The nonlinear susceptibility of a gas of molecules under level crossing in a single-mode laser field is calculated by an iteration procedure. The higher-order solutions up to the fourth order are explicitly given for arbitrary number of nearly degenerate levels. Contributions of the second-, third-, and fourth-order terms are discussed with particular emphasis on the third-order term. The third-order solution reveals the level-crossing effect in saturated absorption with the half-width almost twice as broad as the Lamb clip when the decay rates of the upper and the lower states are different to some extent. Finally the zero-field level-crossing experiment of methane at 3.39 µm by Luntz et al. is reexamined to result in the pressure broadening of its half-width to be 7.4 MHz/Torr.
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
Abstract Starting from a theory in which laser operation is described as the excitation of the natural modes of an open-resonator system, the case of a Fabry-Perot resonator with plane-parallel mirrors is treated. It is shown that, in the case of weakly anisotropic mirrors, the natural modes can be grouped in pairs, such that each pair corresponds to one scalar longitudinal mode. In that case, laser operation can and will be described in terms of these longitudinal modes, which then possess a vectorial field amplitude, in agreement with the usual formalism. The polarization preference in a single-mode gas laser operating on a transition between a singlet and a triplet state is investigated, taking into account differences in the relaxation constants for the various expectation values of atomic variables. A calculation of the effect on the relaxation constants due to interatomic collisions leads to the conclusion that theory and experiment are in good agreement with each other. Equations describing the time evolution of the polarization parameters of both modes in a two-mode operating gas laser are derived. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case in which the single-mode preference is for circular polarization. The influence of two specific mirror anisotropies is discussed. The polarization behaviour of a single-mode gas laser in the presence of (partly) applied, transverse magnetic fields is extensively dealt with. It appears to be essential to distinguish between the case in which the magnetic field is applied only to a fraction of the active medium and the case in which the magnetic field is uniform in the entire medium. This distinction is shown to lead to a satisfactory theoretical description of a certain class of experiments. In the case of two other experiments, good agreement with the theory is obtained, by assuming the presence of mirror anisotropies of acceptable kind and size. Finally, the influence of small anisotropies on the degree of polarization of a single-mode gas laser is theoretically investigated, when the latter is polarized by means of a strong transverse magnetic field.
In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the
J=2 level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the
J=1 level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the
J=2 level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the
Jb=1 level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.
Expressions are developed in this paper which describe the behavior of a gas laser having generalized polarization characteristics. It is found that degeneracies of the atomic energy levels play an important part in determining the behavior of such a laser since significant terms occur in the nonlinear polarization which are attributable to an oscillatory mixing of these levels. As a result, it is found, for example, that for single-mode operation the field intensity is greatest for either plane or circular polarization depending upon whether a $\ensuremath{\Delta}j=\ifmmode\pm\else\textpm\fi{}1$ or $\ensuremath{\Delta}j=0$ atomic transition is involved in the laser action. For two-mode operation, on the other hand, the behavior depends in a complicated way both on the polarization states of the oscillations and on the degree of degeneracy of the energy levels. This behavior is discussed in a number of special cases.
Using classical fields and the density-matrix formalism, we analyze the nonlinear characteristics of a gas laser amplifier subject to an axial magnetic field, operating with two optical-frequency signals of arbitrary polarization. Perturbational solutions, valid for relatively weak intensities, are obtained which describe the saturation interaction of the signals and the generation of combination tones. An arbitrary amount of Doppler broadening is considered throughout. The simple $J=1\ensuremath{\rightarrow}J=0$ model is found convenient to describe the physical processes taking place. In general, however, the interactions are found to depend on the
J values of the levels. We find that only saturation and no combination-tone generation occurs for two opposite circularly polarized signals, while both effects are, in general, present for two linearly or elliptically polarized fields. The limiting case of zero magnetic field is examined separately. It is also found that in many cases the medium is made effectively anisotropic by the nonlinear interactions. Applications to measurements of atomic parameters such as
J values,
g values, and lifetimes are discussed.