The Instability of Molecules in Laser Field and Isotope Separation

1981 ◽  
Vol 36 (8) ◽  
pp. 813-818
Author(s):  
Ke-hsueh Li
Keyword(s):  
Differential Equation ◽  
Dipole Moment ◽  
Laser Pulse ◽  
Nonlinear Differential Equation ◽  
Laser Field ◽  
Isotope Separation ◽  
Schroedinger Equation ◽  
Time Dependent ◽  
Unimolecular Reaction ◽  
Raman Process

Abstract In the present paper the nonlinear differential equation describing the selective decomposition of a molecule as an unimolecular reaction has be deduced from the usual time dependent semi-classical Schroedinger Equation. The selective conditions for the instability of a molecule are discussed. The thresholds of the required laser intensities for ICl and HCl diatomic molecules are estimated respectively, where one type of isotope molecules ought to be decomposed for hundred per cent in a laser pulse for different pulse widths. And possibly selective decomposition of the molecule without permanent dipole moment by Raman process is also discussed briefly.

Recurring Molecular Alignment Induced by Pulsed Nonresonant Laser Fields

2001 ◽  
Vol 66 (7) ◽  
pp. 991-1004 ◽  
Author(s):  
Long Cai ◽  
Břetislav Friedrich
Keyword(s):  
Laser Pulse ◽  
Laser Field ◽  
Analytic Solution ◽  
Short Pulse ◽  
Molecular Alignment ◽  
Time Dependent ◽  
Molecular Axis ◽  
Linear Molecule ◽  
Numerical Computations ◽  
Laser Fields

We examine the rotational wavepackets created by the nonadiabatic interaction of a linear molecule with a pulsed nonresonant laser field. We map out the recurrences of the wavepackets and of the concomitant alignment as a function of the duration and intensity of the laser pulse. We derive an analytic solution to the time-dependent Schrödinger equation in the short-pulse limit and find it to agree quantitatively with our numerical computations. This indicates that the recurrences are favored under an impulsive transfer of action from the radiative field to the molecule. The recurring wavepackets afford field-free alignment of the molecular axis.

Bayesian approach for the optimal control of high-order harmonics for the generation of ultrashort attosecond laser pulses

2021 ◽  
Author(s):  
Wei-Teng Wang ◽  
Yae-Lin Sheu ◽  
Shih-I Chu
Keyword(s):  
Laser Pulse ◽  
Laser Field ◽  
Pseudospectral Method ◽  
Laser Pulses ◽  
Optimization Method ◽  
High Order ◽  
Time Dependent ◽  
Bayesian Optimization ◽  
Time Frequency ◽  
Isolated Attosecond Pulse

Abstract We present an efficient and powerful method to optimize the production of high-order harmonic generation (HHG) and ultrashort single attosecond laser pulses. The system under investigation is the helium atoms that are exposed to the combination of chirped two-color mid-IR laser field and its 34th harmonic. The time-dependent Schrödinger equation is solved accurately and efficiently by means of the time-dependent generalized pseudospectral method and the time-frequency spectrum is obtained by the wavelet transform. We extend the machine-learning based optimization method, called Bayesian optimization (BO), to optimize the incident laser pulse to generate ultrashort attosecond laser pulse successfully for the first time. It is shown that the intensity of HHG power spectrum from the plateau region to the cutoff is enhanced by the optimized laser field by several orders of magnitude. Further, an ultrafast isolated attosecond pulse of 10 attosecond can be generated efficiently by superposing the plateau harmonics.

SOME COMMENTS ABOUT ATOMS INTERACTING WITH LASER

1993 ◽  
Vol 07 (11) ◽  
pp. 747-751 ◽  
Author(s):  
M.A. GRADO CAFFARO ◽  
M. GRADO CAFFARO
Keyword(s):  
Dipole Moment ◽  
Schrödinger Equation ◽  
Laser Field ◽  
Schrodinger Equation ◽  
Amorphous Semiconductors ◽  
Time Dependent ◽  
Single Atom ◽  
Atomic Structures

The interaction of a single atom with a laser field is investigated. In particular, various new results on the time-dependent dipole moment induced in a single atom by the laser are obtained. These results are, in principle, applicable to atomic structures corresponding to certain solids, for instance, amorphous semiconductors. In addition, time-dependent Schrödinger equation is considered with respect to our problem and the interaction Hamiltonian involved in this equation is studied.

scholarly journals Oscillatory behavior of a second order nonlinear advanced differential equation with mixed neutral terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hongwei Shi ◽  
Yuzhen Bai
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

AbstractIn this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form $$ \bigl(r(t) \bigl(z'(t)\bigr)^{\alpha }\bigr)'+q(t)x^{\beta } \bigl(\sigma (t)\bigr)=0,\quad t\geq t_{0}, $$(r(t)(z′(t))α)′+q(t)xβ(σ(t))=0,t≥t0, where $z(t)=x(t)+p_{1}(t)x(\tau (t))+p_{2}(t)x(\lambda (t))$z(t)=x(t)+p1(t)x(τ(t))+p2(t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

Magnetohydrodynamic Squeeze Film Characteristics Between Parallel Circular Plates Containing a Single Central Air Bubble in the Inertial Flow Regime

1999 ◽  
Vol 66 (4) ◽  
pp. 1021-1023 ◽  
Author(s):  
R. Usha ◽  
P. Vimala
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Bubble Radius ◽  
Fluid Film ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Circular Plates ◽  
Air Bubble ◽  
Approximate Analytical Solutions

In this paper, the magnetic effects on the Newtonian squeeze film between two circular parallel plates, containing a single central air bubble of cylindrical shape are theoretically investigated. A uniform magnetic field is applied perpendicular to the circular plates, which are in sinusoidal relative motion, and fluid film inertia effects are included in the analysis. Assuming an ideal gas under isothermal condition for an air bubble, a nonlinear differential equation for the bubble radius is obtained by approximating the momentum equation governing the magnetohydrodynamic squeeze film by the mean value averaged across the film thickness. Approximate analytical solutions for the air bubble radius, pressure distribution, and squeeze film force are determined by a perturbation method for small amplitude of sinusoidal motion and are compared with the numerical solution obtained by solving the nonlinear differential equation. The combined effects of air bubble, fluid film inertia, and magnetic field on the squeeze film force are analyzed.

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