Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theory of the spatial structure of non-linear lasing modes   A self-consistent integral equation is formulated and solved iteratively
which determines the steady-state lasing modes of open multi-mode lasers. These
modes are naturally decomposed in terms of frequency dependent biorthogonal
modes of a linear wave equation and not in terms of resonances of the cold
cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found
to have non-trivial spatial structure even in the single-mode limit. In the
multi-mode regime spatial hole-burning and mode competition is treated exactly.
The formalism generalizes to complex, chaotic and random laser media.

19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ