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Modulated by the spatial phase, Airy-like beams that possess the faster and better self-healing as well as the greater acceleration along the desired arbitrary trajectory are introduced. Airy-like beams have the strong spontaneous-focusing ability and the peak value of the focal plane is 5.4 times that of the initial plane when traveling along the quadratic function trajectory. Besides, the larger quadratic coefficient and the smaller constant term of the quadratic function can enhance the self-healing and the spontaneous-focusing of the beams. When the beams transmit along the snakelike trajectory, the original main lobe separates a new main lobe, and the energy will concentrate on the new main lobe. Airy-like beams, along a hyperbolic-secant trajectory, can remain non-diffraction over long distances. However, when traveling along a hyperbolic trajectory, the evolution process is very similar to that of Airy-Gaussian vortex beams. These excellent properties can be applied to the special beams’ modulation and optimization. Furthermore, it may provide a way for constructing beams along the special trajectory with the desired spontaneous-focusing and self-healing.

We propose an integrated structure with microresonator and slot waveguide to generate high performance supercontinuum harnessing dual-pump scenario. Compared with single pump of CW or soliton pulse, it possesses broader spanning and better coherence.

We propose an on-chip cascaded structure consisting of a microresonator and a slot waveguide to generate the high-performance supercontinuum harnessing the dual pump scenario. Utilizing a single CW pump with the power of only 0.1 W, the dissipative Kerr soliton with the full width at half maximum of 69.2 fs and the peak power of 103.3 W is generated and couples out the microresonator together with the CW pump to serve as a dual pump seed for the supercontinuum generation in the followed slot waveguide. The slot waveguide built upon a silicon-organic hybrid structure is carefully designed to possess remarkable nonlinearity and appropriate dispersion profile for smooth and broadband supercontinuum generation. We have numerically achieved the 1.56 octave-spanning supercontinuum spanning 1 ~ 3 μm with the proposed dual pump scenario. The supercontinuum generated by the dual pump scenario shows flattened, broadband, and quasi-right-angled-trapezoid shape, along with good coherence. Compared with the single pump scenario of CW or soliton pulse only, the supercontinuum generated by the dual pump scenario possesses the much stronger spectrum, broader spanning, and medium coherence. Our work opens up a new path for on-chip and cost-effective supercontinuum generation with the high performance of intensity, bandwidth, and coherence.

We study both analytically and numerically nonparaxial propagation dynamics of the Chirped Airy vortex (CAiV) beams in uniaxial crystal orthogonal to the optical axis. The propagation trajectory, the intensity, the radiation forces, the Poynting vector and the angular momentum (AM) of the CAiV beams are illustrated by numerical examples. The influences of the ratio of the extraordinary refractive index to the ordinary refractive index, the linear chirp factor and the quadratic chirp factor on the nonparaxial evolution of the CAiV beams are examined in detail. Results show that the linear chirp factor provides an intensity concentration, which is totally different with the influence of the quadratic chirp. Besides, the uniaxial crystals with different refractive index ratios can be used to control the intensity of optical lobes. Moreover, the value and the direction of the radiation forces depend on the propagation distance and the chirp factor. The chirp factor acting on the Poynting vector and the AM mainly occurs in the direction of vectors. The nonparaxial propagation characteristics of the CAiV beams provide a convenient method to the intensity modulation and the optical manipulation of micro particles.