What is laser beam quality factor? How to evaluate laser beam quality? Why laser beam quality degrades during propagation? This article will share a bit it.

#### What is laser beam quality

The beam quality of a laser is an important aspect of laser characterization. It can be defined in different ways, but is normally understood as a measure of how tightly a laser beam can be focused under certain conditions. The most common ways to quantify the beam quality are:

- the beam parameter product (BPP), i.e., the product of beam radius at the beam waist with the far-field beam divergence angle
- the M2 factor, defined as the beam parameter product divided by the corresponding product for a diffraction-limited Gaussian beam with the same wavelength

The equation for the divergence, of a pure Gaussian TEM00 unfocused beam propagating through space is given by

where D00 is the diameter of the beam waist, and λ is the wavelength. Higher mode beams often start with a larger beam waist, D0, and/or have a faster divergence Θ0. In this case Equation becomes

where Θ0 and D0 are the divergence and waist of a higher mode beam and M2 is greater than 1 and is named the “Beam Propagation Ratio” per the ISO 11146 standard. When a Gaussian laser beam is focused, the focused spot diameter is defined by

where d00 is the ideal focused spot diameter, f is the focal length of the focusing lens, and D00 is the input beam waist and is placed one focal length from the lens as shown in the figure. However, when a multimode beam is focused, Equation becomes

#### What is the difference between fundamental mode and high order mode laser beam?

With a given divergence angle (i.e. knowing the focal length of the lens), the fundamental mode alone produces the theoretically smallest possible beam waist (green curve). If beam quality worsens (red curve), the beam waist increases. If divergence is fixed, beam waist increases linearly by the factor M2 compared to the underlying Gaussian.

The appropriate power density at z0 is reduced by a factor (M²)². Also the Rayleigh Length increases

by a factor of M².

#### Why laser beam quality degrades during propagation

Using a Gaussian beam is preferred because of its minimum divergence angle and the ability to achieve the minimal focus diameter. Differences to Gaussian shape can be due to

- existence of higher order modes
- amplitude and phase distortions due to inhomogeneous gain medium in lasers
- presence of extraordinary beams

These distortions lead to a larger beam waist compared to Gaussian beams when the same focal lens is used. This results in a lower maximum achievable power density in the focal point.

In the focus (beam waist) of a diffraction-limited beam (i.e., at the location where the beam radius reaches its minimum), the optical wavefronts are flat. Any scrambling of the wavefronts, e.g. due to optical components with poor quality, spherical aberrations of lenses, thermal effects in a gain medium, diffraction at apertures, or by parasitic reflections, can spoil the beam quality. For monochromatic beams, the beam quality could in principle be restored e.g. with a phase mask which exactly compensates the wavefront distortions, but this is usually difficult in practice, even in cases where the distortions are stationary. A more flexible approach is to use adaptive optics in combination with a wavefront sensor.

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