We report experimental realization of high-dimensional chaos in a semi
conductor laser with delayed feedback from a T-shaped cavity. We study
the transition phenomena from regular to high-dimensional chaotic beh
avior and analyze the time series quantitatively. Correlation dimensio
ns up to C-2 similar or equal to 7 are determined reliably from experi
mental data by a combination of a singular value analysis and a Grassb
erger-Procaccia algorithm. Modeling the dynamical behavior using semic
lassical delay rate equations provides a basic understanding of the ob
served delay-induced instabilities.