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Resonant quasiperiodic patterns in a threedimensional lasing medium
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UNSPECIFIED. (1997) Resonant quasiperiodic patterns in a threedimensional lasing medium. PHYSICAL REVIEW A, 56 (1). pp. 803812. ISSN 10502947
Full text not available from this repository.Abstract
Starting from the MaxwellBloch equations for a threedimensional (3D) ringcavity laser, we analyze stability of the nonlasing state and demonstrate that, at the instability threshold, the wave vectors of the critical perturbations belong to a paraboloid in the 3D space. Then, we derive a system of nonlinear evolution equations above the threshold. The nonlinearity in these equations is cubic. For certain sets of four spatial modes whose vectors belong to the critical paraboloid, the cubic nonlinearity gives rise to a resonant coupling between them. This is a nontrivial example of a nonlinear dissipative system in which the cubic terms are resonant. The equations for the four coupled amplitudes have two different solutions that are simultaneously stable: the singlemode one and a solution in which all the amplitudes are equal, while a certain combination of the phases is pi. The latter solution gives rise to a quasiperiodic pattern in the infinite 3D cavity. We also consider effects of the boundary conditions and demonstrate that if the cavity's cross section is a trapezium it may support the quasiperiodic fourmode state rather than suppressing it. Using the Lyapunov function, we find that for the ringlaser configuration the fourmode state is metastable. However, we demonstrate that for a FabryPerot cavity, where diffusion washes out the standingwave grating, this state is absolutely stable. We also consider a number of more complicated patterns. We demonstrate that adding a pair of resonant vectors, or any number of nonresonant ones, always produces an unstable solution. A set containing several resonant quarters without resonant coupling between them may be stable, but it is less energetically favorable than a single quartet.
Item Type:  Journal Article  

Subjects:  Q Science > QC Physics  
Journal or Publication Title:  PHYSICAL REVIEW A  
Publisher:  AMERICAN PHYSICAL SOC  
ISSN:  10502947  
Official Date:  July 1997  
Dates: 


Volume:  56  
Number:  1  
Number of Pages:  10  
Page Range:  pp. 803812  
Publication Status:  Published  
URI:  http://wrap.warwick.ac.uk/id/eprint/17557 
Data sourced from Thomson Reuters' Web of Knowledge
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