The quantum states of the Kapitza pendulum are investigated in the framework of the effective potential obtained by the method of averaging over fast oscillations. An analytical estimate of the energy spectrum of stabilized states is given using a model potential. For the lowest states of the inverted pendulum, an expression is obtained for the spectrum in the form of the energies of a harmonic oscillator, refined according to the perturbation theory. Tunneling corrections to the energies of resonance states in double-well effective potential are found. The results of calculations of the structure of vibrational and rotational spectra of the Kapitza pendulum by the semiclassical method and by the numerical Numerov’s algorithm are compared.
A surface plasmon polariton is an electromagnetic wave that propagates along an interface between two materials with dielectric permittivity of opposite signs. Such waves can be focused by metal waveguides of special geometry. The spatial distribution for a near-field strongly depends on a linear chirp of the laser pulse, which can partially compensate the wave dispersion. Field distribution is calculated for different chirp values, opening angles, and distances. The spatial selectivity of excitation of quantum dots using focused fields is shown using Bloch equations.
The process of the light scattering becomes nonlinear in the fields with relativistic intensity. Nonlinear scattering of
ultrashort relativistic pulses by free electrons is considered. We use the wavelet basis in the form of derivatives from the
Gaussian function for description of ultrashort pulses. The equation of motion, for a charged particle in the field of plane
electromagnetic wave, has the exact solution including the expression for the energy. The approximation of instant
spectrum allows to calculate the Thomson nonlinear scattering for laser pulses of ultrarelativistic intensity. Spectral
distribution for all the pulse duration is the result of integration over the time. Exact solution in the case of laser pulse
with form of the "Mexican hat" gives the velocity and acceleration in the parametrical form as functions of the proper
time. The maximum of radiation for free electron in the fields with intensity 1019-1021 W/ cm2 is concentrated at the
range of ultraviolet spectrum with photons energies 3-12 eV. The part of continuous spectrum reaches the area of large
photon energies. One percent of scattered energy for the laser intensity 1020 W/ cm2 is concentrated at the range
hω > 2,7 x 102 eV, 1021 W/ cm2 - hω > 7,9 x 103 eV, 1022 W/ cm2 - hω > 2,45 x 105 eV. It allows one to use nonlinear
scattering as a source of hard x-ray radiation.
Generation of the electronic waves with high degree of coherence becomes a physical reason for developing holographic
electronic microscopy with high resolution and creating the technology of holography for low energies. This effect opens
an opportunity to design new tools for observation of the nanometer scale objects without destruction. The general
picture can be considered in the approximation of the steady-state wave function. The outgoing wave is described by the
amplitude slowly varying along the trajectory. Quantum formulation of photodetachment of a negative ion as the steady-state
process is equivalent the inhomogeneous Schrödinger equation. Its solution can be expressed in terms of the
Green's function. The exact expression for the Green's three-dimensional function is known in two cases: homogeneous
electric field and the Coulomb field. The detailed picture for distribution of photocurrent in a homogeneous field
demonstrates the advantages of the quantum theory approach. We found the repulsive Coulomb field is more effective
for extension the area of the interference pattern at a small distance from an ion.
The simple analytical formula for description of the scattering of the laser radiation ultrashort pulse with
the shape of the Meyer wavelet by atomic system is obtained. The dependence of the scattered pulse
shape as a function of the system spectral width is discussed.
The scalar problem for a plane wave pulse spreading behind the diaphragm is solved. The calculation is carried out on the base of the non-stationary Kirchhoff-Sommerfeld integral and the expansion of pulse in terms of wavelet. The round and square diaphragm are considered. The pulse propagation under the condition of focusing is calculated. The Green function of the problem for the round diaphragm with and without nonabberative focusing is constructed.
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