Formula for temperature distribution in multi-layer optical fibres for high-power fibre lasers

 High power fibre lasers need to be cooled efficiently to avoid their thermal damage.  Temperature distribution in fibre should be estimated during the fibre laser design process.  The steady-state heat equation in a cylindrical geometry is solved to derive a practical formula for temperature radial distribution in multi-layered optical fibres with arbitrary  number of the layers. The heat source is located in one or more cylindrical domains. The  validity of the analytical formula is tested by comparison with static heat transfer simulations  of typical application examples including octagonal double clad fibre, air-clad fibre, fibre with nonuniform, microstructured core. The accuracy sufficient for practical use is reported  even for cases with not exactly cylindrical domains.