Closed form theory of multicavity reflectors and the output power of external cavity diode lasers

A closed form solution for the transmission and reflection coefficients of a double cavity Fabry-Perot resonator is given. The explicit expressions for these coefficients are used in a formula to give the output power of diode lasers coupled to multiple external cavities. Analysis of a cleaved or etched coupled-cavity laser shows that stable operation depends on proper choice of the phase length of both the gap and the control section. A study of a diode laser coupled to an external waveguide containing a Bragg reflector shows that for correct choice of grating reflectivity only modestly effective antireflection coatings (5 percent on laser facet and 2 percent on waveguide face) are required to allow the grating to dominate the operating wavelength of the laser diode. A single external cavity with loss coupled to a laser diode is also considered. In this case the theory indicates the necessity of proper control of loss or coupling fraction between diode and cavity for there to be effective control of wavelength.