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A Talbot cavity is an external cavity used for the coherent beam combination of output from laser sets. It has been used experimentally for semiconductor laser diodes, carbon dioxide lasers, fiber lasers and solid-state disk lasers arranged in an array. In a simplest version it is constructed with a single mirror at half the Talbot distance from the output facet of the laser array:

$${\displaystyle z_{_{\text{T}}}={\frac {2p^{2}}{\lambda }},}$$

where p is the period of the laser lattice and λ {\displaystyle \lambda } \lambda is the wavelength of laser emission. The constructive interference images the near field of the array back onto the array itself at the Talbot distance, creating optical feedback. This interference feedback forces the lasers in the array to transverse mode lock. The Fresnel number F of the N$${\displaystyle N-}$$ element laser array phase-locked by Talbot cavity is given by:[1]

$${\displaystyle F=N^{2}.}$$

Talbot beam combination is highly sensitive to transverse phase distortions even at λ / 10 {\displaystyle \lambda /10} {\displaystyle \lambda /10} scale. [2] Theory developed for Talbot cavities [3] facilitated the development of thin disk diode-pumped solid-state laser arrays.[4]
References

Okulov, A Yu (1990). "Two-dimensional periodic structures in nonlinear resonator". JOSA B. 7 (6): 1045–1050. doi:10.1364/JOSAB.7.001045.
Okulov, A Yu (1991). "The effect of roughness of optical elements on the transverse structure of alight field in a nonlinear Talbot cavity". J.Mod.Opt. 53 (11): 1887–1890. doi:10.1080/09500349114551991.
Golubentsev, A A; Likhanskii, V V; Napartovich, A P (1980). "Theory of phase locking of an array of lasers". Sov. Phys. JETP. 52 (5): 847.

Okulov, A Yu (1993). "Scaling of diode-array-pumped solid-state lasers via self-imaging". Opt. Comm. 99 (5–6): 350–354. doi:10.1016/0030-4018(93)90342-3.

In-phase coherent coupling of tapered lasers in an external Talbot cavity
Semiconductor laser array in an external Talbot cavity

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