Optical cavity

An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that confines light waves similarly to how a cavity resonator confines microwaves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. They are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times, producing modes with certain resonance frequencies. Modes can be decomposed into longitudinal modes that differ only in frequency and transverse modes that have different intensity patterns across the cross section of the beam. Many types of optical cavities produce standing wave modes. Different resonator types are distinguished by the focal lengths of the two mirrors and the distance between them. Flat mirrors are not often used because of the difficulty of aligning them to the needed precision. The geometry (resonator type) must be chosen so that the beam remains stable, i.e. the size of the beam does not continually grow with multiple reflections. Resonator types are also designed to meet other criteria such as a minimum beam waist or having no focal point (and therefore no intense light at a single point) inside the cavity. Optical cavities are designed to have a large Q factor, meaning a beam undergoes many oscillation cycles with little attenuation. In the regime of high Q values, this is equivalent to the frequency line width being small compared to the resonant frequency of the cavity.

Resonator modes

Light confined in a resonator will reflect multiple times from the mirrors, and due to the effects of interference, only certain patterns and frequencies of radiation will be sustained by the resonator, with the others being suppressed by destructive interference. In general, radiation patterns which are reproduced on every round-trip of the light through the resonator are the most stable. These are known as the modes of the resonator. Resonator modes can be divided into two types: longitudinal modes, which differ in frequency from each other; and transverse modes, which may differ in both frequency and the intensity pattern of the light. The basic, or fundamental transverse mode of a resonator is a Gaussian beam.

Resonator types The most common types of optical cavities consist of two facing plane (flat) or spherical mirrors. The simplest of these is the plane-parallel or Fabry–Pérot cavity, consisting of two opposing flat mirrors. While simple, this arrangement is rarely used in large-scale lasers due to the difficulty of alignment; the mirrors must be aligned parallel within a few seconds of arc, or "walkoff" of the intracavity beam will result in it spilling out of the sides of the cavity. However, this problem is much reduced for very short cavities with a small mirror separation distance (L < 1 cm). Plane-parallel resonators are therefore commonly used in microchip and microcavity lasers and semiconductor lasers. In these cases, rather than using separate mirrors, a reflective optical coating may be directly applied to the laser medium itself. The plane-parallel resonator is also the basis of the Fabry–Pérot interferometer. For a resonator with two mirrors with radii of curvature R1 and R2, there are a number of common cavity configurations. If the two radii are equal to half the cavity length (R1 = R2 = L / 2), a concentric or spherical resonator results. This type of cavity produces a diffraction-limited beam waist in the centre of the cavity, with large beam diameters at the mirrors, filling the whole mirror aperture. Similar to this is the hemispherical cavity, with one plane mirror and one mirror of radius equal to the cavity length. A common and important design is the confocal resonator, with mirrors of equal radii to the cavity length (R1 = R2 = L). This design produces the smallest possible beam diameter at the cavity mirrors for a given cavity length, and is often used in lasers where the purity of the transverse mode pattern is important. A concave-convex cavity has one convex mirror with a negative radius of curvature. This design produces no intracavity focus of the beam, and is thus useful in very high-power lasers where the intensity of the light might be damaging to the intracavity medium if brought to a focus. Less common resonator types include optical ring resonators and whispering-gallery mode resonators, in which a resonance is formed by waves moving in a closed loop rather than reflecting between two mirrors.

Stability

Only certain ranges of values for R1, R2, and L produce stable resonators in which periodic refocussing of the intracavity beam is produced. If the cavity is unstable, the beam size will grow without limit, eventually growing larger than the size of the cavity mirrors and being lost. By using methods such as ray transfer matrix analysis, it is possible to calculate a stability criterion:

0 ⩽ ( 1 − L R 1 ) ( 1 − L R 2 ) ⩽ 1. {\displaystyle 0\leqslant \left(1-{\frac {L}{R_{1}}}\right)\left(1-{\frac {L}{R_{2}}}\right)\leqslant 1.}

Values which satisfy the inequality correspond to stable resonators. The stability can be shown graphically by defining a stability parameter, g for each mirror:

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