This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has ...This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.展开更多
The third-order nonlinear optical properties of water-soluble Cu Se nanocrystals are studied in the near infrared range of 700-980 nm using a femtosecond pulsed laser by the Z-scan technique. It is observed that the n...The third-order nonlinear optical properties of water-soluble Cu Se nanocrystals are studied in the near infrared range of 700-980 nm using a femtosecond pulsed laser by the Z-scan technique. It is observed that the nonlinear optical response of Cu Se nanocrystals is sensitively dependent on the excitation wavelength and exhibits the enhanced nonlinearity compared with other selenides such as ZnSe and CdSe. The W-shaped Z-scan trace, a mixture of the reversed saturated absorption and saturated absorption, is observed near the plasmon resonance band of Cu Se nanocrystals, which is attributed to the state-filling of free carriers generated by copper vacancies (self-doping effect) of Cu Se nanocrystals as well as the hot carrier thermal effect upon intense femtosecond laser excitation. The large nonlinear optical response and tunable plasmonic band make Cu Se nanocrystals promising materials for applications in ultra-fast all-optical switching devices as well as nonlinear nanosensors.展开更多
Two X-type chromophores, 2-[4-(4,5-di(4-nitrophenyl) imidazolyl) phenyl]-4,5-di(4-methoxyphenyl)-imidazole (DNPIPDMOPI), 2-[4-(4,5-di(4-nitrophenyl)-imidazolyl) phenyl]-4,5-di(4-aminophenyl)-imidazole (DNPIPDAPI), wer...Two X-type chromophores, 2-[4-(4,5-di(4-nitrophenyl) imidazolyl) phenyl]-4,5-di(4-methoxyphenyl)-imidazole (DNPIPDMOPI), 2-[4-(4,5-di(4-nitrophenyl)-imidazolyl) phenyl]-4,5-di(4-aminophenyl)-imidazole (DNPIPDAPI), were synthesized and characterized. The results show that they possess good nonlinearity, considerable blue-shifted absorption (385 nm and 379 nm in THF) and high decomposition temperature (377 'C and 405 'C). These mean that the X-type chromophores possess a rather good nonlinearity-transparency-thermal stability trade-off. The multi-step corona-poling technique at elevated temperature and in-situ SHG measurements were used to obtain and evaluate the poled films of these chromophores doped in PMMA. The largest SHG signals appeared at 110-120°C, which are 12.5 pm/V and 16.7 pm/V respectively. The dependence of poling induced orientation stability on temperature was measured by depoling experiments and the results indicate that the poling-induced orientation of the films is stable at about 100°C. Theoretic analyses imply that better orientation stability arises from the X-type structure of chromophore. The X-type chromophore has two crossed intramolecular CT, both β xxx and β xyy can contribute to the second-order susceptibility, and the ratio of the tensorial components (γ= β xyy /β xxx ) is about 1/3, so the orientation decay of the films induced by rising temperature will provide a certain compensation for the contribution of β xyy of chromophores.展开更多
In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditio...In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（super） linearity are assumed. W＇e present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property （X^＋）, which is very important for the existence of periodic solutions and oscillation theory.展开更多
The nonlinear optical crystals of cobalt (Co2+) mixed copper mercury thiocyanate have been grown by slow evaporation method using water and ethanol as solvents. The grown crystals have been subjected to different char...The nonlinear optical crystals of cobalt (Co2+) mixed copper mercury thiocyanate have been grown by slow evaporation method using water and ethanol as solvents. The grown crystals have been subjected to different characterization analyses and the results were compared with pure copper mercury thiocyanate crystal (CMTC), which has been already reported. The single crystal X-ray diffraction shows that the addition of metallic impurity does not alter the basic structure of the parent crystal, but increases the cell volume markedly. The presence of functional groups has been identified using FT-IR analysis. Further the grown crystal is characterized by optical transmission analysis and thermal analysis. The thermal stability of the grown crystal is high, compared to pure CMTC crystal. The optical transparency of the grown crystal is studied by UV-Vis-NIR analysis. This study reveals that Co2+ mixed CMTC crystal has wider transparent waveband than pure CMTC crystal. The relative second harmonic generation efficiency of the Co2+ mixed CMTC crystal has been tested by Kurtz-Perry powder technique.展开更多
Single crystals of pure and Li+ doped L-citrulline oxalate (LCO) crystals are grown successfully by slow evaporation technique. The effect of lithium doping on crystal properties has been studied. The samples are char...Single crystals of pure and Li+ doped L-citrulline oxalate (LCO) crystals are grown successfully by slow evaporation technique. The effect of lithium doping on crystal properties has been studied. The samples are characterized by X-ray powder diffraction, TGA, FTIR, Raman and UV-Vis spectroscopic techniques. The presence of lithium in Li+ doped LCO crystals is estimated using AES. The thermal stability and the optical transparency region are found to be enhanced for the doped samples. The second harmonic generation efficiency of the doped crystal has improved considerably compared to pure L-citrulline oxalate. Lithium doping can hence be considered as a simple and advantageous technique to improve the thermal, optical and non linear optical (NLO) properties of the LCO single crystals.展开更多
Barium metaborate (BaB 2O 4) exists in two forms the high temperature for m α phase and the low temperature form β phase,with the phase transition poi nt at around 925℃.The low temperature phase (β BBO) is an exce...Barium metaborate (BaB 2O 4) exists in two forms the high temperature for m α phase and the low temperature form β phase,with the phase transition poi nt at around 925℃.The low temperature phase (β BBO) is an excellent NLO cryst al for UV region,while the high temperature one (α BBO) is known as a good bir efringent material.α BBO crystal possesses better transparency in the ultravio let region compared with commonly used YVO 4 and CaCO 3 crystals.However,due t o phase transition problem,it is difficult to grow single α BBO crystals by D CZ method,which restricts its wider application.α BBO crystal usually cracks upon cooling resulted from phase transition to β phase.Therefore,it is difficult to grow β BBO single crystals directly from pure BaB 2O 4 mel t;however,to grow single crystals of α BBO is not easy,either. Our recent experiments showed that one could avoid cracking of α BBO cryst als by Sr 2+ doping.This minute amount of Sr 2+ plays the role of structure stabilizer,which inhibits structural reconstruction. In this way,Sr 2+ d op ed BBO single crystals do not subject to phase transition from 925℃ down to roo m temperature. We have mow successfully grown out α BBO single crystals 30mm in diameter by D CZ method from Sr x Ba 1- x BO 4 melt with Sr concentration 0.3 0 .5%.The ratation rate is 10 15r/min,pulling speed is 1 2mm/h.Preliminary tests revealed that its structure and physic chemical properties were almost identic al to those grown from pure melts.These Sr 2+ doped α BBO crystals are no w being widely used in optical isolators.展开更多
基金Partially supported by the NSF(11271154)of China the 985 program of Jilin University
文摘This paper deals with the extinction of weak solutions of the initial and boundary value problem for ut = div（（｜u｜σ ＋ d0）｜ u｜^p（x）-2 u）. When the exponent belongs to different intervals, the solution has different singularity （vanishing in finite time）.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11274302,11474276 and 11674240
文摘The third-order nonlinear optical properties of water-soluble Cu Se nanocrystals are studied in the near infrared range of 700-980 nm using a femtosecond pulsed laser by the Z-scan technique. It is observed that the nonlinear optical response of Cu Se nanocrystals is sensitively dependent on the excitation wavelength and exhibits the enhanced nonlinearity compared with other selenides such as ZnSe and CdSe. The W-shaped Z-scan trace, a mixture of the reversed saturated absorption and saturated absorption, is observed near the plasmon resonance band of Cu Se nanocrystals, which is attributed to the state-filling of free carriers generated by copper vacancies (self-doping effect) of Cu Se nanocrystals as well as the hot carrier thermal effect upon intense femtosecond laser excitation. The large nonlinear optical response and tunable plasmonic band make Cu Se nanocrystals promising materials for applications in ultra-fast all-optical switching devices as well as nonlinear nanosensors.
基金This work was supported by the National Natural Science Foundation of China (No. 90201005).
文摘Two X-type chromophores, 2-[4-(4,5-di(4-nitrophenyl) imidazolyl) phenyl]-4,5-di(4-methoxyphenyl)-imidazole (DNPIPDMOPI), 2-[4-(4,5-di(4-nitrophenyl)-imidazolyl) phenyl]-4,5-di(4-aminophenyl)-imidazole (DNPIPDAPI), were synthesized and characterized. The results show that they possess good nonlinearity, considerable blue-shifted absorption (385 nm and 379 nm in THF) and high decomposition temperature (377 'C and 405 'C). These mean that the X-type chromophores possess a rather good nonlinearity-transparency-thermal stability trade-off. The multi-step corona-poling technique at elevated temperature and in-situ SHG measurements were used to obtain and evaluate the poled films of these chromophores doped in PMMA. The largest SHG signals appeared at 110-120°C, which are 12.5 pm/V and 16.7 pm/V respectively. The dependence of poling induced orientation stability on temperature was measured by depoling experiments and the results indicate that the poling-induced orientation of the films is stable at about 100°C. Theoretic analyses imply that better orientation stability arises from the X-type structure of chromophore. The X-type chromophore has two crossed intramolecular CT, both β xxx and β xyy can contribute to the second-order susceptibility, and the ratio of the tensorial components (γ= β xyy /β xxx ) is about 1/3, so the orientation decay of the films induced by rising temperature will provide a certain compensation for the contribution of β xyy of chromophores.
文摘In this paper the generalized nonlinear Euler differential equation t^2k（tu＇）u＇＇＋ t（f（u） ＋ k（tu＇））u＇ ＋ g（u） = 0 is considered. Here the functions f（u）, g（u） and k（u） satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub（super） linearity are assumed. W＇e present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property （X^＋）, which is very important for the existence of periodic solutions and oscillation theory.
文摘The nonlinear optical crystals of cobalt (Co2+) mixed copper mercury thiocyanate have been grown by slow evaporation method using water and ethanol as solvents. The grown crystals have been subjected to different characterization analyses and the results were compared with pure copper mercury thiocyanate crystal (CMTC), which has been already reported. The single crystal X-ray diffraction shows that the addition of metallic impurity does not alter the basic structure of the parent crystal, but increases the cell volume markedly. The presence of functional groups has been identified using FT-IR analysis. Further the grown crystal is characterized by optical transmission analysis and thermal analysis. The thermal stability of the grown crystal is high, compared to pure CMTC crystal. The optical transparency of the grown crystal is studied by UV-Vis-NIR analysis. This study reveals that Co2+ mixed CMTC crystal has wider transparent waveband than pure CMTC crystal. The relative second harmonic generation efficiency of the Co2+ mixed CMTC crystal has been tested by Kurtz-Perry powder technique.
文摘Single crystals of pure and Li+ doped L-citrulline oxalate (LCO) crystals are grown successfully by slow evaporation technique. The effect of lithium doping on crystal properties has been studied. The samples are characterized by X-ray powder diffraction, TGA, FTIR, Raman and UV-Vis spectroscopic techniques. The presence of lithium in Li+ doped LCO crystals is estimated using AES. The thermal stability and the optical transparency region are found to be enhanced for the doped samples. The second harmonic generation efficiency of the doped crystal has improved considerably compared to pure L-citrulline oxalate. Lithium doping can hence be considered as a simple and advantageous technique to improve the thermal, optical and non linear optical (NLO) properties of the LCO single crystals.
文摘Barium metaborate (BaB 2O 4) exists in two forms the high temperature for m α phase and the low temperature form β phase,with the phase transition poi nt at around 925℃.The low temperature phase (β BBO) is an excellent NLO cryst al for UV region,while the high temperature one (α BBO) is known as a good bir efringent material.α BBO crystal possesses better transparency in the ultravio let region compared with commonly used YVO 4 and CaCO 3 crystals.However,due t o phase transition problem,it is difficult to grow single α BBO crystals by D CZ method,which restricts its wider application.α BBO crystal usually cracks upon cooling resulted from phase transition to β phase.Therefore,it is difficult to grow β BBO single crystals directly from pure BaB 2O 4 mel t;however,to grow single crystals of α BBO is not easy,either. Our recent experiments showed that one could avoid cracking of α BBO cryst als by Sr 2+ doping.This minute amount of Sr 2+ plays the role of structure stabilizer,which inhibits structural reconstruction. In this way,Sr 2+ d op ed BBO single crystals do not subject to phase transition from 925℃ down to roo m temperature. We have mow successfully grown out α BBO single crystals 30mm in diameter by D CZ method from Sr x Ba 1- x BO 4 melt with Sr concentration 0.3 0 .5%.The ratation rate is 10 15r/min,pulling speed is 1 2mm/h.Preliminary tests revealed that its structure and physic chemical properties were almost identic al to those grown from pure melts.These Sr 2+ doped α BBO crystals are no w being widely used in optical isolators.
