Propagation Of Few-cycle Optical Pulses Research Articles

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.

General laws of the propagation of few-cycle optical pulses with orbital angular momentum in free space

We conduct a theoretical study of the propagation of few-cycle, ultrafast vortices (UFVs) carrying orbital angular momentum (OAM) in free space. Our analysis reveals much more complex temporal dynamics than that of few-cycle fundamental Gaussian-like beams, particularly when approaching the single-cycle regime and the magnitude of the topological charge $l$ is high. The recently described lower bound $\sqrt{|l|}$ to the number of oscillations of UFVs with propagation-invariant temporal shape (isodiffracting UFVs) is found to hold on average also for UFVs of general type, with variations along the propagation direction above and below that bound, even vanishing locally. These variations are determined by the so-called Porras factor or $g_0$-factor characterizing the dependence of the Rayleigh distance of the spectral constituents with frequency. With a given available bandwidth, UFVs must widen temporally with increasing magnitude of the topological charge, and must widen or may shrink temporally during propagation as a result of the axially varying, $g_0$-dependent lower bound. Under very restrictive conditions in their generation, an UFV can be shrunk below the lower bound $\sqrt{|l|}$ at a focus into a kind of locally compressed state of OAM, but it broadens well-above $\sqrt{|l|}$ and distorts in a tiny fraction of the depth of focus because of the dispersions introduced by Gouy's phase and wave front mismatch. These propagation phenomena have implications and should be taken into account in experiments and applications of UFVs, such as the generation of high-harmonics and attosecond pulses with high OAM, or in OAM-based ultrafast communications systems, as well as in other areas of physics such as acoustics or electron waves.

Few-cycle optical pulses in a thin film of a topological insulator

In this study we consider the propagation of few-cycle optical pulses in a thin film of a topological insulator. The electrons are described by means of the long-wavelength effective Hamiltonian at low temperatures, and the electromagnetic field is classically considered within the framework of Maxwell׳s equations. The time evolution of the pulse shape is analyzed for different values of its initial velocity and amplitude.

Circularly polarized few-cycle optical rogue waves: Rotating reduced Maxwell-Bloch equations

The rotating reduced Maxwell-Bloch (RMB) equations, which describe the propagation of few-cycle optical pulses in a transparent media with two isotropic polarized electronic field components, are derived from a system of complete Maxwell-Bloch equations without using the slowly varying envelope approximations. Two hierarchies of the obtained rational solutions, including rogue waves, which are also called few-cycle optical rogue waves, of the rotating RMB equations are constructed explicitly through degenerate Darboux transformation. In addition to the above, the dynamical evolution of the first-, second-, and third-order few-cycle optical rogue waves are constructed with different patterns. For an electric field E in the three lower-order rogue waves, we find that rogue waves correspond to localized large amplitude oscillations of the polarized electric fields. Further a complementary relationship of two electric field components of rogue waves is discussed in terms of analytical formulas as well as numerical figures.

Propagation of few-cycle pulses in nonlinear Kerr media: harmonic generation

We apply our recently developed time-transformation method for studying the propagation of few-cycle optical pulses inside a nonlinear Kerr medium after taking into account that changes in the refractive index vary with the electric field as E2 and not by its average over an optical cycle. Our technique correctly predicts carrier-wave shocking and generation of odd-order harmonics inside a Kerr medium, the two features found earlier with directly solving Maxwell's equations using the finite-difference time-domain (FDTD) methods. We extend our method to study the impact of a finite response of the Kerr nonlinearity on harmonic generation and to include chromatic dispersion that cannot be ignored for ultrashort pulses. We show that nonlinear effects can help in controlling the width of an ultrashort pulse, even though it cannot propagate as a fundamental soliton. Our time-transformation method provides an alternative to the FDTD technique, as it deals with the electric field directly but does not require step size to be a small fraction of the wavelength, resulting in much faster computation speeds.

Self-phase modulation and frequency generation with few-cycle optical pulses in nonlinear dispersive media

We analyze nonlinear effects associated with the spatiotemporal propagation of few-cycle optical pulses in nonlinear dispersive media, including nonlinearity-induced self-phase modulation, generation of higher harmonics, and the effects of diffraction. First, we discuss the nonlinear equations governing the spatiotemporal propagation of short pulses in dispersive and diffractive nonlinear media and demonstrate a link between the field equation and the cubic nonlinear Schr\"odinger equation employed for describing the evolution of the pulse envelope. Then, for several different regimes of competitive scales, we study the self-action effects of few-cycle pulses and describe, both analytically and numerically, the pulse self-modulation and self-focusing, including the transformation of the spectral density and harmonic generation in the cases of weak and strong dispersion. Finally, we analyze the effect of the beam diffraction on self-action of the Gaussian few-cycle pulses.