comb line. We find a full-width half-maximum (FWHM) linewidth of around 400 Hz. Moreover, the interferometric measurement between the two signal beams reveals a surprising property: the center of the corresponding RF spectrum is always near zero frequency, even when tuning the pump repetition rate difference or the OPO cavity length. We explain this effect theoretically and discuss its implications for generating stable low-noise idler combs suitable for high-sensitivity mid-infrared dual-comb spectroscopy (DCS).

Timing jitter characterization of free-running dual-comb laser with sub-attosecond resolution using optical heterodyne detection.

Pulse trains emitted from dual-comb systems are designed to have low relative timing jitter, making them useful for many optical measurement techniques such as optical ranging and spectroscopy. However, the characterization of low-jitter dual-comb systems is challenging because it requires measurement techniques with high sensitivity. Motivated by this challenge, we developed a technique based on an optical heterodyne detection approach for measuring the relative timing jitter of two pulse trains. The method is suitable for dual-comb systems with essentially any repetition rate difference. Furthermore, the proposed approach allows for continuous and precise tracking of the sampling rate. To demonstrate the technique, we perform a detailed characterization of a single-mode-diode pumped Yb:CaF2 dual-comb laser from a free-running polarization-multiplexed cavity. This new laser produces 115-fs pulses at 160 MHz repetition rate, with 130 mW of average power in each comb. The detection noise floor for the relative timing jitter between the two pulse trains reaches 8.0 × 10-7 fs2/Hz (∼ 896 zs/Hz), and the relative root mean square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This performance indicates that the demonstrated laser is highly compatible with practical dual-comb spectroscopy, ranging, and sampling applications. Furthermore, our results show that the relative timing noise measurement technique can characterize dual-comb systems operating in free-running mode or with finite repetition rate differences while providing a sub-attosecond resolution, which was not feasible with any other approach before.

51-W average power, 169-fs pulses from an ultrafast non-collinear optical parametric oscillator.

We present a high power optical parametric oscillator (OPO) synchronously pumped by the second-harmonic of a modelocked 1030-nm thin-disk laser (TDL) oscillator. The OPO delivers an average power of 51.1 W around degeneracy (1030 nm) with a 10.2-MHz repetition-rate. After extra-cavity dispersion compensation using dispersive mirrors, we obtain a pulse duration of 169 fs, which is 4.6× shorter than the TDL pulse duration of 770 fs. The TDL has 250 W average power, which is converted to 215 W at the second-harmonic. Hence, the OPO exhibits a high photon conversion efficiency of 47% (ratio of signal photons to 515-nm pump photons). Moreover, the OPO generates a peak power of 26.2 MW, which is very similar to the 28.0-MW peak power of the TDL. To facilitate continuous tuning around degeneracy and convenient extraction of the pump and idler beams, the OPO is operated in a noncollinear configuration. A linear cavity configuration was chosen since it offers easy alignment and straightforward cavity length tuning. To the best of our knowledge, this source has the highest average power generated by any ultrafast OPO, and the shortest pulse duration for any >5-W OPO. This result is an important step to adding wavelength tunability to high power Yb-based laser sources without the complexity of either laser or parametric amplifier systems.

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 -157 dBc/Hz level leading to a tenfold reduction in fCEO-linewidth.

Water-window high harmonic generation with 0.8-µm and 2.2-µm OPCPAs at 100 kHz.

We compare the generation of high-order harmonics in the water window (283-543 eV) with 0.8-µm and 2.2-µm few-cycle lasers at a pulse repetition rate of 100 kHz. Using conventional phase matching with the 2.2-µm driver and what we attribute to nonadiabatic self-phase-matching with the 0.8-µm driver, photons up to 0.6 keV (2 nm) are generated in both cases. Special attention is paid to the understanding of the generation mechanism with the 0.8-µm laser amplifier system. We use the same beamline and pump laser for both drivers, which allows for a direct flux comparison at the two driving wavelengths. For photon energies around 280 eV, a 10-100 times higher flux is obtained from the 2.2-µm versus the 0.8-µm laser system in helium and neon. The crossover at which the 2.2-µm yields a higher flux compared to the 0.8-µm driver is found to be as high as 0.2 keV. Our study supports the common approach of using long-wavelength lasers in a phase-matched regime for efficient generation of water-window harmonics, but also shows that the more widespread 0.8-µm wavelength can be used to generate water-window harmonics with an efficiency close to the one of a less common 2.2-µm source.

Silicate bonding of sapphire to SESAMs: adjustable thermal lensing for high-power lasers.

Silicate bonding is a flexible bonding method that enables room-temperature bonding of many types of materials with only moderate flatness constraints. It is a promising approach for bonding components in high power laser systems, since it results in a thin and low-absorption interface layer between the bonded materials. Here we demonstrate for the first time silicate bonding of a sapphire window to a SEmiconductor Saturable Absorber Mirror (SESAM) and use the composite structure to mode-lock a high-power thin-disk laser. We characterize the fabricated devices both theoretically and experimentally and show how the thermally induced lens of the composite structure can be tuned both in magnitude and sign via the thickness of the sapphire window. We demonstrate mode-locking of a high-power thin-disk laser oscillator with these devices. The altered thermal lens allows us to increase the output power to 233 W, a 70-W-improvement compared to the results achieved with a state-of-the-art SESAM in the same cavity.

High-speed interband cascade infrared photodetectors: photo-response saturation by a femtosecond oscillator.

Interband cascade infrared photodetectors (ICIPs) combine interband optical transitions with fast intraband transport to achieve high-frequency and broad-wavelength operation at room temperature. Here we study the bias-dependent electronic impulse response of ICIPs with a mid-infrared synchronously pumped optical parametric oscillator (OPO). Since the OPO produces ultrashort 104-fs pulses, it is possible to probe the impulse response of the ICIP. From this impulse response, we identify two characteristic decay times, indicating the contribution of electron as well as hole carriers. A reverse bias voltage applied to the ICIP reduces both time scales and leads to an increased electrical cut-off frequency. The OPO emits up to 500 mW average power, of which up to 10 mW is directed to the ICIP in order to test its saturation characteristics under short-pulse illumination. The peak of the impulse response profile as well as the average photocurrent experience a gradual saturation behavior, and we determine the corresponding saturation powers by measuring the photo-response as a function of average power directed to the ICIP. We demonstrate that an increasing reverse bias increases the saturation power as well as the responsivity of the ICIP.

Quality, proximate composition, and sensory characteristics of Dorper, domestic commercial crossbred, and Australian sheep meat: a comparative study.

The objective of this study was to compare the proximate, quality, and sensory attributes of Dorper sheep meat (Dorper), domestic commercial crossbred (DCC) and Australian commercial crossbred (ACC). A total of 60 untrimmed loins from the three sheep sources were purchased (20 sheep loins/source) and processed. The objective color, objective tenderness [Warner-Bratzler Shear Force (WBSF)], and proximate composition of the sheep meat were evaluated. A consumer panel and a trained sensory panel were also conducted to evaluate the sensory attributes. Dorper had greater (P = 0.04) carbohydrate content compared to DCC, but was not (P = 0.86) different from ACC. In addition, Dorper had the greatest WBSF value, followed by DCC, with ACC having the least WBSF out of the three (P < 0.0001). For the consumer panel, Dorper was rated to be less tender than ACC (P = 0.01), but was not different from DCC (P = 0.76). Dorper was also rated with lower flavor acceptability compared to DCC (P = 0.02), but was not different from ACC (P = 0.86). In addition, Dorper had the lowest overall acceptance rating by the consumers (P = 0.01). Trained sensory panel results followed the same trend as the consumer panel results which rated Dorper to be less tender than ACC (P = 0.002), but was not different from DCC (P = 0.10). Dorper was also rated with greater off-flavor intensity compared to DCC (P = 0.009), but was not different from ACC (P = 0.53). Finally, no differences were found for all other attributes evaluated among the sheep sources. The results indicated that consumers did not prefer Dorper over ACC and DCC. However, additional research with a more controlled environment is needed to shed light on the true palatability traits of Dorper.

Watt-level and sub-100-fs self-starting mode-locked 2.4-µm Cr:ZnS oscillator enabled by GaSb-SESAMs.

Femtosecond lasers with high peak power at wavelengths above 2 µm are of high interest for generating mid-infrared (mid-IR) broadband coherent light for spectroscopic applications. Cr2+-doped ZnS/ZnSe solid-state lasers are uniquely suited since they provide an ultra-broad bandwidth in combination with watt-level average power. To date, the semiconductor saturable absorber mirror (SESAM) mode-locked Cr:ZnS(e) lasers have been severely limited in power due to the lack of suitable 2.4-µm SESAMs. For the first time, we develop novel high-performance 2.4-µm type-I and type-II SESAMs, and thereby obtain state-of-the-art mode-locking performance. The type-I InGaSb/GaSb SESAM demonstrates a low non-saturable loss (0.8%) and an ultrafast recovery time (1.9 ps). By incorporating this SESAM in a 250-MHz Cr:ZnS laser cavity, we demonstrate fundamental mode-locking at 2.37 µm with 0.8 W average power and 79-fs pulse duration. This corresponds to a peak power of 39 kW, which is the highest so far for any saturable absorber mode-locked Cr:ZnS(e) oscillator. In the same laser cavity, we could also generate 120-fs pulses at a record high average power of 1 W. A comparable laser performance is achieved using type-II InAs/GaSb SESAM as well. These results pave the way towards a new class of high-power femtosecond SESAM mode-locked oscillators operating directly above 2-µm wavelength.

High-power few-cycle near-infrared OPCPA for soft X-ray generation at 100 kHz.

We present a near-infrared optical parametric chirped-pulse amplifier (OPCPA) and soft X-ray (SXR) high-harmonic generation system. The OPCPA produces few-cycle pulses at a center wavelength of 800 nm and operates at a high repetition rate of 100 kHz. It is seeded by fully programmable amplitude and phase controlled ultra-broadband pulses from a Ti:sapphire oscillator. The output from the OPCPA system was compressed to near-transform-limited 9.3-fs pulses. Fully characterized pulse compression was recorded for an average power of 22.5 W, demonstrating pulses with a peak power greater than 21 GW. Without full temporal characterization, high-power operation was achieved up to 35 W. We demonstrate that at such high repetition rates, spatiotemporally flattened pump pulses can be achieved through a cascaded second-harmonic generation approach with an efficiency of more than 70%. This combination provides a compelling OPCPA architecture for scaling the peak power of high-repetition-rate ultra-broadband systems in the near-infrared. The output of this 800-nm OPCPA system was used to generate SXR radiation reaching 190 eV photon energy through high-harmonic generation in helium.

Power scaling of ultrafast oscillators: 350-W average-power sub-picosecond thin-disk laser.

We report a semiconductor saturable absorber mirror (SESAM)-modelocked thin-disk laser oscillator delivering a record 350-W average output power with 940-fs, 39-µJ pulses at 8.88-MHz repetition rate and 37-MW peak power. This oscillator is based on the Yb:YAG gain material and has a large pump spot on the disk. The cavity design includes an imaging scheme, which results in multiple reflections on the disk gain medium to enable a larger output coupling rate compared to those used in thin-disk oscillators with a single reflection on the disk. This reduces the intracavity power for a given output power, thus decreasing the stress on the intracavity components. We operate the laser in a low-pressure environment in order to limit the disk's thermal lensing and drastically reduce the nonlinearity picked up in the intracavity air medium. The combination of the imaging scheme and low-pressure operation paves the way to further power scaling of ultrafast thin-disk oscillators toward the kW milestone.

Programmable pulse shaping for time-gated amplifiers.

We experimentally demonstrate a novel use of a spatial light modulator (SLM) for shaping ultrashort pulses in time-gated amplification systems. We show that spectral aberrations because of the device's pixelated nature can be avoided by introducing a group delay offset to the pulse via the SLM, followed by a time-gated amplification. Because of phase wrapping, a large delay offset yields a nearly-periodic grating-like phase function (or a phase grating). We show that, in this regime, the phase grating periocidity defines the group delay spectrum applied to the pulse, while the grating's amplitude defines the fraction of light that is delayed. We therefore demonstrate that a one-dimensional (1D) SLM pixel array is sufficient to control both the spectral amplitude and the phase of the amplified pulses.

High-power OPCPA generating 1.7 cycle pulses at 2.5 µm.

We present a high-power mid-infrared (mid-IR) optical parametric chirped-pulse amplifier (OPCPA) generating 14.4 fs pulses centered at 2.5 µm with an average power of 12.6 W and a repetition rate of 100 kHz. The short pulses are obtained without nonlinear pulse compression. This is in contrast to most few-cycle systems operating in the mid-IR. In our case, the ultrashort pulse duration is enabled by a careful design of the gain profile of each amplification stage as well as a precise control of the signal dispersion throughout the system. A pulse shaper is used in the seed beam to adjust the spectral phase at the output of the OPCPA system. This approach allows for a clean temporal profile leading to a high peak power of 6.3 GW.

Gas-lens effect in kW-class thin-disk lasers.

We unveil a gas-lens effect in kW-class thin-disk lasers, which accounts in our experiments for 33% of the overall disk thermal lensing. By operating the laser in vacuum, the gas lens vanishes. This leads to a lower overall thermal lensing and hence to a significantly extended power range of optimal beam quality. In our high-power continuous-wave (cw) thin-disk laser, we obtain single-transverse-mode operation, i.e. M2 < 1.1, in a helium or vacuum environment over an output-power range from 300 W to 800 W, which is 70% broader than in an air environment. In order to predict the magnitude of the gas-lens effect in different thin-disk laser systems and gain a deeper understanding of the effect of the heated gas in front of the disk, we develop a new numerical model. It takes into account the heat transfer between the thin disk and the surrounding gas and calculates the lensing effect of the heated gas. Using this model, we accurately reproduce our experimental results and additionally predict, for the first time by means of a theoretical tool, the existence of the known gas-wedge effect due to gas convection. The gas-lens and gas-wedge effects are relevant to all high-power thin-disk systems, both oscillators and amplifiers, operating in cw as well as pulsed mode. Specifically, canceling the gas-lens effect becomes crucial for kW power scaling of thin-disk oscillators because of the larger mode area on the disk and the resulting higher sensitivity to the disk thermal lens.

Author Correction: Watt-level 10-gigahertz solid-state laser enabled by self-defocusing nonlinearities in an aperiodically poled crystal.

The original version of this Article contained an error in Fig. 3a, in which the delay axis was incorrectly labeled in increments of 0.5 ps instead of the correct 0.2 ps. This has been corrected in both the PDF and HTML versions of the Article.

Decoupling phase-matching bandwidth and interaction geometry using non-collinear quasi-phase-matching gratings.

In optical parametric amplification (OPA) of broadband pulses, a non-collinear angle between the interacting waves is typically introduced in order to achieve broadband phase-matching. Consequently, bandwidth and beam geometry are closely linked. This coupling restricts the geometrical layout of an OPA system. Here, we demonstrate a quasi-phase-matching (QPM) geometry for broadband OPA in which a transverse component is introduced to the QPM grating to impose an additional momentum on the generated wave. This momentum shift detunes the wavelength where the signal and the idler are group-velocity matched, thereby allowing for broadband phase-matching without having to add a non-collinear angle between the interacting waves. We present two experimental configurations making use of this principle, and propose a third configuration with the potential to further simplify ultra-broadband OPA system architectures.