7.4: Cavities

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The amplifying medium can completely fill the space between the mirrors as the top of Figure \(\PageIndex{1}\), or there can be space between the amplifier and the mirrors. For example, if the amplifier is a gas, it may be enclosed by a glass cylinder. The end faces of the cylinder are positioned under the Brewster angle with respect to the axis, as shown in the middle figure of Figure \(\PageIndex{1}\), to minimise reflections. This type of resonator is called a resonator with external mirrors.

Usually one or both mirrors are convex, as shown in the bottom figure of Figure \(\PageIndex{1}\). We state without proof that in that case the distance \(L\) between the mirrors and the radii of curvature \(R_{1}\) and \(R_{2}\) of the mirrors has to satisfy \[0<\left(1-\frac{L}{R_{1}}\right)\left(1-\frac{L}{R_{2}}\right)<1, \nonumber \] or else the laser light will ultimately leave the cavity laterally, i.e. it will escape sideways. This condition is called the stability condition. The curvature of a convex mirror is positive and that of a concave mirror is negative. Clearly, when both mirrors are concave, the laser is always unstable.

7.4.1.jpg — Figure \(\PageIndex{1}\): Three types of laser cavity. The shaded region is the amplifier. The middle case is called a laser with external cavities.