This paper investigates numerically influence of the external-cavity length on the type of the route-to-chaos
of semiconductor lasers under external optical feedback. The study is based on numerical solution of a
time-delay model of rate equations, and the solutions are employed to construct bifurcation diagrams and
to examine the Fourier frequency spectrum of the laser output. The ratio of the relaxation frequency to the
external-cavity resonance frequency is employed to measure the influence of the length of the external
cavity. The route-to-chaos is period doubling when this frequency ratio is less than unity. The route is subharmonic
when the frequency ratio increases up to 2.25. When the frequency ratio increases further, the
transition to chaos becomes quasi-periodic characterized by the compound-cavity frequency and the
relaxation frequency as well as their difference.