Description and interest of open resonators

The role of the laser cavity is to allow the oscillation of the optical wave, generally between two mirrors, so that this wave is amplified at each pass through the amplifying medium inside the cavity. The cavity is also used to extract the useful laser beam through the only partially reflecting outcoupling mirror. Finally, the geometry of the cavity specifies the spatial and spectral characteristics of the laser radiation.

The most simple resonator is a parallelepipedic metallic box (each face is a metallic mirror). In such a cavity, a given number of modes could oscillate, and those modes are determined by the boundary conditions for the wavevectors on the faces of the box (each mode is associated with a wavevector with and the dimensions of the box).

Let us consider an amplifying medium in such a cavity : the modes will oscillate and amplification will take place. However, the number of oscillating modes (in the amplifying medium spectral bandwidth) has to remain low to produce a coherent radiation.

The calculation of the number of modes in this bandwidth shows that it is proportional to the cavity volume and inversely proportional to the square of the wavelength. Numerically, if the wavelength is in the microwave domain (10 cm), we found that about 10 modes could oscillate in a 1 GHz bandwidth for a 10 cm large cubic cavity. Nevertheless, if the wavelength is in the optical range (around 1 µm), as many as 1011 modes could oscillate in the same cavity !

This is the reason why such closed resonators are well-tailored for MASERS (Microwave Amplification by Stimulated Emission of Radiation) but cannot be used with visible light : too many modes will oscillate, or in other terms a quasi-monomode operation will require a very small cavity (around 1 µm).

Consequently, one has to modify the resonator geometry : the idea proposed and developed among others by Schallow and Townes in the fifties is to use a quasi-linear resonator where oscillation is possible only along a single axis : this kind of « open resonator » is in its simplest form composed of two spherical or flat mirrors facing each other in a Fabry-Pérot interferometer configuration.

In a first approach, the modes of this resonator are similar to the closed cavity ones with d>>a, b. Such a Fabry Pérot structure considerably reduces the number of oscillating modes : every optical ray having an important angle with respect to the cavity axis will rapidly escape. However, in a Fabry Perot configuration, the facing flat mirrors have to be perfectly parallel to avoid that all the rays escape the cavity after a few round-trips. To ensure efficient laser operation (and to allow spatial and spectral filtering), some rays have to stay in the cavity long enough : stable cavities are needed (we will come back to this concept later).

The simplest optical cavity is a linear cavity composed of two facing mirrors separated by a distance d. The curvature radii are R1 and R2 , and the diameters D1 et D2 (see figure 1). In this kind of optical cavity, a stationary wave takes place between the mirrors. Some optical elements (lenses, polarisers, active components...) could eventually be inserted inside the cavity. We will call « passive cavity » the optical cavity without the amplifying medium, whereas the « active cavity » will include the amplifying medium.