TY - JOUR
T1 - Computationally determined existence and stability of transverse structures. I. Periodic optical patterns
AU - Harkness, G.K.
AU - Firth, W.J.
AU - Oppo, G.L.
AU - McSloy, J.M.
PY - 2002/10
Y1 - 2002/10
N2 - We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.
AB - We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.
KW - transverse structures
KW - optics
KW - optical cavity
KW - waves
KW - photonics
UR - http://dx.doi.org/10.1103/PhysRevE.66.046605
U2 - 10.1103/PhysRevE.66.046605
DO - 10.1103/PhysRevE.66.046605
M3 - Article
SN - 1063-651X
VL - 66
SP - 46605
EP - 46601
JO - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 4
ER -