تركيب روش توازن هارمونيكي و تفاضل محدود براي شبيه سازي انتشار موج در محيط غير خطي

چكيده انگليسي :

Combining Harmonic Balance and Finite Difference Techniques for Simulation of Wave Propagation in Nonlinear Media Amin Shahverdi a shahverdi@ec iut ac ir Date of Submission 2011 4 18 Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan Iran 84156 83111 Degree M Sc Language FarsiSupervisors name Amir Borji aborji@cc iut ac irAbstractSince the invention of laser propagation of high intensity optical waves which is substantially affected by thenonlinear properties of the medium has been a topic of high interest Nonlinearities of the medium lead tooptical phenomena such as second harmonic generation SHG frequency mixing self refraction self phasemodulation and Soliton which have all found interesting applications in optoelectronics and opticalcommunications In order to study these phenomena wave equation must be solved in nonlinear media Approximate and simplified solutions of the nonlinear wave equation for some of these phenomena alreadyexist These solutions are usually obtained by neglecting higher order harmonics and employing othersimplifying assumptions In this thesis our goal is to solve the nonlinear wave equation considering the effectsof higher order harmonics Harmonic Balance technique HBT is a very well known and effective method forthe analysis of lumped and distributed nonlinear circuits Interactions among different harmonics are taken intoaccount in this method and the number of harmonics is limited by the user In this thesis a new technique whichis inspired by HBT is proposed for solving the nonlinear wave equation First the solution is expanded in termsof multiple temporal harmonics with spatially varying coefficients After balancing the harmonics a system ofnonlinear equations for the coefficients is obtained which is solved by the finite difference method Theproposed method is called HB FD technique Employing this technique enable us to study optical phenomenaprecisely About second harmonic generation phase and intensity of electric field could be extracted fordifferent second order susceptibility This method shows that considering the effects of higher order harmonicschange the variation of first and second harmonics along the media also we can see changes in phase constantof second harmonic due to variation of dispersion This method can be used to study harmonic mixing speciallysum and difference frequency generation and creation of the optical parametric amplification in the absence ofsum frequency Simulation results show that optical parametric amplification is not appeared when sumfrequency generation is considered We use the Manley Rowe relations to calculate total intensity As aconsequence of the Manley Rowe relations the total intensity must be invariant under propagation Furthermore the FD HD technique is used for deriving phase constant variation of first harmonic in the Kerrmedia which is known as a self phase modulation Phase variation of the first harmonic highly depends on thethird order susceptibility and dispersion In this case we can change dispersion to compensate the effect of thethird order susceptibility and derive a suitable condition for creation of Soliton This method is not suitable forsimulation of Soliton propagation along the media so we choose another methods such as fully adaptive wavelettransform FAWT and finite difference time domain FDTD to study this phenomenon however the numberof harmonics are increased in HB FD technique but the calculation time is decreased significantly Also employing same formulation for study different nonlinear phenomena makes HB FD technique more attractive Key Words nonlinear media harmonic balance finite difference harmonic generation harmonic mixing selfphase modulation Soliton

شاهوردي، امين

تركيب روش توازن هارمونيكي و تفاضل محدود براي شبيه سازي انتشار موج در محيط غير خطي

اختلاط فركانس , مدولاسيون فاز خودي , ساليتون