Nonlinear Application Of The One-dimensional Oscillator With Quantized Impedance

At present,the methods of the numerical simulation of the first principle and the perturbation theory of quantum mechanics in dealing with the nonlinear interaction of light-matter(multiphoton absorption for exsample)show a large amount of computation and a very complexity of theoretical derivation.In addition,in the measurement of the atom or molecule multi-photon absorption cross section,a powerful,stable,and tunable laser is usually necessary as an excitation light source,which increases both of the difficulty and the cost of the experiment.The purpose of this paper is to attempt an estimation method of the two-photon absorption cross-section based on the linear absorption spectrum of some matter in order to reduce the complexity and the difficulty of the treatment studying the nonlinear light-matter interaction in a certain range of accuracy.In November 2015,the one-dimensional harmonic oscillator with quantized impedance was proposed,in which the damping coefficient of the oscillator was clarified to be the average collision frequency impacted by other atoms during the electronic transition.Meanwhile a formula of the damping coefficient was suggested in accordance with the collision meaning.The oscillator's simulation of the hydrogen atom emission spectrum is well in agreement with the experimental one.As a development of the harmonic oscillator,the electronic movement along long axis of its elliptical orbit,relative to the atomic nucleus,is futher assumed a one-dimensional an-harmonic oscillator.The restoring force of the oscillator is expressed as the long axis component of Coulomb force acting on the moving electron.As a result,a calculation method for the nonlinear effective parameters of the one-dimensional oscillator was obtained on the basis of Taylor expansion coefficient of the long axis component of Coulomb force.Unfortunately,due to the absence of the measurement report on the two-photon absorption cross section of a hydrogen atom or a hydrogen-like atom,this calculation method has not been experimentally validated.In this dissertation,the one-dimensional oscillator with quantized impedance is used to investigate in detail the two-photon absorption cross section of some typical organic molecules,such as Rhodamine B,chlorin derivative photosensitizer(CDP),and trans-4-[p-(pyrrolidinyl)styryl]-N-methylpyridinium iodide(PSPI).The oscillator's simulation of the cross section is compared and analysed with the experimental one.The major achievements are as follow.1.In a molecule some atom participating in a transition is considered to be a hydrogen-like atom.Its orbits are assumed to comply with the Bohr-Sommerfeld quantization conditions.Relative to the nucleus,the outermost electronic motion along long axis of its elliptical orbit is regarded as a one-dimensional an-harmonic oscillator.The calculation method of the nonlinear effective parameters is re-expressed by taking the atom quantum defect into account in the one-dimensional oscillator with quantized impedance.2.An approach is proposed to determine the jumping quantum numbers of an atom in a molecule.Based on the one-dimensional oscillator with quantized impedance,these quantum numbers may be obtained according to the transition selection rule,the wavelength at the peak and the full width at half maximum of the linear absorption spectrum of the organic molecule,in which there is only one absorption peak.The transition quantum numbers of the jumping atoms in the three organic molecules are calculated and listed in this paper.3.Two-photon absorption cross-section?₂of the three organic molecules has been calculated on the basis of the one-dimensional oscillator with quantized impedance and two-photon transition selection rule.Both theoretical and experimental results are as follows:Rhodamine B:?_2-theory(?=800 nm)=225.3 GM,?_2-experiment(?=800 nm)=150 GM;CDP:?_2-theory(?=800 nm)=19.52 GM,?_2-experiment(?=800 nm)=33.6 GM;PSPI:?_2-theory(?=930nm)=2911 GM,?_2-experiment(?=930 nm)=2850 GM,wherein,GM=10^-50cm⁴·s·photon^-1.The results show that the theoretical values of two-photon absorption section are basically consistent with the experimental ones.The above results suggest that,with the help of the one-dimensional oscillator with quantized impedance,it is perhaps possible for one to carry out estimating two-photon absorption cross section of a molecule based on its linear absorption spectrum with only one absorption peak.