Báo cáo khoa học: Ảnh hưởng của tán sắc bậc ba lên soliton lan truyền trong sợi quang.

Tuyển tập những báo cáo nghiên cứu khoa học hay nhất của trường đại học vinh tác giả: 7. Đinh Xuân Khoa, Bùi Đinh Thuận, Ảnh hưởng của tán sắc bậc ba lên soliton lan truyền trong sợi quang...
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Báo cáo khoa học: "Ảnh hưởng của tán sắc bậc ba lên soliton lan truyền trong sợi quang."§¹i häc Vinh T¹p chÝ khoa häc, tËp XXXVI, sè 2A-2007 INFLUENCE OF THIRD-ORDER DISPERSION ON SOLITONS TRANSMISSION IN OPTICAL FIBERS Dinh Xuan Khoa (a), Bui Dinh Thuan (a) Abstract. In this article, we use split-step Fourrier method to investigate the influence of loss and third-order dispersion on a transmission soliton in optical fibers. 1. Introduction Soliton in optical fibers is formed by the balance between phase self-modulation and dispersion caused by group velocity. The low-loss transmission ofsoliton in optical fibers is described by non-linear Schrodinger equation. The lossand dispersion are main factors which diminish transmission distance and durableof soliton. Normally, we consider only second-order dispersion factor. However,when pulses width is small, higher-order dispersion factors are not negligible.Besides, in optical fibers, material dispersion equals zero at the wavelength of 1300nm. In this case, the change of pulses form and its durable depend on high-orderdispersion. In order to investigate transmission of soliton in optical fibers, we can useback-scattering and perturbation methods. But if the loss is considered, back-scattering method does not give correct solution. In this article, we use Split-StepFourrier algorithm to investigate the transmission of light pulse in non-lineardispersion media, thenceforth investigate the influence of high-order dispersion onsolitons transmission. 2. Transmission equation Pulses transmission in optical fiber is described by equation [1,3] () 2 ∂A  2 ∂A iβ 2 ∂ 2 A β 3 ∂ 3 A α ∂A i∂ 2 − iγ  A A +  (1) = − A − β1 + + A A − TR A 2 ∂t 2 6 ∂t 3 ω 0 ∂t ∂z ∂t ∂t   2  where A=A(z,t) is a complex envelop function of optical field. This function variesslowly with time and z position along optical fiber; α is loss factor of optical fiber; β 1,β 2 and β 3 are first, second and third-order dispersion factors, respectively; γ is non-linear factor of optical fiber, γ/ω0 term describes self-steeping effect, γTR termdescribes Raman scattering effect.NhËn bµi ngµy 19/9/2006. Söa ch÷a xong 18/12/2006. 59§¹i häc Vinh T¹p chÝ khoa häc, tËp XXXVI, sè 2A-2007 Let us consider an optical pulse with the width about some ps. In this case,self-steeping and Raman scattering effects can be negligible. Applying thetransformation t=t-z/vg, (vg is group velocity) equation (1) is re-written as follows: ∂2 A 1 ∂3 A α ∂A i 2 = − A + β 2 2 + β 3 3 − iγ A A . (2) ∂z ∂t ∂t 2 2 6 In general cases, when second-order dispersion factor β 2 is negative andhigher-order dispersion is negligible, the two specific distances of dispersion and 2 t0non-linear effects are approximately equal, LD = 2 , where t0 is the width of β2input pulse [2]. If the loss of optical fiber is small, we can receive pulses whose formdoes not change during transmission process. These pulses are solitons. So that wecan normalize the equation (2) to obtain ∂ u (ξ , τ ) 1 ∂ 2 u (ξ , τ ) ∂ 3 u (ξ , τ ) = − Γ u (ξ , τ ) + i + i u (ξ , τ ) 2 u (ξ , τ ) +B (3) ...