In this paper we consider the influence of higher-order nonlinear effects like third-order dispersion, self-steepening effect on the propagation characteristics of solitons. By solving the higher-order nonlinear Schrödinger equation we show that the self-steepening effect can lead to the breakup of higher-order solitons through the phenomenon of soliton fission. This effect plays an essential role in several nonlinear phenomena, in particular in the so-called supercontinuum generation in optical fibers. Moreover, we can use third order dispersion to compress pulses as well as changing the frequency.

The refractive index of the methanol-water mixture depending on the wavelength at different concentrations was determined by our experimental method using a Michelson interferometer system. A comparative study of Gladstone-Dale, Arago–Biot and Newton relations for predicting the refractive index of a liquid has been carried out to test their validity for the methanol-water mixture with the different concentrations 30%, 40%, 50%, 60%, 80%, and 100%. The comparison shows the good agreement between our experimental results and the results in the expressions studied over the wavelength range approximately from 450 to 850 nm. Full Text: PDF ReferencesS. Sharma, P.B. Patel, R.S. Patel, "Density and Comparative Refractive Index Study on Mixing Properties of Binary Liquid Mixtures of Eucalyptol with Hydrocarbons at 303.15, 308.15 and 313.15 K", E-Journal of Chemistry 4(3), 343 (2007). CrossRef A. Gayathri, T. Venugopal, R. Padmanaban, K. Venkatramanan, R. Vijayalakshmi, "A comparative study of experimental and theoretical refractive index of binary liquid mixtures using mathematical methods", IOP Conf. Series: Materials Science and Engineering 390, 012116 (2018). CrossRef A. Jahan, M.A. Alam, M.A.R. Khan, S. Akhtar, "Refractive Indices for the Binary Mixtures of N, N-Dimethylformamide with 2-Butanol and 2-Pentanol at Temperatures 303.15 K, 313.15 K, and 323.15 K", American Journal of Physical Chemistry 7(4), 55 (2018). CrossRef N. An, B. Zhuang, M. Li, Y. Lu, Z. Wang, "Combined Theoretical and Experimental Study of Refractive Indices of Water–Acetonitrile–Salt Systems", J. Phys. Chem. B 119(33), 10701 (2015). CrossRef M. Upadhyay, S.U. Lego, "Refractive Index of Acetone-Water mixture at different concentrations", American International Journal of Research in Science, Technology, Engineering & Mathematics 20(1), 77 (2017). CrossRef T.H. Barnes, K.Matsumoto, T. Eiju, K. Matsuda, N. Ooyama, "Grating interferometer with extremely high stability, suitable for measuring small refractive index changes", Appl. Opt. 30, 745 (1991). CrossRef B. W. Grange, W. H. Stevenson, R. Viskanta, "Refractive index of liquid solutions at low temperatures: an accurate measurement", Applied Optics 15(4), 858 (1976). CrossRef P. Hlubina, "White-light spectral interferometry with the uncompensated Michelson interferometer and the group refractive index dispersion in fused silica", Optics Communications 193(1-6), 1 (2001). CrossRef P. Hlubina, W. Urbanczyk, "Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry", Meas. Sci. Technol. 16(6), 1267 (2005). CrossRef P. Hlubina, D. Ciprian, L. Knyblová, "Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry", Optics Communications 269(1), 8 (2007). CrossRef S. R. Kachiraju, D. A. Gregory, "Determining the refractive index of liquids using a modified Michelson interferometer", Optics & Laser Technology 44(8), 2361 (2012). CrossRef F. Gladstone, D. Dale, "XXXVI. On the influence of temperature on the refraction of light", Philos. Trans. R. Soc. 148, 887 (1858). CrossRef D.F.J. Arago, J.B. Biot, Mem. Acad. Fr. 15, 7 (1806). CrossRef Kurtz S S and Ward A L J, "The refractivity intercept and the specific refraction equation of Newton. I. development of the refractivity intercept and comparison with specific refraction equations", Franklin Inst. 222, 563-592 (1936). CrossRef K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, D. Triantis, "Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared", Appl. Phys. B 116, 617 (2013). CrossRef S. Kedenburg, M. Vieweg, T. Gissibl, H. Giessen, "Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region", Opt. Mater. Express 2(11), 1588 (2012). CrossRef

Abstract. We consider a model of two coupled ring waveguides with constant linear gain and nonlinear absorption with space-dependent coupling. This system can be implemented in various physical situations as optical waveguides, atomic Bose-Einstein condensates, polarization condensates, etc. It is described by two coupled nonlinear Schrödinger equation. For numerical simulations, we take local two-gaussian coupling.It is found in our previous papers that, depending on the values of involved parameters, we can obtain several interesting nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior. This research will be associated with experimental investigation planned in Freie Universität Berlin, in the group of prof. Michael Giersig.

Abstract:In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in [8] we study in the specific case of Kerr media. An obtained ultrashort pulse propagation equation which is called Generalized Nonlinear Schrödinger Equation usually has a very complicated form and looking for its solutions is usually a "mission impossible". Theoretical methods to solve this equation are effective only for some special cases. As an example we describe the method of a developed elliptic Jacobi function expansion. Several numerical methods of finding approximate solutions are simultaneously used. We focus mainly on the following methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons.