This paper investigates dynamics of
semiconductor lasers under optical feedback during
transitions to chaos. Influence of the external-cavity length
on the route-to-chaos is elucidated. The study is based on
numerical solution of a time-delay model of rate equations.
The route to chaos is period doubling when the ratio of the
relaxation frequency to the external-cavity resonance
frequency is less than unity. The route is sub-harmonic
when the frequency ratio is slightly higher than unity, and
is quasi-periodic characterized by the compound-cavity
frequency and the relaxation frequency as well as their
difference when the ratio is far above unity