Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tight-binding methods for general longitudinally driven photonic
  lattices -- edge states and solitons   A systematic approach for deriving tight-binding approximations in general
longitudinally driven lattices is presented. As prototypes, honeycomb and
staggered square lattices are considered. Time-reversal symmetry is broken by
varying/rotating the waveguides, longitudinally, along the direction of
propagation. Different sublattice rotation and structure are allowed. Linear
Floquet bands are constructed for intricate sublattice rotation patterns such
as counter rotation, phase offset rotation, as well as different lattice sizes
and frequencies. An asymptotic analysis of the edge modes, valid in a
rapid-spiraling regime, reveals linear and nonlinear envelopes which are
governed by linear and nonlinear Schrodinger equations, respectively. Nonlinear
states, referred to as topologically protected edge solitons are unidirectional
edge modes. Direct numerical simulations for both the linear and nonlinear edge
states agree with the asymptotic theory. Topologically protected modes are
found; they possess unidirectionality and do not scatter at lattice defect
boundaries.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys