Optical Solitons With Higher Order Dispersion by Semi-Inverse Variational Principle

Abstract

Abstract-This paper studies optical solitons, in presence of higher order dispersion terms by the aid of He's semi-inverse variational principle. Both Kerr law and power law are taken into consideration. The numerical simulations are also given to complete the analysis.

Evolution and Collapse of a Lorentz Beam in Kerr Medium

“…The collapse dynamics of elliptical beams have been extensively studied [22,24]. These studies pointed out significant differences between quantitative predictions of the aberrationless approximation and actual results obtained from NLS equation simulations [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. From our numerical calculations, we find a simple empirical expression for the critical power of asymmetrical Lorentz beam by fitting the results of the numerical calculation…”

“…In order to investigate further the effect of Kerr nonlinearity [23][24][25][26][27][28][29][30][31][32][33][34][35][36] on the Lorentz beam, we need to solve the NLS equation numerically. Numerical simulations were done using the parameters of wavelength λ = 0.53 µm, n 0 = 1, n 2 = 0.5 × 10 −4 cm 2 /GW, w 0x = 10 µm and z 0 = kw 2 0x /2 = 0.6 mm, respectively.…”

“…Variational technique has been applied to waveguides with effective refractive index method [25] and the study of optical solitons with higher order dispersions [26].…”

Transitional Behaviors of Cqgle Solitons Across Boundaries on a Phase Plane

“…A cubic-quintic (CQGLE) or its variation was used to model dissipative solitons in passively modelocked lasers [5][6][7][8][9]. An exploding soliton is an extreme example of pulsating solitons, which is usually quasi-stable and will grow rapidly over some period [10,11].…”

Optical Soliton Perturbation With Log Law Nonlinearity by He's Semi-Inverse Variational Principle

“…[1][2][3][4][5][6][7][8][9][10] In fact optical solitons are now out of the lab stage and is a reality in many continents. Optical solitons now do propagate over transcontinental and transoceanic distances through underwater optical fibers.…”