Manipulating circular Airy beam dynamics with quadratic phase modulation in fractional systems under some diffraction...

Area of Science:

• Nonlinear Optics
• Quantum Optics
• Mathematical Physics

Background:

• Circular Airy beams (CABs) exhibit unique self-healing and non-diffracting properties.
• Fractional Schrödinger equation (FSE) describes wave propagation in complex optical systems.
• Quadratic phase modulation (QPM) is a technique to manipulate light beam characteristics.

Purpose of the Study:

• To investigate the transmission dynamics of CABs in FSE under diverse diffraction modulations and external potentials.
• To analyze the control effects of QPM on CAB propagation characteristics.
• To explore the frequency domain behavior of QPM-controlled CABs.

Main Methods:

• Split-step Fourier algorithm for simulating beam propagation.
• Investigated various diffraction modulations: periodic, linear, and power function.
• Studied external potentials: parabolic and linear potentials.

Main Results:

• QPM significantly alters CAB focusing, intensity, and trajectory.
• Under periodic modulation, QPM retards beam splitting; under linear modulation, it reduces self-focusing distance and modifies trajectory/width.
• Power function modulation leads to non-diffracting beams, with QPM reducing intensity and increasing width.
• In parabolic potentials, QPM influences autofocusing/defocusing behavior and optical width.
• In linear potentials, QPM causes deflection, periodic evolution, and stabilizes beam width.
• Frequency domain analysis confirms controllable propagation via QPM, modulation coefficients, and potentials.

Conclusions:

• QPM is an effective tool for controlling CAB transmission in FSE optical systems.
• The interplay between QPM, diffraction modulations, and external potentials dictates beam behavior.
• Rational parameter selection allows precise management of CAB propagation dynamics.