The transfer function for transmission through a maser medium is derived. It is valid within the dynamic range of linear maser response and under the assumption of weak dispersion. All signal distortions due to propagation in a maser medium may be canceled by subsequent propagation in a complementary absorbing medium. The signal leaves the cascaded media undistorted with a delay corresponding to propagation at the vacuum velocity of light. This possibility of recovering the speed of light makes it difficult to talk of the propagation of information in a dispersive medium as taking place at a signal velocity below that of light. A potentially useful scheme is shown in which a severely distorting low-noise maser amplifier is used. After further amplification the signal distortions are eliminated by transmission through a complementary absorbing medium. The mathematical form of the transfer functions also leads to a new integral formula involving Bessel functions.
The transfer function for transmission through a maser medium is derived. It is valid within the dynamic range of linear maser response and under the assumption of weak dispersion. All signal distortions due to propagation in a maser medium may be canceled by subsequent propagation in a complementary absorbing medium. The signal leaves the cascaded media undistorted with a delay corresponding to propagation at the vacuum velocity of light. This possibility of recovering the speed of light makes it difficult to talk of the propagation of information in a dispersive medium as taking place at a signal velocity below that of light. A potentially useful scheme is shown in which a severely distorting low-noise maser amplifier is used. After further amplification the signal distortions are eliminated by transmission through a complementary absorbing medium. The mathematical form of the transfer functions also leads to a new integral formula involving Bessel functions.
The 1D problem of propagation of a narrowband signal in a homogeneous dispersing medium is considered. It is shown that there is a direct and immediate relationship between the additional (to vacuum) delay time of the signal and its attenuation during propagation in an absorbing medium. It is shown that with an additional delay time of more than several tens of coherence times of uniformly broadened spectral lines of the medium, the signal weakens by hundreds of decibels and therefore practically disappears. On the other hand, when the delay of the signal is less than the coherence time of the medium, its absorption is small. A similar situation arises in an amplifying (thermodynamically nonequilibrium) environment – of course, with the replacement of signal attenuation with its amplification and the replacement of signal delay with its advance. As an example, the propagation of a narrowband signal, the carrier frequency of which is outside the gain band of the space maser, is considered. It is shown that in this case, due to the long lifetime of the excited states of interstellar gas molecules, the signal propagates at superluminal velocity with practically no change in amplitude, which is very rare in problems of this type.
Recently a measurement of the velocity of longitudinal ultrasonic waves propagating through a phonon maser amplifier showed that the pulse traveled with the maximum or cutoff velocity at resonance. With an approximate dispersion rule for a homogeneously broadened spin-resonance transition, the propagation of the wave is analyzed using a method for the asymptotic expansion of Fourier-type integrals. This analysis, contrary to earlier studies, indicates that the pulse observed, or at least the leading edge of that pulse, was an amplified precursor (transient response). For a sinusoidal imput signal, the asymptotic wave form at a given position is given for all possible values of the time.
For electromagnetic propagation in linear dispersive media, two definitions of energy transport velocity may be introduced. The first is the transport velocity of total stored energy density, and it was first discussed by Brillouin. This concept does not distinguish different forms of energy, but considers only the total. It is equal to the group velocity for the case of a lossless dispersive medium. Its significance is not fully understood for a maser medium where it is either greater than the velocity of light or negative, or for a dissipative dispersive medium where it does not seem to offer a simple description of the propagation process. The second is the transport velocity of electromagnetic energy. It is based on the distinction of propagating energy which is just electric and magnetic field energy, from localized energy which is stored in the degrees of freedom of the dispersive medium. Thus propagation involves electromagnetic propagation per se, plus a transfer of energy between the propagating and localized forms. This transport velocity is always less than the velocity of light, for absorbing and maser media alike. It may be determined through a gain or attenuation measurement since it enters the gain equation of electromagnetic transmission structures.
Abstract This paper considers the question of superluminal (or negative) group velocities of signals in dispersive media, as well as negative group delay times of signals passing through linear filters. It is shown that information can be transmitted only with the help of jumps in the time dependence of a function or its derivatives and, therefore, the information propagation velocity in any (including dispersive, absorbing, or amplifying) medium exactly coincides with the speed of light in vacuum. As for the group velocity of a wave packet, it is only the propagation velocity of its infinitely differentiable envelope, by means of which the transmission of information, strictly speaking, is impossible. Therefore, in regions with anomalous dispersion, the group velocity can be superluminal or negative without violating the “light limitation” of the theory of relativity or the principle of causality. Examples of situations in which superluminal or negative group velocity occurs are given.
Energy exchange between an electromagnetic pulse and dispersive media may result in complicated, yet interesting, phenomena in which the group velocity becomes abnormal (i.e., superluminal or negative). For such cases, signal velocity (velocity of detectable information) remains debatable. In this chapter, we present a systematic study that can be applied to pulse propagation in any dispersive medium in order to quantify the detectable information content and calculate its speed, while accounting for pulse reshaping effects and noise generated in the medium and the detector. Accordingly, we present an operational context within which the constraints of superluminal signaling and its potential applications are shown. We provide scenarios in which the signal velocity is evaluated in microwave circuits with negative group delays and extend the method to include optical pulses in inverted media as well. Such analysis explores the fundamental limitations and capabilities of a broad range of superluminal signaling applications.
The interaction between an electromagnetic (em) pulse and a maser medium is described by a general set of five equations, under the assumption of a homogeneously broadened electric-dipole transition with two Bloch relaxation times T2and T1and of a linear broadband loss mechanism. When the equations are specialized at resonance, their solutions include the results of the previous treatments on the amplifier problem obtained under particular assumptions. The steady-state pulse (S. S. P.) introduced by Wittke and Warter forT_{2}/T_{1} = 0is here generalized forT_{2}/T_{1} \neq 0and it is shown to propagate at the same velocity of the light in the medium. In the caseT_{2}/T_{1} = 0the steady state is described by exact analytical relations. For times short in comparison to the relaxation times, a solution is given which generalizes the usual interaction formula between an em field and a two-level system by introducing propagation effects. In the general case out of resonance, it is shown that an S. S. P. exists, and that its frequency coincides with the frequency of the atomic transition, independent of the frequency of the input field.