Generalized Darboux transformation and the higher-order semirational solutions for a non-linear Schrödinger system in a birefringent fiber

2021 ◽  
pp. 2150013
Author(s):  
Dan-Yu Yang ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yu-Qiang Yuan ◽  
Chen-Rong Zhang ◽  
...  
Keyword(s):  
Darboux Transformation ◽  
Phase Modulation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Four Wave Mixing ◽  
Second Order ◽  
Wave Mixing ◽  
Third Order ◽  
Non Linear ◽  
Schrödinger System

Temporal birefringent effects in the fibers change the crosstalk behaviors inside and between the fiber cores in the linear and non-linear optical power areas. This paper studies a non-linear Schrödinger system with the four-wave mixing term, which describes the optical solitons in a birefringent fiber. We construct the generalized Darboux transformation, and acquire the higher-order semirational solutions consisting of the second- and third-order semirational solutions, which represent the complex amplitudes of the electric fields in the two orthogonal polarizations. We acquire the interactions between/among the two/three solitons. Such interactions are elastic and generate the rogue waves around the interacting regions. We obtain the interactions among the second-/third-order rogue waves and two/three solitons, respectively. When [Formula: see text] decreases, amplitude of the second-order rogue wave increases, with [Formula: see text] and [Formula: see text] accounting for the self-phase modulation and cross-phase modulation, respectively, while [Formula: see text] representing the four-wave mixing effect. With [Formula: see text] kept invariant, when [Formula: see text] increases and [Formula: see text], amplitudes of the second-order rogue wave and two bright solitons increase, while when [Formula: see text] increases and [Formula: see text], amplitudes of the second-order rogue wave and two dark solitons increase, with [Formula: see text] and [Formula: see text] being the constants.

Generation of Non-Classical Light by Four-Wave Mixing in Semiconductors

1998 ◽  
Vol 07 (02) ◽  
pp. 167-180
Author(s):  
A. M. Fox ◽  
M. Dabbicco ◽  
J. F. Ryan
Keyword(s):  
Phase Modulation ◽  
Four Wave Mixing ◽  
Nonlinear Susceptibility ◽  
Squeezed States ◽  
Wave Mixing ◽  
Third Order ◽  
Susceptibility Tensor ◽  
Squeezed Light ◽  
The Third ◽  
Third Order Nonlinear Susceptibility

We describe experiments to generate non-classical quadrature squeezed states of light by four-wave mixing in semiconductors. Squeezing can be achieved with either the diagonal or off-diagonal components of the third-order nonlinear susceptibility tensor. We have demonstrated squeezing by self-phase modulation in ZnS at 780 nm, and by cross-phase modulation in ZnSe at 960 nm. Possibilities for generating squeezed light in other materials by these techniques are discussed.

Third-order non-linear optical suceptibilities by laser self-trapping and degenerate four-wave mixing in oligothienyldicyanovinylene solutions

1993 ◽  
Vol 57 (1) ◽  
pp. 3974-3979 ◽  
Author(s):  
Makarand V. Joshi ◽  
Michael P. Cava ◽  
M.V. Lakshmikantham ◽  
Robert M. Metzger ◽  
Hossain Abdeldayem ◽  
...  
Keyword(s):  
Four Wave Mixing ◽  
Wave Mixing ◽  
Third Order ◽  
Non Linear ◽  
Self Trapping ◽  
Linear Optical ◽  
Degenerate Four Wave Mixing

Generalized Darboux transformation and rogue wave solution of the coherently-coupled nonlinear Schrödinger system

2016 ◽  
Vol 30 (13) ◽  
pp. 1650208 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Sha-Sha Yuan ◽  
Yue Wang
Keyword(s):  
Darboux Transformation ◽  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Rogue Wave Solution ◽  
Bright Soliton Solution ◽  
Generalized Darboux Transformation ◽  
Schrödinger System

In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS system.

Impact of System Parameters of Optical Fiber Link on Four Wave Mixing

2019 ◽  
Vol 13 ◽  
Author(s):  
Anil Kumar ◽  
Karamjit Kaur
Keyword(s):  
System Performance ◽  
Phase Modulation ◽  
Four Wave Mixing ◽  
Wave Mixing ◽  
Channel Spacing ◽  
Spacing Distance ◽  
Non Linear ◽  
Quality Of Transmission ◽  
The Mathematical Model

Background: The invention of WDM technology in optical communication system has completely revolutionized the telecomm industry through its high data carrying capacity and efficiency of transmission. Advanced optical modulation formats with high spectral efficiency, advanced components like Reconfigurable Optical Add Drop Multiplexers (ROADMS), OXC, and large bandwidth requirements contributed significantly in existence of dynamic, flexible translucent and transparent networks. In these networks, it is common practice to increase the power levels as much as possible to overcome the power penalty effects and better transmission, but this introduces several non-linear impairments in the link and hence degrades the quality of signal flowing. These impairments arise when several high strength optical fields of different wavelengths interact with molecular vibrations and acoustic waves. The different non-linear impacts include Self Phase Modulation (SPM), Cross Phase Modulation (XPM), Four Wave Mixing (FWM) and scattering effects like Stimulated Raman Scattering (SRS), Stimulated Brillouin Scattering (SBS. The main cause of these impairments is variation in refractive index of fiber (also called Kerr effect) due to intensity of signal flowing through fiber. Due to the degradation impact posed by these impairments, it is crucial to analyze their cause, their influence on system performance and mitigation techniques so as to improve the overall quality of transmission. The monitoring of impairments is quite a challenging task due to their dependency on time, present state of network, signals flowing in adjoining channels and fibers. Objective: The present work aims to identify and describe the role of FWM in optical networks. The mathematical model of FWM is studied to know the parameters influencing the overall impact on system performance. The power of optical source, channel spacing, distance of transmission and presence of dispersion are considered as key factors influencing FWM power being developed. Their impact on FWM power and hence, FWM efficiency is calculated. In addition, the influence of FWM on Quality of transmission is quantified in terms of BER and Q-factor. Method: The analysis is done through a two-channel transmitter system with varied power, channel spacing, distance of transmission and presence of other degradation factors (dispersion) is taken into account. The corresponding optical spectrums are analysed. Result & Conclusion: In this paper, the non-linear impairment FWM posing degradation effect on the signal quality has been discussed. The basics involved are presented along with the mathematical model. It has been found that FWM results in power transfer from one channel to generation of new waves which may lead to power depletion and interference. The new waves generated depend on the number of wavelengths travelling in the fiber and channel spacing. The influence of FWM on system performance is presented in terms of BER and Q-value. It has been concluded that the increased power of transmission and decreased channel spacing are the crucial factors increasing the magnitude of FWM and need to be closely monitored. On the other hand, increased distance of propagation and presence of certain level of dispersion leads to decrease in FWM power. Therefore, if selected carefully, they may act as source of FWM mitigation without requiring any external compensating device

scholarly journals Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Song ◽  
W. Zhang ◽  
P. Wang ◽  
Y. K. Xue
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Fifth Order

The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.

scholarly journals Highly efficient THz four-wave mixing in doped silicon

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Nils Dessmann ◽  
Nguyen H. Le ◽  
Viktoria Eless ◽  
Steven Chick ◽  
Kamyar Saeedi ◽  
...  
Keyword(s):  
Four Wave Mixing ◽  
Wave Mixing ◽  
Optical Nonlinearities ◽  
Third Order ◽  
Picosecond Pulses ◽  
Light Pulses ◽  
A Value ◽  
Doped Silicon ◽  
Perturbative Regime ◽  
Silicon Doped

AbstractThird-order non-linearities are important because they allow control over light pulses in ubiquitous high-quality centro-symmetric materials like silicon and silica. Degenerate four-wave mixing provides a direct measure of the third-order non-linear sheet susceptibility χ(3)L (where L represents the material thickness) as well as technological possibilities such as optically gated detection and emission of photons. Using picosecond pulses from a free electron laser, we show that silicon doped with P or Bi has a value of χ(3)L in the THz domain that is higher than that reported for any other material in any wavelength band. The immediate implication of our results is the efficient generation of intense coherent THz light via upconversion (also a χ(3) process), and they open the door to exploitation of non-degenerate mixing and optical nonlinearities beyond the perturbative regime.

Sign in / Sign up

Export Citation Format

Share Document