Formation Of Dispersive Waves Research Articles

Zero dispersion Kerr solitons in optical microresonators

Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems from BEC to hydrodynamics, and fall into two separate classes: bright solitons existing in anomalous group velocity dispersion, and switching waves forming ‘dark solitons’ in normal dispersion. Bright solitons in particular have been relevant to chip-scale microresonator frequency combs, used in applications across communications, metrology, and spectroscopy. Both have been studied, yet the existence of a structure between this dichotomy has only been theoretically predicted. We report the observation of dissipative structures embodying a hybrid between switching waves and dissipative solitons, existing in the regime of vanishing group velocity dispersion where third-order dispersion is dominant, hence termed as ‘zero-dispersion solitons’. They are observed to arise from the interlocking of two modulated switching waves, forming a stable solitary structure consisting of a quantized number of peaks. The switching waves form directly via synchronous pulse-driving of a Si3N4 microresonator. The resulting comb spectrum spans 136 THz or 97% of an octave, further enhanced by higher-order dispersive wave formation. This dissipative structure expands the domain of Kerr cavity physics to the regime near to zero-dispersion and could present a superior alternative to conventional solitons for broadband comb generation.

Tailored Multi‐Color Dispersive Wave Formation in Quasi‐Phase‐Matched Exposed Core Fibers (Adv. Sci. 8/2022)

Dispersive Waves The optical properties of optical fibers with exposed cores can be straightforwardly tuned by the deposition of high refractive index nano-films (green) inducing tailored resonances. In article number 2103864 by Markus A. Schmidt and co-workers, a precise dispersion design and tailored supercontinuum generation is enabled through periodically structured nano-films. Multicolor, user-defined femtosecond frequency conversion to higher order dispersive waves by quasi-phase matching is demonstrated.

Tailored Multi-Color Dispersive Wave Formation in Quasi-Phase-Matched Exposed Core Fibers.

Widely wavelength‐tunable femtosecond light sources in a compact, robust footprint play a central role in many prolific research fields and technologies, including medical diagnostics, biophotonics, and metrology. Fiber lasers are on the verge in the development of such sources, yet widespan spectral tunability of femtosecond pulses remains a pivotal challenge. Dispersive wave generation, also known as Cherenkov radiation, offers untapped potentials to serve these demands. In this work, the concept of quasi‐phase matching for multi‐order dispersive wave formation with record‐high spectral fidelity and femtosecond durations is exploited in selected, partially conventionally unreachable spectral regions. Versatile patterned sputtering is utilized to realize height‐modulated high‐index nano‐films on exposed fiber cores to alter fiber dispersion to an unprecedented degree through spatially localized, induced resonances. Nonlinear optical experiments and simulations, as well as phase‐mismatching considerations based on an effective dispersion, confirm the conversion process and reveal unique emission features, such as almost power‐independent wavelength stability and femtosecond duration. This resonance‐empowered approach is applicable to both fiber and on‐chip photonic systems and paves the way to instrumentalize dispersive wave generation as a unique tool for efficient, coherent femtosecond multi‐frequency conversion for applications in areas such as bioanalytics, life science, quantum technology, or metrology.

Dispersive waves and radiation trapping in optical fibers with a zero-nonlinearity wavelength

The formation of dispersive waves and radiation trapping are two most relevant phenomena in supercontinuum generation. In spite the fact that the nonlinear coefficient of many waveguides depends strongly on wavelength and even changes sign, the influence of a frequency-dependent nonlinearity on these phenomena have seldom been studied. The goal of this work is to fill this gap in the literature by thoroughly studying the behavior of dispersive waves and radiation trapping in the presence of a zero-nonlinearity wavelength (ZNW). Although the generalized nonlinear Schrödinger equation (GNLSE) is widely used to model optical pulse propagation in waveguides, it has been shown that the GNLSE may lead to unphysical results in the case of frequency-dependent nonlinearities. For this reason, we perform our analysis by resorting to the newly introduced photon-conserving generalized nonlinear Schrödinger equation (pcGNLSE). Further, we discuss results obtained with both equations and put in evidence the inadequacy of the GNLSE to appropriately account for radiation trapping.

Numerical and Experimental Demonstration of Intermodal Dispersive Wave Generation

AbstractEvidence of intermodal dispersive wave generation mediated by intermodal cross‐phase modulation (iXPM) between different transverse modes during supercontinuum generation in silicon nitride waveguides is presented. The formation of a higher‐order soliton in one strong transverse mode leads to phase modulation of a second, weak transverse mode by iXPM. The phase modulation enables not only supercontinuum generation but also dispersive wave generation within the weak mode, that otherwise has insufficient power to facilitate dispersive wave formation. The nonlinear frequency conversion scheme presented here suggests phase‐matching conditions beyond what is currently known, which can be exploited for extending the spectral bandwidth within supercontinuum generation.

Understanding Nonlinear Pulse Propagation in Liquid Strand-Based Photonic Bandgap Fibers

Ultrafast supercontinuum generation crucially depends on the dispersive properties of the underlying waveguide. This strong dependency allows for tailoring nonlinear frequency conversion and is particularly relevant in the context of waveguides that include geometry-induced resonances. Here, we experimentally uncovered the impact of the relative spectral distance between the pump and the bandgap edge on the supercontinuum generation and in particular on the dispersive wave formation on the example of a liquid strand-based photonic bandgap fiber. In contrast to its air-hole-based counterpart, a bandgap fiber shows a dispersion landscape that varies greatly with wavelength. Particularly due to the strong dispersion variation close to the bandgap edges, nanometer adjustments of the pump wavelength result in a dramatic change of the dispersive wave generation (wavelength and threshold). Phase-matching considerations confirm these observations, additionally revealing the relevance of third order dispersion for interband energy transfer. The present study provides additional insights into the nonlinear frequency conversion of resonance-enhanced waveguide systems which will be relevant for both understanding nonlinear processes as well as for tailoring the spectral output of nonlinear fiber sources.

Higher-order mode supercontinuum generation in dispersion-engineered liquid-core fibers

Supercontinuum generation enabled a series of key technologies such as frequency comb sources, ultrashort pulse sources in the ultraviolet or the mid-infrared, as well as broadband light sources for spectroscopic methods in biophotonics. Recent advances utilizing higher-order modes have shown the potential to boost both bandwidth and modal output distribution of supercontinuum sources. However, the strive towards a breakthrough technology is hampered by the limited control over the intra- and intermodal nonlinear processes in the highly multi-modal silica fibers commonly used. Here, we investigate the ultrafast nonlinear dynamics of soliton-based supercontinuum generation and the associated mode coupling within the first three lowest-order modes of accurately dispersion-engineered liquid-core fibers. By measuring the energy-spectral evolutions and the spatial distributions of the various generated spectral features polarization-resolved, soliton fission and dispersive wave formation are identified as the origins of the nonlinear broadening. Measured results are confirmed by nonlinear simulations taking advantage of the accurate modeling capabilities of the ideal step-index geometry of our liquid-core platform. While operating in the telecommunications domain, our study allows further advances in nonlinear switching in emerging higher-order mode fiber networks as well as novel insights into the sophisticated nonlinear dynamics and broadband light generation in pre-selected polarization states.

Controlled soliton formation in a femtosecond optical parametric oscillator with positive group delay dispersion

Soliton formation in a femtosecond optical parametric pumped by the second harmonic of a Yb: KGW solid-state oscillator was investigated. The intracavity group delay dispersion was positive, and the soliton condition was satisfied by introducing negative nonlinearity from cascaded quadratic nonlinearity (CQN). Controllable CQN was induced by an additional second-harmonic-generating nonlinear crystal inside the same resonator. Close to zero-phase mismatch, high CQN allows higher-order soliton formation, which leads to output power increase, self-phase modulation phase-matched dispersive wave formation, pulse splitting under perturbations of higher orders of nonlinear phase, and stable time/spectral domain oscillations with soliton period. Numerical simulations were employed to aid interpretations of the experimental data.

Directional supercontinuum generation: the role of the soliton

In this paper we numerically study supercontinuum generation by pumping a silicon nitride waveguide, with two zero-dispersion wavelengths, with femtosecond pulses. The waveguide dispersion is designed so that the pump pulse is in the normal-dispersion regime. We show that because of self-phase modulation, the initial pulse broadens into the anomalous-dispersion regime, which is sandwiched between the two normal-dispersion regimes, and here a soliton is formed. The interaction of the soliton and the broadened pulse in the normal-dispersion regime causes additional spectral broadening through formation of dispersive waves by non-degenerate four-wave mixing and cross-phase modulation. This broadening occurs mainly towards the second normal-dispersion regime. We show that pumping in either normal-dispersion regime allows broadening towards the other normal-dispersion regime. This ability to steer the continuum extension towards the direction of the other normal-dispersion regime beyond the sandwiched anomalous-dispersion regime underlies the directional supercontinuum notation. We numerically confirm the approach in a standard silica microstructured fiber geometry with two zero-dispersion wavelengths.

Intermode Breather Solitons in Optical Microresonators

The observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Octave-spanning dissipative Kerr soliton frequency combs in Si_3N_4 microresonators

Octave-spanning, self-referenced frequency combs are applied in diverse fields ranging from precision metrology to astrophysical spectrometer calibration. In the past decade, Kerr frequency comb generators have emerged as alternative scheme offering chip-scale integration, high repetition rate and bandwidths that are only limited by group velocity dispersion. The recent observation of Kerr frequency combs operating in the dissipative Kerr soliton (DKS) regime, along with dispersive wave formation, has provided the means for fully coherent, broadband Kerr frequency comb generation with engineered spectral envelope. Here, by carefully optimizing the photonic Damascene fabrication process, and dispersion engineering of $\mathrm{Si_{3}N_{4}}$ microresonators with $1\,\mathrm{THz}$ free spectral range, we achieve bandwidths exceeding one octave at low powers ($\mathcal{O}(100\,\mathrm{mW})$) for pump lasers residing in the telecom C-band ($1.55\,\mathrm{\mu m}$), as well as for the first time in the O-band ($1.3\,\mathrm{\mu m}$). Equally important, we find that for THz repetition rate comb states, conventional criteria applied to identify DKS comb states fail. Investigating the coherence of generated, octave-spanning Kerr comb states we unambiguously identify DKS states using a response measurement. This allows to demonstrate octave-spanning DKS comb states at both pump laser wavelengths of $1.3\mathrm{\,\mu m}$ and $1.55\,\mathrm{\mu m}$ including the broadest DKS state generated to date, spanning more than $200\,\mathrm{THz}$ of optical bandwidth. Octave spanning DKS frequency combs can form essential building blocks for metrology or spectroscopy, and their operation at $1.3\mathrm{\,\mu m}$ enables applications in life sciences such as Kerr comb based optical coherence tomography or dual comb coherent antistokes Raman scattering.

Coherent ultra-violet to near-infrared generation in silica ridge waveguides

Short duration, intense pulses of light can experience dramatic spectral broadening when propagating through lengths of optical fibre. This continuum generation process is caused by a combination of nonlinear optical effects including the formation of dispersive waves. Optical analogues of Cherenkov radiation, these waves allow a pulse to radiate power into a distant spectral region. In this work, efficient and coherent dispersive wave generation of visible to ultraviolet light is demonstrated in silica waveguides on a silicon chip. Unlike fibre broadeners, the arrays provide a wide range of emission wavelength choices on a single, compact chip. This new capability is used to simplify offset frequency measurements of a mode-locked frequency comb. The arrays can also enable mode-locked lasers to attain unprecedented tunable spectral reach for spectroscopy, bioimaging, tomography and metrology.