Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry, stability, and computation of degenerate lasing modes   We present a general method to obtain the stable lasing solutions for the
steady-state ab-initio lasing theory (SALT) for the case of a degenerate
symmetric laser in two dimensions (2d). We find that under most regimes (with
one pathological exception), the stable solutions are clockwise and
counterclockwise circulating modes, generalizing previously known results of
ring lasers to all 2d rotational symmetry groups. Our method uses a combination
of semi-analytical solutions close to lasing threshold and numerical solvers to
track the lasing modes far above threshold. Near threshold, we find closed-form
expressions for both circulating modes and other types of lasing solutions as
well as for their linearized Maxwell--Bloch eigenvalues, providing a simple way
to determine their stability without having to do a full nonlinear numerical
calculation. Above threshold, we show that a key feature of the circulating
mode is its "chiral" intensity pattern, which arises from spontaneous
symmetry-breaking of mirror symmetry, and whose symmetry group requires that
the degeneracy persists even when nonlinear effects become important. Finally,
we introduce a numerical technique to solve the degenerate SALT equations far
above threshold even when spatial discretization artificially breaks the
degeneracy.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph