  For the asymptotic string solution in AdS_3 which is represented by the AdS_3
Poincare coordinates and yields the planar multi-gluon scattering amplitude at
strong coupling in arXiv:0904.0663, we express it by the AdS_4 Poincare
coordinates and demonstrate that the hexagonal and octagonal Wilson loops
surrounding the string surfaces take closed contours consisting of null vectors
in R^{1,2} owing to the relations of Stokes matrices. For the tetragonal Wilson
loop we construct a string solution characterized by two parameters by solving
the auxiliary linear problems and demanding a reality condition, and analyze
the asymptotic behavior of the solution in R^{1,2}. The freedoms of two
parameters are related with some conformal SO(2,4) transformations.
