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Annalen der Physik

Quantenmechanische Behandlung des Lasers mit nichtresonanter Rückkopplung. I Berechnung von Photonenzahl und Amplitudenfluktuation

W. Brunner, Henryk Paul

Published Jan 1, 1969• 6 citations
Publisher

Abstract

The interaction between M modes of the radiation field and an active medium in a laser with nonresonant feedback (one of the laser mirrors is substituted by a diffusely reflecting medium) is studied in the HEISENBERG picture. In agreement with [3] the amplitude of the total radiation is found to be stabilized due to the nonlinear interaction, while the radiation corresponding to any of the M modes has properties characteristic of thermal radiation.

DOI
10.1002/andp.19694780306

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In the model introduced in a preceding paper [1] (in which only the homogeneous broadening of the atomic levels is taken into account and the radiation field is assumed to be monochromatic) the first and second order correlation functions for the radiation field in one mode as well as for the total field are calculated explicitly by solving the HEISENBERG equations for the photon creation and annihilation operators b+λ, bλ and the operator \documentclass{article}\pagestyle{empty}\begin{document}$ Q \equiv \sum\limits_\lambda {b_\lambda ^ + } b_\lambda $\end{document} representing the total photon number. The linewidth of the radiation (which is the same for a single mode and the total radiation field) is found to be 2M‐times (M number of modes) larger than in the corresponding case of 1‐mode operation with the same total photon number.

Annalen der Physik•Jan 1, 1969•5 citations
The interaction between M modes of the radiation field and an active medium in a laser with nonresonant feedback (one of the laser mirrors is substituted by a diffusely reflecting medium) is studied in the HEISENBERG picture. In agreement with [3] the amplitude of the total radiation is found to be stabilized due to the nonlinear interaction, while the radiation corresponding to any of the M modes has properties characteristic of thermal radiation.
Abstract Using the quantum mechanical equations describing the laser process we calculate the photon number and the amplitude fluctuations of the laser radiation for the stationary case, if the atomic frequencies are assumed to be distributed inhomogeneously in form of a LORENTZ line. It is shown, that, on principle, the results in comparision with the case of homogeneously broadened atomic line are unchanged. However, the photon number and therefore especially the threshold condition for the laser effect as well as the amplitude fluctuations are changed quantitatively in general due to the dependence of the line width 2ϵ of the LORENTZ line.
Abstract Making use of the eigenfunctions of the total Hamiltonian, the correlation function 〈𝔈̂(−) (t1) 𝔈̂(+) (t2)〉 is calculated explicitly for a one‐mode radiation field interacting incessantly with an atom. In the frequency spectrum following from this correlation function there appear frequency shifts corresponding, just as in [7], in one case, to a change of the effective dielectric constant within the cavity due to the atom, and, in the other case, to an amplitude modulation due to the alternating absorption and emission of a photon by the atom.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
The spectral perturbation is considered in a semiconductor active medium in the vicinity of the frequency of a strong electromagnetic wave. The nonlinear interaction of waves via the dynamic interference grating, or nonlinear scattering by population waves leads to the shift of resonance frequencies, which is manifested, in particular, in a change of the mode-beating spectrum of the laser. The spectral profile of this perturbation depends on the amplitude—phase coupling factor α. For large α, the profile becomes symmetrical in detuning from the strong-mode frequency. A change in the group refractive index corresponding to the 'slowing' of light is also calculated.
In the model introduced in a preceding paper [1] (in which only the homogeneous broadening of the atomic levels is taken into account and the radiation field is assumed to be monochromatic) the first and second order correlation functions for the radiation field in one mode as well as for the total field are calculated explicitly by solving the HEISENBERG equations for the photon creation and annihilation operators b+λ, bλ and the operator \documentclass{article}\pagestyle{empty}\begin{document}$ Q \equiv \sum\limits_\lambda {b_\lambda ^ + } b_\lambda $\end{document} representing the total photon number. The linewidth of the radiation (which is the same for a single mode and the total radiation field) is found to be 2M‐times (M number of modes) larger than in the corresponding case of 1‐mode operation with the same total photon number.