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Journal of Communications Technology and Electronics

On the Distortion of the Leading Edge of a Quasi-Monochromatic Signal in a Resonantly Absorbing Medium

Nikolai S. Bukhman

Published Mar 1, 2019• 2 citations
Publisher

Abstract

Abstract The paper is concerned with the distortion of a sharp leading edge of a quasi-monochromatic electromagnetic (light or radio) signal (wave packet) propagating in a medium with an absorption line (or band). It is shown that the frontal jump of the complex envelope of a radio signal propagates without changing its magnitude. Behind the leading edge, the signal level decreases with a rate increasing with the path length. As a result, the leading and trailing (if it exists) edges of the signal acquire tooth kinks, which become more and more acute with increasing path length. Such tooth kinks are formed not only at the points of discontinuity of the real amplitude of a signal but also at the points of discontinuity of its phase; therefore, the propagation of a phase-shift keyed radio signal in a resonantly absorbing medium is accompanied by its “self-disclosure”.

DOI
10.1134/s1064226919030045

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Abstract The paper is concerned with the distortion of a sharp leading edge of a quasi-monochromatic electromagnetic (light or radio) signal (wave packet) propagating in a medium with an absorption line (or band). It is shown that the frontal jump of the complex envelope of a radio signal propagates without changing its magnitude. Behind the leading edge, the signal level decreases with a rate increasing with the path length. As a result, the leading and trailing (if it exists) edges of the signal acquire tooth kinks, which become more and more acute with increasing path length. Such tooth kinks are formed not only at the points of discontinuity of the real amplitude of a signal but also at the points of discontinuity of its phase; therefore, the propagation of a phase-shift keyed radio signal in a resonantly absorbing medium is accompanied by its “self-disclosure”.
Propagation of a short quasi-monochromatic electromagnetic (light or radio) signal (wave packet) is considered. The carrier frequency of the signal is close to the frequency of the absorption spectral line (or group of lines) of a medium, and the spectrum width is large relative to the width of this spectral line (or group of lines). Analytic formulas for the temporal dependence of the signal are derived and numerically confirmed for paths of various lengths. It is shown that the signal is substantially distorted long before it noticeably decays owing to absorption. The signal’s temporal dependence turns out to be rather universal with respect to the form factor of the spectral line, the optical thickness of the substance layer, and the initial temporal dependence of the signal.
The propagation of a narrow-band signal (wave packet) in a medium with population inversion is considered. It is shown that in an optically thick medium layer the signal decomposes into the initial and amplified signals propagating at different velocities and having different durations. The initial signal propagates without distortions at the velocity c / n 0 ( n 0 is the refractive index of the medium away from the resonance frequency) and plays the role of a precursor of the amplified signal. The amplified signal moves at a lower velocity. It lags behind the initial signal during propagation and acquires a universal Gaussian shape (irrespective of the shape of the initial signal and the spectral line profile). The appearance of the amplified signal, which substantially differs from the initial signal in all the parameters, as well as the interference between the amplified and initial signals looks like a 'extra-distortion' of the initial signal.
It is shown that, when a narrow-band signal with a non-Gaussian envelope propagates in a medium with a strong dispersion, the signal envelope being distorted due to the dispersion of the gain (or) absorption in the medium. Nevertheless, the amplitude-modulated signal having a symmetric (even) intensity envelope remains the same. The propagation velocity of the `middle point' (i.e., the symmetry centre) of the signal coincides with the real group velocity of the wave with a given carrier frequency in the medium and can be subluminal, superluminal or negative. Therefore, the concept of a real group velocity (including the superluminal or negative velocity) is also applicable in media with a strong dispersion of the gain (or absorption).
It is shown that the absorbtion of a weak field in a thick resonant absorber is a reversible process even in the case of the homogeneous broadening of the absorption line. As an example, the propagation of a long rectangular pulse with sharp edges in an optically dense resonant medium is studied theoretically in the linear response approximation. Transient nutation (TN), free induction decay (FID), and transients, induced by the phase switch of the incident pulse, are considered. It is shown that in exact resonance the amplitude of FID increases with the length of the medium. FID arises due to the scattered radiation field (dipoles ringing). In a thick medium the scattered field is almost of the same amplitude but opposite in phase with the incident radiation field. Both fields interfere destructively to produce what is seen as radiation damping at the output of the medium. The scattered field needs time to develop. Therefore, the leading edge of the pulse is not absorbed, demonstrating temporal transparency followed by TN. Phase shift (180${}^{\ensuremath{\circ}}$) of the pulse brings the incident pulse in phase with the scattered radiation. Constructive interference of the pulse with the scattered radiation field produces a short pulse with an amplitude that is two times larger than the amplitude of the incident pulse. If the input pulse is detuned from resonance, for a particular detuning and optical thickness of the medium the amplitude of the transient pulse, induced by the phase shift, is nearly three times larger than the amplitude of the incident pulse. This is explained by the interference of the scattered field, the phase-shifted input field, and the slowly propagating part of the pulse, developed before the phase shift.
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.
The phenomena which take place during the time of propagation of a monochromatic pulse of a resonance radiation through optically dense on the transition frequency medium containing resonance absorbing centers are considered. Due to the action of the pulse of the resonance radiation the saturation of absorption in the layer of the medium takes place. As a result the absorption decreases in the layer and the radiation penetrates into the next layer. Thus translucent region continuously moves deeper into the medium and the process is wavelike.When the density of the initial photon flux is constant and the distribution of absorbing centers is homogeneous the absorption coefficient and the photon density in the depth of the media depends only on the variable $t\phantom{\rule{0.15em}{0ex}}\ensuremath{-}\phantom{\rule{0.15em}{0ex}}x/v$. The velocity of translucency wave v may be by several orders of magnitude less than the velocity of light. The mechanism of the saturation can be various. The small value of the loss of photons in the transluced region of the medium is the necessary condition for the rise of translucent waves. The condition of realization of translucent wave is fulfilled for a large number of condensed states having intense absorption lines. These conditions are the most favourable in the case of presence of methastable levels between the levels 1 and 2 (type-ruby system). The effect of the translucent waves is general for various ranges of spectrum of electromagnetic radiation and may be realized in astrophysical scale.