Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is imp...Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.展开更多
A novel soluble π-conjugated polymer, poly [(3-acetylpyrrole-2, 5-diyl) p-(N, N-dimethylamino) azobenzylidene] (PAPDMAABE), was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4'-dimethylaminoaz...A novel soluble π-conjugated polymer, poly [(3-acetylpyrrole-2, 5-diyl) p-(N, N-dimethylamino) azobenzylidene] (PAPDMAABE), was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4'-dimethylaminoazobenzene (ADMAA). The chemical structure of PAPDMAABE was characterized by Fourier transform infrared spectroscopy (FTIR), ^1H-NMR, and UV-Vis-NIR spectra. Transmission electron microscope (TEM) analysis for PAPDMAABE indicates that part of PAPDMAABE is in crystal state, due to the short-range order of the polymer. Thermogravimetric analysis (TGA) curve shows that the polymer has good thermal stability and its decomposition temperature is 248℃. The optical band gap of PAPDMAABE obtained from the optical absorption spectrum is about 1.73 eV. The resonant third-order nonlinear optical property of PAPDMAABE at 532 nm was studied using degenerate four-wave mixing (DFWM) technique. The resonant third-order nonlinear optical susceptibility of the polymer is about 7.48×10^-8 esu.展开更多
We quantitatively investigate the third-order optical nonlinear response of Co-doped ZnO thin films prepared by magnetron sputtering using the Z-scan method. The two-photon absorption and optical Kerr effect are revea...We quantitatively investigate the third-order optical nonlinear response of Co-doped ZnO thin films prepared by magnetron sputtering using the Z-scan method. The two-photon absorption and optical Kerr effect are revealed to contribute to the third-order nonlinear response of the Co-doped ZnO films. The nonlinear absorption coefficient β is determined to be approximately 8.8 × 10-5 cm/W and the third-order nonlinear susceptibility X(3) is 2.93 × 10-6 esu. The defect-associated energy levels within the band gap are suggested to be responsible for the enhanced nonlinear response observed in Co-doped ZnO films.展开更多
Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrat...Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrated information-processing chip,high optical nonlinearity is indispensable for various fundamental functionalities,such as all-optical modulation,high order harmonic generation,optical switching and so on.Here we study the third-order optical nonlinearity of free-standing h-BN thin films,which is an ideal platform for on-chip integration and device formation without the need of transfer.The films were synthesized by a solution-based method with abundant functional groups enabling high third-order optical nonlinearity.Unlike the highly inert pristine h-BN films synthesized by conventional methods,the free-standing h-BN films could be locally oxidized upon tailored femtosecond laser irradiation,which further enhances the third-order nonlinearity,especially the nonlinear refraction index,by more than 20 times.The combination of the free-standing h-BN films with laser activation and patterning capability establishes a new promising platform for high performance on-chip photonic devices with modifiable optical performance.展开更多
UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing g...UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group -CF3 and -C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of -OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the -C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.展开更多
The third-order optical nonlinearity of two sandwich-type phthalocyaninato and porphyrinato europium com- plexes, including double- and triple-deckers (Eu[Pc(OC5H11)8]2, Eu2(Pc)(TPP)2, Pc=phthalocyanine, TPP=5,...The third-order optical nonlinearity of two sandwich-type phthalocyaninato and porphyrinato europium com- plexes, including double- and triple-deckers (Eu[Pc(OC5H11)8]2, Eu2(Pc)(TPP)2, Pc=phthalocyanine, TPP=5, 10, 15, 20- tetraphenylporphyrinate), was investigated by using the femtosecond time-resolved optical Kerr gate method at 830 nm wavelength. Their second-order hyperpolarizability is estimated to be 0.74× 10^-30esu and 3.0× 10^-3esu respectively. This exhibits an evident enhancement in comparison with 0.47×10^-30esu for one-decker Eu(Pc)(acac) (acac=acetylacetonate), which is also measured under the same conditions. The enhancement is attributed to the introduction of lanthanide metal to the large π-conjugated system, intermacrocycle interaction and two-photon resonance etc.展开更多
The optical wave breaking (OWB) characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion (TOD) and quinti...The optical wave breaking (OWB) characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion (TOD) and quintic nonlinearity (QN) are numerically calculated. The results show that the TOD causes the asymmetry of the temporal- and spectral-domain, and the chirp characteristics. The OWB generally appears near the pulse center and at the trailing edge of the pulse, instead of at the two edges of the pulse symmetrically in the case of no TOD. With the increase of distance, the relation of OWB to the TOD near the pulse center increases quickly, leading to the generation of ultra-short pulse trains, while the OWB resulting from the case of no TOD at the trailing edge of the pulse disappears gradually. In addition, the positive (negative) QN enhances (weakens) the chirp amount and the fine structures, thereby inducing the OWB phenomena to appear earlier (later). Thus, the TOD and the positive (negative) QN are beneficial (detrimental) to the OWB and the generation of ultra-short pulse trains.展开更多
Nonlinear polarizability of erythrocytes in non-uniform alternating electric field (NUAEF) was proved theoretically and experimentally by dielectrophoresis method. The paper presents experimental evidence of the nonli...Nonlinear polarizability of erythrocytes in non-uniform alternating electric field (NUAEF) was proved theoretically and experimentally by dielectrophoresis method. The paper presents experimental evidence of the nonlinear polarizability of erythrocytes in the non-uniform alternating electric field. The rotation of erythrocyte around its own axis at more than one revolution per second in the non-uniform alternating electric field in the frequency range and the electric field intensity?is the evidence of its nonlinear polarizability. The theoretical analysis of the density of electric charges capable of overcoming the membrane potential was carried out on the basis of statistical mechanics, the thermal equilibrium in which the particle stays. The nonlinear polarizability of the erythrocyte emerges if the voltage on the membrane exceeds?, which was theoretically proved. The alternating electric field from the donor erythrocyte with the amplitude exceeding forms the constant component of the current? in the cytoplasm of the recipient erythrocyte whose energy can be considered as a signal one. The nonlinear equivalent electric circuit of the cell was proposed.展开更多
A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D ty...A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.展开更多
In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method...In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.展开更多
The third-order nonlinear optical properties of two dmit organometallic complexes, [(CH3)4N] [Au(C3S5)2] (MeAu) and [(CH3)4N][Ni(C3S5)2] (Me Ni) in acetone solutions, were characterized us- ing a short pulse Z-scan te...The third-order nonlinear optical properties of two dmit organometallic complexes, [(CH3)4N] [Au(C3S5)2] (MeAu) and [(CH3)4N][Ni(C3S5)2] (Me Ni) in acetone solutions, were characterized us- ing a short pulse Z-scan technique at 1064 nm wavelength. Self-defocusing effects were found in both samples and stronger saturable absorp-tion was observed in MeNi solution comparing with that of MeAu. The origins were analyzed for the differences between the results. Two figures of merit W and T were also calculated to evalu-ate the suitability of two materials for all-optical integrated devices. The results of W=22.84 and T≈0 of MeAu make it an excellent candidate for the all-optical applications.展开更多
A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-nitrobenzylidene] (POPNBE), was synthesized by a five-step reaction. As a result of introducing a long acyl to pyrrole at 3-position, the poly...A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-nitrobenzylidene] (POPNBE), was synthesized by a five-step reaction. As a result of introducing a long acyl to pyrrole at 3-position, the polymer can be easily solved in polar solvents and be processed into films. The chemical structures of the intermediates and POPNBE were characterized by FTIR, 1H NMR, and UV-Vis-NIR spectrometries. The absorption band in the range of 400-600 nm in the UV-Vis-NIR spectrum is due to the π-π * band gap transition. The optical band gap of POPNBE obtained from the optical absorption is about 1.72 eV. The resonant third-order nonlinear optical property of POPNBE at 532 nm was studied by using the degenerate four-wave mixing(DFWM) technique. The resonant third-order nonlinear optical susceptibility of POPNBE is about 3.42×10 -8 esu.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
Third-order nonlinear optical (NLO) materials have broad application prospects in high-density data storage, optical computer, modern laser technology, and other high-tech industries. The structures and frequencies of...Third-order nonlinear optical (NLO) materials have broad application prospects in high-density data storage, optical computer, modern laser technology, and other high-tech industries. The structures and frequencies of Dinaphtho[2,3-b:2’,3’-d]thiophene-5,7,12,13-tetraone (DNTTRA) and its 36 derivatives containing azobenzene were calculated by using density functional theory B3LYP and M06-2X methods at 6-311++g(d, p) level, respectively. Besides, the atomic charges of natural bond orbitals (NBO) were analyzed. The frontier orbitals and electron absorption spectra of A-G5 molecule were calculated by TD-DFT (TD-B3LYP/6-311++g(d, p) and TD-M06-2X/6-311++g(d, p)). The NLO properties were calculated by effective finite field FF method and self-compiled program. The results show that 36 molecules of these six series are D-π-A-π-D structures. The third-order NLO coefficients γ (second-order hyperpolarizability) of the D series molecules are the largest among the six series, reaching 10<sup>7</sup> atomic units (10<sup><span style="color:#4F4F4F;font-family:-apple-system, " font-size:14px;white-space:normal;background-color:#ffffff;"="">-</span>33</sup> esu) of order of magnitude, showing good third-order NLO properties. Last, the third-order NLO properties of the azobenzene ring can be improved by introducing strong electron donor groups (e.g. -N(CH<sub>3</sub>)<sub>2</sub> or -NHCH<sub>3</sub>) in the azobenzene ring, so that the third-order NLO materials with good performance can be obtained.展开更多
The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations...The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.展开更多
The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks(ANNs)with the use of global search particle swarm optimization(PSO)along with the...The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks(ANNs)with the use of global search particle swarm optimization(PSO)along with the competent local search interior-point programming(IPP)called as ANN-PSOIPP.The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model(TON-DD-EFM).The TON-DD-EFM is based on two types along with the particulars of shape factor,delayed terms,and singular points.A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM.The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM.The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07.Furthermore,the statistical-based assessments for 100 trials are provided to compute the accuracy,stability,and constancy of the ANNPSOIPP for solving the TON-DD-EFM.展开更多
The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The p...The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.展开更多
We report the modulation of epsilon-near-zero(ENZ)wavelength and enhanced third-order nonlinearity in indium tin oxide(ITO)/Au multilayer films.The samples consisting of five-layer 40 nm ITO films spaced by four-layer...We report the modulation of epsilon-near-zero(ENZ)wavelength and enhanced third-order nonlinearity in indium tin oxide(ITO)/Au multilayer films.The samples consisting of five-layer 40 nm ITO films spaced by four-layer ultrathin Au films of different thickness,i.e.,ITO(40 nm)/[Au(x)/ITO(40 nm)]4,were prepared by magnetron sputtering at room temperature.The ENZ wavelength in the multilayer films is theoretically calculated and experimentally confirmed.The nonlinear refractive index and nonlinear absorption coefficient of the samples of x=0,2,3,4 nm were determined using the Z-scan method at a wavelength of 1.064μm.The large nonlinear refractive index n2=1.12×10^(−13) m^(2)=W and nonlinear absorption coefficient β=−1.78×10^(−7) m=W in the sample of x=4 nm are both four times larger than those in the single-layer ITO film.The large optical nonlinearity due to the ENZ enhancement and carrier concentration is discussed.The results indicate that the ITO/Au multilayer films are promising for advanced all-optical devices.展开更多
The third-order optical nonlinearities of [(CH3)4N]Au(dmit)2 (dmit = 4,5-dithiolate-1,3-dithiole-2-thione) at 532 nm and 1064 nm are investigated using the Z-scan technique with pulses of picoseconds duration. T...The third-order optical nonlinearities of [(CH3)4N]Au(dmit)2 (dmit = 4,5-dithiolate-1,3-dithiole-2-thione) at 532 nm and 1064 nm are investigated using the Z-scan technique with pulses of picoseconds duration. The Z-scan spectra reveal a strong nonlinear absorption (reverse saturable absorption) and a negative nonlinear refraction at 532 nm. No nonlinear absorption is observed at 1064 nm. The molecular second-order hyperpolarizability γ for the [(CH3)4N]Au(dmit)2 molecule at 532nm is estimated to be as high as (2.1 ±0.1) × 10^-31 esu, which is nearly three times larger than that at 1064 nm. The mechanism responsible for the difference between the results is analysed. Nonlinear transmission measurements suggest that this material has potential applications in optical limiting.展开更多
Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, un...Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.展开更多
文摘Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.
基金the National Natural Science Foundation of China for financial support of this work(No.60277002).
文摘A novel soluble π-conjugated polymer, poly [(3-acetylpyrrole-2, 5-diyl) p-(N, N-dimethylamino) azobenzylidene] (PAPDMAABE), was synthesized by condensation of 3-acetylpyrrole with 4-aldehyde-4'-dimethylaminoazobenzene (ADMAA). The chemical structure of PAPDMAABE was characterized by Fourier transform infrared spectroscopy (FTIR), ^1H-NMR, and UV-Vis-NIR spectra. Transmission electron microscope (TEM) analysis for PAPDMAABE indicates that part of PAPDMAABE is in crystal state, due to the short-range order of the polymer. Thermogravimetric analysis (TGA) curve shows that the polymer has good thermal stability and its decomposition temperature is 248℃. The optical band gap of PAPDMAABE obtained from the optical absorption spectrum is about 1.73 eV. The resonant third-order nonlinear optical property of PAPDMAABE at 532 nm was studied using degenerate four-wave mixing (DFWM) technique. The resonant third-order nonlinear optical susceptibility of the polymer is about 7.48×10^-8 esu.
基金Supported by National Basic Research Program of China under Grant Nos 2011CB922200 and 2013CB922303
文摘We quantitatively investigate the third-order optical nonlinear response of Co-doped ZnO thin films prepared by magnetron sputtering using the Z-scan method. The two-photon absorption and optical Kerr effect are revealed to contribute to the third-order nonlinear response of the Co-doped ZnO films. The nonlinear absorption coefficient β is determined to be approximately 8.8 × 10-5 cm/W and the third-order nonlinear susceptibility X(3) is 2.93 × 10-6 esu. The defect-associated energy levels within the band gap are suggested to be responsible for the enhanced nonlinear response observed in Co-doped ZnO films.
基金We are grateful for financial supports from the Australian Research Council through the Discovery Project scheme(Grant No.DP190103186 and FT210100806)the Australian Research Council through Industrial Transformation Training Centres scheme(IC180100005).
文摘Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrated information-processing chip,high optical nonlinearity is indispensable for various fundamental functionalities,such as all-optical modulation,high order harmonic generation,optical switching and so on.Here we study the third-order optical nonlinearity of free-standing h-BN thin films,which is an ideal platform for on-chip integration and device formation without the need of transfer.The films were synthesized by a solution-based method with abundant functional groups enabling high third-order optical nonlinearity.Unlike the highly inert pristine h-BN films synthesized by conventional methods,the free-standing h-BN films could be locally oxidized upon tailored femtosecond laser irradiation,which further enhances the third-order nonlinearity,especially the nonlinear refraction index,by more than 20 times.The combination of the free-standing h-BN films with laser activation and patterning capability establishes a new promising platform for high performance on-chip photonic devices with modifiable optical performance.
基金supported by the National Natural Science Foundation of China(21172161)
文摘UV-Vis spectrum and the third-order nonlinear optical properties of the chiral camphor-derived β-diketonate have been studied at the B3LYP/6-31G* level. The results showed that the introduction of electron-drawing group -CF3 and -C3F7 on β-diketonate made the strongest absorption peak red-shift and the lowest energy absorption blue-shied. Introduction of -OC2H5 on the benzene or pyridine ring made the lowest energy absorption blue-shift. When the -C2H3 was introduced on the benzene or pyridine ring, the lowest energy absorption was red-shifted. Introduction of electron-donating group on β-diketonate can enlarge their nonlinear optical properties. On the contrary, the introduction of electron-drawing group dropped it down.
基金Project supported by the National Key Research Program of China (Grant No TG1999075209) and the National Natural Science Foundation of China (Grant Nos 10434020, 90206003 and 60378012).
文摘The third-order optical nonlinearity of two sandwich-type phthalocyaninato and porphyrinato europium com- plexes, including double- and triple-deckers (Eu[Pc(OC5H11)8]2, Eu2(Pc)(TPP)2, Pc=phthalocyanine, TPP=5, 10, 15, 20- tetraphenylporphyrinate), was investigated by using the femtosecond time-resolved optical Kerr gate method at 830 nm wavelength. Their second-order hyperpolarizability is estimated to be 0.74× 10^-30esu and 3.0× 10^-3esu respectively. This exhibits an evident enhancement in comparison with 0.47×10^-30esu for one-decker Eu(Pc)(acac) (acac=acetylacetonate), which is also measured under the same conditions. The enhancement is attributed to the introduction of lanthanide metal to the large π-conjugated system, intermacrocycle interaction and two-photon resonance etc.
基金supported by the Postdoctoral Fund of China(Grant No.2011M501402)the National Natural Science Foundation of China(Grant No.61275039)+2 种基金the 973 Program of China(Grant No.2012CB315702)the Key Project of the Chinese Ministry of Education,China(Grant No.210186)the Major Project of the Natural Science Foundation supported by the Educational Department of Sichuan Province,China(Grant Nos.13ZA0081 and 12ZB019)
文摘The optical wave breaking (OWB) characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion (TOD) and quintic nonlinearity (QN) are numerically calculated. The results show that the TOD causes the asymmetry of the temporal- and spectral-domain, and the chirp characteristics. The OWB generally appears near the pulse center and at the trailing edge of the pulse, instead of at the two edges of the pulse symmetrically in the case of no TOD. With the increase of distance, the relation of OWB to the TOD near the pulse center increases quickly, leading to the generation of ultra-short pulse trains, while the OWB resulting from the case of no TOD at the trailing edge of the pulse disappears gradually. In addition, the positive (negative) QN enhances (weakens) the chirp amount and the fine structures, thereby inducing the OWB phenomena to appear earlier (later). Thus, the TOD and the positive (negative) QN are beneficial (detrimental) to the OWB and the generation of ultra-short pulse trains.
文摘Nonlinear polarizability of erythrocytes in non-uniform alternating electric field (NUAEF) was proved theoretically and experimentally by dielectrophoresis method. The paper presents experimental evidence of the nonlinear polarizability of erythrocytes in the non-uniform alternating electric field. The rotation of erythrocyte around its own axis at more than one revolution per second in the non-uniform alternating electric field in the frequency range and the electric field intensity?is the evidence of its nonlinear polarizability. The theoretical analysis of the density of electric charges capable of overcoming the membrane potential was carried out on the basis of statistical mechanics, the thermal equilibrium in which the particle stays. The nonlinear polarizability of the erythrocyte emerges if the voltage on the membrane exceeds?, which was theoretically proved. The alternating electric field from the donor erythrocyte with the amplitude exceeding forms the constant component of the current? in the cytoplasm of the recipient erythrocyte whose energy can be considered as a signal one. The nonlinear equivalent electric circuit of the cell was proposed.
文摘A novel Schiff base ligand (HL) derived from S-methyldithiocabazate and pmethoxylbenzaldehyde was prepared and characterized. The Schiff base ligand acts as a single negatively charged bidentate ligand fondng D-M-D type comPlex (D=donor, M=metal). Single crystal X-ray diffraction analysis of the copper(Ⅱ) complex established that the geometry around Cu (Ⅱ) is square-planar with two equivalent M-N and M-S bonds. The two phenyl rings and the coordinated plane are almost in one plane fotheng an electronic delocalization system. Their thirdorder response was also studied.
文摘In this paper, a new two-step Newton-type method with third-order convergence for solving systems of nonlinear equations is proposed. We construct the new method based on the integral interpolation of Newton’s method. Its cubic convergence and error equation are proved theoretically, and demonstrated numerically. Its application to systems of nonlinear equations and boundary-value problems of nonlinear ODEs are shown as well in the numerical examples.
文摘The third-order nonlinear optical properties of two dmit organometallic complexes, [(CH3)4N] [Au(C3S5)2] (MeAu) and [(CH3)4N][Ni(C3S5)2] (Me Ni) in acetone solutions, were characterized us- ing a short pulse Z-scan technique at 1064 nm wavelength. Self-defocusing effects were found in both samples and stronger saturable absorp-tion was observed in MeNi solution comparing with that of MeAu. The origins were analyzed for the differences between the results. Two figures of merit W and T were also calculated to evalu-ate the suitability of two materials for all-optical integrated devices. The results of W=22.84 and T≈0 of MeAu make it an excellent candidate for the all-optical applications.
文摘A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-nitrobenzylidene] (POPNBE), was synthesized by a five-step reaction. As a result of introducing a long acyl to pyrrole at 3-position, the polymer can be easily solved in polar solvents and be processed into films. The chemical structures of the intermediates and POPNBE were characterized by FTIR, 1H NMR, and UV-Vis-NIR spectrometries. The absorption band in the range of 400-600 nm in the UV-Vis-NIR spectrum is due to the π-π * band gap transition. The optical band gap of POPNBE obtained from the optical absorption is about 1.72 eV. The resonant third-order nonlinear optical property of POPNBE at 532 nm was studied by using the degenerate four-wave mixing(DFWM) technique. The resonant third-order nonlinear optical susceptibility of POPNBE is about 3.42×10 -8 esu.
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.
文摘Third-order nonlinear optical (NLO) materials have broad application prospects in high-density data storage, optical computer, modern laser technology, and other high-tech industries. The structures and frequencies of Dinaphtho[2,3-b:2’,3’-d]thiophene-5,7,12,13-tetraone (DNTTRA) and its 36 derivatives containing azobenzene were calculated by using density functional theory B3LYP and M06-2X methods at 6-311++g(d, p) level, respectively. Besides, the atomic charges of natural bond orbitals (NBO) were analyzed. The frontier orbitals and electron absorption spectra of A-G5 molecule were calculated by TD-DFT (TD-B3LYP/6-311++g(d, p) and TD-M06-2X/6-311++g(d, p)). The NLO properties were calculated by effective finite field FF method and self-compiled program. The results show that 36 molecules of these six series are D-π-A-π-D structures. The third-order NLO coefficients γ (second-order hyperpolarizability) of the D series molecules are the largest among the six series, reaching 10<sup>7</sup> atomic units (10<sup><span style="color:#4F4F4F;font-family:-apple-system, " font-size:14px;white-space:normal;background-color:#ffffff;"="">-</span>33</sup> esu) of order of magnitude, showing good third-order NLO properties. Last, the third-order NLO properties of the azobenzene ring can be improved by introducing strong electron donor groups (e.g. -N(CH<sub>3</sub>)<sub>2</sub> or -NHCH<sub>3</sub>) in the azobenzene ring, so that the third-order NLO materials with good performance can be obtained.
基金Project supported by the National Natural Science Foundation of China(Nos.11872186 and11272126)the Fundamental Research Funds for the Central Universities(No.HUST:2016JCTD114)
文摘The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.
基金This project is funded by National Research Council of Thailand(NRCT)and Khon Kaen University:N42A650291.
文摘The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks(ANNs)with the use of global search particle swarm optimization(PSO)along with the competent local search interior-point programming(IPP)called as ANN-PSOIPP.The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model(TON-DD-EFM).The TON-DD-EFM is based on two types along with the particulars of shape factor,delayed terms,and singular points.A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM.The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM.The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07.Furthermore,the statistical-based assessments for 100 trials are provided to compute the accuracy,stability,and constancy of the ANNPSOIPP for solving the TON-DD-EFM.
基金the National Science Foundation of China (69978021), Fujian Provincial National Science Foundation of China (E9910030) and State
文摘The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients (i, (ij, (ijk and (ijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.
基金supported by the National Natural Science Foundation of China(No.12174228)Natural Science Foundation of Shandong Province(No.ZR2019MA024).
文摘We report the modulation of epsilon-near-zero(ENZ)wavelength and enhanced third-order nonlinearity in indium tin oxide(ITO)/Au multilayer films.The samples consisting of five-layer 40 nm ITO films spaced by four-layer ultrathin Au films of different thickness,i.e.,ITO(40 nm)/[Au(x)/ITO(40 nm)]4,were prepared by magnetron sputtering at room temperature.The ENZ wavelength in the multilayer films is theoretically calculated and experimentally confirmed.The nonlinear refractive index and nonlinear absorption coefficient of the samples of x=0,2,3,4 nm were determined using the Z-scan method at a wavelength of 1.064μm.The large nonlinear refractive index n2=1.12×10^(−13) m^(2)=W and nonlinear absorption coefficient β=−1.78×10^(−7) m=W in the sample of x=4 nm are both four times larger than those in the single-layer ITO film.The large optical nonlinearity due to the ENZ enhancement and carrier concentration is discussed.The results indicate that the ITO/Au multilayer films are promising for advanced all-optical devices.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60377016 and 60476020) and the National High Technology Development Program of China (Grant No 2002AA313070).
文摘The third-order optical nonlinearities of [(CH3)4N]Au(dmit)2 (dmit = 4,5-dithiolate-1,3-dithiole-2-thione) at 532 nm and 1064 nm are investigated using the Z-scan technique with pulses of picoseconds duration. The Z-scan spectra reveal a strong nonlinear absorption (reverse saturable absorption) and a negative nonlinear refraction at 532 nm. No nonlinear absorption is observed at 1064 nm. The molecular second-order hyperpolarizability γ for the [(CH3)4N]Au(dmit)2 molecule at 532nm is estimated to be as high as (2.1 ±0.1) × 10^-31 esu, which is nearly three times larger than that at 1064 nm. The mechanism responsible for the difference between the results is analysed. Nonlinear transmission measurements suggest that this material has potential applications in optical limiting.
基金supported by the National Natural Science Foundation of China (Grants 11402126, 11502122, and 11290152)the Scientific Research Foundation of the Inner Mongolia University of Technology (Grant ZD201410)
文摘Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.