| It describes the absorption and fluorescence spectrum of all-transβ-carotene molecules, the influence of the fluorescence from all-transβ-carotene molecules on the threshold and saturated values of stimulated Raman Stokes lines of CS2,and on multiple Stokes outputs in this doctoral dissertation. And, both of different coupled wave equations on stimulated Raman scattering (SRS) were used to fit the experimental results. We explained the physical reasons that the fluorescence seeding from all-transβ-carotene molecules influences the SRS of CS2.Moreover, the approximation conditions and the scope of applications of the coupled waves equations were also given.This dissertation can be divided into three parts:(1)All-transβ-carotene molecule is a linearπ-electron-conjugated chain-like polyene molecule with C2h symmetry and has eleven conjugated double bonds.The absorption band of the solution of all-transβ-carotene in the solvent of CS2 at a concentration of 10-7mol/L was shown in Fig.1.The resonance absorption band lied within from 440nm to 540nm.It has two roles in the experiments of the fluorescence seeding of SRS:One side, it could emit the fluorescence signals by absorptions of the pump photons because the pump light (532nm) is within Fig.1:The UV-VIS absorption spectrum of the solution of all-transβ-carotene in the solvent of CS2the resonance absorption band of all-transβ-carotene.The fluorescence-seeding signals will influence the spontaneous Raman noise at different Stokes frequencies. On the other side,all stokes lines were out of the absorption band except that the 1st Stokes line was in the non-resonance absorption band. Then, these output Stokes lines could escape from the high absorption from the solution so that they were able to be obtained more efficiently.The fluorescence spectrum of the solution of all-transβ-carotene in CS2 at a concentration of 10-7mol/L was shown in Fig.2.It also had two roles: One side, all Stokes lines of CS2 molecule were in the fluorescence band and would benefit from the fluorescence seeding from all-transβ-carotene molecules. On the other side, due to the short life of the second electronic excited state S2(1Bu+) of all-transβ-carotene molecule,there is no lasing process like Rhodamine molecules. Thus, there is no other nonlinear optical process.such as the lasing. which could compete with SRS on the pump energy. For the solution of all-transβ-carotene in CS2,the pump photon would sufficiently interact with the CS2 molecules for Fig.2:The fluorescence spectrum of the solution of all-transβ-carotene in CS2the efficient outputs of the Stokes lines.(2)The pump line was within the resonance absorption band and the 1st Stokes line was within the non-resonance absorption band. Here,the influence of the absorption and fluorescence characteristics of all-transβ-carotene at different concentrations on the threshold and saturated values were made research. We chosen liquid-core optical fiber with the length of 110cm (i.d.100/μm.o.d.300μ) as the sample.(2.1)The threshold of 1st Stokes line changes with the concentration of all-trans-beta-carotene in the solution. When the concentration is below 10-8 mol/1. the absorption and fluorescence at the pump and Stokes frequencies are both weak due to a small amount of all-trans-beta-carotene molecules in the solution, and the Sokes signal approaches the level of pure CS2-core. However, when the solution of beyond 10-6 mol/1 is used, the intense absorption would suppress the development of 1st Stokes line.It is observed by experiment that the threshold at 10-6 mol/L is 1.5 times as much as that of pure CS2,and that the threshold of 1st Stokes rises with the increase of the concentration,see Fig.3.A threshold power model of 1st Fig. 3: Thresholds of 1st Stokes at different concentrations by experiment. Stokes is used as follows,see Eq.(1):(?)(1)where ap,aS1 denote the absorption coefficient of pump and 1st Stokes lines respectively,gR is the Raman gain factor,Aeff the effective area of the fiber mode, L is the length of LCOF,and G is the net gain factor (G = gRLP/Aeff).The fitted result was shown in Fig.4. Then, in Fig.4,the numerically simulation shows the good agreement with experimental values. When the concentration becomes high, the absorption is more intense. More of the pump photons would be absorbed by all-trans-beta-carotene molecules because the pump line overlaps with the absorption band of the solution,and then the proportion of pump photons practically generating SRS of CS2 molecule would relatively decrease. Thus, with the increase of the concentration,the total quantity of pump photons, including those interacting with all-trans-beta-carotene and CS2 molecules, had to be raised in order that there is enough pump energy for the onset of SRS of CS2 molecules. Fig.4:Theoretical fittiug of the thresholds of 1st Stokes at different concentrations.(2.2) In Fig.5,the 2nd Stokes of CS2 is barely noticeable in pure CS2 solution and only the strong 1st Stokes line of CS2 is observed even at 2.85mJ of pump energy. However, with the addition of all-trans-beta-carotene in CS2 solution, the signal of 2nd Stokes line is enhanced by the fluorescence from all-trans-beta-carotene and could be observed at a low pump energy. As is shown in Fig.6. the 2nd Stokes line of CS2 in 10-7mol/L solution can be obtained at 1.76mJ of pump energy.Considering the contribution of the spontaneous Raman noise PN,(i=p. s1,s2 for the pump, first and second Stokes respectively) at Stokes frequencies,a set of differential equations can be written as follows,see Eq.(2):(?)(?)(2)(?)where ai is the absorption coefficient,gi is the gain factor, Pi is the power,and Fig. 5:The 1st and 2nd Stokes lines of CS2 in pure CS2 (Ep=2.85mJ)Fig. 6:The 1st and 2nd Stokes lines of CS2 in the solutions of 10-7 mol/L all-trans-beta-carotene in CS2 (Ep=1.76mJ). the anti-Stokes lines,the 3rd and higher-order Stokes lines are ignored,PNi is the equivalent noise input within the Raman bandwidth, which is responsible for the growth of spontaneous emission at the Stokes frequencies. Note that if the spontaneous Raman noise of some n-order Stokes line has developed enough to have significant amplification(such as when the Stokes line is within the fluorescence band) PNi can be viewed as equivalent input Stokes signals and it can lower the threshold of the n-order Stokes line as the seeding,or the amplified noise signal . In our experiment, all-trans-beta-carotene offer fluorescence seeding of the 2nd Stokes line of CS2 at 1310cm-1.which is outside the absorption band of the solution and is spectrally situated at the peak of the fluorescence envelope. Fluorescence seeding can provide a large number of initial photons at 2nd Stokes frequency. Thus,the fluorescence Pfluorescence from all-trans-beta-carotene acts as the role of the spontaneous Raman noise power PNS2 at 2nd Stokes frequency and the 2nd Stokes light PS2 starts from not the spontaneous Raman noise but the fluorescence Pfluourescence.(Normally Pfluorescence is greater than PNS2 due to the larger cross section of the fluorescence molecule even at low concentrations.) In Eq.(2), instead of the spontaneous Raman noise at 2nd Stokes frequency, the signal of fluorescence from all-trans-beta-carotene can be viewed as a new and amplified PNS2, which contributes to the decrease of threshold of 2nd Stokes line. Then, the pump threshold of 2nd Stokes line is not as high as that in pure CS2.The theoretical computations about the threshold of 2nd Stokes light is given below through Eq.(2)(see Fig.7).In Fig.7(a), up to 3.0mJ of pump energy,the 2nd Stokes line begins to slightly develop. With the fluorescence seeding of the 2nd Stokes line (Fig.7(b)),it preferentially starts at as low as 1.7mJ of pump energy.The simulation shows that the fluorescence seeding can effectively lower the threshold of 2nd Stokes light. At low pump energy, the 2nd Stokes line can be more easily observed than that without fluorescence seeding.(2.3) The saturation intensities of 1st Stokes at the different concentrations are Fig.7:The theoretical computations of thresholds of 2nd Stokes (a) without the fluorescence seeding,(b) with the fluorescence seeding. Fig.8:The experimental curve of the intensity dependence of 1st Stokes line on pump energy.investigated. Fig.8 shows the intensity dependence of 1st Stokes on pump energy. In the case of pure CS2 liquid, one can observe no sign of saturation besides the intense 1st Stokes line at a pump energy of 2.0 mJ. In 10-7mol/L solution. the saturation of 1st Stokes is observed and its intensity apparently decreases. At 10-6mol/L.the lower saturation intensity is obtained. These phenomenons mainly result from the following reasons: Firstly, it conies from the influence of the absorption at 1st Stokes frequency. While it is amplified by GR,part of the 1st Stokes is simultaneously depleted owing to the absorptionαS1 by all-trans-beta-carotene.For one thing,αS1 will weaken the intensity of the 1st Stokes line to some certain extent and make it develop not as intensely as that in pure CS2 liquid or in the solutions of lover concentrations. For another, the intensity of the fluorescence can be increased by the additional absorption of the 1st Stokes light besides the pump light. Thus the fluorescence seeding of 2nd Stokes line will also be enhanced. Secondly,it results from the preferential emergence of 2nd Stokes line in the influence of fluorescence seeding. The seeding of 2nd Stokes line will cause it to build faster than that in pure CS2.When the concentration of all-trans-beta-carotene in CS2 becomes higher,the development of 2nd Stokes will be faster owing to the strong seeding effect. Thus, the preferential energy transfer process from 1st Stokes to 2nd Stokes due to seeding effect will inhibit the further development to a higher level of 1st Stokes line.The third one is the influence of the gain quantity GR of 1st Stokes. In pure CS2 liquid, almost all of pump energy acts on CS2 molecules. However, in the solution of all-trans-beta-carotene in CS2,some of pump energy had to be absorbed to give rise to fluorescence by all-trans-beta-carotene. With the increase of concentration, more pump photons will be absorbed to emit the intense fluorescence. Thus, the actual number of pump photons np generating SRS of CS2 molecules will relatively decrease. According to the steady-state Raman gain quantity, GR will become low. In addition,the number of 1st Stokes photons nS1 is given by Eq.(3)(?)(3)While the concentration gets high, due to the increasing absorption aS1 from all-trans-beta-carotene at 1st Stokes frequency and low GR factor mentioned above,the quantity of (GR-αS1) becomes small and the growth of 1st Stokes photons slows down. Accordingly, in the condition of the fixed length of LCOF and the limited pump energy in our experiments, with the increase of the concentration, the slower growth rate of lst Stokes line will also limit the final number of nS1.(3) We made a research of the output of multiple Stokes lines under the fluorescence seeding and the corresponding coupled wave equations model.The LCOF was quartz fiber with the inner diameters of 260μm and output diameters of 400μm. The solution of all-trans-beta-carotene in CS2 at a concentration of 4×10-6mol/L was injected into this LCOF of 90-centimeter. In the limit pump energy of 0 to 5 mJ,we got the 1st,2nd,3rd Stokes lines under the fluorescence seeding (see Fig.9) and the trend in the dependence of the intensity of the 1st,2nd. 3rd Stokes lines on the pump energy (see Fig.10). In Fig.10, the threshold of the 1st Stokes line is almost 1.0mJ,and the 2nd Stokes line is about 1.5mJ.It means that the 1st Stokes starts before the saturation of the 2nd Stokes line. And the 3rd Stokes line starts at a pump energy of 3.5mJ before the saturation of the 2nd Stokes line, when the 1st Stokes line saturates. However,in the liquid core of pure CS2,only an intense the 1st Stokes line was observed at 4mJ of pump energy. So, the fluorescence seeding effect plays an important role in the acquisition of multiple Stokes lines. It not only lowers the thresholds of these Stokes lines, but also influences the original cascaded transfer process of the energy between these Stokes lines. In theory, we introduced the terms of the spontaneous Raman noise, the interaction between the pump wave and the Stokes waves and the interaction among all Stokes waves. The new set of equations are as follows,see Eq.(4)(?)(?)(?)(?)(4)where S3 denotes the 3rd Stokes line,αS3 is the absorption loss at the 3rd Stokes frequency,gS3 is the gain factor at the 3rd Stokes frequency, NS3 represents the spontaneous Raman noise at the 3rd Stokes frequency. The fitting result is shown in Fig.11.The fitting result agrees well with the experimental results. When we applied the model of Eq.(2), the fitting results were not as good as the model of Eq.(4). It means that the interactions will be not only limited between two adjacent Stokes lines but be among all Stokes lines or between the pump and all Stokes lines. So, there arc two factors which come from the influence of the fluorescence Fig.9:The 1st,2nd, 3rd Stokes lines of CS2 under the fluorescence seeding. Fig.10: The trend in the dependence of the intensity of the 1st., 2nd, 3rd Stokes lines of CS2 on the pump energy.Fig.11: The theoretical fitting of the development trends of the 1st,2nd. 3rd Stokes lines as the pump energy. seeding:one is the influence of the. spontaneous noise at, Stokes frequencies,the other is the multiple interactions between all lines, which causes the change of energy transfer rule.As a proof, we applied the model of Eq.(4) to the fitting of the threshold of 2nd Stokes line at different concentrations.We could get good fitting using the model of Eq.(4) under different circumstances. However, in the case of the model of Eq.(2),it can only be applied in the solution of low concentrations, where the interactions are not too intense. When the concentration becomes high, only the model of Eq.(4) is valid.In conclusion, we have got the following view points:(1)All-transβ-carotene molecules are applied in the research of SRS as new liquid core material. This type of molecule can not only supply the fluorescence-seeding at different Stokes frequencies, but also has no lasing process, which may compete with the SRS.(2)Through the comparison between two different coupled wave models, the physical reasons that the fluorescence seeding influences SRS in LCOF is as follows:the fluorescence seeding not only influences the spontaneous Raman noise at different Stokes frequencies, but also influences the energy transfer process,which is realized through the multiple interactions among all lines.(3)We. have obtained the different coupled wave equations under different approximation conditions and their scopes of applications. It will make contributions to the theoretical developments and experimental analysis of fiber lasers based on SRS. |
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