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溶液中の高速移動境界によるレーザ光のドップラー効果

Hiroshi Ito, 辰夫 八木, Shinji Kaitsuka, Kazunori Murakami

Published Jan 1, 1982• 0 citations
Publisher

Abstract

The Doppler frequency shift of an optical wave can be made, not only by moving media, but by a moving boundary in a stationary medium. Especially, the reflected wave by the boundary is shifted by a large amount of the frequency, as the velocity of the boundary approaches the one of the light. The moving boundary in a stationary medium can be produced in a liquid, in nitro-benzene (C_6H_5NO_2) for example, by a high voltage pulse, transmitted along a strip line which is installed in a cell filled with the liquid. This paper describes, theoretically and experimentally, the Doppler frequency shift of a He-Ne laser by the moving boundary. The frequency of the light transmitted to the end of the cell is shifted by about 15MHz. The shifted frequency of the reflected light by the boundary has not, however, been observed yet, because the variation of the refractive index of the medium is too little. From the results of this paper the large amount of the frequency shift of the laser is highly expected if the medium with the large kerr constant is discovered in the near future.

DOI
10.34429/00001873

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The Doppler frequency shift of an optical wave can be made, not only by moving media, but by a moving boundary in a stationary medium. Especially, the reflected wave by the boundary is shifted by a large amount of the frequency, as the velocity of the boundary approaches the one of the light. The moving boundary in a stationary medium can be produced in a liquid, in nitro-benzene (C_6H_5NO_2) for example, by a high voltage pulse, transmitted along a strip line which is installed in a cell filled with the liquid. This paper describes, theoretically and experimentally, the Doppler frequency shift of a He-Ne laser by the moving boundary. The frequency of the light transmitted to the end of the cell is shifted by about 15MHz. The shifted frequency of the reflected light by the boundary has not, however, been observed yet, because the variation of the refractive index of the medium is too little. From the results of this paper the large amount of the frequency shift of the laser is highly expected if the medium with the large kerr constant is discovered in the near future.
Broadening of the satellites of the Hg green line $\ensuremath{\lambda}5461$ was observed when the light passed between the plates of a Kerr cell on which was impressed a varying E.M.F. having a frequency of 2\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 ${\mathrm{sec}}^{\ensuremath{-}1}$. The E.M.F. was obtained by superposing the output of a vacuum tube oscillator upon a steady potential of about 7000 volts. The maximum oscillator voltage was about 5000 volts. With this voltage the fine structure of the Hg green line became so diffuse that two satellites having a separation of 0.045A were scarcely resolved by the Lummer-plate. The broadening was observed to increase rapidly with the oscillator voltage. The observed effect is predicted by the classical electromagnetic theory and the quantum theories of dispersion of Kramers-Heisenburg, Schr\"odinger, and Dirac. The high frequency voltage effects a rapid variation of the refractive index of the nitrobenzene in the Kerr cell which in turn produces a corresponding variation in optical path, giving the source a virtual velocity, and thereby producing a Doppler effect. The magnitude of the observed boradening is in agreement with the predictions of theory.
In Chaps. 8 and 9, we considered a laser medium consisting of homo­ geneously broadened, stationary atoms. When the lasing atoms move as in a gas, they see an electric field with shifted frequency due to the Doppler effect, as shown in Fig. 10-1. One might argue that it is merely necessary to average the complex polarization or the susceptibility Xn over the frequency range corresponding to the velocity distribution, that is, calculate a new ^ n , for which Here the frequency co = coo + Kv, where coo is the frequency at atomic line (1) center, v is the component of velocity along the laser (z) axis, and the frequen­ cy distribution is determined by a Maxwell-Boltzmann velocity distribution W(y) = ( w)-1 exp [ - (v/w)2]. (2) Here u is the most probable speed of the atom, and K is the wave number. The simple recipe (1) is, in fact, valid for an inhomogeneously broadened mediumt consisting of stationary atoms such as ruby at low temperatures. However, in the standing-wave laser, the atoms not only see Doppler-shifted frequencies, but also move through the standing-wave electric field, effectively seeing an amplitude-modulated field. Equivalently, each atom sees two frequencies, for the standing-wave field is the sum of oppositely directed running waves, one of which appears to be Doppler upshifted, one down­ shifted. Hence it is necessary to consider both the frequency shift and the time dependence of the atomic z coordinate when calculating the polarization of a gaseous medium.
We report the experimental observation of a self-reflected wave inside a dense saturable absorber. A femtosecond pulse saturates the absorption and causes a density front to penetrate into the semiconductor. The dielectric constant change across the boundary between areas of low and high densities results in internal reflection. Due to the front propagation the self-reflected light is shifted by the Doppler effect. The Doppler shift makes it possible to distinguish between surface reflection and self-reflection and is used to experimentally verify the dynamic nonlinear skin effect. The measurements are in agreement with our theory which is within the framework of the reduced semiconductor Maxwell-Bloch equations.
In this Rapid Communication, we theoretically discuss a large Doppler shift in a signal slow-light pulse in a photonic-crystal waveguide by considering its reflection at a quasilight speed mirror. The mirror is formed by the photonic band-gap shift induced by the high nonlinearity of a control slow-light pulse, which could be possible in a realistic device. In the simulation, the Doppler shift appears at multiple frequencies due to the Bloch nature of the photonic lattice. Larger but inefficient Doppler shifts occur through nonadiabatic processes, whereas the smallest but more efficient shift (i.e., the intraband Doppler shift) occurs through an adiabatic process. The occurrence of the intraband shift depends on whether the adiabatic process produces a complete reflection of the incident pulse, despite the fact that the pulse penetrates the mirror. A large band-gap shift and a moderately slow mirror satisfy this condition; otherwise, the shift ends at the halfway point.