arXiv subjects

Günter Steinmeyer

Publications and source records attributed to Günter Steinmeyer.

17 recordsLinked to original sources

arXiv2026

Geometric Parametric Instability in Nonlinear Multipass Cells

Geometric parametric instability (GPI) is the resonant growth of discrete spectral sidebands enabled by longitudinally periodic multimode evolution and has been studied primarily in graded-index fibers. Here we show theoretically and numerically that GPI can occur in gas-filled nonlinear multipass cells (MPCs). By mapping a mode-matched MPC onto an equivalent waveguide, we derive a Floquet quasi-phase-matching condition governed by the single-pass Gouy-phase imbalance of the signal--idler pair relative to the pump pair. The theory predicts the small-signal gain and bandwidth. A pump-depleted coupled-mode model (CMM) further relates the maximum converted fraction to the residual phase mismatch. The CMM predicts multiple geometrically tunable sideband pairs associated with different radial indices and Floquet orders. For argon at $5$~bar, varying the cavity geometry shifts the sideband detuning from approximately $96$ to $46$~THz when the $p_{\mathrm{s}}=1$, $h=0$ branch is considered. A truncated multimode generalized nonlinear Schrödinger equation (MMGNLSE) model is used for numerical simulations with a semiclassical stochastic seed corresponding to one photon per spectral mode. The MMGNLSE simulations reproduce the predicted sideband frequencies and reveal pump depletion and competition among the retained radial channels. GPI in MPCs may therefore limit spatial beam quality in nonlinear pulse compression while providing a tunable mechanism for broadband multicolor generation.

physics.optics↗

arXiv2026

Photon-conserving Raman soliton attractors in focusing and defocusing Kerr media

The sign of the Kerr nonlinear coefficient has long been regarded as irrelevant to the direction of the Raman-induced soliton self-frequency shift. Yet the standard generalized nonlinear Schrödinger equation (GNLSE) predicts a frequency shift that depends on the sign of the nonlinearity, which leads to an unphysical blue shift in the defocusing case. We resolve this inconsistency by deriving the time-domain form of the photon-conserving GNLSE (pcGNLSE) from its established frequency-domain counterpart. The derivation reveals that photon-number conservation imposes two sign modifications relative to the standard GNLSE: the Raman-shift coefficient acquires the absolute value of the Kerr nonlinear coefficient in place of its signed counterpart, and the self-steepening-Raman dissipation term likewise carries an absolute-value prefactor rather than a signed one. These two modifications jointly guarantee a universal spectral redshift and monotonically decreasing pulse energy during propagation, irrespective of the signs of the Kerr nonlinear coefficient and its frequency derivative. Applying the method of moments to the time-domain pcGNLSE with appropriate chirped ansätze, we derive closed-form evolution equations for five pulse parameters and establish explicit attractor conditions under which bright or dark Raman solitons propagate with constant peak power. Direct numerical integration of the pcGNLSE confirms all analytical predictions and demonstrates that the standard GNLSE fails qualitatively, predicting unphysical energy growth and spectral blueshift in the negative-nonlinearity regime. The results provide a rigorous analytical framework for Raman soliton dynamics in materials with negative third-order susceptibility, with direct implications for soliton-based devices in emerging semiconductor waveguide and microresonator platforms.

physics.optics↗

arXiv2024

Bose-Einstein condensation of an optical thermodynamic system into a solitonic state

Recent years have seen a resurgence of interest in multimode fibers due to their intriguing physics and applications, with spatial beam self-cleaning (BSC) having received special attention. In BSC light condenses into the fundamental fiber mode at elevated intensities. Despite extensive efforts utilizing optical thermodynamics to explain such counterintuitive beam reshaping process, several challenges still remain in fully understanding underlying physics. Here we provide compelling experimental evidence that BSC in a dissipative dual-core fiber can be understood in full analogy to Bose-Einstein condensation (BEC) in dilute gases. Being ruled by the identical Gross-Pitaevskii Equation, both systems feature a Townes soliton solution, for which we find further evidence by modal decomposition of our experimental data. Specifically, we observe that efficient BSC only sets in after an initial thermalization phase, causing converge towards a Townes beam profile once a threshold intensity has been surpassed. This process is akin to a transition from classical to quantum-mechanical thermodynamics in BEC. Furthermore, our analysis also identifies dissipative processes as a crucial, yet previously unidentified component for efficient BSC in multimode fiber. This discovery paves the way for unprecedented applications of multimode-fiber based systems in ultrafast lasers, communications, and fiber-based delivery of high-power laser beams.

physics.optics↗

arXiv2021

Chaotic synchronization in optical frequency combs

Using a discrete mode approach we investigate the intermodal dynamics in a frequency comb with nonlinear coupling due to four-wave mixing. In the presence of sufficient saturable absorption, phase space collapses into a single state, and all modes tightly lock with identical phase. In case of a purely reactive nonlinearity, a less constrained locking mechanism emerges, which keeps phase differences of neighboring modes loosely bounded and leads to the formation of quasi-periodic breathers. Analysis of the underlying nonlinear correlations identifies a chaotic synchronization process as the origin of this previously unreported locking mechanism. Despite their rather large Lyapunov exponent and correlation dimension, the highly chaotic dynamics may be easily overlooked by common diagnostic approaches for laser mode-locking. This finding may finally explain numerous unexplained reports on laser self mode-locking in the absence of an effective saturable absorber mechanism and the formation of self-frequency modulated combs in semiconductor lasers.

physics.optics↗

arXiv2021

Spatial cage solitons -- taming light bullets

Multimode nonlinear optics offers to overcome a long-standing limitation of fiber optics, tightly phase locking several spatial modes and enabling the coherent transport of a wavepacket through a multimode fiber. A similar problem is encountered in the temporal compression of multi-mJ pulses to few-cycle duration in hollow gas-filled fibers. Scaling the fiber length to up to six meters, hollow fibers have recently reached 1 TW of peak power. Despite the remarkable utility of the hollow fiber compressor and its widespread application, however, no analytical model exists to enable insight into the scaling behavior of maximum compressibility and peak power. Here we extend a recently introduced formalism for describing mode-locking to the spatially analogue scenario of locking spatial fiber modes together. Our formalism unveils the coexistence of two soliton branches for anomalous modal dispersion and indicates the formation of stable spatio-temporal light bullets that would be unstable in free space, similar to the temporal cage solitons in mode-locking theory. Our model enables deeper understanding of the physical processes behind the formation of such light bullets and predict the existence of multimode solitons in a much wider range of fiber types than previously considered possible.

physics.optics↗

arXiv2020

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.

physics.optics↗

arXiv2020

Spontaneous emission noise in mode-locked lasers and frequency combs

Amplified spontaneous emission (ASE) causes fluctuations of pulse energy, of the optical phase and of the timing of the pulse intensity envelope in a mode-locked laser or frequency comb. Starting from the assumption of one ASE photon per longitudinal laser mode and roundtrip, we rederive analytic equations for the three fundamental types of quantum noise in a laser. To this end, we analyze the interference of the coherent intracavity field and a spectrally localized ASE photon as a function of wavelength and phase of the latter. Performing an integration over all wavelengths and phases and taking stochastic noise into account, we compute ASE-induced jitters for all quantities considered. Continuing this approach, we then derive an expression for the resulting carrier-envelope phase noise of the comb, for which so far only numerical estimates exist. We further compute analytical estimates for ASE induced pulse chirp and duration variations and address the issue of resulting pulse contrast in a mode-locked laser and the resulting coherence properties. Considering three example cases, we finally compute estimates for all quantities analyzed. Taken together, our analysis provides a comprehensive view of ASE effects in a mode-locked laser, which unites numerous scattered reports across the literature.

physics.optics↗

arXiv2019

Linear chirp instability analysis for ultrafast pulse metrology

Pulse train instabilities have often given rise to confusion in misinterpretation in ultrafast pulse characterization measurements. Most prominently known as the coherent artifact, a partially mode-locked laser with non-periodic waveform may still produce an autocorrelation that has often been misinterpreted as indication for a coherent pulse train. Some modern pulse characterization methods easily miss the presence of a coherent artifact, too. Here we address the particularly difficult situation of a pulse train with chirp-only instability. This instability is shown to be virtually invisible to autocorrelation measurements, but can be detected with FROG, SPIDER, and dispersion scan. Our findings clearly show that great care is necessary to rule out a chirp instability in lasers with unclear mode-locking mechanism and in compression experiments in the single-cycle regime. Among all dynamical pulse train instabilities analyzed so far, this instability appears to be the best hidden incoherence and is most difficult to detect.

physics.optics↗

arXiv2019

Comment on "Retrieval of phase relation and emission profile of quantum cascade laser frequency combs''

A recent publication on arXiv:1905.00668 suggests that the phase relationship within a frequency comb can be reconstructed from a heterodyne measurement using a reference comb. In principle, following this approach, such retrieval of optical phases appears possible, but should give rise to a temporally constant signal. Instead, arXiv:1905.00668 provides experimental evidence for a pronounced relative drift of the phases, which indicates that the modes of the comb are not coherently phase-locked. This temporal drift can be explained if the comb under test is not equidistant. This further means that the underlying temporal waveform is not repetitive and cannot be compressed into a coherent short pulse. This artifact severely hampers suggested applications of quantum cascade lasers in precision metrology. Moreover, the notion of designating multi-mode quantum cascade lasers as frequency combs appears questionable.

physics.optics↗

arXiv2017

Advanced phase retrieval for dispersion scan: a comparative study

Dispersion scan is a self-referenced measurement technique for ultrashort pulses. Similar to frequency-resolved optical gating, the dispersion scan technique records the dependence of nonlinearly generated spectra as a function of a parameter. For the two mentioned techniques, these parameters are the delay and the dispersion, respectively. While dispersion scan seems to offer a number of potential advantages over other characterization methods, in particular for measuring few-cycle pulses, retrieval of the spectral phase from the measured traces has so far mostly relied on the Nelder-Mead algorithm, which has a tendency of stagnation in a local minimum and may produce ghost satellites in the retrieval of pulses with complex spectra. We evaluate three different strategies to overcome these retrieval problems, namely regularization, use of a generalized-projections algorithm, and an evolutionary retrieval algorithm. While all these measures are found to improve the precision and convergence of dispersion scan retrieval, differential evolution is found to provide the best performance, enabling the near-perfect retrieval of the phase of complex supercontinuum pulses within less than ten seconds, even in the presence of strong detection noise and limited phase-matching bandwidth of the nonlinear process.

physics.ins-det↗

arXiv2017

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 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.

physics.optics↗

arXiv2015

Random walks across the sea: the origin of rogue waves?

Ocean rogue waves are large and suddenly appearing surface gravity waves, which may cause severe damage to ships and other maritime structures. Despite years of research, the exact origin of rogue waves is still disputed. Linear interference of waves with random phase has often been cited as one possible explanation, but apparently does not satisfactorily explain the probability of extreme events in the ocean. Other explanations therefore suggested a decisive role of a nonlinearity in the system. Here we show that linear interference of a finite and variable number of waves may very well explain the heavy tail in the wave height distribution. Our model can explain all prototypical ocean rogue waves reported so far, including the "three sisters" as well as rogue holes. We further suggest nonlinear time series analysis for estimation of the characteristic number of interfering waves for a given sea state. If ocean dynamics is ruled by interference of less than ten waves, rogue waves cannot appear as a matter of principle. In contrast, for larger numbers, their appearance is much more likely than predicted by parameterless models or longterm observation. The pronounced threshold behavior of our model enables effective forecasting of extreme ocean waves.

physics.ao-ph↗

arXiv2015

On the predictability of rogue events

Using experimental data from three different rogue wave supporting systems, determinism and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the Draupner platform in the North Sea as well as time series from two optical systems in our analysis. One of the latter was measured in the infrared tail of optical fiber supercontinua, the other in the fluence profiles of multifilaments. All three data sets exhibit extreme-value statistics and exceed the significant wave height in the respective system by a factor larger than two. Nonlinear time series analysis indicates a different degree of determinism in the systems. The optical fiber scenario is found to be driven by quantum noise whereas rogue waves emerge as a consequence of turbulence in the others. With the large number of rogue events observed in the multifilament system, we can systematically explore the predictability of such events in a turbulent system. We observe that rogue events do not necessarily appear without a warning, but are often preceded by a short phase of relative order. This surprising finding sheds some new light on the fascinating phenomenon of rogue waves.

physics.ao-ph↗

arXiv2014

Phase retrieval via regularization in self-diffraction based spectral interferometry

A novel variant of spectral phase interferometry for direct electric-field reconstruction (SPIDER) is introduced and experimentally demonstrated. Other than most previously demonstrated variants of SPIDER, our method is based on a third-order nonlinear optical effect, namely self-diffraction, rather than the second-order effect of sum-frequency generation. On one hand, self-diffraction (SD) substantially simplifies phase-matching capabilities for multi-octave spectra that cannot be hosted by second-order processes, given manufacturing limitations of crystal lengths in the few-micrometer range. On the other hand, however, SD SPIDER imposes an additional constraint as it effectively measures the spectral phase of a self-convolved spectrum rather than immediately measuring the fundamental phase. Reconstruction of the latter from the measured phase and the spectral amplitude of the fundamental turns out to be an ill-posed problem, which we address by a regularization approach. We discuss the numerical implementation in detail and apply it to measured data from a Ti:sapphire amplifier system. Our experimental demonstration used 40-fs pulses and a 500 $μ$m thick BaF${}_2$ crystal to show that the SD SPIDER signal is sufficiently strong to be separable from stray light. Extrapolating these measurements to the thinnest conceivable nonlinear media, we predict that bandwidths well above two optical octaves can be measured by a suitably adapted SD SPIDER apparatus, enabling the direct characterization of pulses down to single-femtosecond pulse durations. Such characteristics appear out of range for any currently established pulse measurement technique.

physics.optics↗

arXiv2013

Regularization of an autoconvolution problem in ultrashort laser pulse characterization

An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically required extension of the deautoconvolution problem beyond the classical case usually discussed in literature: (i) For measurements of ultrashort laser pulses with the self-diffraction SPIDER method, a stable approximate solution of an autocovolution equation with a complex-valued kernel function is needed. (ii) The considered scenario requires complex functions both, in the solution and the rhs of the integral equation. Since, however, noisy data are available not only for amplitude and phase functions of the rhs, but also for the amplitude of the solution, the stable approximate reconstruction of the associated smooth phase function represents the main goal of the paper. An iterative regularization approach is described that is specifically adapted to the physical situation in pulse characterization, using a non-standard stopping rule for the iteration process of computing regularized solutions. Our approach is illustrated by several case studies for synthetic noisy data and physically realistic complex-valued kernel functions. Based on an example with focus on amplitude perturbations, we show that the autoconvolution equation is locally ill-posed everywhere. To date, the analytical treatment of the impact of noisy data on phase perturbations remains an open question. However, we show its influence with the help of numerical experiments. Moreover, we formulate assertions on the non-uniqueness of the complex-valued autoconvolution problem, at least for the simplified case of a constant kernel. The presented results and figures associated with case studies illustrate the ill-posedness phenomena also for the case of non-trivial complex kernel functions.

math-ph↗

arXiv2012

The coherent artifact in modern pulse measurements

We simulate multi-shot intensity-and-phase measurements of unstable ultrashort-pulse trains using frequency-resolved-optical-gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER). Both techniques fail to reveal the pulse structure. FROG yields the average pulse duration and suggests the instability by exhibiting disagreement between measured and retrieved traces. SPIDER under-estimates the average pulse duration but retrieves the correct average pulse spectral phase. An analytical calculation confirms this behavior.

physics.optics↗

arXiv2011

Comment on arXiv:1105.6334 "Optical nonlinearity in Ar and N$_2$ near the ionization threshold"

In a recent publication [Phys. Rev. Lett. 107, 103901 (2011)], Wahlstrand et al. reported to observe no indications for the appearance of the higher-order Kerr effect in a parameter regime that was previously found to display this phenomenon [Opt. Express 17, 13429 (2009)]. Here we show that careful analysis of the original experimental data of Wahlstrand et al. reveals a 22% saturation, i.e., direct proof for the appearance of the higher-order Kerr effect. In the light of these findings, the validity of Wahlstrand et al.'s main conclusions appears highly questionable.

physics.optics↗