This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappin...This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.展开更多
Analytic formula of the efficiency of optical-optical double-color double-resonance multi-photon ionization （OODR-MPI） is derived from the dynamic rate equation about the interaction of photon and material. Based on...Analytic formula of the efficiency of optical-optical double-color double-resonance multi-photon ionization （OODR-MPI） is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the influence of characteristic of the pump and probe laser on the ionization efficiency of （1＋2＋1） OODR-MPI process is simulated theoretically. It is shown that the pump laser will affect the ionization efficiency by the number control of the molecules excited to the first resonance state. The ionization efficiency is decided by the probe laser directly. Both of the excited molecules and ionization efficiency increase with the intensity and pulse duration of the laser until saturation. It is also found that the longer the delay time of the probe laser to the pump one is, the lower the ionization efficiency would be. The delay time ought to be smaller than the lifetime of the excited molecule in the practical use of the OODR-MPI technique.展开更多
This Letter reports the formation of periodic surface structures on Ni–Fe film irradiated by a single femtosecond laser pulse. A concave lens with a focus length of-150 mm is placed in front of an objective（100×...This Letter reports the formation of periodic surface structures on Ni–Fe film irradiated by a single femtosecond laser pulse. A concave lens with a focus length of-150 mm is placed in front of an objective（100×, NA=0.9）,which transforms the Gaussian laser field into a ring distribution by the Fresnel diffraction. Periodic ripples form on the ablation area after the irradiation of a single femtosecond laser pulse, which depends on the laser polarization and laser fluence. We propose that the ring structure of the laser field leads to a similar transient distribution of the permittivity on the sample surface, which further launches the surface plasmon polaritons. The interaction of the incident laser with surface plasmon polaritons dominates the formation of periodic surface structures.展开更多
The analytic formula of the ionization efficiency in the process of double resonance enhanced multi-photon ionization （DREMPI） is derived from the dynamic rate equation about the interaction of photon and material. ...The analytic formula of the ionization efficiency in the process of double resonance enhanced multi-photon ionization （DREMPI） is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the ionization efficiency and the laser power index versus laser intensity in the DREMPI process of NO molecule, via A2E and S2E intermediate resonant states, is numerically simulated. It is shown that the ionization efficiency of NO molecule increases with the laser intensity until getting saturation, while the laser power index decreases with the enhancement of the laser intensity and changes to zero at last. The variation of the laser power index with the laser intensity indicates that the ionization efficiency reaches saturation in the one, two, and three excitation steps respectively. It is also found that the narrower the laser pulse duration is, the higher becomes the laser intensity for saturation.展开更多
Gold nanoparticles （NPs） have highly efficient multi-photon-induced luminescence. In this paper, we record the two-photon images of gold NPs, lymphoma cell line Karpas 299, and Karpas 299 incubated with 30-nm-diamet...Gold nanoparticles （NPs） have highly efficient multi-photon-induced luminescence. In this paper, we record the two-photon images of gold NPs, lymphoma cell line Karpas 299, and Karpas 299 incubated with 30-nm-diameter gold NPs and ACT-1 antibody conjugates （Au30-ACT-1 conjugates） by using a multi-photon microscopy system. Due to the specific conjugation of ACT-1 antibody and cell membrane receptor CD25, gold NPs are only bound to the surface of cell membrane of Karpas 299. The luminescence intensity of gold NPs is higher than that of cells at 750-nm laser excitation. By comparing the images of Karpas 299 cells incubated with and without gold NPs, it is found that by means of gold NPs, we can get clear cell images with lower excitation power. Their excellent optical and chemical properties make gold NPs an attractive contrast agent for cellular imaging.展开更多
We present the measurement of the third-order nonlinearity of Bi203-B^O3-BaO glasses using the single Z-scan method with femtosecond laser pulses at 750 - 850 nm. Both third-order nonlinear refraction γ and two photo...We present the measurement of the third-order nonlinearity of Bi203-B^O3-BaO glasses using the single Z-scan method with femtosecond laser pulses at 750 - 850 nm. Both third-order nonlinear refraction γ and two photon absorption coefficient β are investigated. The γ shows an increasing tendency with increasing BaO content, and the largest value is estimated to be 7.2×10^-14 cm^2/W, which is as large as those of chalcogenide glasses. The dependence of 13 on the normalized photon energy is studied.展开更多
An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of Ts 〈 Td 〈 Tm, where Td is the dead time o...An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of Ts 〈 Td 〈 Tm, where Td is the dead time of each detector and Tm is the laser pulse repetition period. And each single photon detector cannot detect more than one photon in each pulse. The approach can sufficiently eliminate the influences of the detector＇s dead time on photon statistics. At last, the photon statistics of coherent field is experimentally determined.展开更多
Theretical analysis of the helicity inversion of laser （photons） during reflection is made by quantum theory for laser （photons） through an optical helix. The result reveals that the helicity inversion of the las...Theretical analysis of the helicity inversion of laser （photons） during reflection is made by quantum theory for laser （photons） through an optical helix. The result reveals that the helicity inversion of the laser （photons） occurs when the wave vector of the laser （photon） rotates at an extremely high angular velocity. The dynamic factor that dominates the process is the Coriolis coupling between the spin of the photon and the rotation of the wave vector. This non-intertial effect is treated successfully by simplification of the Maxwell equation in the rotational frame. In addition, the implication of the helicity inversion in information theory is discussed.展开更多
Photoelectron angular distributions （PADs） from two-photon ionization of atoms in linearly polarized strong laser fields are obtained in accordance with the nonperturbative quantum scattering theory. We also study t...Photoelectron angular distributions （PADs） from two-photon ionization of atoms in linearly polarized strong laser fields are obtained in accordance with the nonperturbative quantum scattering theory. We also study the influence of laser wavelength on PADs. For two-photon ionization very close to the ionization threshold, most of the ionized electrons are vertically ejected to the laser polarization. PADs from two- photon ionization of atoms are determined by the second order generalized phased Bessel function at which the ponderomotive parameter plays a key role. In terms of dependence of PADs on laser wavelength, corresponding variations for the ponderomotive parameter are demonstrated.展开更多
Two-photon photopolymerization （TPP） with femtosecond laser is a promising method to fabricate threedimensional （3D） photonic crystals （PCs）. Based on the TPP principle, the micro-fabrication system has been bui...Two-photon photopolymerization （TPP） with femtosecond laser is a promising method to fabricate threedimensional （3D） photonic crystals （PCs）. Based on the TPP principle, the micro-fabrication system has been built. The 3D woodpile PCs with rod space of 2000 nm are fabricated easily and different defects are introduced in order to form the cross-waveguide and the micro-laser structure PCs. Simulation results of the optical field intensity distributions using finite-difference time domain （FDTD） method are given, which support the designs and implementation of the PC of two types in theory.展开更多
We provide the first demonstration of pure red emission in the visible light region via three-photon excitation in monodisperse N a3 ZrF7：Er nanoparticles （NPs） by using a laser operating in the telecommunication b...We provide the first demonstration of pure red emission in the visible light region via three-photon excitation in monodisperse N a3 ZrF7：Er nanoparticles （NPs） by using a laser operating in the telecommunication band. NPs of -22 nm in diameter are synthesized at 260℃ by the thermal decomposition method. The experimental results reveal that the Na3ZrF7：Er NPs exhibit pure red emission in the visible region under 1480 nm laser excitation, and the emission intensity is significantly influenced by the Er3＋ ion concentration. The decay times of the 4S3/2 → 4F15/2 and 4F9/2 → 4F15/2 transitions of the Er3＋ ions at 540 and 655 nm, respectively, are reduced by increasing the Er3＋ ion concentration in the Na3ZrF7：Er NPs. The suppressed emission intensity result from the defect-related quenching effect： when trivalent Er3＋ ions replac tetravalent Zr4＋ ions, extra Na＋ ions and F- vacancies are formed to re-balance the charge in the Na3ZrF7 matrix. The emission color of the Na3ZrF7：Er NPs is related to the cross relaxation between Er3＋ ions. These results provide an important step toward more ef- fective biological imaging and photodynamic therapy by minimizing the scattering of the excitation light and increasing the penetration depth.展开更多
We propose a new mechanism/scheme to explain the ultrafast population inversion of molecular ions which takes place in a time scale comparable to the femtosecond laser pulse. The nonlinear pumping process including th...We propose a new mechanism/scheme to explain the ultrafast population inversion of molecular ions which takes place in a time scale comparable to the femtosecond laser pulse. The nonlinear pumping process including the pump photons and the self-generated harmonic photons of the pump laser would be responsible for building up population inversion to realize remote molecule lasers in femtosecond laser filaments in gases. It is shown that the remote laser emissions in molecular ions of gases may be a universal process in the femtosecond laser filament.展开更多
文摘This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.
基金supported by the National Natural Science Foundation of China (No.10647130)the Doctoral Foundation of North China Electric Power University (200612003)
文摘Analytic formula of the efficiency of optical-optical double-color double-resonance multi-photon ionization （OODR-MPI） is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the influence of characteristic of the pump and probe laser on the ionization efficiency of （1＋2＋1） OODR-MPI process is simulated theoretically. It is shown that the pump laser will affect the ionization efficiency by the number control of the molecules excited to the first resonance state. The ionization efficiency is decided by the probe laser directly. Both of the excited molecules and ionization efficiency increase with the intensity and pulse duration of the laser until saturation. It is also found that the longer the delay time of the probe laser to the pump one is, the lower the ionization efficiency would be. The delay time ought to be smaller than the lifetime of the excited molecule in the practical use of the OODR-MPI technique.
基金supported by the National Natural Science Foundation of China (Nos. 11474097, 11274116, 11104178, 44108280, and 51132004)the National Special Science Research Program of China (No. 2011CB808105)
文摘This Letter reports the formation of periodic surface structures on Ni–Fe film irradiated by a single femtosecond laser pulse. A concave lens with a focus length of-150 mm is placed in front of an objective（100×, NA=0.9）,which transforms the Gaussian laser field into a ring distribution by the Fresnel diffraction. Periodic ripples form on the ablation area after the irradiation of a single femtosecond laser pulse, which depends on the laser polarization and laser fluence. We propose that the ring structure of the laser field leads to a similar transient distribution of the permittivity on the sample surface, which further launches the surface plasmon polaritons. The interaction of the incident laser with surface plasmon polaritons dominates the formation of periodic surface structures.
基金supported by the National Natural Science Foundation of China (No.10647130)the Doctoral Foundation of North China Electric Power University (No.200612003).
文摘The analytic formula of the ionization efficiency in the process of double resonance enhanced multi-photon ionization （DREMPI） is derived from the dynamic rate equation about the interaction of photon and material. Based on this formula, the ionization efficiency and the laser power index versus laser intensity in the DREMPI process of NO molecule, via A2E and S2E intermediate resonant states, is numerically simulated. It is shown that the ionization efficiency of NO molecule increases with the laser intensity until getting saturation, while the laser power index decreases with the enhancement of the laser intensity and changes to zero at last. The variation of the laser power index with the laser intensity indicates that the ionization efficiency reaches saturation in the one, two, and three excitation steps respectively. It is also found that the narrower the laser pulse duration is, the higher becomes the laser intensity for saturation.
基金supported by a grant from the National Natural Science Foundation of China under Grant No.60578026,60878056.
文摘Gold nanoparticles （NPs） have highly efficient multi-photon-induced luminescence. In this paper, we record the two-photon images of gold NPs, lymphoma cell line Karpas 299, and Karpas 299 incubated with 30-nm-diameter gold NPs and ACT-1 antibody conjugates （Au30-ACT-1 conjugates） by using a multi-photon microscopy system. Due to the specific conjugation of ACT-1 antibody and cell membrane receptor CD25, gold NPs are only bound to the surface of cell membrane of Karpas 299. The luminescence intensity of gold NPs is higher than that of cells at 750-nm laser excitation. By comparing the images of Karpas 299 cells incubated with and without gold NPs, it is found that by means of gold NPs, we can get clear cell images with lower excitation power. Their excellent optical and chemical properties make gold NPs an attractive contrast agent for cellular imaging.
基金supported by the National Natural Science Foundation of China(Nos.60978058,60908032, and 60972064)the Natural Science Foundation of Zhejiang Province(No.Y1090996)the Scientific Research Foundation of Graduate School of Ningbo University, and the K.C.Wong Magna Fund in Ningbo University
文摘We present the measurement of the third-order nonlinearity of Bi203-B^O3-BaO glasses using the single Z-scan method with femtosecond laser pulses at 750 - 850 nm. Both third-order nonlinear refraction γ and two photon absorption coefficient β are investigated. The γ shows an increasing tendency with increasing BaO content, and the largest value is estimated to be 7.2×10^-14 cm^2/W, which is as large as those of chalcogenide glasses. The dependence of 13 on the normalized photon energy is studied.
基金the National Natural Science Foundation of China(No.10674086)"973"Program(No.2006CB921102)+1 种基金NCET,PCSIRT(No.IRT0516)the Shanxi Provincial Foundation for Leaders of Disciplines in Science,and the Natural Science Foundation of Shanxi Province(No.2007011006)
文摘An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of Ts 〈 Td 〈 Tm, where Td is the dead time of each detector and Tm is the laser pulse repetition period. And each single photon detector cannot detect more than one photon in each pulse. The approach can sufficiently eliminate the influences of the detector＇s dead time on photon statistics. At last, the photon statistics of coherent field is experimentally determined.
文摘Theretical analysis of the helicity inversion of laser （photons） during reflection is made by quantum theory for laser （photons） through an optical helix. The result reveals that the helicity inversion of the laser （photons） occurs when the wave vector of the laser （photon） rotates at an extremely high angular velocity. The dynamic factor that dominates the process is the Coriolis coupling between the spin of the photon and the rotation of the wave vector. This non-intertial effect is treated successfully by simplification of the Maxwell equation in the rotational frame. In addition, the implication of the helicity inversion in information theory is discussed.
基金supported by the National Natural Science Foundation of China under Grant Nos.60908006,10804067,and 60407007
文摘Photoelectron angular distributions （PADs） from two-photon ionization of atoms in linearly polarized strong laser fields are obtained in accordance with the nonperturbative quantum scattering theory. We also study the influence of laser wavelength on PADs. For two-photon ionization very close to the ionization threshold, most of the ionized electrons are vertically ejected to the laser polarization. PADs from two- photon ionization of atoms are determined by the second order generalized phased Bessel function at which the ponderomotive parameter plays a key role. In terms of dependence of PADs on laser wavelength, corresponding variations for the ponderomotive parameter are demonstrated.
基金supported by the National Natural Science Foundation of China (No. 50375068 and 50775104)the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 96039)the Natural Science Foundation of Jiangsu Province
文摘Two-photon photopolymerization （TPP） with femtosecond laser is a promising method to fabricate threedimensional （3D） photonic crystals （PCs）. Based on the TPP principle, the micro-fabrication system has been built. The 3D woodpile PCs with rod space of 2000 nm are fabricated easily and different defects are introduced in order to form the cross-waveguide and the micro-laser structure PCs. Simulation results of the optical field intensity distributions using finite-difference time domain （FDTD） method are given, which support the designs and implementation of the PC of two types in theory.
基金supported by the National Basic Research Program of China(No.2015CB352005)the National Natural Science Foundation of China(Nos.61525503,61378091,61405123,and 61405062)+1 种基金the Guangdong Natural Science Foundation Innovation Team(No.2014A030312008)the Shenzhen Basic Research Project(Nos.JCYJ20150324141711561,JCYJ20150930104948169,ZDSYS20140430164957663,and KQCX20140509172719305)
文摘We provide the first demonstration of pure red emission in the visible light region via three-photon excitation in monodisperse N a3 ZrF7：Er nanoparticles （NPs） by using a laser operating in the telecommunication band. NPs of -22 nm in diameter are synthesized at 260℃ by the thermal decomposition method. The experimental results reveal that the Na3ZrF7：Er NPs exhibit pure red emission in the visible region under 1480 nm laser excitation, and the emission intensity is significantly influenced by the Er3＋ ion concentration. The decay times of the 4S3/2 → 4F15/2 and 4F9/2 → 4F15/2 transitions of the Er3＋ ions at 540 and 655 nm, respectively, are reduced by increasing the Er3＋ ion concentration in the Na3ZrF7：Er NPs. The suppressed emission intensity result from the defect-related quenching effect： when trivalent Er3＋ ions replac tetravalent Zr4＋ ions, extra Na＋ ions and F- vacancies are formed to re-balance the charge in the Na3ZrF7 matrix. The emission color of the Na3ZrF7：Er NPs is related to the cross relaxation between Er3＋ ions. These results provide an important step toward more ef- fective biological imaging and photodynamic therapy by minimizing the scattering of the excitation light and increasing the penetration depth.
基金supported by the financial supports from NSERC,Canada Research Chairs,CIPI,CFI,FQRNTthe National Natural Science Foundation of China(Nos.11074098,11134010,60825406,and10974213)+2 种基金NCET-09-0429,the fundamental research funds of Jilin Universitytwo grants from the Ministry of Education,Culture,Sports,Science and Technology(MEXT),Japan the Grant-in-Aid for Specially Promoted Research on Ultrafast Hydrogen Migration (No. 19002006)the Grant-in-Aid for Global COE Program for Chemistry Innovation
文摘We propose a new mechanism/scheme to explain the ultrafast population inversion of molecular ions which takes place in a time scale comparable to the femtosecond laser pulse. The nonlinear pumping process including the pump photons and the self-generated harmonic photons of the pump laser would be responsible for building up population inversion to realize remote molecule lasers in femtosecond laser filaments in gases. It is shown that the remote laser emissions in molecular ions of gases may be a universal process in the femtosecond laser filament.
