Nonlinear compression of few-cycle multi-mJ 5 µm pulses in ZnSe around zero-dispersion.

We present a compact nonlinear compression scheme for the generation of millijoule few-cycle pulses beyond 4 µm wavelength. For this purpose 95 fs pulses at 5 µm from a 1 kHz midwave-IR optical parametric chirped pulse amplifier (OPCPA) are spectrally broadened due to a self-phase modulation in ZnSe. The subsequent compression in a bulk material yields 53 fs pulses with 1.9 mJ energy. The compression succeeds efficiently with only slight beam distortions and an energy throughput of 85%, which results in a peak power of 34 GW. The nonlinear refractive index of ZnSe was derived from the nonlinear compression and self-focusing measurements. Furthermore, we explore to which extent multiphoton absorption affects the nonlinear compression regime.

Creating the perfect plasmonic wave.

Exploiting a plasmonic resonance, near-perfect grating structures have been reported, with a regularity that exceeds typical commercially available diffraction gratings.

Kinetics of excitation transfer from Cr2+ to Fe2+ ions in co-doped ZnSe.

The transfer of electronic excitations from Cr2+ to Fe2+ ions in co-doped epitaxially grown ZnSe is studied by time-resolved photoluminescence (PL) spectroscopy with unprecedented sub-10 ns time resolution. Upon excitation of Cr2+ ions by a picosecond pulse at 2.05 µm wavelength, PL from Fe2+ ions displays a delayed onset and a retarded decay in comparison to Fe2+ PL directly excited at 3.24 µm. We measure an extremely rapid 60 ns buildup of the Fe2+ luminescence, which is followed by a slower relaxation on the few micrometer scale. The experimental results are analyzed in the framework of Förster radiationless resonant energy transfer. Directly connecting to the work of Fedorov et al. [Opt. Mater. Express9, 2340 (2019)10.1364/OME.9.002340], the 60-ns buildup time of energy transfer is found to correspond to a Cr2+-Fe2+ distance of 0.95 nm, close to the length of the space diagonal of the ZnSe unit cell. This result demonstrates a significant density of spatially correlated Cr2+-Fe2+ ion pairs at short distance, in parallel to ions with a random distribution at a larger mutual separation.

Milliradian precision ultrafast pulse control for spectral phase metrology.

A pulse-shaper-based method for spectral phase measurement and compression with milliradian precision is proposed and tested experimentally. Measurements of chirp and third-order dispersion are performed and compared to theoretical predictions. The single-digit milliradian accuracy is benchmarked by a group velocity dispersion measurement of fused silica.

Long-term hybrid stabilization of the carrier-envelope phase.

Controlling the carrier envelope phase (CEP) in mode-locked lasers over practically long timescales is crucial for real-world applications in ultrafast optics and precision metrology. We present a hybrid solution that combines a feed-forward technique to stabilize the phase offset in fast timescales and a feedback technique that addresses slowly varying sources of interference and locking bandwidth limitations associated with gain media with long upper-state lifetimes. We experimentally realize the hybrid stabilization system in an Er:Yb:glass mode-locked laser and demonstrate 75 hours of stabilization with integrated phase noise of 14 mrad (1 Hz to 3 MHz), corresponding to around 11 as of carrier to envelope jitter. Additionally, we examine the impact of environmental factors, such as humidity and pressure, on the long-term stability and performance of the system.

Carrier-envelope phase stabilization of an Er:Yb:glass laser via a feed-forward technique.

Few-cycle pulsed laser technology highlights the need for control and stabilization of the carrier-envelope phase (CEP) for applications requiring shot-to-shot timing and phase consistency. This general requirement has been achieved successfully in a number of free-space and fiber lasers via feedback and feed-forward (FF) methods. Expanding on existing results, we demonstrate CEP stabilization through the FF method applied to a SESAM mode-locked Er:Yb:glass laser at 1.55 µm with a measured ultralow timing jitter of 2.9 as (1-3 MHz) and long-term stabilization over a duration of 8 h. Single-digit attosecond stabilization at telecom wavelengths opens a new direction in applications requiring ultra-stable frequency and time precision such as high-resolution spectroscopy and fiber timing networks.

Influence of the Doppler effect of a periodically moving mirror on the carrier-envelope frequency of a pulse train.

We investigate the influence of the optical Doppler effect on the carrier-envelope frequency (CEF) of a mode-locked pulse train. The laser pulses are Doppler-shifted in frequency during reflection off a periodically moving mirror that is driven by an electro-dynamical exciter inside an f-2f interferometer. Depending on the relative movement of the mirror at the instant of reflection, we experimentally demonstrate a CEF shift of the laser pulses up to ±69 kHz, which is sufficient for the carrier-envelope phase control of laser amplifiers with repetition rates of 10 kHz and beyond. Using piezoelectric thick films, we show that the scheme also appears to be adaptable to the megahertz repetition rates of typical oscillators. As the phase control is exerted extra-cavity, Doppler-induced CEF modulation is virtually free of any side effects of traditional stabilization schemes that typically act on the pump power. Finally, the Doppler scheme may overcome servo loop bandwidth limitations associated with pump power control.

Retrieving the coherent artifact in frequency-resolved optical gating.

When confronted with a pulse train whose intensity and/or phase versus time varies from pulse to pulse, multi-shot pulse-measurement techniques usually exhibit a coherent artifact (CA), which substantially complicates the interpretation of the measurement. In frequency-resolved optical gating (FROG), such instabilities are indicated by discrepancies between the measured and retrieved FROG traces. Here we consider the simultaneous retrieval of the CA and the average pulse characteristics from a single FROG trace in the limit of significant fluctuations. We use a modified generalized projections algorithm. Two electric fields are simultaneously retrieved, while the data constraint is updated as the algorithm progresses using only the assumption that the trace can be modeled as the sum of two spectrograms, one corresponding to the pulse and the other corresponding to the CA. An additional flat-spectral-phase constraint is added to one of the fields to ensure that it only reacts to the presence of the CA. Using this novel retrieval method, the complete retrieval of the characteristics of pulses in an unstable train from FROG traces is demonstrated.

Active f-to-2f interferometer for record-low jitter carrier-envelope phase locking.

The f-to-2f interferometer plays a key role for carrier-envelope phase (CEP) measurement and subsequent stabilization. The CEP measurement typically relies on the application of two optical nonlinearities, namely supercontinuum generation and second-harmonic generation. Then the cascadation of these nonlinearities often leads to signal levels on the order of a few photons per pulse. We experimentally demonstrate that the introduction of optical gain into the infrared arm of an f-to-2f interferometer can mitigate this detection bottleneck and improve signal-to-noise ratios by 20 dB compared to purely passive schemes. We further show that this measure allows for residual phase jitters between the carrier and envelope of about 10 mrad, corresponding to record-breaking timing jitters in the single attosecond regime. Moreover, the method appears generally applicable to a wide range of oscillators in the near-infrared and may enable stable CEP locking of mode-locked oscillators that so far have resisted stabilization. Finally, we propose a parametric variant of the active f-to-2f interferometer that can be used for laser amplifiers with kilohertz repetition rates and below.

100-kHz, dual-beam OPA delivering high-quality, 5-cycle angular-dispersion-compensated mid-infrared idler pulses at 3.1 µm.

We demonstrate a dual-beam infrared optical parametric source featuring a noncollinear KTA booster amplifier and straightforward angular dispersion compensation of the idler beam. Through careful beam and pulse characterization, and high-harmonic generation in a crystalline solid, we show that the corrected idler beam is diffraction-limited, astigmatism-free, and compressible to its transform-limited, 5-cycle pulse duration. Pumped by only 40-µJ pulses at 1.03 µm, the parametric source delivers 7.8-µJ, 38-fs, 1.53-µm and 2.3-µJ, 53-fs, CEP-stable, 3.1-µm pulses at a repetition rate of 100 kHz. The scheme provides a promising route to scale the pulse energy and average power beyond PPLN- or KTA-based collinear OPA architectures.

1.34 µm VECSEL mode-locked with a GaSb-based SESAM.

Mode locking of a 1.34 µm vertical external cavity surface emitting laser is demonstrated using a GaSb-based semiconductor saturable absorber mirror (SESAM). The SESAM includes six AlGaSb quantum wells (QWs) with an absorption edge at ∼1.37 µm. The proposed approach has two key benefits: the QWs can be grown lattice matched, and only a small number of Bragg reflector layers is required to provide high reflectivity. Pump-probe measurements also reveal that the AlGaSb/GaSb structure exhibits an intrinsically fast absorption recovery on a picosecond timescale. The mode-locked laser pulse train had a fundamental repetition rate of 1.03 GHz, a pulse duration of ∼5 ps, and a peak power of ∼1.67 W. The demonstration paves the way for exploiting GaSb-based SESAMs for mode locking in the 1.3-2 µm wavelength range, which is not sufficiently addressed by GaAs and InP material systems.

High-detectivity optical heterodyne method for wideband carrier-envelope phase noise analysis of laser oscillators.

Broadband characterization of the carrier-envelope phase (CEP) noise spectral density of free-running mode-locked lasers is essential for advanced low-noise optical frequency comb designs. Here we present a direct method that utilizes an optical heterodyne beat between a pair of repetition-rate-locked mode-locked lasers for CEP noise characterization, without requiring an f-2f interferometer or nonlinear optical conversion steps. A proof-of-principle experiment in a femtosecond Yb-fiber laser achieves CEP noise spectral density characterization with >270 dB dynamic range over a Fourier frequency range from 5 mHz to 8 MHz. The measurement noise floor is well below 1 µrad/√Hz, enabling dependable detection down to a quantum-limited noise floor. The method can resolve various noise mechanisms that cause specific CEP noise spectral shapes. The underlying mechanisms are further analyzed in terms of spurious temporal correlation to distinguish between technical and stochastic noise signatures. Moreover, a Hadamard deviation analysis reveals a varying degree of frequency stability in the measured CEP time series.

Pulse retrieval algorithm for interferometric frequency-resolved optical gating based on differential evolution.

A novel algorithm for the ultrashort laser pulse characterization method of interferometric frequency-resolved optical gating (iFROG) is presented. Based on a genetic method, namely, differential evolution, the algorithm can exploit all available information of an iFROG measurement to retrieve the complex electric field of a pulse. The retrieval is subjected to a series of numerical tests to prove the robustness of the algorithm against experimental artifacts and noise. These tests show that the integrated error-correction mechanisms of the iFROG method can be successfully used to remove the effect from timing errors and spectrally varying efficiency in the detection. Moreover, the accuracy and noise resilience of the new algorithm are shown to outperform retrieval based on the generalized projections algorithm, which is widely used as the standard method in FROG retrieval. The differential evolution algorithm is further validated with experimental data, measured with unamplified three-cycle pulses from a mode-locked Ti:sapphire laser. Additionally introducing group delay dispersion in the beam path, the retrieval results show excellent agreement with independent measurements with a commercial pulse measurement device based on spectral phase interferometry for direct electric-field retrieval. Further experimental tests with strongly attenuated pulses indicate resilience of differential-evolution-based retrieval against massive measurement noise.

Interferometric time-domain ptychography for ultrafast pulse characterization.

A novel pulse characterization method is presented, favorably combining interferometric frequency-resolved optical gating (FROG) and time-domain ptychography. This new variant is named ptychographic-interferometric frequency-resolved optical gating (πFROG). The measurement device is simple, bearing similarity to standard second-harmonic FROG, yet with a collinear beam geometry and an added bandpass filter in one of the correlator arms. The collinear beam geometry allows tight focusing and circumvents possible geometrical distortion effects of noncollinear methods, making πFROG especially suitable for the characterization of unamplified few-cycle pulses. Moreover, the direction-of-time ambiguity afflicting most second-order FROG variants is eliminated. Possible group delay dispersion of pulses leads to a characteristic tilt in the πFROG traces, allowing the detection of uncompensated dispersion without a retrieval. Using nanojoule, three-cycle pulses at 800 nm, the πFROG method is tested, and the results are compared with spectral phase interferometry for direct electric field reconstruction measurements. Measured pulse durations agree within a fraction of a femtosecond. As a further test, the πFROG measurements are repeated with added group delay dispersion, and found to accurately reproduce the dispersion computed with Sellmeier equations.

Excess carrier-envelope phase noise generation in saturable absorbers.

Attosecond spectroscopy and precision frequency metrology depend on the stabilization of the carrier-envelope phase (CEP) of mode-locked lasers. Unfortunately, the phase of only a few types of lasers can be stabilized to jitters in the few-hundred millirad range. In a comparative experimental study, we analyze a femtosecond Ti:sapphire laser and three mode-locked fiber lasers. We numerically demodulate recorded time series of the free-running carrier-envelope beat note. Our analysis indicates a correlation between amplitude and frequency fluctuations at low Fourier frequencies for essentially all lasers investigated. While this correlation typically rolls off at frequencies beyond 100 kHz, we see clear indications for a broadband coupling mechanism in one of the fiber lasers. We suspect that the observed coupling mechanism acts to transfer intracavity power fluctuations into excess phase noise. This coupling mechanism is related to the mode-locking mechanism employed and not to the gain medium itself. We further verify this hypothesis by numerical simulations, which identify resonances of the saturable absorber mirror as a possible explanation for the coupling mechanism. Finally, we discuss how to avoid a detrimental influence of such resonances.

Role of Intrapulse Coherence in Carrier-Envelope Phase Stabilization.

The concept of coherence is of fundamental importance for describing the physical characteristics of light and for evaluating the suitability for experimental application. In the case of pulsed laser sources, the pulse-to-pulse coherence is usually considered for a judgment of the compressibility of the pulse train. This type of coherence is often lost during propagation through a highly nonlinear medium, and pulses prove incompressible despite multioctave spectral coverage. Notwithstanding the apparent loss of interpulse coherence, however, supercontinua enable applications in precision frequency metrology that rely on coherence between different spectral components within a laser pulse. To judge the suitability of a light source for the latter application, we define an alternative criterion, which we term intrapulse coherence. This definition plays a limiting role in the carrier-envelope phase measurement and stabilization of ultrashort pulses. It is shown by numerical simulation and further corroborated by experimental data that filamentation-based supercontinuum generation may lead to a loss of intrapulse coherence despite near-perfect compressibility of the pulse train. This loss of coherence may severely limit active and passive carrier-envelope phase stabilization schemes and applications in optical high-field physics.

Simple route toward efficient frequency conversion for generation of fully coherent supercontinua in the mid-IR and UV range.

Fiber supercontinua represent light sources of pivotal importance for a wide range of applications, ranging from optical communications to frequency metrology. Although spectra encompassing more than three octaves can be produced, the applicability of such spectra is strongly hampered due to coherence degradation during spectral broadening. Assuming pulse parameters at the cutting edge of currently available laser technology, we demonstrate the possibility of strongly coherent supercontinuum generation. In a fiber with two zero-dispersion wavelengths a higher-order soliton experiences a temporal breakdown, without any compression or splitting behavior, which leads to nearly complete conversion of input solitonic radiation into resonant nonsolitonic radiation in the dispersive wave regime. As the process is completely deterministic and shows little sensitivity to input noise, the resulting pulses appear to be compressible down to the sub-cycle level and may thus hold a new opportunity for direct generation of attosecond pulses in the visible to near ultraviolet wavelength range.

Intracavity measurement of the electro-optic Kerr effect via carrier-envelope phase demodulation.

Placing a sinusoidally driven air capacitor in the intracavity beam path of a mode-locked few-cycle Ti:sapphire oscillator, we measure the influence of the electro-optical Kerr effect on the carrier-envelope phase of the laser pulses. Using a capacitor length of only 8 cm at atmospheric pressure, we observe a Kerr-induced frequency modulation of the carrier-envelope beat note. From the measured frequency excursion, we determine a Kerr constant of the order of 10-27 m2/V2, which is found to agree with theoretically computed hyperpolarizabilities of the nitrogen and oxygen molecules. The carrier-envelope phase only depends on the dispersion of the hyperpolarizability, which has been previously found very challenging to measure in the gas phase. Our substantially more sensitive measurement method for the electro-optic Kerr effect in air may prove a valuable tool for non-contact measurements of high voltages in power grids and even for monitoring atmospheric electric fields during thunderstorms.

Ocean rogue waves and their phase space dynamics in the limit of a linear interference model.

We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.

Controlling formation and suppression of fiber-optical rogue waves.

Fiber-optical rogue waves appear as rare but extreme events during optical supercontinuum generation in photonic crystal fibers. This process is typically initiated by the decay of a high-order fundamental soliton into fundamental solitons. Collisions between these solitons as well as with dispersive radiation affect the soliton trajectory in frequency and time upon further propagation. Launching an additional dispersive wave at carefully chosen delay and wavelength enables statistical manipulation of the soliton trajectory in such a way that the probability of rogue wave formation is either enhanced or reduced. To enable efficient control, parameters of the dispersive wave have to be chosen to allow trapping of dispersive radiation in the nonlinear index depression created by the soliton. Under certain conditions, direct manipulation of soliton properties is possible by the dispersive wave. In other more complex scenarios, control is possible via increasing or decreasing the number of intersoliton collisions. The control mechanism reaches a remarkable efficiency, enabling control of relatively large soliton energies. This scenario appears promising for highly dynamic all-optical control of supercontinua.