The relation of line narrowing and chirp reduction resulting from the coupling of a semiconductor laser to passive resonator

We present a theory of adiabatic chirp reduction and narrowing of the Lorentzian laser line that occurs when a laser is coupled to an external passive resonator. Chirp reduction and line narrowing are simply related. We show that the reduction in the Lorentzian line width is equal to the square of the reduction in adiabatic chirp. Both are strongly enhanced near resonances of the external cavity.