Lax pair, Darboux transformation and rogue-periodic waves of a nonlinear Schrödinger–Hirota equation with the spatio-temporal dispersion and Kerr law nonlinearity in nonlinear optics

2021 ◽  
pp. 2150451 ◽  
Author(s):  
Cheng-Cheng Wei ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Su-Su Chen ◽  
Dan-Yu Yang
Keyword(s):  
Darboux Transformation ◽  
Periodic Wave ◽  
Lax Pair ◽  
Third Order ◽  
Periodic Wave Solutions ◽  
The Third ◽  
Third Order Dispersion ◽  
Wave Solutions ◽  
Minimum Amplitude ◽  
Order Dispersion

For a nonlinear Schrödinger–Hirota equation with the spatio-temporal dispersion and Kerr law nonlinearity in nonlinear optics, we derive a Lax pair, a Darboux transformation and two families of the periodic-wave solutions via the Jacobian elliptic functions dn and cn. We construct the linearly-independent and non-periodic solutions of that Lax pair, and substitute those solutions into the Darboux transformation to get the rogue-periodic-wave solutions. When the third-order dispersion or group velocity dispersion (GVD) or inter-modal dispersion (IMD) increases, the maximum amplitude of the rogue-periodic wave remains unchanged. From the rogue-dn-periodic-wave solutions, when the GVD decreases, the minimum amplitude of the rogue-dn-periodic wave decreases. When the third-order dispersion decreases, the minimum amplitude of the rogue-dn-periodic wave rises. Decrease of the IMD causes the period of the rogue-dn-periodic wave to decrease. From the rogue-cn-periodic-wave solutions, when the GVD increases, the minimum amplitude of the rogue-cn-periodic wave decreases. Increase of the third-order dispersion or IMD leads to the decrease of the period.

Alignment of a petawatt-class pulse compressor with the third-order dispersion completely compensated

2016 ◽  
Vol 13 (5) ◽  
pp. 055302 ◽  
Author(s):  
Yanlei Zuo ◽  
Kainan Zhou ◽  
Zhaohui Wu ◽  
Xiao Wang ◽  
Na Xie ◽  
...  
Keyword(s):  
Third Order ◽  
Pulse Compressor ◽  
The Third ◽  
Third Order Dispersion ◽  
Order Dispersion

Suppression and Compensation of the Third-Order Dispersion Effect on Polarization Modes in Birefringent Fibres

2001 ◽  
Vol 18 (9) ◽  
pp. 1222-1224 ◽  
Author(s):  
Xu Wen-Cheng ◽  
Chen Wei-Cheng ◽  
Luo Ai-Ping ◽  
Cui Hu ◽  
Chen Yong-Zhu ◽  
...  
Keyword(s):  
Dispersion Effect ◽  
Third Order ◽  
The Third ◽  
Third Order Dispersion ◽  
Order Dispersion

Stable anti-dark light bullets supported by the third-order dispersion

1998 ◽  
Vol 248 (2-4) ◽  
pp. 203-207 ◽  
Author(s):  
D.J Frantzeskakis ◽  
K Hizanidis ◽  
B.A Malomed ◽  
C Polymilis
Keyword(s):  
Third Order ◽  
Dark Light ◽  
The Third ◽  
Third Order Dispersion ◽  
Light Bullets ◽  
Order Dispersion

scholarly journals Dispersion Characteristic of Spatiotemporal Sharply Autofocused Vector Airy-Circular Airy Gaussian Vortex Wave Packets

2021 ◽  
Vol 9 ◽  
Author(s):  
Dong Li ◽  
Xin Chen ◽  
Chengquan Wei ◽  
Peng Li ◽  
Jianlin Zhao
Keyword(s):  
Wave Packet ◽  
Dispersion Coefficient ◽  
Initial Position ◽  
Main Peak ◽  
Third Order ◽  
The Third ◽  
Third Order Dispersion ◽  
Peak Intensity ◽  
Order Dispersion ◽  
Evolution Trajectory

The spatiotemporal vector Airy-Circular Airy Gaussian vortex wave packet is constructed by solving the (3 + 1)D Schrodinger equation in free space. The wave packet can simultaneously autofocus in space and time by setting the appropriate initial pulse velocity υ and the initial position of the main lobe T0. This kind of wave packet has low intensity before focusing, but the intensity at focus is about 80 times of the initial plane intensity. Our results may have potential applications in particle manipulation, laser processing, and other fields. Furthermore, the influence of the third-order dispersion coefficient on the evolution trajectory, the focus position, and the main peak intensity at the focus of the focusing pulse vector field is analyzed. The results show that the change of the initial velocity, the initial position, and the third-order dispersion coefficient can accurately control the evolution trajectory and the focus position, while the main peak intensity at the focus can only be controlled by adjusting the third-order dispersion coefficient. This means that the pulse vector light field can be manipulated precisely for precise processing by adjusting the third-order dispersion effect.

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