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Supercontinuum generation in the anomalous group-velocity dispersion regime is widely considered to be inherently unstable against input pulse fluctuations. This constraint has compelled a coherent supercontinuum to be triggered by femtosecond pulses. In this work, conditions for breaking this fundamental limitation are analytically derived and realized in a silicon waveguide by exploiting the Kerr nonlinearity dispersion. On this basis, coherent supercontinuum generation with picosecond pulses and anomalous group-velocity dispersion is numerically demon-strated, which crosses a long-standing frontier in nonlinear optics. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Coherent supercontinuum generation from picosecond pulses pumped in the anomalous dispersion regime is numerically demonstrated in a silicon waveguide by canceling modulation instability through the Kerr nonlinear-index dispersion.

Accurate knowledge of the nonlinear coefficient is extremely important to make reliable predictions about optical pulses propagating along waveguides. Nevertheless, determining this parameter when dispersion and loss are as important as nonlinear effects brings both theoretical and experimental challenges that have not yet been solved. A general method for measuring the nonlinear coefficient of waveguides under these demanding conditions is here derived and demonstrated experimentally in a kilometer-long standard silica fiber pumped close to 2 µm.

Nonlinear propagation of light pulses can excite dispersive waves anchored at frequencies determined by the chromatic dispersion curve. In this work, conditions enabling dispersive-wave self-frequency shift over the propagation distance are analytically derived in the normal dispersion regime. Importantly, this novel, to the best of our knowledge, scenario is not found by solving the complex dynamics of the pulse, but by studying the evolution of the nonlinear and dispersive length scales. This approach allows a simpler, yet consistent and insightful, analysis that may also be very useful in other nonlinear regimes. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Measuring the nonlinear coefficient γ of any guiding medium, regardless of the sign and magnitude of its group-velocity dispersion parameter β 2 , is challenging because of the lack of general solutions of the nonlinear Schrodinger equation (NLSE). Indeed, existing approaches typically need to disregard chromatic-dispersion effects to determine γ [1] . Here we propose an all-encompassing approach to measure the ratio β 2 /γ and prove our method in polarization-maintaining (PM) and single-mode (SM) fibers with positive and negative β 2 .

Graphene exhibits a strong nonlinear-optical refractive response to light pulses, but its impact on the pulses' spatiotemporal evolution is challenging to analyze and predict. We solve this issue using non-perturbative calculations and spectral broadening experiments.

No general approach is available yet to measure directly the ratio between chromatic dispersion and the nonlinear coefficient, and hence the soliton number for a given optical pulse, in an arbitrary guiding medium. Here we solve this problem using continuum generation. We experimentally demonstrate our method in polarization-maintaining and single-mode fibers with positive and negative chromatic dispersion. Our technique also offers new opportunities to determine the chromatic dispersion of guiding media over a broad spectral range while pumping at a fixed wavelength. (C) 2020 Optical Society of America

Geometrical and material - i.e., external and internal - scaling symmetries are exploited to obtain approximated analytical expressions for the mode effective index, group index, and chromatic dispersion of a scaled fiber. Our results include material refractive index scaling that changes the numerical aperture. First, the analytical expressions are successfully tested with a conventional step index fiber in a broadband range of wavelengths, from 1 to 2 mu m. Then, we establish a procedure to adapt the analytical expressions to photonic crystal fibers (PCFs) and illustrate its application in a triangular PCF with circular holes. These adapted analytical expressions show good agreement with a rigorous numerical solution of the fundamental fiber mode. Finally, we demonstrate how powerful these expressions are for the design of PCFs. In particular, we illustrate our approach designing, in four iterations or less, PCFs with flattened dispersion profile over 300 nm or high dispersion slope over 40 nm, with different chromatic dispersion values. (c) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene’s electronic third-order susceptibility χ(3) cannot, however, be explained using the relatively modest χ(3) value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ(3)-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices., Graphene enables extraordinary nonlinear-optical refraction, far exceeding predictions based on conventional nonlinear-susceptibility theory. Here, Vermeulen et al. show that rather than the nonlinear susceptibility, a complex saturable refraction process is central to graphene’s unusual behavior.

Nonlinear-optical refraction is typically described by means of perturbation theory near the material's equilibrium state. Graphene, however, can easily move far away from its equilibrium state upon optical pumping, yielding strong nonlinear responses that cannot be modeled as mere perturbations. So far, one is still lacking the required theoretical expressions to make predictions for these complex nonlinear effects and to account for their evolution in time and space. Here, this long-standing issue is solved by the derivation of population-recipe-based expressions for graphene's nonperturbative nonlinearities. The presented framework successfully predicts and explains the various nonlinearity magnitudes and signs observed for graphene over the past decade, while also being compatible with the nonlinear pulse propagation formalism commonly used for waveguides., 1 figure, 1 table

We numerically show that diamond-on-insulator (DOI) is more suitable than silicon-nitride waveguides to obtain a zero-dispersion wavelength in the VIS and hence to achieve VIS supercontinuum generation (SCG). We simulate SCG reaching 453 nm in DOI.

We solve the long-standing discrepancy between the theoretically predicted and experimentally observed performance of nonlinear-optical refraction in graphene. Hereto we study self-phase modulation in silica-core waveguides covered with graphene.

We numerically show the advantages of using diamond-on-insulator (DOI) waveguides to design compact supercontinuum (SC) light sources for the visible (VIS) wavelength range. We conclude that the DOI platform is more suitable than silicon nitride waveguides for tailoring the dispersion in such a way that a zero-dispersion wavelength (ZDW) is obtained in the VIS, as is required to achieve efficient VIS SC generation (SCG). After designing a DOI waveguide that features a ZDW at ∼600 nm, we exploit it to numerically obtain a smooth SC ranging from 453 nm to 1030 nm above the -30 dB point after propagation over 4 mm. Our result extends beyond the state-of-the-art shortest VIS wavelengths induced by SCG in integrated waveguides, while using ∼26 times lower input energy and a shorter waveguide length, thus showcasing the potential of the DOI platform for on-chip VIS SC light sources.

A fully analytical toolbox for supercontinuum generation relying on scenarios without pulse splitting is presented. Furthermore, starting from the new insights provided by this formalism about the physical nature of direct and cascaded dispersive wave emission, a unified description of this radiation in both normal and anomalous dispersion regimes is derived. Previously unidentified physics of broadband spectra reported in earlier works is successfully explained on this basis. Finally, a foundry-compatible few-millimeters-long silicon waveguide allowing octave-spanning supercontinuum generation pumped at telecom wavelengths in the normal dispersion regime is designed, hence showcasing the potential of this new analytical approach. (C) 2016 Optical Society of America

We experimentally demonstrate a negative Kerr nonlinearity for quasiundoped graphene. Hereto, we introduce the method of chirped-pulse-pumped self-phase modulation and apply it to graphene-covered silicon waveguides at telecom wavelengths. The extracted Kerr-nonlinear index for graphene equals n(2,gr) = -10(-13) m(2) = W. Whereas the sign of n(2,gr) turns out to be negative in contrast to what has been assumed so far, its magnitude is in correspondence with that observed in earlier experiments. Graphene's negative Kerr nonlinearity strongly impacts how graphene should be exploited for enhancing the nonlinear response of photonic (integrated) devices exhibiting a positive nonlinearity. It also opens up the possibility of using graphene to annihilate unwanted nonlinear effects in such devices, to develop unexplored approaches for establishing Kerr processes, and to extend the scope of the "periodic poling" method often used for second-order nonlinearities towards third-order Kerr processes. Because of the generic nature of the chirped-pulse-pumped self-phase modulation method, it will allow fully characterizing the Kerr nonlinearity of essentially any novel (2D) material.

We present a novel theoretical framework where dispersive wave emission in normal and anomalous dispersion is interpreted based on four-wave mixing processes. It is a powerful tool for designing supercontinuum sources along analytical guidelines.

A new approach to design waveguides for supercontinuum generation through dispersive wave emission from optical wave-breaking is proposed in this work. In two steps, the spectral broadening is analytically related to the dispersion curve, and the cross-section of a waveguide is optimized in a few iterations to fit such dispersion profile and, consequently, the target output bandwidth. This strategy does not only improve the efficiency of design tasks, but also provides new insights into the underlying nonlinear processes.

The control of the pulse spectrum at the output of nonlinear fibers is crucial in many applications. In this contribution we implement a new strategy based on optical wave-breaking to map the group-velocity-dispersion curve of highly nonlinear fibers to the spectral profile of the output pulsed light. So we efficiently manipulate the spectral characteristics of the emerging pulsed light by engineering the dispersion function of the waveguide.

In this work we recognize new strategies involving optical wave-breaking for controlling the output pulse spectrum in nonlinear fibers. To this end, first we obtain a constant of motion for nonlinear pulse propagation in waveguides derived from the generalized nonlinear Schrödinger equation. In a second phase, using the above conservation law we theoretically analyze how to transfer in a simple manner the group-velocity-dispersion curve of the waveguide to the output spectral profile of pulsed light. Finally, the computation of several output spectra corroborates our proposition.

Four-wave-mixing processes enabled during optical wave-breaking (OWB) are exploited in this paper for supercontinuum generation. Unlike conventional approaches based on OWB, phase-matching is achieved here for these nonlinear interactions, and, consequently, new frequency production becomes more efficient. We take advantage of this kind of pulse propagation to obtain numerically a coherent octave-spanning mid-infrared supercontinuum generation in a silicon waveguide pumping at telecom wavelengths in the normal dispersion regime. This scheme shows a feasible path to overcome limits imposed by two-photon absorption on spectral broadening in silicon waveguides.

We present a numerical tool that searches an optimal cross section geometry of silicon-on-insulator waveguides given a target dispersion profile. The approach is a gradient-based multidimensional method whose efficiency resides on the simultaneous calculation of the propagation constant derivatives with respect to all geometrical parameters of the structure by using the waveguide mode distribution. The algorithm is compatible with regular mode solvers. As an illustrative example, using a silicon slot hybrid waveguide with 4 independent degrees of freedom, our approach finds ultra-flattened (either normal or anomalous) dispersion over 350 nm bandwidth in less than 10 iterations.

We present a novel approach for measuring nonlinear coefficients in fibers with significant pulse broadening. We perform a proof-of-concept demonstration for 200-m-long polarization-maintaining and single-mode fibers pumped at 1060 nm with ps pulses.

We present a numerical tool to find the cross-section geometry of silicon-oninsulator waveguides that leads to a target dispersion profile. In < 10 iterations, we achieve geometries providing ultraflattened dispersion over 350 nm bandwidth.

Microresonator combs exploit parametric oscillation and nonlinear mixing in an ultrahigh-Q cavity. This new comb generator offers unique potential for chip integration and access to high repetition rates. However, time-domain studies reveal an intricate spectral coherence behavior in this type of platform. In particular, coherent, partially coherent or incoherent combs have been observed using the same microresonator under different pumping conditions. In this work, we provide a numerical analysis of the coherence dynamics that supports the above experimental findings and verify particular design rules to achieve spectrally coherent microresonator combs. A particular emphasis is placed in understanding the differences between so-called Type I and Type II combs.

We provide a quantitative analysis of the coherence in microresonator frequency combs. We show how to achieve coherent transform-limited pulses on-chip without actively manipulating the pump setting conditions in the course of comb formation.

We theoretically find the third order dispersion that optimizes the spectral broadening induced by optical wave-breaking. It produces supercontinuum spectra spanning beyond 2=3 of an octave in a silicon waveguide pumping at 1550 nm.

The generation of multiple tones using four-wave mixing (FWM) has been exploited for many applications, ranging from wavelength conversion to frequency comb generation. FWM is a coherent process, meaning that its dynamics strongly depends on the relative phase among the waves involved. The coherent nature of FWM has been exploited for phase-sensitive processing in different waveguide structures, but it has never been studied in integrated microresonators. Waveguides arranged in a resonant way allow for an effective increase in the wavelength conversion efficiency (at the expense of a reduction in the operational bandwidth). In this letter, we show that phase shaping of a three-wave pump provides an extra degree of freedom for controlling the FWM dynamics in microresonators. We present experimental results in single-mode, normal-dispersion high-Q silicon nitride resonators, and numerical calculations of systems operating in the anomalous dispersion regime. Our results indicate that the wavelength conversion efficiency and modulation instability gain in microcavities pumped by multiple waves can be significantly modified with the aid of simple lossless coherent control techniques.

The physics of nonlinear-optical refraction in graphene has remained unclear for almost a decade now. We solve this issue through self-phase modulation experiments in graphene-covered waveguides, revealing the extra-ordinary free-carrier interactions that underpin the refraction process.