Evolution of the model basing on the nonlocal response functions has been accessed according to the (2+1)d schrödinger equation in cartesian coordinates .this paper presents the singular laguerre-gaussian beams modulated by the airy functions in free space. It is possible to solve process the space-time multiple beams propagating in the medium using the superposition principle. Even more, it provides the theoretical basis for all-optical control technology.
Evolution of the model basing on the nonlocal response functions has been accessed according to the (2+1)d schrödinger equation in cartesian coordinates. This paper presents the singular laguerre-gaussian beams modulated by the airy functions in free space. Their propagation characteristics have been discussed with split-step fourier method. It is possible to solve process the space-time multiple beams propagating in the medium using the superposition principle. Even more, it provides the theoretical basis for all-optical control technology.
The Airy-Gaussian wave packets are the Airy wave packets modulated by the Gaussian wave packets. Basing on the separating variable method, the analytical solution has been accessed according to solving the paraxial beam equation in cylindric coordinates in free space. The Airy-Gaussian wave packets with complex variables are combing the Airy function with the complex variables and the Gaussian beams. The propagation characteristics of the complex variables Airy-Gaussian wave packets are studied. The complex variables Airy-Gaussian wave packets will rotate with the increase of propagating distance. Poynting vector reveals the essence of this phenomenon.
The space-time Airy-Ince-Gaussian Beams are the Ince-Gaussian beams, which is their intensity distribution at the cross-section showing as the Ince functions in the space domain, are modulated by the Airy pulses with initial velocity in the time domain. The solutions of the space-time Airy-Ince-Gaussian functions basing on the initial velocity, the power ratio about the critical power and the input power, and the ellipticity have been accessed according to solving the cylindric coordinates’ (1+3)D Schrödinger equations in Highly Nonlocal Nonlinear Media. Their propagation characteristics are studied in the paper. According to the incident power of the beam is not equal to the critical power, the beam width changes periodically when the beam is propagating. The Poynting vector of the propagating beams at cross section reveals the essence of physics.
The space-time complex variables Airy-Laguerre-Gaussian wave packets are the Laguerre-Gaussian wave packets, which is their intensity distribution at the cross section showing as the complex variables Laguerre-Gaussian functions in the space domain, are modulated by the Airy pulses in the time domain. The method of separating variables is a mathematical method to obtain this solution. According to solving the (1+3)D Pxi-axis equations, the analytical solution of the space-time complex variables Airy-Laguerre-Gaussian wave packets in free space has been accessed. When the initial incident power of the space-time complex variables Airy-Laguerre-Gaussian wave packets is not equal to the critical power, the wave packets’ width will fluctuate periodically. Poynting vector reveals the essence of this phenomenon.
The solutions for the example basing on the initial velocity, the power ratio about the critical power and the input power, and the ellipticity have been accessed according to solving the cylindric coordinates’ (1+3)D pxi-axis equations. The CAiIG wave packets are attained about the combinatorial solution by the Ince-Gaussian(IG) beams if we get it in the space domain and the Airy pulses with initial velocity if we get it in the time domain.
Analytical solution based on the separating variable method has been accessed according to solving the paraxial beam equation in cylindric coordinates in free space. The Airy- Gaussian wave packets with complex variables are combing the Airy function with the complex variables and the Gaussian beams.
Analytical solution basing on the separating variable method has been accessed according to solving the (1+3)D Pxi-axis equations in cylindrical coordinate system. The self-decelerating Airy-Elegant-Laguerre-Gaussian wave packets are constructed by the Airy pulses in temporal domain and the Elegant-Laguerre-Gaussian wave packets in spatial domain.
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