Passive Optical Resonators

This chapter deals with the theory of passive optical resonators i.e. where no active medium is present within the cavity. The most widely used laser resonators have either plane or spherical mirrors of rectangular (or, more often, circular) shape, separated by some distance L. Typically, L may range from a few centimeters to a few tens of centimeters, while the mirror dimensions range from a fraction of a centimeter to a few centimeters. Laser resonators thus differ from those used in the microwave field (see e.g. Sect. 2.2.1) in two main respects: (1) The resonator dimensions are much greater than the laser wavelength. (2) Resonators are usually open, i.e. no lateral surfaces are used. The resonator length is usually much greater than the laser wavelength because this wavelength usually ranges from a fraction of a micrometer to a few tens of micrometers. A laser cavity with length comparable to the wavelength would then generally have too low a gain to allow laser oscillation. Laser resonators are usually open because this drastically reduces the number of modes which can oscillate with low loss. In fact, with reference to example 5.1 to be considered below, it is seen that even a narrow linewidth laser such as a He-Ne laser would have a very large number of modes ( ≈ 109) if the resonator were closed. By contrast, on removing the lateral surfaces, the number of low-loss modes reduces to just a few ( ≈ 6 in the example). In these open resonators, in fact, only the very few modes corresponding to a superposition of waves traveling nearly parallel to the resonator axis will have low enough losses to allow laser oscillation.