Polarization states and coherent effects in a coherently pumped J 9 Ä 1 \J Ä 0 \J 8 Ä 1 isotropic-cavity laser A. Kul’minskii, 1, * R. Vilaseca, 1 R. Corbala ´ n, 2 and N. Abraham 3 1 Departament de Fı ´sica i E. N., Universitat Polite ´cnica de Catalunya, Colom 11, E-08222 Terrassa, Barcelona, Spain 2 Departament de Fı ´sica, Universitat Auto `noma de Barcelona, E-08193 Bellaterra, Spain 3 Physics Department, DePauw University, Greencastle, Indiana 46135-0037 ~Received 24 May 1999; revised manuscript received 22 October 1999; published 17 August 2000! We have theoretically explored the behavior of a coherently pumped J 9 51 →J 50 →J 8 51 isotropic cavity laser and compared it with the behavior of other related laser systems involving atomic or molecular levels with angular quantum numbers 0 and 1. It is shown that at low and moderate pumping strengths it behaves very differently from the J 9 50 →J 51 →J 8 50 laser exhibiting no pump-induced gain anisotropy and allow- ing for linearly polarized ~LP! solutions with arbitrary azimuth and circularly polarized ~CP! solutions, de- pending on the values of the molecular relaxation rates. Above the instability threshold, a variety of dynamic regimes involving the polarization degree of freedom can be found, including LP states with rotating azimuth ~as in incoherently pumped J 50 →J 8 51 or J 51 →J 8 50 lasers!, antiphase dynamics, and full polarization chaos. PACS number~s!: 42.55.Lt, 42.60.Mi, 42.25.Ja, 42.55.Ye I. INTRODUCTION The dynamical behavior of lasers is markedly different in two large classes distinguished by their pumping methods. One method involves incoherent processes ~such as, for in- stance, electrical discharge or light from conventional lamps!, whereas the other one is based on a coherent pump- ing process ~typically by means of the light from another laser! in which the pumping and lasing transitions share the common upper level. Two fundamental differences between coherently ~optically! and incoherently pumped lasers are known. First, since a laser is generally a source of polarized emission, a polarized pumping beam can break the cylindri- cal symmetry of the optically pumped laser, even in the case of a perfectly isotropic cavity. Second, coherent pumping induces two-photon ~Raman! processes which are absent in an incoherently pumped laser. The dynamic behavior of these types of lasers has been a subject of extensive investigations @1–3#. However, the prob- lem was typically simplified by the assumption that the laser field had fixed polarization, reducing the vector problem to a scalar one. This simplification was justified by the fact that many lasers were fabricated with Brewster’s angle windows or other anisotropic elements which imposed a fixed polar- ization state. Recently, the situation has changed. The benefits of the polarization ~or vector! degrees of freedom for solving dif- ferent fundamental and applied problems has renewed the interest in vector systems in general, and in laser systems in particular @4–6#. A large amount of work has already been devoted to different aspects of the static and dynamic behav- ior of vector laser systems, although most of the work has been devoted to lasers with incoherent pumping. The influ- ence of the vectorial degrees of freedom on the behavior of lasers with coherent pumping has been less well studied @7–11#, although it is evident that polarization freedom should greatly affect their behavior. Until recently, theoretical studies of vectorial coherently pumped lasers have been restricted to the simplest case which permits full vectorial behavior. In particular, this is the case in which the gain medium is modeled by three-level J 9 50 →J 51 →J 8 50 atoms with the pumping acting on the J 9 50 →J 51 transition which is adjacent to the laser ( J 51 →J 8 50) transition. The Zeeman structure of the upper manifold ( J 51) enables one to take into account the vecto- rial degrees of freedom for both pumping and emitted fields. Strong gain anisotropy that favors emission with polarization identical to that of the pump field @7#, polarization switching @8#, and even full polarization chaos @9,10# have been found in such a system. However, one may wonder whether the interesting polar- ization phenomena encountered in the coherently pumped laser are specific to the particular atomic configuration con- sidered, i.e., the J 9 50 →J 51 →J 8 50 level scheme, or are more general, i.e., weakly sensitive on the particular values of the atomic level quantum numbers J, J 8 , J 9 . This is an interesting question that arises naturally in the case of, for instance, optically pumped far-infrared molecular lasers. Most of these lasers are coherently pumped by means of a CO 2 or N 2 O laser @with wavelengths ranging in the midin- frared ( l;10 m m) # and their emission wavelength lies in the range 502500 m m @12#. With, for instance, the NH 3 laser ~one of the most efficient far-infrared lasers!, landmark contributions to nonlinear dynamics have been achieved in the past, in particular the first experimental demonstration, in science, of the dynamics of the paradigmatic Lorenz model @13#. The dynamics of this laser, however, are strongly sen- sitive to the quantum numbers of the molecular levels in- volved in the pumping-lasing process @for instance, Lorenz- *Permanent address: Institute of Molecular and Atomic Physics, National Academy of Sciences, F. Skarina Ave., 70, 220072 Minsk, Belarus. PHYSICAL REVIEW A, VOLUME 62, 033818 1050-2947/2000/62~3!/033818~13!/$15.00 ©2000 The American Physical Society 62 033818-1