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Advances in Solid-State Lasers: Development and Applicationsduration and in the end limits Part 11

Tham khảo tài liệu 'advances in solid-state lasers: development and applicationsduration and in the end limits part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 392 Advances in Solid-State Lasers Development and Applications where o E a.u. 42n nỈ2 c v 2 U 2Uh V2 2K-3 2e2K-Vo o j2 K - Vo IoK Io eonocEo I 2 25 26 where o is the electric permittivity of free space c is the speed of light in vacuum. 3. Simulation on gradient temperature Song et al. 2008a Song et al. 2008b 3.1 Model of simulation In our simulation model to simplify the calculation and hold the essential physical dynamic characteristics we just only consider the fundamental mode the spatial profile of which is not changing along propagation of the coupled leaky modes propagating in the hollow fiber. We also neglect the interaction and energy transfer between the fundamental and high-order modes because the attenuation length of high-order modes is much smaller than that of the fundamental. We use the standard nonlinear 1 1 dimension Schrodinger equation to simulate and analyze the evolution dynamic of the pulse propagation both in temporal and spectra domain. The nonlinear Schrodinger equation for the electric field envelope u z t in a reference frame moving at the group velocity vg takes the following form assuming propagation along the z axis Agrawal 2OO7 du a ifi2 ổ2u . r 2. i d 1 2 . ổ u 2 u _ iri u u u u -T u 27 dz 2 2 ỔT2 1 1 o a1 dT The terms on the right hand side of the equation are the loss second order dispersion selfphase modulation self-steepening and Raman scattering respectively. Here c is the speed of light in vacuum ao the central angle frequency a the loss p2 the GVD group velocity dispersion and TR is related to the slope of the Raman gain spectrum. The nonlinear coefficient Y n2a cAeff where n2 is the nonlinear refractive index and Aeff the effective cross section area of the hollow fiber. Equation 27 and the parameters in the equation characterize propagation of the fundamental mode. The initial envelop of the pulse is in the following form Tempea Brabec 1998 Courtois et al. 2OO1 which is a simplification expression of Eq. 4 2P t u O t J .