Normal Dispersion Regime Research Articles

Influence of stimulated Raman scattering on Kerr domain walls and localized structures

We investigate the influence of the stimulated Raman scattering on the formation of bright and dark localized states in all-fiber resonators subject to a coherent optical injection, when operating in the normal dispersion regime. In the absence of the Raman effect, and far from any modulational instability, localized structures form due to the locking of domain walls connecting two coexisting continuous wave states, and undergo a particular bifurcation structure known as collapsed snaking. The stimulated Raman scattering breaks the reflection symmetry of the system, and modifies the dynamics, stability, and locking of domain walls. This modification leads to the formation of, not only dark, but also bright moving localized states, which otherwise are absent. We perform a detailed bifurcation analysis of these localized states, and classify their dynamics and stability as a function of the main parameters of the system.

Multi-octave-spanning supercontinuum generation through high-energy laser filaments in YAG and ZnSe pumped by a 2.4 μm femtosecond Cr:ZnSe laser

Abstract We present experimental and numerical investigations of high-energy mid-infrared filamentation with multi-octave-spanning supercontinuum generation (SCG), pumped by a 2.4 μm, 250 fs Cr:ZnSe chirped-pulse laser amplifier. The SCG is demonstrated in both anomalous and normal dispersion regimes with YAG and polycrystalline ZnSe, respectively. The formation of stable and robust single filaments along with the visible-to-mid-infrared SCG is obtained with a pump energy of up to 100 μJ in a 6-mm-long YAG medium. To the best of the authors’ knowledge, this is the highest-energy multi-octave-spanning SCG from a laser filament in a solid. On the other hand, the SCG and even-harmonic generation based on random quasi-phase matching (RQPM) are simultaneously observed from the single filaments in a 6-mm-long polycrystalline ZnSe medium with a pump energy of up to 15 μJ. The numerical simulations based on unidirectional pulse propagation equation and RQPM show excellent agreement with the measured multi-octave-spanning SCG and even-harmonic generation. They also reveal the temporal structure of mid-infrared filaments, such as soliton-like self-compression in YAG and pulse broadening in ZnSe.

Designing tunable narrowband parametric source in Chalcogenide-based dynamic fiber geometry

We numerically investigate the generation of spectrally isolated narrowband tunable parametric sources by continuous-wave pumping a specially designed gelatin-coated chalcogenide-silica dynamic fiber in the normal dispersion regime. The relative humidity (RH) dependent phase matching dominated by fourth order dispersion has been exploited for the first time, to the best of our knowledge, to produce far-detuned new wavelengths. A tunable source in the range of 0.96–2.5 μm with a tuning rate of 1.3 THz/%RH has been designed by milliwatt pumping a 30 cm long fiber at 1.395 μm. Additionally, the sideband tailorability of about 50 THz close to the visible band was achieved by selectively exciting higher-order fiber modes (HE21) in the anomalous dispersion regime at 0.91 μm. We emphasize that the parametric sources from the proposed host would be extremely useful in short-wave infrared spectroscopy and biomedical applications.

Spectral extension and synchronization of microcombs in a single microresonator

Broadband optical frequency combs are extremely versatile tools for precision spectroscopy, ultrafast ranging, as channel generators for telecom networks, and for many other metrology applications. Here, we demonstrate that the optical spectrum of a soliton microcomb generated in a microresonator can be extended by bichromatic pumping: one laser with a wavelength in the anomalous dispersion regime of the microresonator generates a bright soliton microcomb while another laser in the normal dispersion regime both compensates the thermal effect of the microresonator and generates a repetition-rate-synchronized second frequency comb. Numerical simulations agree well with experimental results and reveal that a bright optical pulse from the second pump is passively formed in the normal dispersion regime and trapped by the primary soliton. In addition, we demonstrate that a dispersive wave can be generated and influenced by cross-phase-modulation-mediated repetition-rate synchronization of the two combs. The demonstrated technique provides an alternative way to generate broadband microcombs and enables the selective enhancement of optical power in specific parts of a comb spectrum.

High-energy normal-dispersion fiber optical parametric chirped-pulse oscillator.

We demonstrate a fiber optical parametric chirped-pulse oscillator (FOPCPO) pumped in the normal-dispersion regime by chirped pulses at 1.036 µm. Highly chirped idler pulses tunable from 1210 nm to 1270 nm with energies higher than 250 nJ are generated from our system, along with signal pulses tunable from 870 nm to 910 nm. Numerical simulations demonstrate that further energy scaling is possible and paves the way for the use of such FOPCPOs for applications requiring high-energy, compact, and low-noise sources, such as in biophotonics or spectroscopy.

Passive mode locking in fiber lasers due to the polarization-dependent losses.

Weak polarization dependence exists in most fiber components. We numerically demonstrated passive mode locking in fiber lasers based on weak polarization dependence down to polarization-dependent loss of 1.76 dB. Different polarization dependences are investigated to unveil its role for achieving passive mode locking. The anomalous dispersion region and the normal dispersion regime are both tested. It is found that, independent of operating dispersion regime, stronger gain is required for achieving mode locking with lower polarization dependence. Our numerical demonstration confirms previous experimental results and broadens the knowledge on additive-pulse mode locking.

Higher order effects on constant intensity waves of nonlinear Schrödinger equation with [formula omitted] symmetric potential

Constant intensity solutions of nonlinear Schrödinger equation that includes terms accounting for third order dispersion, self steepening, self frequency shift and PT symmetric potential are obtained. The complex potential is constructed as a solution to an inverse problem which predicts the potential supporting the desired solution. These constant intensity waves are then used to perform a modulational instability analysis both in anomalous and normal dispersion regime. The linear stability results are supplemented with direct numerical simulations. The role of third order dispersion, self steepening and self frequency shift on modulational instability of the constant intensity states has been investigated. Effect of variation of amplitude of constant intensity solutions on modulational instability is studied too.

Spatio-temporal control of dispersive waves trapping by solitons in graded-index multimode fibers

We investigate the impact of the spatial beam oscillations in a graded-index multimode fiber (MMF) upon the trapping and blue-shifting of dispersive pulses by a multimode soliton. We find that the dispersive pulses trapped by solitons can be controlled through adjusting the degree of compression of the spatial beam. This can provide an explanation for the enhanced blue spectral extension observed in the typical supercontinuum generation in graded-index MMFs. Besides, the spatial-temporal nonlinear effect may provide an additional degree of freedom for the spectrally tailored light generation and the ultrashort pulse generation with tunable wavelengths in the normal dispersion regime.

Modulation instability in nonlinear metamaterials modeled by a cubic-quintic complex Ginzburg-Landau equation beyond the slowly varying envelope approximation.

Considering the theory of electromagnetic waves from the Maxwell's equations, we introduce a (3+1)-dimensionsal cubic-quintic complex Ginzburg-Landau equation describing the dynamics of dissipative light bullets in nonlinear metamaterials. The model equation, which is derived beyond the slowly varying envelope approximation, includes the effects of diffraction, dispersion, loss, gain, cubic, and quintic nonlinearities, as well as cubic and quintic self-steepening effects. The modulational instability of the plane waves is studied both theoretically, using the linear stability analysis, and numerically, using direct simulations of the Fourier space of the proposed nonlinear wave equation, based on the Drude model. The linear theory predicts instability for any amplitude of the primary wave. Also, in the linear stability analysis, self-steepening effects of different orders are confronted and one discusses their effects on the behavior of the gain spectrum under both normal and anomalous group-velocity dispersion regimes. Analytical results are equally confronted to direct numerical simulations and fully agree with the predictions from the gain spectra. Modulational instability is manifested by clusters of solitons and multihump and dromion-like structures, whose emergence and features depend not only on system parameters, such as the cubic and quintic self-steepening coefficients, but also on the propagation distance under a suitable balance between nonlinear and dispersive effects.

Few-cycle optical pulses in negative index materials with dispersive permittivity and permeability

Propagation of few-cycle optical pulses in nonlinear optical Kerr (cubic) and non-Kerr (quintic) type metamaterials, exhibiting frequency-dependent dielectric susceptibility and magnetic permeability, is considered. Considering the theory of electromagnetic waves from Maxwell’s equations, a new nonlinear evolution equation describing the combined influences of higher-order nonlinearities and higher-order linear and nonlinear dispersions, appropriate for electromagnetic ultrashort pulse propagation in negative index materials, is derived beyond the slowly varying envelope approximation. A fully numerical simulation of the newly derived model equation, based on the lossy Drude model, shows the propagation of soliton-like stable few-cycle optical pulses under some parameter values. The change in types of self-steepening parameters induces structural changes of the initial input pulse, characterized by a soliton molecule made of either asymmetric or symmetric optical pulses. Also, the mutual balancing between Kerr and non-Kerr nonlinearities and higher-order dispersions is found to support the formation of soliton-molecules in both the normal and anomalous group velocity dispersion regimes.

Dissipative-Soliton-Resonance generation in anomalous-dispersion fiber lasers based on spectral filtering effect

In this article, we numerically research the generation of Dissipative-Soliton-Resonance (DSR) pulse in anomalous dispersion regime based on spectral filtering effect. We find that a strong spectral filtering effect can limit the spectrum broadening and avoid the pulse breaking up in the high effective gain of the cavity, which leads to the formation of DSR pulse. Meanwhile, we also find that the peak power of DSR pulse increases with the saturation power, which is in line with the case in normal dispersion regime. As a comparison, the DSR pulse cannot be obtained in the absence of spectral filtering effect, which proves that the generation of DSR pulse needs strong spectral filtering effect in anomalous dispersion regime. We believe that our work can be served as a theoretically guideline to investigate the generation of DSR pulse in anomalous dispersion regime.

Heterodyne interferometry applied to the characterization of nonlinear integrated waveguides.

We demonstrate that heterodyne interferometry makes it possible to accurately measure minute nonlinear phase shifts with little constraint on the propagation loss or chromatic dispersion. We apply this technique to characterize the effective nonlinearity of silicon nitride rib waveguides in the normal and anomalous dispersion regimes.

Harmonic dissipative soliton resonance in an Yb doped fiber laser with 110 W all fiber polarization-maintaining amplifier

The formation of harmonic dissipative soliton resonance (DSR) is experimentally investigated in an Yb-doped fiber laser operating in large normal dispersion regime. The DSR is observed at a fundamental frequency of 221 KHz, which delivered square-shaped with of 18.7–98.5 ns and single pulse energy of 0.25 μJ at 1056 nm. By adjusting the PCs, the DSR square pulses could be split into their harmonic mode-locked (HML) counterparts. These experimental results provide a new viewpoint for the further understanding of the mechanism and characteristics of HML square pulses. Based on a two-stage all-fiber PM master oscillator power amplifier (MOPA) system seeded by this oscillator, the pulses are amplified up to 110 W output power with the polarization extinction ratio (PER) of 18.7 dB at different frequencies ranging from 221KHz to 663 KHz and a record pulse energy of 0.51 mJ at the frequency of 221 KHz is achieved.

Buildup and dissociation dynamics of dissipative optical soliton molecules

Solitons can self-assemble into stable bound states, also denoted as soliton molecules that exhibit molecule-like dynamics. Soliton molecules have been predominantly investigated in the anomalous dispersion mode-locked fiber lasers. However, the soliton molecule dynamic evolution is still largely unexplored in the normal dispersion regime. We reveal here that, in the normal dispersion regime, the buildup and dissociation dynamics of soliton molecules. Our theoretical prediction indicates that, under different transmission functions of a saturable absorber (SA), a pair of solitons can be formed directly from background noise and then evolve into a soliton molecule through intense repulsive interaction, or a soliton molecule can be triggered to dissociate into a single soliton with transient annihilation and energy transfer. The experimental observation of short-time soliton molecule buildup and a new soliton molecule dissociation process corroborate the theoretical prediction. Furthermore, a long-time soliton molecule buildup ( ∼ 900 m s ) is discovered with single soliton splitting and soliton pair attraction. The buildup time is over four orders of magnitude longer than that of the short-time soliton molecule ( ∼ 21 µ s ). Our work unveils new perspectives into the ultrafast transient process and the interaction dynamics of soliton molecules in complex nonlinear systems.

Combining FDTD and coupled-mode theory for self-pulsing modeling in coupled nonlinear microring resonators

By means of finite-difference time-domain (FDTD) simulations, the stationary and dynamic responses of coupled optical microring resonators made with a material exhibiting an instantaneous Kerr nonlinearity are numerically investigated. We compare the results with the coupled-mode theory (CMT) and find good agreement. We demonstrate by integrating Maxwell’s equations that this system can show a self-pulsing operation in the normal dispersion regime. Finally, this work shows that FDTD simulations can be combined with a CMT analysis for the purpose of designing optical functions whose operation is based on nonlinear coupled micro-resonators.

Higher dimensional nonlinear Schrödinger equations in anomalous dispersion and normal dispersive regimes: Bright and dark optical solitons

In this paper, we are concerned with a higher order nonlinear Schrödinger equations existing in the anomalous dispersion regimes and the normal dispersive regimes. Applying the variational iteration method (VIM) we present bright soliton solutions for the anomalous case and dark optical soliton solutions for the normal dispersive regime. We address the constraint conditions that arise from the parameters involved in the model. Other solitonic, singular, and exponential solutions are derived as well.

Periodic power variation induced sideband instability in a single mode fiber laser

We report on the experimental observation of a type of parametric spectral sideband generation in a continuous wave (CW) fiber laser operating in the normal dispersion regime. The appearance of the sidebands is a threshold effect and their spectral shifts from the CW wavelength vary with the cavity length and CW power. We show that the sideband formation is induced by the periodic power variation of the light in the laser cavity.

Nonlinear beam self-imaging and self-focusing dynamics in a GRIN multimode optical fiber: theory and experiments.

Beam self-imaging in nonlinear graded-index multimode optical fibers is of interest for many applications, such as implementing a fast saturable absorber mechanism in fiber lasers via multimode interference. We obtain a new exact solution for the nonlinear evolution of first and second order moments of a laser beam of arbitrary transverse shape carried by a graded-index multimode fiber. We have experimentally directly visualized the longitudinal evolution of beam self-imaging by means of femtosecond laser pulse propagation in both the anomalous and the normal dispersion regime of a standard telecom graded-index multimode optical fiber. Light scattering out of the fiber core via visible photo-luminescence emission permits us to directly measure the self-imaging period and the beam dynamics. Spatial shift and splitting of the self-imaging process under the action of self-focusing are also revealed.

Modulational-instability-free pulse compression in anti-resonant hollow-core photonic crystal fiber.

Gas-filled hollow-core photonic crystal fiber (PCF) is used for efficient nonlinear temporal compression of femtosecond laser pulses, two main schemes being direct soliton-effect self-compression and spectral broadening followed by phase compensation. To obtain stable compressed pulses, it is crucial to avoid decoherence through modulational instability (MI) during spectral broadening. Here, we show that changes in dispersion due to spectral anti-crossings between the fundamental-core mode and core wall resonances in anti-resonant-guiding hollow-core PCF can strongly alter the MI gain spectrum, enabling MI-free pulse compression for optimized fiber designs. The results are important, since MI cannot always be suppressed by pumping in the normal dispersion regime.

Nonlinear Absorbing-Loop Mirror in a Holmium-Doped Fiber Laser

Nonlinear amplifying-loop mirror (NALM) and nonlinear optical loop mirror (NOLM) are two basic Sagnac interferometers widely used in mode-locked fiber lasers. Here we construct a variant by replacing the amplifier in an NALM with an absorber, which forms a type of nonlinear absorbing-loop mirror (NAbLM). The optical waves counter-propagating within an ideal NAbLM possess equal optical powers when they return and interfere inside the used fiber coupler owing to the equal absorptions. Meanwhile, their nonlinear phase shifts can still differ adequately if an asymmetric distribution of the absorber is employed. We theoretically predict that, in comparison to typical NALM and NOLM, the NAbLM can achieve relatively higher extinction ratio and larger modulation depth, resting on the unique equal-power interference. We then first used it as a saturable absorber in a holmium-doped fiber laser and achieved passively mode-locked operations in both normal and anomalous dispersion regimes. In the normal dispersion regime, h-shaped pulse was generated; whereas in the anomalous dispersion regime, both noise-like and dissipative-soliton-resonance-like pulses were achievable with polarization manipulation. NAbLM enables more options in nonlinear fiber optics especially when a high extinction ratio or large modulation depth is required.