tailieunhanh - Nonlinear Dynamics Part 2

Tham khảo tài liệu 'nonlinear dynamics part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 18 Nonlinear Dynamics Time s Fig. 11. The same experiment as in figure 10 but with an intermediate dye concentration x D and the same values of irradiation intensity. Here the solid lines are not fits but theoretical plots of equation 14 for a 60 20 and 4 for the decreasing I0 respectively. Serra Terentjev 2008b At a lower concentration of chromophore corresponding to D mm and x D the transmitted intensity is about 1 10 of the incident intensity figure 11 shows the similar features of the non-linearity which are especially evident at very short times. Again all curves start at the same I 10 . At higher irradiation intensities we achieve the saturation and the steady-state value I x corresponding to the solution of equation 6 . The change of curvature notable in figures 8 and 10 is not so clear here even at the highest I0. However in the comparative analysis of data we now take a different approach. Assuming all the parameters for the curves are now known y and x D from independent measurements and a from the fitting in figure 10 we simply plot the theoretical equation 14 on top of the experimental data. It is clear that the theory is in excellent agreement with the data. Finally we study the case of low dye concentration D 91 mm x D in figure 12 this is also the case which is more relevant for biological spectroscopy studies where the concentration of chromophore is usually small. In this exemplified case the initial transmittance is very high almost 85 of the incident light goes through the sample. Here the complicated integral equation 14 simplifies dramatically since at small x D 1 the difference between A ln 10 ln I0 I and x D which is the range of integration in 14 is also small. The integration can then be carried out analytically giving In Io x 1 _ a i-t _ e-T 1 t D 1 a 19 which gives in the stationary state the correct solution of equation 6 approximated at small x D In ĩiĩìẦ X D Io 1 a Nonlinear Absorption of Light in Materials with .