Laser spatial coherence is one of the key parameters for laser applications, and is often quantitatively described by the beam quality factor M2. In the article we define a theoretical basis for the generalization of the beam quality factor M2 to three-dimensional (3D) space, which we call M6 formalism, by defining a new quality parameter Mz2 representing the axial component of the overall beam quality.
This quality represents the effect of component that change the depth of focus of the beam, such as Bessel-like beam generators (Axicons), multi-focal diffractive optics and even the contribution of the standard (transverse) quality factor to depth of focus.
The overall beam quality of the laser is defined as , with the Rayleigh range for a multimode beam with Z axis components has the form of , where ZR0 is the single mode beam Rayleigh range.
This formalism gives an elegant explanation of non-diffractive beams such as Bessel-like beams and Airy beams, as private examples of axial beam shaping, with increased axial beam quality factor. Numerical examples are provided for a Bessel-like beam case.
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