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Physical Review A

Study of the Frequency-Locking Region of a Monomode Anisotropic Zeeman Laser

A. Le Floch, Guy Michel Stéphan

Published Aug 1, 1972• 14 citations
Publisher

Abstract

The experimental study of polarization in a Zeeman laser with strong $x\ensuremath{-}y$-type anisotropies makes evident the rotations of the electric field vector greater than the limiting value of $\frac{1}{4}\ensuremath{\pi}$ which is fixed by the self-consistent theory. The results are in agreement with the vectorial theory based on the resonance condition, which is necessary for the representation of such a type of quantum oscillator with nonreciprocal effects (including anisotropies). The self-consistent theory appears to provide a limit which becomes valid only for very weak anisotropies. Only the polarization of the so-called "Lamb's vector" can be described by the self-consistent theory and its rotation effectively attains $\frac{1}{4}\ensuremath{\pi}$ whatever the value of the anisotropy.

DOI
10.1103/physreva.6.845

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Physical Review A•Jul 1, 1992•36 citations
The experimental study of polarization in a Zeeman laser with strong x\ensuremath−yx\ensuremath{-}yx\ensuremath−y-type anisotropies makes evident the rotations of the electric field vector greater than the limiting value of 14\ensuremathπ\frac{1}{4}\ensuremath{\pi}41​\ensuremathπ which is fixed by the self-consistent theory. The results are in agreement with the vectorial theory based on the resonance condition, which is necessary for the representation of such a type of quantum oscillator with nonreciprocal effects (including anisotropies). The self-consistent theory appears to provide a limit which becomes valid only for very weak anisotropies. Only the polarization of the so-called "Lamb's vector" can be described by the self-consistent theory and its rotation effectively attains 14\ensuremathπ\frac{1}{4}\ensuremath{\pi}41​\ensuremathπ whatever the value of the anisotropy.
It has already been reported that a laser subject to an axial magnetic field and having end mirrors which exhibit relatively high $x\ensuremath{-}y$-type loss anisotropy can be described by two theoretical methods. The first method uses self-consistent-field equations with distributed losses, whereas the second one is based on a resonance condition for a complete round-trip pass. The following study of a Zeeman laser with different $x\ensuremath{-}y$-type loss anisotropy at each mirror shows that the localization of the losses and the nonreciprocal character of the Farady rotation require a different formulation for each initial system. The rotation of the plane of polarization is different at each end of the laser, but it is shown that there always exists for central tuning a real or virtual average polarization vector which obeys Lamb's theory. The equivalence of the two methods is discussed.
The Lamb theory of the optical maser is applied to circularly polarized atomic transitions, and used to consider the beat frequencies and the coherence properties of such orthogonal fields when axial magnetic fields are applied to the gaseous laser. The beat frequency approaches zero in near-zero magnetic fields and synchronization can then occur between the right- and left-handed circularly polarized oscillations. For a resonator with no undue polarization constraint, such a strong coupling gives rise to a linearly polarized output, and to a rotation of the plane of polarization with increasing magnetic field. A self-consistent expression is derived for this rotation under steady-state conditions, and a maximum rotation of $\ifmmode\pm\else\textpm\fi{}\frac{1}{4}\ensuremath{\pi}$ with magnetic field is indicated before the synchronization breaks down and circularly polarized beat phenomena appear. The rotation with magnetic field depends on the laser intensity, on the anisotropy in the cavity losses, and on the position of the cavity resonance within the Doppler linewidth. Also, the angle of rotation is indeterminate unless such anisotropy is present. Other regions of such coherence can occur at higher magnetic fields, where the beat frequency again approaches zero. These depend on the detailed shape of the various dispersion curves of the laser medium. The results derived from the theory used are in general agreement with experimental observations on the 1.153-\ensuremath{\mu} He-Ne laser transition.
The dynamics of a quasi-isotropic continuous-wave solid-state laser sustaining the oscillation of two orthogonally polarized eigenstates is experimentally investigated. A set of phase-sensitive vectorial Maxwell-Bloch equations is developed to describe theoretically the evolution of such a laser. Different temporal behaviors for the output intensities are observed, depending on the relative amounts and orientations of the phase and loss anisotropies and on the frequency of relaxation oscillations. Namely, the frequency locking of the two orthogonally linearly polarized eigenstates is shown to lead to a surprising pulsed mode-locked oscillation regime. In addition, for different values of the parameters, other peculiar operation regimes are found, such as cw circularly polarized, double-pulsed, or triple-pulsed output intensities. These experimental results, obtained using a diode-pumped Nd:YAG (YAG denotes yttrium aluminum garnet) laser, are well confirmed by the theoretical model.
The all-optical control of the polarization in a vectorial bistable monomode laser by injection with a second laser is analyzed theoretically and performed experimentally. The polarization is shown to switch following either an externally induced rotation or an externally induced inhibition mechanism. The usual theory of scalar-locking phenomena is extended to vectorial systems. We show that there is a single locking range in the induced rotation process occurring for low phase anisotropy values, whereas there are two distinct locking ranges in the induced inhibition process for higher anisotropy values. The theoretical results are in good agreement with experiments realized with 3He–20Ne lasers. By scanning the injected signal frequency, optical gates with high signal-to-noise ratios are experimentally obtained.
The general theory of a Zeeman laser given in part I is used to analyze laser operation in axial and transverse magnetic fields. The analysis is illustrated by graphs of intensities and beat frequencies versus cavity detuning and magnetic field strength. Among the topics discussed are frequency-locking effects due to cavity anisotropy, the dependence of competition between polarization modes on magnetic field strength for various atomic angular momenta, and the measurement of atomic decay rates and ggg values using a laser in a magnetic field.
The basic mechanisms of the polarization switching in vectorial bistable lasers are studied both theoretically and experimentally versus internal parameters. In particular, by scanning the frequency of a gas laser with two linearly polarized eigenstates, two quite different flipping processes with hysteresis occur according to the linear-phase-anisotropy value of the cavity. Indeed, when the anisotropy increases, rotation and inhibition mechanisms appear successively. The variations of the hysteresis loop for different anisotropy and excitation values are theoretically found to be opposed in the two processes. Additional evolutions of the polarization, such as multiple switchings in the inhibition mechanism and ``hybrid'' hysteresis loops, are predicted. The experiments, essentially performed on a monomode 3.39-\ensuremath{\mu}m $^{3}\mathrm{\ensuremath{-}}^{20}$Ne laser containing an adjustable linear phase anisotropy, confirm the existence of the two processes and their corresponding properties. These processes may also occur in other quasi-isotropic lasers versus other internal parameters, such as, for instance, the injection current in semiconductor lasers. In this case the TE and TM modes flip only in the inhibition mechanism when the bistability conditions are satisfied. The knowledge of the basic flipping mechanisms in the laser itself enables us to understand and realize the external optical-polarization control by an anisotropic feedback (one-frequency systems). Induced-rotation and induced-inhibition mechanisms are then theoretically predicted and experimentally verified. Sensitive optical gates are realized by varying the feedback phase in both processes.