The problem of the quantization of evanescent waves, which appear in the angular spectrum representation of the electromagnetic field in a half-space, is discussed. Although evanescent waves are associated with material sources, scatterers, etc., we are able to treat the electromagnetic field, including the evanescent waves, effectively as a free field, by making use of the idea of the refractive index of a passive, macroscopically continuous medium. We consider a space which is filled with a homogeneous dielectric to the left of the plane $z=0$ , and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.The problem of the quantization of evanescent waves, which appear in the angular spectrum representation of the electromagnetic field in a half-space, is discussed. Although evanescent waves are associated with material sources, scatterers, etc., we are able to treat the electromagnetic field, including the evanescent waves, effectively as a free field, by making use of the idea of the refractive index of a passive, macroscopically continuous medium. We consider a space which is filled with a homogeneous dielectric to the left of the plane $z=0$, and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJan 15, 1971251 citations

Dynamics of quantum waves in the field of a nonstationary well

Alexander S. Chikhachev

Journal of Russian Laser ResearchMay 1, 20103 citations

Time dependence of evanescent quantum waves

Juan Gonzalo Muga, Μ. Büttiker

The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymptotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling already plays a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency-band-limited sources and (b) the short-time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymptotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling already plays a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency-band-limited sources and (b) the short-time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.

arXiv:quant-ph/0001039Physical Review AJul 19, 200041 citations

z=0

, and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.