Formation Of Light Bullets Research Articles

Optical crystals and light-bullets in Kerr resonators

Stable light bullets and clusters of them are presented in the monostable regime using the mean-field Lugiato–Lefever equation [Gopalakrishnan, Panajotov, Taki, and Tlidi, Phys. Rev. Lett. 126, 153902 (2021)]. It is shown that three-dimensional (3D) dissipative structures occur in a strongly nonlinear regime where modulational instability is subcritical. We provide a detailed analysis on the formation of optical 3D crystals in both the super- and sub-critical modulational instability regimes, and we highlight their link to the formation of light bullets in diffractive and dispersive Kerr resonators. We construct bifurcation diagrams associated with the formation of optical crystals in both monostable and bistable regimes. An analytical study has predicted the predominance of body-centered-cubic (bcc) crystals in the intracavity field over a large variety of other 3D solutions with less symmetry. These results have been obtained using a weakly nonlinear analysis but have never been checked numerically. We show numerically that indeed the most robust structures over other self-organized crystals are the bcc crystals. Finally, we show that light-bullets and clusters of them can occur also in a bistable regime.

Total internal reflection of the mid-IR near single-cycle light bullet in LiF.

Mid-IR light bullets formation and self-reconstruction after total internal reflection in LiF is investigated experimentally and through numerical simulations. The experiment showed that spatial-temporal deformations of the wave packet in inhomogeneous wave on a reflecting interface can be neglected for this process and a near single-cycle light bullet can be formed or recovered after a distance determined by its energy loss for ionization and supercontinuum radiation. The estimation of the reconstruction distance by an empirical formula for self-focusing distance on the base of the peak power and the radius of the LB numerical simulation are in a good agreement with experimental data received.

Short-wavelength cutoff of the light bullet spectrum in calcium fluoride

For the first time, we studied the change in a short-wavelength cutoff of a mid-IR pulse spectrum with an increase in a nonlinear optical interaction length in calcium fluoride. We investigate a transformation of an anti-Stokes wing in a pulse spectrum during light bullet formation under anomalous group velocity dispersion. An experimental scheme allowing a variation of a pulse propagation length in dielectric sample was employed. We compare results of numerical simulations provided by both, slowly-evolving-wave approximation method and unidirectional pulse propagating equation, under experimental conditions. It was found that a short-wavelength cutoff of an isolated anti-Stokes wing in light bullet’s spectrum shifts towards short-wave region by several hundred nanometers during light bullet formation. Moreover, the shift of a short-wavelength cutoff is 100 nm per 100 μm of a pulse propagation length in a sample at the initial stage of light bullet appearance. The short-wavelength cutoff of already formed propagating light bullet changes slightly. With an increase in pulse energy, the short-wavelength cutoff decreases. The observed shift of the cutoff wavelength during the light bullet formation exhibits a general behaviour for all considered pulse energies.

Spatiotemporal localizations of light in quadratically nonlinear media with transversal inhomogeneity

In the current study with the help of mathematical modeling we investigate the generation of second optical harmonic provided various group velocity dispersion (GVD) and third order dispersion effects taken into account. Varying values and signs of the third-order dispersion at quasi-zero values of GVD we reveal the conditions of light bullet formation and stable propagation. To this end we use a generalization of the well-known system of the second harmonic generation in quasi-optical approach. Particular attention is paid to the case when GVD at the second harmonic is close to zero. In addition, we investigate these cases using both focusing and defocusing waveguide which means the presence of transversal inhomogeneity.

Dependence of the short-wavelength cutoff in the mid-IR pulse spectrum on the interaction length in SiO2 and CaF2

This paper presents the results of experimental and numerical study of the anti-Stokes wing formation and the evolution of the short-wavelength cutoff in the 1900 nm pulse spectrum during its propagation and filamentation in fused silica and calcium fluoride. It is found that during the light bullet formation the short-wavelength cutoff in the supercontinuum spectrum is shifted to the anti-Stokes region with an increase in the nonlinear optical interaction length with the medium. However, change in the short-wavelength cutoff in the formed light bullet spectrum throughout its further propagation is insignificant.

Interference effects in the formation of the light bullet spectrum under axicon focusing

Specific features of the anti-Stokes band of the light bullet supercontinuum spectrum under filamentation of 1900-nm femtosecond pulses, focused by an axicon in fused silica and calcium fluoride, have been experimentally, numerically, and analytically investigated. It is found that the formation of two or more light bullets in a filament leads to modulation of spectral components’ intensity. The oscillation period of spectral components, defined as the wavelength interval between adjacent intensity minima, decreases with decreasing their wavelength. On a logarithmic scale, the relative change in the oscillation period in the spectrum is proportional to the spectral component wavelength and is independent of the pulse energy and the position of the light bullet formation region in the filament. It is established that the modulation in the spectrum is due to the interference of the broadband supercontinuum emitted by light bullets, and its period decreases with increasing interval between them.

Formation of Annular Light Bullets in a Femtosecond Vortex Beam

The formation of annular light bullets during the filamentation of femtosecond optical vortices in a LiF crystal under conditions of anomalous group velocity dispersion is considered. Features of the spatiotemporal dynamics of pulses are described. Quantitative estimates of the parameters of light bullets are given. The mechanism of the formation of a light bullet in the first nonlinear focus is analyzed. Models of a stationary optical vortex and a slit beam are considered.

Regimes of two-color light bullet formation in a gradient waveguide

In this paper we concentrate on the remarkable role of a gradient waveguide in two-color light bullet formation. We study generation of the second harmonic in such an inhomogeneous nonlinear medium, taking into account diffraction and relatively weak temporal dispersion. Using the averaged Lagrangian method we consider all possible combinations of the range of group velocities (normal or anomalous dispersion) and waveguide geometry (focusing or defocusing waveguide). Stability conditions for a propagating two-color light bullet are derived analytically. We demonstrate the formation of a stable two-component light bullet in a parabolic planar quadratically nonlinear waveguide either at anomalous or at normal group velocity dispersion. We discuss also the results of numerical simulation confirming our analytical findings. Besides that, simulation allows us to expand the scope of the study and to show light bullet propagation at a certain phase mismatching and the formation of a stable coupled localized structure from a signal at the fundamental frequency as well.

Chirp-controlled filamentation and formation of light bullets in the mid-IR.

Formation of light bullets-tightly localized in space and time light packets, retaining their spatiotemporal shape during propagation-is, for the first time, experimentally observed and investigated in a new regime of mid-infrared filamentation in ambient air. It is suggested that the light bullets generated in ambient air by multi-mJ, positively chirped 3.9-μm pulses originate from a dynamic interplay between the anomalous dispersion in the vicinity of CO2 resonance and positive chirp, both intrinsic, carried by the driver pulse, and accumulated, originating from nonlinear propagation in air. By adjusting the initial chirp of the driving pulses, one can control the spatial beam profile, energy losses, and spectral-temporal dynamics of filamenting pulses and deliver sub-3-cycle mid-IR pulses in high-quality beam on a remote target.

Effect of Scale Characteristics of a Femtosecond Mid-IR Wave Packet on the Threshold Power of Filamentation

The dependence of the formation process of a light bullet on the relation between diffraction and dispersion lengths of the femtosecond mid-IR wave packet during its propagation in transparent dielectrics is studied. It is found that the ratio of the diffraction length of the wave packet to its dispersion length is the similarity parameter for the light bullet formation under conditions of anomalous dispersion of the group velocity. The value of the filamentation threshold power taken relative to the critical power of stationary self-focusing is also defined by the introduced similarity parameter and increases with it.

Stable single light bullets and vortices and their active control in cold Rydberg gases

Realizing single light bullets and vortices that are stable in high dimensions is a long-standing goal in the study of nonlinear optical physics. On the other hand, the storage and retrieval of such stable high dimensional optical pulses may offer a variety of applications. Here we present a scheme to generate such optical pulses in a cold Rydberg atomic gas. By virtue of electromagnetically induced transparency, strong, long-range atom-atom interaction in Rydberg states is mapped to light fields, resulting in a giant, fast-responding nonlocal Kerr nonlinearity and the formation of light bullets and vortices carrying orbital angular momenta, which have extremely low generation power, very slow propagation velocity, and can stably propagate, with the stability provided by the combination of local and the nonlocal Kerr nonlinearities. We demonstrate that the light bullets and vortices obtained can be stored and retrieved in the system with high efficiency and fidelity. Our study provides a new route for manipulating high-dimensional nonlinear optical processes via the controlled optical nonlinearities in cold Rydberg gases.

Formation of Light Bullets and the Generation of a Broadband Supercontinuum upon the Filamentation of Femtosecond IR Pulses

The formation of light bullets and the generation of a broadband supercontinuum with the minimum wavelength in the UV region are observed upon the filamentation of a femtosecond laser pulse in transparent dielectrics under conditions of an anomalous dispersion of group velocity. The duration of a light bullet, measured via laser coloration, is around one period of the light field’s oscillation, and its diameter is less than 10 μm. Numerically calculated parameters of the light bullet are in good agreement with experimentally measured values.

Light bullets in a time-delay model of a wide-aperture mode-locked semiconductor laser.

Recently, a mechanism of formation of light bullets (LBs) in wide-aperture passively mode-locked lasers was proposed. The conditions for existence and stability of these bullets, found in the long cavity limit, were studied theoretically under the mean field (MF) approximation using a Haus-type model equation. In this paper, we relax the MF approximation and study LB formation in a model of a wide-aperture three section laser with a long diffractive section and short absorber and gain sections. To this end, we derive a non-local delay-differential equation (NDDE) model and demonstrate by means of numerical simulations that this model supports stable LBs. We observe that the predictions about the regions of existence and stability of the LBs made previously using MF laser models agree well with the results obtained using the NDDE model. Moreover, we demonstrate that the general conclusions based upon the Haus model that regard the robustness of the LBs remain true in the NDDE model valid beyond the MF approximation, when the gain, losses and diffraction per cavity round trip are not small perturbations anymore.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Similarity parameter for the process of mid-IR light bullet formation

We study the influence of the ratio of diffraction and dispersion lengths of a femtosecond mid-IR wave packet on the filamentation threshold power and the light bullet (LB) formation upon nonlinear optical interaction with solid-state dielectrics under the conditions of anomalous group velocity dispersion. It is found that the ratio of the threshold power of filamentation and LB formation to the critical power of stationary self-focusing is independent of the radiation wavelength and the medium characteristics and is determined by the similarity parameter, equal to the ratio of the diffraction length to the dispersion one. With an increase in the similarity parameter, the threshold power of filamentation and light bullet formation increases.

Spatial instabilities of light bullets in passively-mode-locked lasers

Recently, the existence of robust three-dimensional light bullets (LBs) was predicted theoretically in the output of a laser coupled to a distant saturable absorber. In this manuscript, we analyze the stability and the range of existence of these dissipative localized structures and provide guidelines and realistic parameter sets for their experimental observation. In order to reduce the complexity of the analysis, we first approximate the three-dimensional problem by a reduced equation governing the dynamics of the transverse profile. This effective theory provides an intuitive picture of the LB formation mechanism. Moreover, it allows us to perform a detailed multi-parameter bifurcation study and to identify the different mechanisms of instability. It is found that the LBs experience dominantly either homogeneous oscillation or symmetry breaking transversal waves radiation. In addition, our analysis reveals several non-intuitive scaling behaviors as functions of the linewidth enhancement factors and the saturation parameters. Our results are confirmed by direct numerical simulations of the full system.

Stability of Gaussian-type light bullets in the cubic-quintic-septimal nonlinear media with different diffractions under $${\mathcal {PT}}$$ PT -symmetric potentials

From the governing equation $$-(3+1)$$ -dimensional nonlinear Schrodinger equation with cubic-quintic-septimal nonlinearities, different diffractions and $${\mathcal {PT}}$$ -symmetric potentials, we obtain two kinds of analytical Gaussian-type light bullet solutions. The septimal nonlinear term has a strong impact on the formation of light bullets. The eigenvalue method and direct numerical simulation to analytical solutions imply that stable and unstable evolution of light bullets against white noise attributes to the coaction of cubic-quintic-septimal nonlinearities, dispersion, different diffractions and $${\mathcal {PT}}$$ -symmetric potential.

Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrodinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.

Light bullets formation accompanied by odd harmonics generation under Mid-IR femtosecond filamentation in LiF

The formation of light bullets in mid-IR femtosecond filamentation is investigated numerically by means of the unidirectional pulse propagation equation (UPPE). A general approach for light bullets formation is presented for condensed media under anomalous GVD. The main parameters of the light bullets are evaluated. The features of super continuum and odd harmonic generation accompanying the light bullets formation are analyzed.

Filamentation and light bullet formation dynamics in solid-state dielectric media with weak, moderate and strong anomalous group velocity dispersion

We present a series of measurements, which characterize filamentation dynamics of intense ultrashort laser pulses in the space–time domain, as captured by means of three-dimensional imaging technique in sapphire and fused silica, in the wavelength range of 1.45–2.25 μm, accessing the regimes of weak, moderate and strong anomalous group velocity dispersion (GVD). In the regime of weak anomalous GVD (at 1.45 μm), pulse splitting into two sub-pulses producing a pair of light bullets with spectrally shifted carrier frequencies in both nonlinear media is observed. In contrast, in the regimes of moderate (at 1.8 μm) and strong (at 2.25 μm) anomalous GVD we observe notably different transient dynamics, which however lead to the formation of a single self-compressed quasistationary light bullet with an universal spatiotemporal shape comprised of an extended ring-shaped periphery and a localized intense core that carries the self-compressed pulse.

Visible supercontinuum radiation of light bullets in the femtosecond filamentation of IR pulses in fused silica

We report experimental and theoretical investigations of visible supercontinuum generation in the formation of light bullets in a filament produced by IR pulses. In the filamentation of a pulse in fused silica, bright tracks are recorded resulting from the recombination glow of carriers in the laser plasma produced by a sequence of light bullets and from the scattering in silica of the visible supercontinuum generated by the light bullets. It is found that the formation of a light bullet is attended with an outburst of a certain portion of supercontinuum energy in the visible range. The energy outburst is the same for all bullets in the sequence and becomes smaller with increasing pulse wavelength.