Identification of the laser beam fi eld in the emission plane and in the measurement plane

The article considers an important practical problem that allows expanding the information on the laser beam parameters required for manufacturing and certification of laser sources. The only existing standardized numerical characteristic, the М 2 measure (GOST R ISO 11146-1-2008 “Lasers and laser installations (systems). Methods for measuring widths, divergence angles and propagation coefficients of laser beams”), which determines the quality of a laser beam, allows estimating the degree of similarity of the measured spatial distribution of the beam intensity only with the spatial distribution of the Gaussian intensity in the measurement plane. An alternative measure of similarity of the measured spatial distribution of the laser beam amplitude with a uniform distribution in the emitter plane or a spatial distribution of intensity with an arbitrary distribution in the measurement plane has been developed. It has been shown that the alternative measure of similarity when located in the emitter plane coincides with the aberration factor determining the source with the greatest axial luminous intensity. The proposed measure is universal and has a wider application than the М 2 measure, since it is associated with the characteristic of the field distribution homogeneity, the generalized area and the generalized diameter of the laser beam, which is an alternative to the beam diameter determined by GOST R ISO 11146-1-2008.

1. Lingqiang Meng, Qingqing Kong, Kunhao Ji et al. Characterization of beam quality of unstable laser beams with the multiple hyperbolas method.

2. Results in Physics, 12, 38– 45 (2019).

3. https://doi.org/10.1016/j.rinp.2018.11.044

4. Hinton R. Laser Beam Quality: Beam propagation and quality factors: A primer. Laser Focus World (2019).

5. Potemkin A. K. et al. Calculation of the laser-beam М 2 factor by the method of moments. Quantum Electronics, 35(11),

6. –1044 (2005). http://dx.doi.org/10.1070/QE2005v035n11ABEH012788

7. Raitsin A.M., Ulanovskii M.V. Bases for the identification of spatial distributions of intensity laser beams. Measurement Techniques, 65(4), 258–265 (2022). https://doi.org/10.1007/s11018-022-02077-6.

8. Raitsin, A.M. Cumulant method for identifying spatial distributions of laser beam intensity. Meas Tech 67, 597–607 (2024). https://doi.org/10.1007/s11018-024-02380-4

9. Anan’ev Yu. A. Opticheskie rezonatory i lazernye puchki. Nauka, Moscow (1990). (In Russ.)

10. Anan'ev Yu.A. Opticheskie rezonatory i problema rashodimosti lazernogo izluchenija. Nauka, Moscow (1979). (In Russ.)

11. Gudmen Dzh. Vvedenie v fur'e-optiku. Mir, Moscow (1970). (In Russ)

12. Tsypkin Ya. Z., Informatsionnaya teoriya identifi katsii. Fizmatlit, Moscow (1995). (In Russ.)

13. Ahmanov S.A., Nikitin S.Ju. Fizicheskaja optika. Nauka, Moscow (2004). (In Russ.)

14. Raitsin, A. M, Frolovichev S.M. The problem of correct measurements of the width and diverge angle of a laser beam. Optics and Spectroscopy 132.5 (2024): 494-500.

15. Kirgetov M.V. Measurement of spot diameter and divergence of laser beam by shadow method using generalized parameters. Meas. Tech., 65 (11), 819 (2023). DOI: 10.1007/s11018-023-02156-2]

16. Grjaznov M.I. Integral'nyj metod izmerenija impul'sov. Sov. radio, Moscow (1975). (In Russ.)

17.