Space-time singularities represent points where the local structure of a wave field becomes locally undefined, and are central to phenomena ranging from fluid dynamics to cosmology. In optics, spatiotemporal optical vortices (STOVs) provide a versatile setting in which to study such singularities, but their controlled manipulation during nonlinear frequency conversion has remained elusive. Here we show that the evolution of STOV singularities in second-harmonic generation can be continuously engineered through spatial Gouy-phase control. In a 4f system, translating a thin nonlinear crystal about the Fourier plane imposes a tunable Gouy phase that governs the orientation, splitting, and trajectories of singularities in the second-harmonic field. A Hermite-Gaussian modal description identifies Gouy-phase-dependent mechanism underlying these dynamics, in agreement with spatiotemporal interferometry measurements. Beyond integer-order inputs, fractional-order inputs (l=0.5) result in a distinct regime in which Gouy-phase bias drives topological reconfiguration and directional energy redistribution. Our results establish the Gouy phase as a simple yet powerful control knob for space-time singularities, opening new opportunities for structured-light engineering in nonlinear and ultrafast photonics.

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.

Nonlinear optical mixing effects have been identified as the driving force behind beam self-cleaning (BSC), as experimentally observed in multimode fibers with a parabolic index profile. Optical thermodynamics emerged as a theoretical framework for describing this phenomenon statistically. Here we observe that spatial coherence increases significantly during BSC, leading to a decrease in the beam profile’s entropy and an apparent violation of the second law of thermodynamics. Using a full polarimetric analysis, a concomitant reduction in the degree of polarization is experimentally demonstrated, thereby demystifying the apparent loss of entropy as a transfer from the spatial to the polarization domain. We conclude that depolarization is caused by intrapulse Raman scattering, which is incoherently seeded by vacuum fluctuations with random polarization and subsequently experiences a Raman self-frequency shift in the anomalous dispersion regime.

Abstract As photonic systems grow more complex, it becomes increasingly difficult to capture their behaviour within the conventional four dimensions of space and time, particularly for systems operating at the nanometer scale, where strong confinement effects, near-field interactions, and subwavelength structuring introduce additional layers of complexity. The concept of 5D photonics reflects this shift by incorporating additional physical, material, computational, adaptive, and quantum degrees of freedom as active components in design, control, and function. Rather than defining a single extra coordinate, higher-dimensional photonics is about operating photonic systems within expanded, dynamically accessible state spaces where multiple dimensions can interact and evolve together. This roadmap brings together perspectives ranging from modeling and design concepts to experimental platforms, materials, components, and system-level implementations. It covers a wide spectrum of synthetic and structured dimensions, nonlinear and strong-field regimes, adaptive and reconfigurable architectures, cyber-physical and engineering approaches, as well as inherently high-dimensional quantum and excitonic systems. Across all these areas, higher-dimensional thinking emerges not as an abstract construct but as a practical tool for enabling new functionalities, overcoming conventional design limitations, and bridging physical systems with digital and AI-driven layers. By framing these diverse developments within a shared higher-dimensional perspective, the roadmap aims to provide orientation in a rapidly expanding field, reveal conceptual connections between traditionally separate areas of photonics, and highlight common challenges and opportunities. In doing so, it positions higher-dimensional photonics as a central paradigm for developing future photonic technologies that are increasingly adaptive, intelligent, and integrated across physical and virtual domains.

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_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.

Thermal transients in optical amplifiers can lead to spurious frequency shifts of frequency combs. Mitigating this effect, we demonstrate a comb with an offset frequency stability exceeding best demonstrated optical clocks by an order of magnitude.

Frequency metrology with optical comb sources heavily relies on mode-locked fiber lasers. However, suitable fiber lasers only exist for two wavelength bands around 1.03 and 1.55 μm, and nonlinear conversion mechanisms have to be employed to access out-of-band wavelengths. To this end, parametric amplification appears appealing as it allows for high conversion efficiency. Nevertheless, optical parametric amplifiers (OPAs) require coherent seed light at the signal wavelength, and this seed light has to be deduced from the pump light by spectral broadening in highly nonlinear optical fibers, which can easily destroy favorable coherence properties. Here we demonstrate an alternative approach, using a single-frequency seed laser with 8 mW output power. Despite limited seed power, surprisingly low carrier-envelope phase (CEP) jitters of only 82 mrad result.

Nonlinear optics in multimode fibers has recently attracted increased attention. One particularly intriguing phenomenon is beam self-cleaning [1]. Upon nonlinear propagation in the multimode fiber, an initially noisy speckled input beam [Fig. 1b] contracts into a much cleaner profile with significantly enhanced fundamental mode contents [Fig. 1e]. This process has often been discussed using a thermodynamic picture and explained by convergence to a Rayleigh-Jeans distribution [2], [3]. However, this explanation has been controversially received as it relies on the absence of dissipative mechanisms and therefore does not allow a decrease of entropy during nonlinear propagation. Here we now show that much stronger beam self-cleaning is possible in a dual-clad multimode fiber with dissipative core. Starting at an initial occupation of 34% for linear propagation, a total of 92% of the energy condenses in a Townes profile for nonlinear propagation at maximum available power, see Fig. 1c,d,f. Concomitantly, we observe a dramatic decrease of entropy from 78% to below 20% in the system. In order to evaluate the thermodynamic behavior of the system, we fit Bose-Einstein distributions to modal decompositions, cf. Fig. 1c,f. This analysis indicates an abrupt drop of the chemical potential of the system by two orders of magnitude at a threshold temperature of 43.5 nK, i.e., a clear indication for an underlying phase transition.

Frequency metrology and high-field physics heavily depend on reliable stabilization of the carrier-envelope offset frequency $(f_{\text{ceo}})$ of optical combs. To this end, passively stabilized frequency combs are particularly appealing as they promise zero offset frequency [1]. However, this theoretical expectation has never been put to a thorough test yet. Here we demonstrate an f-2f interferometer with additional frequency shift for a long term measurement of $f_{\text{ceo}}$ [2]. In particular, our analysis provides an indication for a non-deterministic shift of $f_{\text{ceo}}$ in passively stabilized frequency combs. Our method can easily be adapted for the analysis of other passively stabilized optical sources, e.g., parametric or difference frequency generated mid- IR combs.

Due to their controllable optical path length and flexible adjustment of optical nonlinearity, multipass cells (MPCs) have emerged as an effective platform for investigations of strong-field nonlinear optics with few-cycle pulses. Prior compression schemes frequently employed hollow core fibers. Propagation in these fibers is effectively single transverse mode, which greatly simplifies numerical modeling. Here we tackle the problem of transverse-multimode nonlinear propagation in solid-state MPCs, employing a suitably expanded unidirectional pulse propagation equation. Our numerical investigation reveals a peculiar spatiotemporal optical wave breaking mechanisms, which is intricately linked to energy transfer dynamics from the fundamental to higher-order modes. This intermodal energy reallocation results in mode-specific pulse compression, depending on the energy in each mode. Remarkably, this process induces a rapid expansion of the beam size, which leads to a mitigation of adverse thermal effects. Our study provides deeper theoretical insights into multimode nonlinear propagation in solid-state MPCs. The observed spatiotemporal phenomena as well as the observed energy transfer dynamics offer valuable guidance for the design and application of MPCs in pulse compression.

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 revived attention. In BSC initially multimode light condenses into the fundamental fiber mode at elevated intensities. Nevertheless, BSC found little application as even the best demonstrations so far did not reach more than 75% fundamental mode content. Here we present a method for sufficiently enhancing the beam quality in BSC by employing a dissipative double-clad fiber. Using this fiber, we demonstrate a record-breaking LP₀₁ content of 98%, which constitutes the best demonstrated BSC to date. Concomitantly, transmission reaches 34% for maximum injected powers, which clearly improves over low-power transmission values of less than 10%. Saturable absorption of the erbium-doped fiber core there appears to play a pivotal role in enabling much more efficient BSC.

Femtosecond laser ablation-driven periodic surface structuring offers a promising method for large-scale and high-throughput nanolithography technique. However, the self-organized periodic structures typically manifest constraints in terms of tunable period and depth, as well as suboptimal regularity, which restricts their broader application potential. Here, in terms of a rarely explored laser-induced photochemical mechanism for nonablative structuring, we demonstrate manufacturing of sub-wavelength oxidative grating structures on silicon films with active structural modulation. In this scenario, the plasmonic field plays a pivotal role in dragging oxygen ions from surface into the silicon, greatly speeding up oxidation rates. While high oxygen doping levels can already be achieved with single-pulse exposure, far superior results are obtained with the application of 40-MHz burst mode pulse trains, mitigating the formation of excessively large nanocrystallites. Furthermore, it is revealed that the periodicity and modulation depth of laser-writing nanograting are both dependent on the number of pulse per burst. This offers a convenient scheme for actively controlling laser plasmonic lithography.

Relying on the nonlinear optical effect of difference-frequency generation, passively carrier-envelope stabilized comb systems are currently considered the simplest option for generating combs with zero carrier-envelope offset frequency fceo, that is, without relying on electronic servo loops or additional acousto-optic shifters. However, recent measurements indicated statistically significant deviations from a perfect vanishing fCEO. Here we show that temperature-drift induced refractive index changes in subsequent distribution or booster amplifiers may give rise to an effective Doppler shift of the measured fCEO, thwarting precision frequency measurements up to the mHz level. Comparing this hypothesis with temperature-dependent refractive index data and gain spectra, we find excellent quantitative agreement with measurements. Mitigating these problems by allowing for sufficient warm-up times of the external amplifiers, the fceo mean value of a difference frequency comb is measured as –0.55±1.55 µHz, which is statistically equivalent to 0. The corresponding stability supersedes the current best optical clocks, with an overlapping Allan deviation of <1×10-17 at 1 second and 5.36×10−21 at 100,000 s. Previously often considered negligible, the temperature drift of external distribution or booster amplifiers plays a critical role in obtaining similar stabilities in frequency metrology for all kind of fCEO-stabilized combs.

The past two decades have seen rapid development of optical atomic clocks with fractional performance at 10(-18) level or even below. Dissemination of optical atomic clocks into microwave domain and their intercomparisons using optical frequency combs as clockwork requires precise measurements of their carrier-envelope offset frequencies (f(ceo)). To this end, passive stabilization to zero offset frequency has been considered as a promising approach. However, previous studies often indicate imperfections in passive stabilization schemes. Therefore, in this Letter, aiming to unveil the in-depth noise performance and origin of f(ceo) of passively stabilized frequency combs, a frequency-shifted f-2f interferometer is presented to characterize the f(ceo) frequency stability, frequency shift, frequency uncertainty, linewidth, and phase noise. The stability observed amounts to 2.46 x 10(-17) and 4.05 x 10(-20) in 1 and 10 000 s, respectively. The linewidth of f(ceo) is 3.7 mHz, with resulting phase noise of - 40 dBrad(2)/Hz and -64 dBrad(2)/Hz at 1 and 10 Hz offset frequency, respectively. The phase noise at > 1 kHz is confirmed to be of stochastic origin through correlation analysis. The measured f(ceo) is conclusively determined as -75(14) mu Hz. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

Acoustic modulation of atmospheric air enables the deflection of laser pulses with a peak power of 20 gigawatts, expanding the acousto-optics toolbox to high-power laser manipulation in ambient air.

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.

Optical frequency combs have revolutionized frequency metrology and spectroscopic measurements, enabling the most precise measurements of all physical quantities. However, precision frequency metrology heavily relies on mode-locked laser combs, which are only directly available for a few selected near-infrared wavelength ranges. Recently, a strong tendency emerged for combs in the mid-infrared molecular fingerprint region. To this end, several methods for wavelength conversion have been proposed and demonstrated, which nevertheless cost a degradation of coherence properties. Here a first approach is presented toward measuring resulting phase noise fluctuations, exploiting the temporal resolution of the dispersive temporal interferometry (DTI) technique for experimentally unveiling the carrier-envelope phase dynamics of a cw-seeded femtosecond optical parametric amplifier (OPA). Particularly, it is experimentally demonstrated for the first time that unexpectedly low seed power levels suffice to exceed vacuum fluctuations by more than an order of magnitude, resulting in pulse-to-pulse phase fluctuations of 82 mrad at rather moderate cw seed levels of 8 mW. Additionally, a formula is provided that allows exact prediction of the experimentally observed noise levels. This study therefore provides new insight into the role of vacuum fluctuations in OPAs, which open up an avenue for coherent dual-comb systems in the mid-infrared and beyond. A first approach is presented toward measuring resulting phase noise fluctuations, taking advantage of the temporal resolution of the dispersive temporal interferometry (DTI) technique for experimentally unveiling the carrier-envelope phase dynamics of a cw-seeded femtosecond optical parametric amplifier. image

Spectrally broad laser radiation from continuous wave (cw) lasers can exhibit second-order autocorrelation traces virtually indistinguishable from those of mode-locked lasers. Consequently, based only on autocorrelations, one might erroneously conclude that a cw laser is mode-locked. Such misinterpretations can be avoided by carefully characterizing radio frequency transients and spectra. However, optoelectronics are often too slow for lasers with an axial mode spacing in the multi-GHz range. Carefully evaluated autocorrelations then remain the last resort for validating mode locking. We compare autocorrelation measurements and calculations of a mode-locked titanium-sapphire (Ti:Sa) laser and a spectrally broad monolithic cw Ti:Sa laser to illustrate the ambiguity of optical autocorrelation.

With the rapid advance of ultrafast laser technology, high-energy few-cycle pulses are becoming increasingly accessible [1]. Recently, the interest of generating high-energy few-cycle pulse has increasingly shifted towards even longer wavelengths in the $2\ \mu \mathrm{m}$ range [2]. However, given the rather narrow band amplification range, gain narrowing effects during the amplification process limit the pulse duration of lasers system to about 2 ps, requiring hundredfold compression to reach the few-cycle range [3]. In the following, we numerically revisit the scenario of pulse compression in solid-state nonlinear media inside multipass cells (MPC). Multi-photon absorption, thermal conductivity, and linear absorption at $2\ \mu \mathrm{m}$ range are considered for silica, sapphire, YAG and diamond.

Recently, mode-locking and frequency comb formation of semiconductor lasers [1], in particular, quantum cascade lasers (QCL) was reported independently by several groups [2]. Subsequently, these claims were also extended to dissipative soliton formation [3] and the observation of passive CEP stability [4]. While these reports were highly controversially received by the ultrafast community, neither party in this controversy was able to deliver a convincing explanation for the reported experimental findings so far. Here we apply the proven Haus Master Equation (HME) approach [5] to a system with dispersion, Kerr nonlinearity, and fast gain saturation to explain the experimental observation of apparent mode-locking. Nevertheless, as this locking process only provides a frequency lock rather than a phase lock, applications of mode-locked QCLs in the time domain or the claim for solitons remain elusive.