Gentec-eo Beamage-M2 Manuel d'utilisateur télécharger pdf (Page 10)

Beamage-M

User Manual Revision 2.0 10

2. Theory

2.1. Understanding the M

Factor

The M

factor, which is unitless, can be considered as a quantitative indicator of laser beam quality. It indicates

the deviation of the measured beam from a theoretical Gaussian beam of the same wavelength. It can

mathematically be defined as the ratio between the Beam Parameter Product (beam waist radius w

multiplied

by divergence half-angle θ) of the measured beam with the theoretical Gaussian beam. Thus, for a single mode

ideal TEM

theoretical Gaussian beam, the M

factor

is exactly one. Since an ideal Gaussian beam diverges more

slowly than any other beam, the M

value is always greater than one. An M

value very close to 1 indicates an

excellent beam quality. This is associated with a low divergence and a good ability to focus. Multimode lasers

have higher M

factors.

2.1.1. Propagation Parameters

In the following equations, ‘’th’’ refers to theoretical values and ‘’exp’’ to experimental or real values.

The beam waist is defined as the location along the beam propagation axis where the beam radius reaches its

minimum value (see Figure 2-1). For a theoretical Gaussian beam, the beam radius w

(z) at any position z along

the beam axis is given by the following equation:

Where λ is the laser wavelength and w

0th

the theoretical beam waist radius.

As depicted by Figure 2-1, the theoretical Rayleigh length Z

Rth

is the distance (along the propagation axis)

between the beam waist and the position where the beam radius is times larger than the beam waist

(doubled cross-section).

Figure 2-1 Beam Propagation Diagram

Mathematically, it is given by the following equation:

1 2 ... 5 6 7 8 9 10 11 12 13 14 15 ... 49 50

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Gentec-eo Beamage-M2 Manuel d'utilisateur Page 10