A topical review of numerical and experimental studies of supercontinuum generation in photonic crystal fiber is presented over the full range of experimentally reported parameters, from the femtosecond to the continuous-wave regime. Results from numerical simulations are used to discuss the temporal and spectral characteristics of the supercontinuum, and to interpret the physics of the underlying spectral broadening processes. Particular attention is given to the case of supercontinuum generation seeded by femtosecond pulses in the anomalous group velocity dispersion regime of photonic crystal fiber, where the processes of soliton fission, stimulated Raman scattering, and dispersive wave generation are reviewed in detail. The corresponding intensity and phase stability properties of the supercontinuum spectra generated under different conditions are also discussed.

Supercontinuum generation, photonic crystal fiber

The dynamic characteristics of pure-quartic solitons and soliton molecules

Ultrashort pulse generation hinges on the careful management of dispersion. Traditionally, this has exclusively involved second-order dispersion, with higher-order dispersion treated as a nuisance to be minimized. Here, we show that this higher-order dispersion can be strategically leveraged to access an uncharted regime of ultrafast laser operation. In particular, our mode-locked laser—with an intracavity spectral pulse shaper—emits pure-quartic soliton pulses that arise from the interaction of fourth-order dispersion and the Kerr nonlinearity. Phase-resolved measurements demonstrate that their pulse energy scales with the third power of the inverse pulse duration. This implies a strong increase in the energy of short pure-quartic solitons compared with conventional solitons, for which the energy scales as the inverse of the pulse duration. These results not only demonstrate a novel approach to ultrafast lasers, but more fundamentally, they clarify the use of higher-order dispersion for optical pulse control, enabling innovations in nonlinear optics and its applications. By suppressing the second- and third-order intracavity dispersion using an intracavity spectral pulse shaper, a mode-locked laser that emits pure-quartic soliton pulses that arise from the interaction of the fourth-order dispersion and the Kerr nonlinearity is demonstrated.

The pure-quartic soliton laser

In this paper, we investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu) according to analytical and approximate simulation. We study the dynamic of the separation phase for the ternary alloys of iron. The dynamical process of this separation has been described in a mathematical model called the Cahn–Hilliard equation. The minor element behavior in the process has been described by the Cahn–Hilliard equation. It describes the process of phase separation for two components of a binary fluid in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu). We implement a modified auxiliary equation method and the cubic B-spline scheme on this mathematical model to show the dynamical process of phase separation and the concentration of one of two components in a system. We try obtaining the solitary and approximate solutions of this model to show the relation between the components in this phase. We discuss our solutions in view of a Stefan, Thomas-Windle, and Navier–Stokes models. Whereas, these models describe the motion of viscous fluid substance.

Analytical and numerical simulations for the kinetics of phase separation in iron (Fe-Cr-X (X=Mo, Cu)) based on ternary alloys

We numerically solve a generalized nonlinear Schrodinger equation and find a family of pure-quartic solitons (PQSs), existing through a balance of positive Kerr nonlinearity and negative quartic dispersion. These solitons have oscillatory tails, which can be understood analytically from the properties of linear waves with quartic dispersion. By computing the linear eigenspectrum of the solitons, we show that they are stable, but that they possess a nontrivial internal mode close to the radiation continuum. We also demonstrate evolution into a PQS from Gaussian initial conditions. The energy-width scaling of PQSs differs strongly from that for conventional solitons, opening up possibilities for PQS lasers.

Stationary and dynamical properties of pure-quartic solitons.

The generation of ultrashort pulses hinges on the careful management of dispersion. Traditionally, this has exclusively involved second-order dispersion, while higher-order dispersion was treated as a nuisance to be minimized. Here we show that high-order dispersion can be strategically leveraged to access an uncharted regime of ultrafast laser operation. In particular, we demonstrate a mode-locked laser, with an intra-cavity spectral pulse-shaper, that emits pure-quartic soliton pulses, which arise from the interaction of the fourth-order dispersion and the Kerr nonlinearity. Using phase-resolved measurements we demonstrate that the energy of these pulses is proportional to the third power of the inverse pulse duration. This implies a dramatic increase in the energy of ultrashort pulses compared to those emitted by soliton lasers to date. These results not only demonstrate a novel approach to ultrafast lasers, but more fundamentally, they clarify the use of higher-order dispersion for optical pulse control, opening up a plethora of possibilities in nonlinear optics and its applications.

A family of solitons in fourth-order dispersive Kerr media is predicted and thoroughly analyzed. The found solutions unify many previously known classes of solitons, and present favorable characteristics for the dispersion engineering of ultrafast soliton lasers.

Generalized dispersion Kerr solitons

We consider solutions to the nonlinear Schrodinger equation with quadratic and quartic dispersion, and discover a temporal soliton family that includes recently discovered pure quartic solitons and solitons with only quadratic dispersion.

Kevin K. K. Tam

Papers

The pure-quartic soliton laser

Stationary and dynamical properties of pure-quartic solitons.

The pure-quartic soliton laser

Generalized dispersion Kerr solitons

Solitary wave solutions in nonlinear media with quartic and quadratic dispersion—implications for high-power lasers