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Journal of Electromagnetic Waves and Applications

On the Pulse Velocity in Absorbing and Nonlinear Media and Parallels With the Quantum Mechanics - Abstract

Ioseph Gurwich

Published Jan 1, 2001• 6 citations
Publisher

Abstract

A novel definition of pulse propagation velocity is introduced. It is shown that the present definition does not lead to confusing results such as complex velocity or velocity exceeding the light velocity in the vacuum. Also shown are the parallels of this definition to the classical and quantum mechanics conceptions. Using the present definition reveals certain analogies between electromagnetic pulse propagation in the classical physics and de Broglie wave-packets propagation in the quantum mechanics, thus adding support to its validity.

DOI
10.1163/156939301x00805

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On the Pulse Velocity in Absorbing and Nonlinear Media and Parallels with the Quantum Mechanics

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A novel definition of pulse propagation velocity is introduced.It is shown that the present definition does not lead to confusing results such as complex velocity or velocity exceeding the light velocity in the vacuum.Also shown are the parallels of this definition to the classical and quantum mechanics conceptions.Using the present definition reveals certain analogies between electromagnetic pulse propagation in the classical physics and de Broglie wave-packets propagation in the quantum mechanics, thus adding support to its validity.

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The velocity is a macroscopic concept. The question what is the meaning of velocity in Quantum Mechanics( QM) ,this problem itself is inno answersituation. In the semi-classical theory,for the reconstruction of the velocity definition,we have v→= ▽S / m[m is the particle's mass and ψ = Aexp( j S /h) ]. This method builds the relation of velocity and wave function,but it is not the necessary and useful concept of wave's speed. The velocity of light in vacuum is a common basic constant of physics,however QM also need this parameter obviously,i. e. the new wave mechanics is on need of this physical quantity.The process and result of people's practice show that,scientist has intended to bring forth in the measurement of c with very high accuracy does stand out,if he used the scalar equation c = fλ. Modern physics maintain that the wave velocities( phase velocityvp、group velocity vg) are scalars,not vectors.The wave has its special scientific features; the regular pattern is different from the Classical Mechanics( CM). It needs supports of the QM,but it is not identical with the serious QM. Now,it has not only a theory that can explain the wave problems perfectly,so it is support by the classical physics and quantum physics.The quantization process of EM fields explains the particle-wave duality mathematically. Post quantization,from the EM fields we obtained the photons. But scientist still is puzzled by a difficult question:what is photon. As the common knowledge,the matter waves of photon still a paradox in physics. In addition,the electronic probability waves corresponding the Schrdinger equation,but people says the photonic probability waves have not that wave equation. In other words,the physical meanings of matter wave's phase velocity are not clear,and why the phase velocity of de Broglie waves is faster-than-light,many explanations will be needed.Many instances similar to these examples make the particle-wave duality still the magic ghost in modern physics. Finally,the study on negative wave velocity( NWV) in recent years has a great deal of experience on wave sciences,and bring the new chance on theoretical thinking.

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Summary form only given. According to the conventional expression the group velocity of optical pulses in resonantly absorbing media can exceed the light velocity in the vacuum and even become negative. Recently a new definition of group velocity has been proposed by means of the saddle point method. We observed the propagation of femtosecond optical pulses in a dye solution and experimentally tested the new definition of the group velocity.

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•Jan 1, 2000•12 citations
A novel definition of pulse propagation velocity is introduced. It is shown that the present definition does not lead to confusing results such as complex velocity or velocity exceeding the light velocity in the vacuum. Also shown are the parallels of this definition to the classical and quantum mechanics conceptions. Using the present definition reveals certain analogies between electromagnetic pulse propagation in the classical physics and de Broglie wave-packets propagation in the quantum mechanics, thus adding support to its validity.
A novel definition of pulse propagation velocity is introduced.It is shown that the present definition does not lead to confusing results such as complex velocity or velocity exceeding the light velocity in the vacuum.Also shown are the parallels of this definition to the classical and quantum mechanics conceptions.Using the present definition reveals certain analogies between electromagnetic pulse propagation in the classical physics and de Broglie wave-packets propagation in the quantum mechanics, thus adding support to its validity.
The velocity is a macroscopic concept. The question what is the meaning of velocity in Quantum Mechanics( QM) ,this problem itself is inno answersituation. In the semi-classical theory,for the reconstruction of the velocity definition,we have v→= ▽S / m[m is the particle's mass and ψ = Aexp( j S /h) ]. This method builds the relation of velocity and wave function,but it is not the necessary and useful concept of wave's speed. The velocity of light in vacuum is a common basic constant of physics,however QM also need this parameter obviously,i. e. the new wave mechanics is on need of this physical quantity.The process and result of people's practice show that,scientist has intended to bring forth in the measurement of c with very high accuracy does stand out,if he used the scalar equation c = fλ. Modern physics maintain that the wave velocities( phase velocityvp、group velocity vg) are scalars,not vectors.The wave has its special scientific features; the regular pattern is different from the Classical Mechanics( CM). It needs supports of the QM,but it is not identical with the serious QM. Now,it has not only a theory that can explain the wave problems perfectly,so it is support by the classical physics and quantum physics.The quantization process of EM fields explains the particle-wave duality mathematically. Post quantization,from the EM fields we obtained the photons. But scientist still is puzzled by a difficult question:what is photon. As the common knowledge,the matter waves of photon still a paradox in physics. In addition,the electronic probability waves corresponding the Schrdinger equation,but people says the photonic probability waves have not that wave equation. In other words,the physical meanings of matter wave's phase velocity are not clear,and why the phase velocity of de Broglie waves is faster-than-light,many explanations will be needed.Many instances similar to these examples make the particle-wave duality still the magic ghost in modern physics. Finally,the study on negative wave velocity( NWV) in recent years has a great deal of experience on wave sciences,and bring the new chance on theoretical thinking.
The classical theory of dispersive signal propagation by Sommerfeld and Brillouin proposed in 1914 provided the first proof within the classical Maxwell–Lorentz theory that an electromagnetic signal could not propagate faster than the vacuum speed of light in a causal dielectric, also introducing the signal velocity and the precursor fields (or forerunners). Modern asymptotic theory has extended these results, providing a physically meaningful definition of the signal velocity while showing the critical role that the precursor fields play in the observed pulse dynamics. Their role in defining the observed pulse velocity is presented and compared with the classical group velocity as well as with other pulse velocity measures that yield superluminal results.
Propagation of a Gaussian wave packet in an absorbing medium is examined in order to shed light on the physical basis of group velocity which exhibits a singular behavior. It is found that the velocity of the wave packet, defined as the traveling distance of the peak amplitude divided by its flight time, decreases in the absorption range of frequency, although the group velocity becomes infinite in the same range. Fast pulse propagation, which was observed by Chu and Wong and is characterized by a packet velocity faster than the light velocity, turns out to be a characteristic in the early stage of the flight and is understood in terms of packet distortion due to damping of Fourier-component waves in an anomalous dispersion region. It also turns out that slow pulse propagation characterized by a packet velocity less than the light velocity appears for long traveling distance. The results provided a unified picture of wave-packet propagation in an absorbing medium.
In two models it is shown that a light pulse propagates from a vacuum into certain media with velocity greater than that of a light in a vacuum (c). By numerical calculation the propagating properties of such a light are given. Recently L. J. Wang and his collaborators in their experiment [1] have found that the group velocity of a laser pulse in particularly prepared atomic caesium gas can much exceed that of light in a vacuum (c). Here we will explore the problem from a theoretical piont of view. Many years ago A. Sommerfeld rigorously proved [2] that the velocity of light pulse can not exceed c in absorption media. We call this conclusion as basic theorem afterwardz. In the following we will first examine why usually the basic theorem holds and in what condition it will be violated. Then two models are proposed, where with precise numerical calculation we will show that the basic theorem is indeed violated. Therefore the properties of light propagating in media of the models are given. We believe that these properties may appears in more realistic models. 1 Let a light pulse propagating along x axis toward its positive direction in a vacuum (x < 0), at time t = 0 arriving at x = 0, and then entering into a medium (x ≥ 0) afterwards. At x = 0, the amplitude of the light pulse changes with time t as ⎨ F(t) t ≥ 0 f(t) = ⎩ 0 t < 0. Usually f(t) can be rigorously expressed in Fourier integration as f(t) = Re A(n)e −int dn. (2) 0 For simplicity suppose there is no reflection of light at x = 0. The amplitude of the light pulse entering into the medium (x ≥ 0) is [2] f(t, x) = Re A(n)e −int+ikx dn, (3)