Over the last dozen years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations, but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing) and are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing, among others.

Airy beams and accelerating waves: an overview of recent advances

The dynamics of wave packets in the fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in the fractional Schrodinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional input chirped Gaussian beams is not harmonic. In one dimension, the beam propagates along a zigzag trajectory in real space, which corresponds to a modulated anharmonic oscillation in momentum space. In two dimensions, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display an increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero.

Propagation Dynamics of a Light Beam in a Fractional Schrödinger Equation.

Optical Solitons From Fibers To Photonic Crystals

Optical vortices exhibit a corkscrew-like shape as they travel. The study of this phenomenon, known as singular optics, is now extended to the high-power regime where high-harmonic processes become evident. This type of radiation could help illuminate novel attosecond phenomena in atoms and molecules.

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Strong-field physics with singular light beams

Beams of ``squeezed'' light have important applications in quantum metrology and gravitational-wave detection. The authors generate twin beams of correlated photons using parametrically amplified four- and six-wave mixing in a nonlinear optical crystal. This medium offers several advantages, such as better on-chip integration than atomic vapors, plus a longer coherence time than traditional optical materials. These achievements can also find potential application in all-optical communication and quantum storage of light in photonic circuits.

Controlled Correlation and Squeezing in Pr 3 + : Y 2 SiO 5 to Yield Correlated Light Beams

We study periodic inversion and phase transition of normal, displaced, and chirped finite energy Airy beams propagating in a parabolic potential. This propagation leads to an unusual oscillation: for half of the oscillation period the Airy beam accelerates in one transverse direction, with the main Airy beam lobe leading the train of pulses, whereas in the other half of the period it accelerates in the opposite direction, with the main lobe still leading – but now the whole beam is inverted. The inversion happens at a critical point, at which the beam profile changes from an Airy profile to a Gaussian one. Thus, there are two distinct phases in the propagation of an Airy beam in the parabolic potential – the normal Airy and the single-peak Gaussian phase. The length of the single-peak phase is determined by the size of the decay parameter: the smaller the decay, the smaller the length. A linear chirp introduces a transverse displacement of the beam at the phase transition point, but does not change the location of the point. A quadratic chirp moves the phase transition point, but does not affect the beam profile. The two-dimensional case is discussed briefly, being equivalent to a product of two one-dimensional cases.

Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential.

We theoretically investigate the dually dressed electromagnetically induced transparency, and the multidressed four-wave mixing (FWM) and six-wave mixing (SWM) processes in an inverted-$Y$-type atomic system with Zeeman sublevels. The results show that the Zeeman degeneracy of the dark states can be lifted by the dressing field as its intensity is increased. Moreover, the derived analytical expressions indicate that one can, for example, selectively create secondary dark states on the multi-Zeeman-sublevel dark states (by tuning the coupling field), distinguish two different types of dark states generated in two FWM processes (by properly controlling the coupling field intensity), and selectively enhance multi-FWM signals coming from various paths consisting of split Zeeman sublevels (by tuning the dressing field). The SWM signals can be either enhanced or suppressed by controlling the dressing field.

Controlling four-wave mixing and six-wave mixing in a multi-Zeeman-sublevel atomic system with electromagnetically induced transparency

We experimentally demonstrate the vortex solitons of four-wave mixing (FWM) in multi-level atomic media created by the interference patterns with superposing three or more waves. The modulation effect of the vortex solitons is induced by the cross-Kerr nonlinear dispersion due to atomic coherence in the multi-level atomic system. These FWM vortex patterns are explained via the three-, four- and five-wave interference topologies.

Modulated vortex solitons of four-wave mixing

We report the competition between the spontaneous parametric four-wave mixing and second- or fourth-order fluorescence (FL) signals in Pr3+:Y2SiO5 crystal. By changing the powers of controlling fields and blocking different fields, the competitive two signals can be identified through the dressing effect. Meanwhile, the delay of fourth-order FL in the time domain results from splitting the energy level. Such results can find potential applications in optical information storage and processing on a photonic chip.

http://iopscience.iop.org/article/10.1088/1612-2011/12/1/015404/pdf

Competition between spontaneous parametric four-wave mixing and fluorescence in Pr3+:YSO

We show that the four-wave mixing (FWM) processes in a multi-Zeeman level atomic system can be enhanced and suppressed by changing the polarization of one of the pump beams. Different polarization states of the pump beams will act on different transition pathways among the multi-Zeeman levels with different transition strengths, which affect the FWM efficiencies. An additional dress field applied to the adjacent transition can cause energy level splitting and therefore control the enhancement and suppression of the FWM processes in the system. The experimental results are in good agreement with our theoretical calculations.

Ruimin Wang

Papers

Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential.

Controlling four-wave mixing and six-wave mixing in a multi-Zeeman-sublevel atomic system with electromagnetically induced transparency

Modulated vortex solitons of four-wave mixing

Competition between spontaneous parametric four-wave mixing and fluorescence in Pr3+:YSO

Controlling enhancement and suppression of four-wave mixing via polarized light