Coherent addition

The addition of lasers reduces the number of longitudinal modes in the output beam; the more lasers are combined, the smaller is the number of longitudinal modes in the output. The simple estimates show that the number of output modes reduces exponentially with the number of lasers combined. Of order of eight lasers can be combined in such a way.[3] The future increase of number of combined lasers requires the exponential growth of the spectral bandwidth of gain and/or length of partial lasers. The same conclusion can be made also on the base of more detailed simulations. [4] Practically, the combination of more than ten lasers with a passive combining arrangement appears to be difficult. However, active coherent combining of lasers has the potential to scale to very large numbers of channels.[5]

Nonlinear interactions of light waves are used widely to synchronize the laser beams in multichannel optical systems. Self-adjusting of phases may be robustly achievable in binary-tree array of beam-splitters and degenerate four-wave mixing Kerr Phase conjugation[6] in Chirped pulse amplification extreme light facilities.[7] This phase-conjugating Michelson interferometer increases the brightness as ${\displaystyle N^{2}}$,[8] where ${\displaystyle N}$ is the number of phase-locked channels.

Constructive interference due to Talbot self-imaging forces the lasers in the array to transverse mode locking. The Fresnel number ${\displaystyle F}$ of the one-dimensional ${\displaystyle N-}$ element laser array phase-locked by Talbot cavity is given by[9] ${\displaystyle F=N^{2}.}$ For the two-dimensional ${\displaystyle N^{2}-}$ element laser array phase-locked by Talbot cavity Fresnel number ${\displaystyle F}$ scales as ${\displaystyle F=N^{2}}$ as well. Talbot phase-locking techniques are applicable to thin disk diode-pumped solid-state laser arrays.[10]

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