Władysław Żakowicz
Time-dependent scattering of finite duration wave packets on a rigid cylinder is studied using exact solutions of the corresponding Schrödinger equation. The similarity between the time evolution of the total wavefunction and evolution of the corresponding classical ensemble of particles is exposed. Special attention is paid to a discussion of the differences between the total wavefunction dynamics and the dynamics of the scattered part of the wavefunction, the part which is commonly used for the evaluation of scattering cross-sections. This discussion emphasizes the necessity of using the total wavefunction in the description of scattering.
J. Phys. B: At. Mol. Opt. Phys. 37 L153-L159
Showing posts with label Władysław Żakowicz. Show all posts
Showing posts with label Władysław Żakowicz. Show all posts
Jan 5, 2004
Feb 20, 2003
Classical properties of quantum scattering
Władysław Żakowicz
Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.
J. Phys. A vol. 36, 4445-4464 (2003)
Quantum elastic potential scattering of a particle is re-examined taking into account exact solutions of the corresponding Schrödinger equation. In addition to the scattering of stationary plane waves and stationary finite-width wave beams, nonstationary wave packets having finite duration times are studied and some corresponding examples are presented. The role of interference between the scattered wave and the advancing incident beam is studied. Several two-dimensional scattering problems, involving axially symmetric, generic examples of nonuniform attractive and repulsive potentials, are discussed in more detail. This discussion concentrates on finding proper conditions when the solutions of the Schrödinger equation may resemble the corresponding solutions of the classical Newton equation. Examples are shown where such similarities occur.
J. Phys. A vol. 36, 4445-4464 (2003)
Aug 5, 2002
Graphical examples of geometrical and wave optics
Władysław Żakowicz
A simple method of the description of optical pulses of finite dimensions and finite duration time is presented. The pulses are given by superpositions of the known analytical as well as numerical solutions of the Maxwell equations. The examples show optical properties of scattering in detail. In the general case the wide pulses split in the scattering processes. The description of these phenomena requires a full wave approach. The pulses (or their fragments) that do not split but move smoothly through the optical system (or its fragment) may be described with the help of the geometrical optics theory.
Acta Phys. Polon. B 33, 2059 (2002)
A simple method of the description of optical pulses of finite dimensions and finite duration time is presented. The pulses are given by superpositions of the known analytical as well as numerical solutions of the Maxwell equations. The examples show optical properties of scattering in detail. In the general case the wide pulses split in the scattering processes. The description of these phenomena requires a full wave approach. The pulses (or their fragments) that do not split but move smoothly through the optical system (or its fragment) may be described with the help of the geometrical optics theory.
Acta Phys. Polon. B 33, 2059 (2002)
Jul 3, 2001
Spontaneous Emission by Atoms in Simple Environments
Władysław Żakowicz
Spontaneous radiation by atoms in the presence of the planar dielectric--vacuum interface, planar dielectric waveguides and cylindrical dielectric waveguides are discussed in the frame of cavity quantum electrodynamics in full analogy with that in free space. However, quantization of the electromagnetic field should be based on the modes appropriate to the selected space structure. These quantizations are usually based on incoming waves. However, the discussion of the angular intensity pattern of spontaneous emission can be simplified if the quantization is based on outgoing modes. Using these outgoing photons the angular emission radiation pattern has been obtained from a straightforward application of the perturbative method of the quantum radiation theory. Adding a contribution of the waveguiding photons attached to the waveguides (when they are present) the total emission of the spontaneous radiation and excitation decay rates of atoms radiating in these systems have been derived.
Acta Phys. Polon. A 101, 119 (2002)
Spontaneous radiation by atoms in the presence of the planar dielectric--vacuum interface, planar dielectric waveguides and cylindrical dielectric waveguides are discussed in the frame of cavity quantum electrodynamics in full analogy with that in free space. However, quantization of the electromagnetic field should be based on the modes appropriate to the selected space structure. These quantizations are usually based on incoming waves. However, the discussion of the angular intensity pattern of spontaneous emission can be simplified if the quantization is based on outgoing modes. Using these outgoing photons the angular emission radiation pattern has been obtained from a straightforward application of the perturbative method of the quantum radiation theory. Adding a contribution of the waveguiding photons attached to the waveguides (when they are present) the total emission of the spontaneous radiation and excitation decay rates of atoms radiating in these systems have been derived.
Acta Phys. Polon. A 101, 119 (2002)
Jun 23, 2001
On the extinction paradox
Władysław Żakowicz
The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σQ=2πa2=2σC for ka>>1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrödinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w>>a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R>>waλ. Moderately narrow beams, but also that the transverse width of beams of de Broglie's waves is small.
Acta Phys. Polon. A 101, 369 (2002)
The extinction paradox, the difference of classical and quantum scattering cross-sections for the scattering of particles by a rigid sphere (σQ=2πa2=2σC for ka>>1), is analyzed in a simpler 2D model of a rigid cylindrical potential. Rigorous solutions of the Schrödinger equation for particle beams, including also finite width beams, are derived and employed in the description of the scattering process. The scattering particle fluxes, with a thorough treatment of the forward directions, are being studied. It is pointed out that for wide beams (w>>a) the scattered flux can reach the value determined by the quantum theory, provided that it is measured at distances R>>waλ. Moderately narrow beams, but also that the transverse width of beams of de Broglie's waves is small.
Acta Phys. Polon. A 101, 369 (2002)
May 10, 2001
Light rays and imaging in wave optics
Władysław Żakowicz
An interpretation of focusing and image formation on scattering of electromagnetic waves by a dielectric cylinder (a cylindrical lens) is proposed on the basis of the full Maxwell theory. It is centered on analysis of the behavior of integral curves of the Poynting vector here called wave rays. These wave rays cannot intersect so that the focusing and imaging spots are identified with regions of high flow concentration. Two-dimensional examples of wave rays and wave fronts in the scattering of plane and cylindrical electromagnetic waves as well as of Gaussian beams by a dielectric cylinder derived from rigorous solution of the Maxwell equations for incident waves perpendicular to and uniform along the scatterer are given. Their qualitative comparison with geometrical and diffraction approximations are provided. Fixed points and vortex structure of the Poynting flow are investigated. An example of (Gaussian-beam) scattering with transparent multiple internal reflections and multiple wave splitting is given.
Phys. Rev. E 64, 066610 (2001)
An interpretation of focusing and image formation on scattering of electromagnetic waves by a dielectric cylinder (a cylindrical lens) is proposed on the basis of the full Maxwell theory. It is centered on analysis of the behavior of integral curves of the Poynting vector here called wave rays. These wave rays cannot intersect so that the focusing and imaging spots are identified with regions of high flow concentration. Two-dimensional examples of wave rays and wave fronts in the scattering of plane and cylindrical electromagnetic waves as well as of Gaussian beams by a dielectric cylinder derived from rigorous solution of the Maxwell equations for incident waves perpendicular to and uniform along the scatterer are given. Their qualitative comparison with geometrical and diffraction approximations are provided. Fixed points and vortex structure of the Poynting flow are investigated. An example of (Gaussian-beam) scattering with transparent multiple internal reflections and multiple wave splitting is given.
Phys. Rev. E 64, 066610 (2001)
May 18, 2000
New concept of waveguide for inverse free electron laser accelerator
Władysław Żakowicz
A segmented waveguide formed by a periodic system of pairs of wedge prisms with a gap between them is proposed. The prisms are made of single-crystal sapphire for which the refraction index ν<1 for CO2 laser radiation (λ=10.6 μm). The attenuation of 0.1 db/m can be estimated for a 5 mm diameter radiation beam for which the Rayleigh distance is approximately 1 m. The gap between adjacent prisms can be useful in FEL-like applications.
Nucl. Instr. Meth. Phys. Res. A 445, 313 (2000)
A segmented waveguide formed by a periodic system of pairs of wedge prisms with a gap between them is proposed. The prisms are made of single-crystal sapphire for which the refraction index ν<1 for CO2 laser radiation (λ=10.6 μm). The attenuation of 0.1 db/m can be estimated for a 5 mm diameter radiation beam for which the Rayleigh distance is approximately 1 m. The gap between adjacent prisms can be useful in FEL-like applications.
Nucl. Instr. Meth. Phys. Res. A 445, 313 (2000)
Jan 27, 2000
Spontaneous emission in the presence of a dielectric cylinder
Władysław Żakowicz and Maciej Janowicz
Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.
Phys. Rev. A 62, 013820 (2000)
Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.
Phys. Rev. A 62, 013820 (2000)
Mar 5, 1999
Interference without interference: Directional properties of spontaneous emission
A. Orlowski and W. Zakowicz
A fully quantum-mechanical description of the spontaneous emission from an excited two-level atom placed in front of the two slit interferometer is given. Global modes of the electromagnetic field in a two slit system are derived within the Kirchhoff-Huygens diffraction approximation, serving as a base for the field quantization. The standard Fermi’s golden rule, supplemented by a factor coming from the nontrivial mode structure caused by the presence of the two slit interferometer, is used to show that interference results from the position dependent coupling between the atom and different field modes of the system.
Opt. Spectrosc. 87, 500 (1999)
A fully quantum-mechanical description of the spontaneous emission from an excited two-level atom placed in front of the two slit interferometer is given. Global modes of the electromagnetic field in a two slit system are derived within the Kirchhoff-Huygens diffraction approximation, serving as a base for the field quantization. The standard Fermi’s golden rule, supplemented by a factor coming from the nontrivial mode structure caused by the presence of the two slit interferometer, is used to show that interference results from the position dependent coupling between the atom and different field modes of the system.
Opt. Spectrosc. 87, 500 (1999)
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