1. The M2 parameter in space ---beam quality factor
Chengao Wang

2. Review of the fundamental Gaussian modes in laser beams
Amplitude distribution at beam waist
Amplitude distribution at any position

3. Review of the fundamental Gaussian modes in laser beams
Rayleigh Range
Propagation of the beam

4. Review of the fundamental Gaussian modes in laser beams
In the far field,
Divergence angle:

5. Review of the fundamental Gaussian modes in laser beams
Rewrite the propagation of the beam using the definition of the divergence angle:

6. The interpretation for “beam quality”
How the beam diverges in the far-field and how it focuses in the near-field

7. Uncertainty Relationship

8. Uncertainty relationship in Gaussian beams

9. Uncertainty relationship in Gaussian beams
By Fourier transformation

10. Uncertainty relationship in Gaussian beams

11. Definition of the parameters in real laser beams
spot size
Divergence angle

12. The definition of M
M is named as times diffraction limit number, which characterize the beam quality for a real laser beam

13. Propagation function for a real laser beam
For Gaussian beam
For real laser beams

14. Introduction to the instrument

15. Applications Quality control Process control
Product or process development

16. Thanks