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Journal of Optoelectronics·laser

Transverse Effect of Field in an Open V-type Inversionless Lasing System

Fan Xi

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The transverse effect of the fields was studied by densitymatrix equations of motion in an open Vtype system and Hurwitz criteria.The result shows that comparing with the case in the plane wave approximation,the transverse profile of the field leads to an obvious variation of the fashion that the system obtains inversionless lasing through instability of nonlasing solution,and makes the system more easy to obtain inversionless lasing through instability of pitchfork bifurcation;the value of the ratio of the active medium transverse section to the beam waist has a determinant effect on size of the instability region in which inversionless lasing arises,and the Raman inversion region increases with increasing of value of the ratio;the effects of unsaturated gain,loss of laser cavity,the ratio of atomic injection rates and atomic exit rate varying on the instability region in which inversionless lasing arises are much different from that in the plane wave approximation case.

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The transverse effect of the fields was studied by densitymatrix equations of motion in an open Vtype system and Hurwitz criteria.The result shows that comparing with the case in the plane wave approximation,the transverse profile of the field leads to an obvious variation of the fashion that the system obtains inversionless lasing through instability of nonlasing solution,and makes the system more easy to obtain inversionless lasing through instability of pitchfork bifurcation;the value of the ratio of the active medium transverse section to the beam waist has a determinant effect on size of the instability region in which inversionless lasing arises,and the Raman inversion region increases with increasing of value of the ratio;the effects of unsaturated gain,loss of laser cavity,the ratio of atomic injection rates and atomic exit rate varying on the instability region in which inversionless lasing arises are much different from that in the plane wave approximation case.
Begin with the density matrix equations of motion under the conditions of the rotating wave,slowly varying amplitude and mean field approximations,by using the numerical calculation results,the time evolution laws of the probe laser field and populations corresponding to two cases in producing inversionless lasing (i.e.,through the Pitchfork bifurcation giving rise to continuous wave lasing emission and through the Hopf bifurcation giving rise to self-pulsing lasing emission) in an open V-type resonant system are studied,and the effects of the system parameters varying on the time evolution laws are discussed.
A way resulting in lasing without inversion (LWI) in an open resonant ?-type system from a nonlinear dynamics viewpoint is investigated. The destabilization of the non-lasing solution can occur not only through pitchfork bifurcation, giving rise to continuous wave LWI, but also through Hopf bifurcation, giving rise to self-pulsing LWI. This is much different from that of the corresponding closed resonant ?-type system in which the destabilization of the non-lasing solution can occur only through pitchfork bifurcation. The effects of the unsaturated gain coefficient, cavity loss coefficient, atomic injection and exit rates on the two bifurcations are discussed.
A way resulting in lasing without inversion (LWI) in an open resonant A-type system from a nonlinear dynamics viewpoint is investigated. The destabilization of the non-lasing solution can occur not only through pitchfork bifurcation, giving rise to continuous wave LWI, but also through Hopf bifurcation,giving rise to self-pulsing LWI. This is much different from that of the corresponding closed resonant A-type system in which the destabilization of the non-lasing solution can occur only through pitchfork bifurcation. The effects of the unsaturated gain coefficient, cavity loss coefficient, atomic injection and exit rates on the two bifurcations are discussed.
Theoretical model of an open four-level atomic system driven by two fields was presented. The density matrix equations of motion were obtained by the electric dipole and the rotating wave approximations. Under resonance of corresponding fields, the physical mechanism of lasing without inversion (LWI) was discussed and its linear analytical solution was obtained. By numerical results, we studied the effects of the spontaneous decay rates between atomic levels, incoherent pump rate, the injection rates, and the exit rate on the gain without inversion and the population difference of the system. The difference between the linear and nonlinear gain and the population difference of the system were discussed. A LWI gain was got during the region of the spontaneous decay rates between atomic levels. The LWI gain can obtain by adjusting suitably incoherent pump rate, the atomic injection ratio and the exit rate. The curves of the linear gain and the nonlinear gain were similar with the Rabi frequencies of the driving fields. The curves of the linear population difference and the nonlinear population difference were similar too. The linear stable value of the gain was larger than the nonlinear stable value of the gain.
The model of an open four-level atomic system is presented on the basis of the closed four-level atomic system. In the rotating wave, slowly varying envelope and mean field approximations, the density-matrix motion equations of the system are solved, and the linear analytical solution in the steady state is obtained. The numerical calculation from the steady-state solution of the open system is presented. It is shown that a change from LWI to lasing with inversion action can occur due to the Rabi frequency of the driving field increasing; another change from lasing with inversion to LWI action can also occur as the exit rate or ratio of injection rates increases; high refractive index without absorption can be obtained; the curve of ρ33-ρ11(vs Δ2) presents the shape of the rectangle wave.