Coherent manipulation of spatial bright solitons of reflection and transmission using control fields of Milnor Gaussian polynomials

The generation of spatial bright solitons of reflection and transmission pulses and their intensities are investigated in a sodium atomic medium using Gaussian Milnor polynomial control fields. Significant bright and dark ring-shaped solitons are controlled by balancing nonlinearity and dispersion along two spatial coordinates. The intensity is more localized along one of the spatial coordinates due to larger nonlinearity and spread along other spatial coordinates due to smaller nonlinearity in the reflection pulse. A circular, crater-type bright soliton intensity is also maintained around the origin of the x and y coordinates, exhibiting varying intensity along the circumference. A large, bright intensity peak is observed around the origin, with the intensity minima at the center in reflection. The intensity peaks are enhanced in one of the spatial coordinates and localized in another coordinate in reflection. A large Gaussian-type bright solitonic intensity distribution is investigated at approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mi>λ</mml:mi></mml:mrow></mml:math> throughout the variation along the x-axis in the transmission pulse pattern. The reflection and transmission pulse intensities vary from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mn>0</mml:mn><mml:mi>%</mml:mi></mml:mrow></mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mn>40</mml:mn><mml:mi>%</mml:mi></mml:mrow></mml:math> , and at least <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mn>20</mml:mn><mml:mi>%</mml:mi></mml:mrow></mml:math> of the intensity of the incident pulse is lost by attenuation. The modified results are useful in optical communications, fiber optics, optical computation, signal processing, radar technology, and artificial neural networks.