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现代传播:中国传媒大学学报

Discussions of the Evanescent States

Huang Zhi

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The evanescent states are common in the electro-magnetic environments,it's basic feature is the field strength decrease according to the exponential law from orginal position to far away.The electro-magnetic waves propagate through the reactive medium are common situations,corresponding wave propagation in the guided wave modes,dispersion mediums,and the ionic gases.In 1897,Lord Rayleigh's calculation predicated the evanescent states appear to propagate in rectangular metal waveguides.In order to analyze the phenomenon of waveguide below cut-off(WBCO),it seems that the evanescent states have a imaginary wave vector(a imaginary wave number).And so,we can say it is like a standing wave,the variation of field occurs in every position simultaneously,this means that they do not experience a phase shift in propagate direction.But the behaviour of WBCO was a bit strange,sometimes the phase constant β is negative,then in THz experiments the pulse delay is negative.Although the phase velocity of waveguide to be superluminal is well-known,the theoretical discussion does not explain why the phase velocity and the phase refractive index becomes negative.In quantum mechanics(QM),in barrier the evanescent states also have a imaginary wave parame-ter.This state can be explained by the Schrdinger equation,it is analogy with the Helmholtz equation in classical electro-magnetic theory.In practice,quantum tunnelling is the most popular physical process,it can be observed in many cases: the propagation of the graded index optical fiber,the two glass prisms of Bose experiment,etc.In scientist's opinion,to defy the light-speed limit is possible;for example,photons tunnel across a gap between two prisms yet arrive at same time as reflected photons that travelled a shorter distance,that means an ultra-fast transit between the two prisms:so much faster than the speed of light.As well-known,we are used the virtual particles in microscopic interaction processes since R.Feynman,but now we perhaps demonstrated here an example in the macroscopic range of a meter since G.Nimtz's experiment.

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Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.

现代传播:中国传媒大学学报•Jan 1, 2013•0 citations
The evanescent states are common in the electro-magnetic environments,it's basic feature is the field strength decrease according to the exponential law from orginal position to far away.The electro-magnetic waves propagate through the reactive medium are common situations,corresponding wave propagation in the guided wave modes,dispersion mediums,and the ionic gases.In 1897,Lord Rayleigh's calculation predicated the evanescent states appear to propagate in rectangular metal waveguides.In order to analyze the phenomenon of waveguide below cut-off(WBCO),it seems that the evanescent states have a imaginary wave vector(a imaginary wave number).And so,we can say it is like a standing wave,the variation of field occurs in every position simultaneously,this means that they do not experience a phase shift in propagate direction.But the behaviour of WBCO was a bit strange,sometimes the phase constant β is negative,then in THz experiments the pulse delay is negative.Although the phase velocity of waveguide to be superluminal is well-known,the theoretical discussion does not explain why the phase velocity and the phase refractive index becomes negative.In quantum mechanics(QM),in barrier the evanescent states also have a imaginary wave parame-ter.This state can be explained by the Schrdinger equation,it is analogy with the Helmholtz equation in classical electro-magnetic theory.In practice,quantum tunnelling is the most popular physical process,it can be observed in many cases: the propagation of the graded index optical fiber,the two glass prisms of Bose experiment,etc.In scientist's opinion,to defy the light-speed limit is possible;for example,photons tunnel across a gap between two prisms yet arrive at same time as reflected photons that travelled a shorter distance,that means an ultra-fast transit between the two prisms:so much faster than the speed of light.As well-known,we are used the virtual particles in microscopic interaction processes since R.Feynman,but now we perhaps demonstrated here an example in the macroscopic range of a meter since G.Nimtz's experiment.
Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tunneling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.
Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tunneling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.
Feynman one of the founders of Quantum Electronic Dynamics (QED) introduced in his diagrams virtual particles as intermediate states of an interaction process. Such virtual particles are not observable, however, from the theoretical point of view they represent necessary intermediate states between observable real states. Such virtual particles were introduced for describing the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual photons are evanescent modes known from optics. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes are present in the optical processes of total reflection and in undersized wave guides for instance. The most prominent example of the occurrence of evanescent modes is frustrated total internal reflection at double prisms. In 1949 Sommerfeld \cite{Sommerfeld} pointed out that this optical phenomenon represents the analogy of quantum mechanical tunneling. The evanescent modes and tunneling violate the theory of special relativity, obviously, they represent the exception which proves the special theory of relativity. We demonstrate the quantum mechanical behavior of evanescent modes \textbf{with digital microwave} signals at a macroscopic scale of the order of a meter and show that evanescent modes are well described by virtual photons as predicted by former QED calculations.
Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.
The analogy between quantum tunneling of particles and evanescent electromagnetic waves can be used to study particle tunneling. Possibilities for the measurement of the time delay resulting from the transmission of waves through an evanescent region, say with lower dielectric constant, are discussed. In contrast to particle tunneling, an electromagnetic pulse can consist of many photons and can be probed in a noninvasive way. We emphasize the delay of the centroid of an electromagnetic pulse transmitted below cutoff through a portion of a waveguide with the same cross section as the adjacent propagating guides. The boundary conditions at the interface between the propagating and the evanescent region lead to the same transmission and reflection coefficients as for a square-barrier tunneling problem. For a pulse restricted to a narrow frequency range, the time delay depends only on the frequency derivative of the phase shift associated with transmission. The delay of a centroid is just that; there is no deeper physical sense which links the incoming centroid to the outgoing centroid. For sufficiently long evanescent regions, the delay is independent of thickness.
Recently,there has been interest in modifying the group velocity of optical pulses,resulting in stopped,slow,and fast(superluminal)light.According to the physical theory,fast appears in the anomalous medium,and then it so called light medium.There are many experimeuts to produce fast light,this situation opens up new perspectives for the so called dispersion engineering.For example,signal propagating with a group velocity that exceeds the speed of light in vacuum(c) is intriguing for scientists.And then,the traveling of short wave pulses,microwave pulses and light pulses with group velocity vg,whose values exceed infinity,so called negative group velocity(NGV) propagation.Such circumstance occurs when the peak of a pulse traveling through DUT,exits before the peak of the input pulse has reached the beginning of DUT.This effect is counterintuitive,but it is a discover under the experimental basis.When the group velocity of light in a material is negative,it is the NGV medium. Although NGV are possible particularly in gain systems,there have been some experimental demonstrations of that phenomenon in passive systems,such as the coaxial cables,waveguides,micro-strip lines,and optical fibers,etc.If the experimental configuration used with a higher impedance mismatch,then it permits larger group delays,and a corresponding NGV.If n is the effective refraction index of the medium,we wantfn |f/ndn/df|1 to obtain the NGV. Many experiments showed the group velocity can surpass the light speed c,but scientists still lack the further understanding of the results.In 2001,Scientists obtained the formula v-e=|T|2vg,where v-e is average energy velocity,T is transmission coeficient of the system.If we want v-ec,the condition is vgc|T|-2.Hence it can be concluded that only vg/c is very large,the energy velocity can surpass c.This demonstration opens the door to interesting possibilities. The definition of signal velocity by Brillouin,mathemalical meaning exceeds physical meaning.We argue that undistorted wave group(wave packet) propagation are the first consideration.According to this viewpoint,the theoretical analysis show that superluminal propagation(i.e.superluminal communication) was observed by authors of many NGV researchers.……The superluminal group velocity wave propagation,the negative group velocity wave propagation——each of the two cases has its own use.Now,scientists do research works in these fields: such as optical communication,squeezed light and quantum entanglement.The condusion tell us that,a hight efficiency and low-loss fast light scheme may explore potential applications.