The fundamental equations describing the coherent light injection locking in semiconductor lasers are derived from semi-classical theory, the multi-branch structure and its stability, the steady modulation characteristic and its stability, several kinds of instability phenomena inside and outside the locking region and their distribution in the parametric plane representing the light injection condition are investigated. It is found that the stability region can only exist near the lower boundary and the right side in the locking region of the highest branch, and a self-pulsation region exists near to it. In the central portion in the rest part of the locking region there exists a chaotic region, between self-pulsation and chaotic regions is the transition region. In this transition region and outside the locking region there are bifurcation of self pulsation of 2p type and non-2p type, beat frequency self-modulation, and their mixed forms, the intermitant relaxation oscilation and intermiting chaos, etc., and several new routes to chaos.
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