Normal Group Velocity Dispersion Research Articles

Quartic Kerr cavity combs: bright and dark solitons.

We theoretically investigate the dynamics, bifurcation structure, and stability of localized states in Kerr cavities driven at the pure fourth-order dispersion point. Both the normal and anomalous group velocity dispersion regimes are analyzed, highlighting the main differences from the standard second-order dispersion case. In the anomalous regime, single and multi-peak localized states exist and are stable over a much wider region of the parameter space. In the normal dispersion regime, stable narrow bright solitons exist. Some of our findings can be understood using a new, to the best of our knowledge, scenario reported here for the spatial eigenvalues, which imposes oscillatory tails to all localized states.

Platicon microcomb generation using laser self-injection locking

The past decade has witnessed major advances in the development and system-level applications of photonic integrated microcombs, that are coherent, broadband optical frequency combs with repetition rates in the millimeter-wave to terahertz domain. Most of these advances are based on harnessing of dissipative Kerr solitons (DKS) in microresonators with anomalous group velocity dispersion (GVD). However, microcombs can also be generated with normal GVD using localized structures that are referred to as dark pulses, switching waves or platicons. Compared with DKS microcombs that require specific designs and fabrication techniques for dispersion engineering, platicon microcombs can be readily built using CMOS-compatible platforms such as thin-film (i.e., thickness below 300 nm) silicon nitride with normal GVD. Here, we use laser self-injection locking to demonstrate a fully integrated platicon microcomb operating at a microwave K-band repetition rate. A distributed feedback (DFB) laser edge-coupled to a Si3N4 chip is self-injection-locked to a high-Q ( > 107) microresonator with high confinement waveguides, and directly excites platicons without sophisticated active control. We demonstrate multi-platicon states and switching, perform optical feedback phase study and characterize the phase noise of the K-band platicon repetition rate and the pump laser. Laser self-injection-locked platicons could facilitate the wide adoption of microcombs as a building block in photonic integrated circuits via commercial foundry service.

The large-mode-area multicore fiber with low and flat normal dispersion profile at 1.5–2.3 μm

For the purpose of realizing the large-mode-area (LMA) fibers with low and flat normal group velocity dispersion (GVD) profiles, the approach based on the multicore fiber (MCF) consisting of identical cores is proposed. The contribution of the coupling between two adjacent cores to tailoring the GVD of the MCF can be analyzed by using the dispersive equation, which is evaluated by the coupled mode theory (CMT) and can describe the GVD relation between the MCF and single-core waveguide. Furthermore, the designed 19- and 37-core MCFs with the step-index waveguides exhibit extremely flat normal GVD profiles with values of close to 0 ps/nm·km in the wavelength range of 1500 – 2300 nm, while the effective mode area of the 37-core MCF can reach 440 μm2 at 1900 nm. For the case of the MCF based on the photonic crystal fiber (PCF) structure, the 7-core MCFs can offer the concave-shaped normal GVD profiles in the 1900-nm wavelength region, where the minimum GVD values are around −46 ps/nm·km, and the wavelengths of the dip center can shift from 1880 to 2110 nm by tuning the core spacing. The effective mode areas are increased beyond 170 μm2 at 1900 nm. The proposed LMA normal-dispersion MCFs have potential applications in high-power ultrashort-pulse fiber lasers and amplifiers.

Consequences of non-differentiable angular dispersion in optics: tilted pulse fronts versus space-time wave packets.

Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields, thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle[s] associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets - pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined - have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does not possess a derivative at some wavelength. Here we investigate the consequences of introducing non-differentiable AD into a pulsed field and show that it is the crucial ingredient required to realize group velocities that deviate from c (the speed of light in vacuum) along the propagation axis in free space. In contrast, the on-axis group velocity for conventional pulsed fields in free space is always equal to c. Furthermore, we show that non-differentiable AD is needed for realizing anomalous or normal group-velocity dispersion along the propagation axis, while simultaneously suppressing all higher-order dispersion terms. We experimentally verify these and several other consequences of non-differentiable AD using a pulsed-beam shaper capable of introducing AD with arbitrary spectral profile. Non-differentiable AD is not an exotic phenomenon, but is rather an accessible, robust, and versatile resource for sculpting pulsed optical fields.

Generation of vector flat-top solitons and hybrid bright–flat-top soliton complexes in optical microresonators via modulated pump

We demonstrate numerically the possibility of generation of vector platicons (or vector flat-top solitons) having orthogonally polarized components by the modulated pump at normal group velocity dispersion (GVD). Dynamics of this process can be controlled by pump polarization and depends on both the spectral interval between pumped modes and the difference of their free spectral ranges. We also show the possibility of the excitation of the hybrid soliton-platicon complexes (or hybrid complexes of bright and flat-top solitons) if pumped modes have alternating signs of the GVD coefficient.

Realizing normal group-velocity dispersion in free space via angular dispersion.

It has long been thought that normal group-velocity dispersion (GVD) cannot be produced in free space via angular dispersion. Indeed, conventional diffractive or dispersive components such as gratings or prisms produce only anomalous GVD. We identify the conditions that must be fulfilled by the angular dispersion introduced into a plane-wave pulse to yield normal GVD. We then utilize a pulsed-beam shaper capable of introducing arbitrary angular-dispersion profiles to symmetrically produce normal and anomalous GVD in free space, which are realized here on the same footing for the first time, to our knowledge.

Normal-dispersion CS2-filled silica fiber with broadband single-polarization property

The CS2-filled silica fiber with two air holes in the cladding can offer high nonlinearity, high birefringence and normal group velocity dispersion (GVD) profiles for both two orthogonally polarized fundamental modes (FMs) by an appropriate choice of the fiber parameters. Furthermore, the highly birefringent CS2-filled fiber assisted by two subwavelength-diameter gold wires can exhibit broadband single-polarization (SP) property because that, only the y-polarized FM guided in the CS2-core can couple to the fundamental surface plasmon polariton (SPP) modes with the field vectors along the radial direction, and then has a much larger losses than the x-polarized FM in the wavelength region beyond 1500 nm. The numerical results show that when the 25-kW 0.1-ps pulse at 1920 nm is coupled into the 0.035-m fiber and linearly polarized along the fast axis, the output pulse exhibits over one-octave supercontinuum (SC) spectrum linearly polarized in the fast axis, and can maintain a linear polarization state across the whole SC spectrum even though the input polarization angle increases to 15° from the fast axis.

Supercontinuum generation in single-crystal YAG fibers pumped around the zero-dispersion wavelength.

Yttrium aluminum garnet (YAG) is a common host material for both bulk and single-crystal fiber lasers. With increasing interest in developing optical technologies in the short-wave infrared and mid-infrared wavelength range, YAG may be a potential supercontinuum medium for these applications. Here, we characterize femtosecond laser pumped supercontinuum generation with 1200-2000 nm pump wavelengths (λp) for undoped, single-crystal YAG fibers, which are representative of the normal, zero, and anomalous-dispersion regimes. Supercontinuum was observed over the spectral region of about 0.2 to 1.6λp. Z-scan measurements were also performed of bulk YAG, which revealed little dispersion of the nonlinear index of refraction (n2) in the region of interest. The measured values of n2 (∼1×10-6cm2/GW) indicate a regime in which the nonlinear length, LNL, is less than the dispersion length, LD, (LNL≪LD). We report intensity clamping of the generated filament in the normal group velocity dispersion (GVD) regime and an isolated anti-Stokes peak in the anomalous GVD regime, suggesting further consideration is needed to optimize supercontinuum generation in this fiber medium.

Investigation into the impact of the recovery time of a saturable absorber for stable dissipative soliton generation in Yb-doped fiber lasers.

In this study, we conduct a numerical evaluation of the impact of the recovery time of a saturable absorber (SA) on the output performance of an Yb-doped fiber laser operating in the dissipative soliton regime. Particularly, we evaluate the output pulse characteristics, such as the pulse width, spectral bandwidth, pulse peak power, and pulse energy depending on the change in recovery time. Applying a too-slow SA recovery time above a certain critical value is shown to make the output pulse unstable and broken. Furthermore, we demonstrate that there is an optimum recovery time range for stable dissipative soliton pulse generation, depending on the cavity dispersion and modulation depth of the SA. Further, we perform an additional numerical simulation of the pulse compression to demonstrate the relationship between the output dechirped pulse width and SA recovery time. The optimum approach for the generation of the shortest dechirped pulses in the dissipative soliton regime will be to construct a fiber laser cavity with a small normal cavity group velocity dispersion and use an SA with an appropriate recovery time.

Modulational instability in optical fibers with randomly kicked normal dispersion

We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.

Thermally induced generation of platicons in optical microresonators.

We demonstrate a numerically novel mechanism providing generation of the flat-top solitonic pulses, platicons, in optical microresonators at normal group velocity dispersion (GVD) via negative thermal effects. We found that platicon excitation is possible if the ratio of the photon lifetime to the thermal relaxation time is large enough. We show that there are two regimes of the platicon generation depending on the pump amplitude: the smooth one and the oscillatory one. Parameter ranges providing platicon excitation are found and analyzed for different values of the thermal relaxation time, frequency scan rate, and GVD coefficient. Possibility of the turn-key generation regime is also shown.

Gaussian Pulse Propagation via Bright and Dark Solitons through an Atomic Medium

We study the Gaussian pulse propagation and its absorption, dispersion, and distortion in an atomic medium for advanced optical technology. The output pulse intensity distribution in time and Rabi oscillations, as well as the phase of control fields, show significant dark and bright forms of soliton shapes. We investigate the localized intensity of dark and bright solitons with the intensity of control fields in time domain within the normal and anomalous group velocity dispersion regions. Uniform undistorted pulse intensity and bright soliton are noted in time domain with the phase variation of control fields. These theoretical results are useful for optical fibers due to their minimum losses of the signal quality.

Femtosecond infrared supercontinuum generation in 6H-SiC crystal

We report on supercontinuum generation in silicon carbide (6H-SiC), pumped by tunable femtosecond pulses in the wavelength range of 1.3 - 2.4 μm, which cover the regions of normal, zero, and anomalous group velocity dispersion of the material. More than an octave spanning infrared supercontinuum spectra were measured, demonstrating almost constant blue cut-offs around 0.9 μm. Low energy thresholds for supercontinuum generation (depending on the pump wavelengths, but generally below 200 nJ) were demonstrated due to large nonlinear refractive index of the material (n2 = 97 ± 19 × 10−16 cm2/W), which was experimentally evaluated by measurement of the nonlinear transmission at 2.0 μm.

Frequency conversion dynamics of vector modulation instability in normal-dispersion high-birefringence fibers

We investigate the frequency conversion associated with the nonlinear stage of vector modulational instability in high-birefringence fibers with normal group-velocity dispersion. A complex heteroclinic structure of instability reveals all possible dynamic trajectories of frequency conversion. It is shown that different Fermi–Pasta–Ulam recurrent regimes are separated by Akhmediev breathers corresponding to a separatrix on the heteroclinic structure. We also demonstrate that the optimal frequency conversion unexpectedly occurs outside the parametric gain bandwidth when the input light is polarized close to 45° from a principal axis of the fiber, whereas the optimal conversion frequency gradually shifts into the gain region when the polarization direction of input light tilts toward the principal axis of the fiber.

Diffraction-Ray Optics of Femtosecond Laser Pulses Propagating in Air Under the Influence of the Normal Group Velocity Dispersion

Results of theoretical study of the femtosecond Ti:Sa laser pulse propagation in air under the influence of the normal group velocity dispersion are presented. The use of the diffraction-ray tube method for an analysis of numerical solutions of the nonlinear Schrodinger equation in chromatic dispersion medium with the Kerr and plasma nonlinearity makes it possible to determine the main regularities of the femtosecond laser pulse selffocusing and filamentation in air for various pulse durations, initial beam radii, and peak powers. It is shown that under the influence of the group velocity dispersion, the filamentation terminates with an increase in the initial radius of the laser beam even at high values of supercritical powers. With an increase in the dispersion distortions of the pulse, the radius of the energetically replenishing diffraction-ray tube, the angular divergence of the post-filamentation light channel, and the nonlinear focus coordinate normalized to the Rayleigh length increase in the central time slices of the laser pulse and its integral pattern.

Spatiotemporal solitons in dispersion-managed multimode fibers

We develop the scheme of dispersion management (DM) for three-dimensional (3D) solitons in a multimode optical fiber. It is modeled by the parabolic confining potential acting in the transverse plane in combination with the cubic self-focusing. The DM map is adopted in the form of alternating segments with anomalous and normal group-velocity dispersion. Previously, temporal DM solitons were studied in detail in single-mode fibers, and some solutions for 2D spatiotemporal ‘light bullets’, stabilized by DM, were found in the model of a planar waveguide. By means of numerical methods, we demonstrate that stability of the 3D spatiotemporal solitons is determined by the usual DM-strength parameter, S: they are quasi-stable at , and completely stable at . Stable vortex solitons are constructed too. We also consider collisions between the 3D solitons, in both axial and transverse directions. The interactions are quasi-elastic, including periodic collisions between solitons which perform shuttle motion in the transverse plane.

Four-wave mixing in high-Q tellurium-oxide-coated silicon nitride microring resonators

We report the first-time observation, to the best of our knowledge, of four-wave mixing (FWM) in hybrid tellurium oxide coated silicon nitride ring resonators with internal Q factors of 1.7 × 105 to 1.0 × 106. We show oscillation at NIR wavelengths ranging from 1020 nm to 2530 nm under 1590 nm pumping. The FWM process has been investigated for TeO2-coated Si3N4 ring resonators with a 600 µm radius and FWM is observed for threshold launched pump powers as low as 25 mW with normal group velocity dispersion (GVD). With the potential for engineering of the GVD to the anomalous regime, a phase-matched and more efficient FWM process can be realized, which can pave the way for broadband frequency comb generation in this platform. These results suggest further promise of higher performance and lower threshold power nonlinear devices on a low-loss CMOS compatible platform with the possibility of co-integration of active functionalities due to high solubility of rare earth dopants in tellurium oxide.

Numerical study of solitonic pulse generation in the self-injection locking regime at normal and anomalous group velocity dispersion.

We developed an original model describing the process of the frequency comb generation in the self-injection locking regime and performed numerical simulation of this process. Generation of the dissipative Kerr solitons in the self-injection locking regime at anomalous group velocity dispersion was studied numerically. Different regimes of the soliton excitation depending on the locking phase, backscattering parameter and pump power were identified. It was also proposed and confirmed numerically that self-injection locking may provide an easy way for the generation of the frequency combs at normal group velocity dispersion. Generation of platicons was demonstrated and studied in detail. The parameter range providing platicon excitation was found.

Generation and properties of dissipative Kerr solitons and platicons in optical microresonators with backscattering.

Generation and properties of dissipative Kerr solitons and platicons in optical microresonators are studied in the presence of the backscattering using the original analytical model considering a linear forward-backward waves coupling and nonlinear cross-action. We reveal that the backscattering may suppress the generation of the solitonic pulses or destabilize them for both anomalous and normal group velocity dispersion. We also demonstrate the possibility of switching between different soliton states. The influence of the linear and nonlinear coupling is analysed. It is shown that while the impact of the nonlinear coupling on the generation of the bright solitons is rather weak, it is significantly more pronounced for the platicon excitation process.

Stability Analysis and Transient Attraction Dynamics of Flat-Top Solitons via Modulated Driving Fields in Normal Dispersion Microcavity

We theoretically and numerically investigate the stability and transient attraction dynamics of flat-top solitons (or platicons) in normal group velocity dispersion (GVD) microcavity via modulation-assisted four wave mixing instead of mode interaction. The spatial bifurcation structure of the stationary states depending on modulation power, pump power and cavity detuning is mapped, indicating a significantly extended existence range by the modulation-assisted approach. We explore the transformation between discrete energy spectrum of dark solitons and a quasi-continuous spectrum of platicons with and without a third-order dispersion and identify the connections between these two states. Robust trapping and manipulation of temporal platicons is also verified by implementation of phase modulation, and explained by transient attraction dynamics. One may manipulate the duration of the pulse by varying modulation power, pump power, or cavity detuning. Specifically, the effect of high-order dispersion on Kerr frequency comb generation is studied, and the results show that different orders of GVD term affect the 3dB comb bandwidth, repetition rate, spectral position of dispersive waves, as well as temporal profile and pulse peak power.