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**1.3 Cavity modes Axial modes λ = 2d / n ν = nc / 2d n = 2d / λ**

The cavity provides positive feedback which is necessary to amplify light travelling in a given direction – that is, along the cavity axis. Cavity axis d Mirrors can be planar or curved To avoid destructive interference of photons of different phases, we need an exact integer number, n, of half wavelengths spanning the mirror separation, d. That is, λ = 2d / n ν = nc / 2d n = 2d / λ Waves that fulfil these conditions are the axial modes of the cavity.

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**Example: (cf. 9.1 in Hollas) **

Cavity modes Example: (cf. 9.1 in Hollas) A laser cavity is cm long and operates at a wavelength of nm. (a) How many half wavelengths are there along the length of the cavity? (b) What is the next longer wavelength that will be a mode of the cavity? (c) What is the difference in frequency between these two consecutive modes? (d) What is the time taken for a photon to make a round trip in the cavity?

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**How do the cavity modes affect the laser emission?**

It can readily be shown that the separation of allowed frequencies is: Δν = c / 2d The cavity transmission (and laser modes) thus looks like: How do the cavity modes affect the laser emission?

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**As a result, lasers often produce a multimode spectrum **

Cavity modes The Gain profile must be combined with the cavity modes to determine the laser output. As a result, lasers often produce a multimode spectrum Single mode operation can be achieved, but the laser power is generally lower.

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Cavity modes Transverse modes There are also cavity modes perpendicular to the cavity axis. These modes are the transverse modes of the cavity and are usually labelled TEMij (transverse electromagnetic) modes. These modes describe the spatial distribution of the cavity modes. The subscripts i and j describe the number of nodes along each axis: TEM00 is most commonly encountered – it describes a Gaussian beam profile.

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