Interferometric Locating the Waist of a Laser Beam
Abstract
An interferometric method for determining the location of a laser beam waist has been developed, which implements the dependence of the wavefront curvature on its distance to the waist. The initial laser beam, the waist location of which must be determined, is split by a shear interferometer into reference and information beams, which form a spatially non-localized interference field in reflected light. The period of the interference fringes observed in any cross-section of the interference field carries information about the location of the waist of the initial laser beam relative to this section. The distance from the waist to the plane of recording the period of the interference fringes is calculated using the formulas of Gaussian optics. The fundamental difference of this method from currently known ones allows for increasing the accuracy of the obtained result while simultaneously reducing the laboriousness of the measurement process.
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References
Mohl, S. Kaldun, C. Kunz, F. A. Muller, U. Fuchs, and S. Graf, “Tailored focal beam shaping and its application in laser material processing”, J. Laser Appl. 31, 042019 (2019). https://doi.org/10.2351/1.5123051
Y. Mi, S. Mahade, F. Sikstrom, I. Choquet, S. Joshi, and A. Ancona, “Conduction mode laser welding with beam shaping using a deformable mirror”, Opt. Laser Technol. 148, 107718 (2022). https://doi.org/10.1016/j.optlastec.2021.107718
N. Levichev, P. Herwig, A. Wetzig, and J.R. Duflou, “Towards robust dynamic beam shaping for laser cutting applications”, Proc. CIRP, 111, 746 (2022). https://doi.org/10.1016/j.procir.2022.08.116
A.R. Bakhtari, H.K. Sezer, O.E. Canyurt, O. Eren, M. Shah, and S. Marimuthu, “A review on laser beam shaping application in laser-powder bed fusion”, Adv. Eng. Mater. 26, 2302013 (2024). https://doi.org/10.1002/adem.202302013
O. Savchenko, in: Laser technologies in orthodontic practice – Achievements and prospects, Conference proceedings of the International scientific and practical conference (Seoul, Republic of Korea, 2019), pp. 109-114, https://doi.org/10.36074/22.12.2019.v1.35
K.J. Gasvik, Optical Metrology, 3rd ed., (John Wiley & Sons, Ltd, 2002).
H. Le, P. Penchev, A. Henrottin, D. Bruneel, V. Nasrollahi, J.A. Ramos-de-Campos, and S. Dimov, “Effects of top-hat laser beam processing and scanning strategies in laser micro-structuring”, Micromachines, 11, 221 (2020). https://doi.org/10.3390/mi11020221
A. Forbes, F. Dickey, M. DeGama, and A. du Plessis, “Wavelength tunable laser beam shaping”, Opt. Lett. 37, 49 (2012). https://doi.org/10.1364/OL.37.000049
M.A. Moiseev, E.V. Byzov, S.V. Kravchenko, and L. L. Doskolovich, “Design of LED refractive optics with predetermined balance of ray deflection angles between inner and outer surfaces”, Optics Express, 23, A1140 (2015), https://doi.org/10.1364/OE.23.0A1140
C. Rosales-Guzmán, and A Forbes, “How to shape light with spatial light modulators,” SPIE, 30, 57 (2017).
T. Häfner1, J. Strauß, C. Roider, J. Heberle, and M. Schmidt, “Tailored laser beam shaping for efficient and accurate microstructuring”, Applied Physics A, 124, 111 (2018). https://doi.org/10.1007/s00339-017-1530-0
C. Halbhuber, “Heat conduction joining with the multispot focusing lens: Joining plastics and metal”, PhotonicsViews, 19, 60 (2022). https://doi.org/10.1002/phvs.202200044
A.G. Nalimov, V.V. Kotlyar, S.S. Stafeev, and E.S. Kozlova, “Metalens for detection of a topological charge”, Optical Memory and Neural Networks, 32, S187 (2023). https://doi.org/10.3103/S1060992X23050144
I.V. Petrusenko, and Yu.K. Sirenko, “Generalized mode-matching technique in the theory of guided wave diffraction. Part 3: wave scattering by resonant discontinuities”, Telecommunications and Radio Engineering, 72, 555 (2013). https://doi.org/10.1615/TelecomRadEng.v72.i7.10
A.E. Mandel, and A.S. Perin, Study of the efficiency of radiation input and losses at the joints of optical fiber, (TUSUR, Tomsk, 2018). https://studfile.net/preview/16874330 (in Russian)
O.B. Kovalev, I.O. Kovaleva, and V.V. Belyaev, “Ray tracing method for simulation of laser beam interaction with random packings of powders”, AIP Conf. Proc., 1939, 020028 (2018).https://doi.org/10.1063/1.5027340
H. Kogelnik, and T. Li, “Laser beams and resonators”, Appl. Opt. 5, 1550 (1966). https://doi.org/10.1364/AO.5.001550
J.A. Arnaud, “Gaussian laser beam-waist radius measuring apparatus”, Patent United States No. 13,612,885 (10 Dec. 1969).
J.A. Arnaud, “Apparatus for locating and measuring the beam waist radius of a Gaussian laser beam”, Patent United States No. 3617755A (11 Febr., 1971).
E.H.A. Granneman, and M.J. van der Wiel, “Laser beam waist determination by means of multiphoton ionization”, Rev. Sci. Instrum. 46, 332 (1975). https://doi.org/10.1063/1.1134202
Y. Suzaki, and A. Tachibana, “Measurement of the Gaussian laser beam divergence,” Appl. Opt. 16, 1481 (1975). https://doi.org/10.1364/AO.16.001481
G.N, Vinokurov, V.A. Gorbunov, V.P. Dyatlov, V.N. Sizov, and A.D. Starikov, “Method for the determination of the position of the focal plane of converging laser beams”, Soviet Journal of Quantum Electronics, 6, 364 (1976). https://doi.org/10.1070/QE1976v006n03ABEH011092
E. Stijns, “Measuring the spot size of a Gaussian beam with an oscillating wire”, IEEE J. Quantum Electron. QE-16, 1298 (1980). https://doi.org/10.1109/JQE.1980.1070431
Y.C. Kiang, and R.W. Lang, “Measuring focused Gaussian beam spot sizes: a practical method”, Appl. Opt., 22, 1296 (1983). https://doi.org/10.1364/AO.22.001296
J.T. Luxon, D.E. Parker, and J. Karkheck, “Waist location and Rayleigh range for higher-order mode laser beams”, Appl. Opt. 23, 2088 (1984). https://doi.org/10.1364/AO.22.001296
S. Nemoto, “Determination of waist parameters of a Gaussian beam”, Appl. Opt. 25, 3859 (1986). https://doi.org/10.1364/AO.25.003859
S. Nemoto, “Waist shift of a Gaussian beam by plane dielectric interfaces”, Appl. Opt. 27, 1833 (1988). https://doi.org/10.1364/AO.27.001833
P.D. Gupta, and S. Bhargava, “An experiment with Gaussian laser beam”, Am. J. Phys. 56, 563 (1988). https://doi.org/10.1119/1.15555
S. Nemoto, “Waist shift of a Gaussian beam by a dielectric plate”, Appl. Opt. 28, 1643 (1989). https://doi.org/10.1364/AO.28.001643
P.B. Chipple, “Beam waist and M2 measurement using a finite slit”, Opt. Eng. 33, 461 (1994). https://doi.org/10.1117/12.169739
C.R.C. Wang, C.C. Hsu, W.Y. Liu, W.C. Tsai, and W.B. Tzeng, “Determination of laser beam waist using photoionization time-of-flight”, Rev. Sci. Instrum. 65, 2776 (1994). https://doi.org/10.1063/1.1144615
J. P. Landry, “Optical oblique-incidence reflectivity difference microscopy: Application to label-free detection of reactions in biomolecular microarrays, (University of California, Davis 2008).
J. Wang and J. P. Barton, “Actual focal length of a symmetric biconvex microlens and its application in determining the transmitted beam waist position”, Appl. Opt. 49, 5828 (2010). https://doi.org/10.1364/AO.49.005828
A.B. Ortega, M.L.A. Carrasco, J.A.D. Pintle, M.M.M. Otero, and M.D.I. Castillo, “New method to characterize Gaussian beams”, Proc. SPIE, 8011, in: 22nd Congress of the International Commission for Optics: Light for the Development of the World, 80114X (2011). https://doi.org/10.1117/12.902192
Y. You, J. Urakawa, A. Rawankar, A. Aryshev, H. Shimizu, Y. Honda, L. Yan, W. Huang, and C. Tang, “Measurement of beam waist for an optical cavity based on Gouy phase”, Nuclear Instruments and Methods in Physics Research Section A, 694, 6 (2012). https://doi.org/10.1016/j.nima.2012.07.022
E.A. Bibikova, N. Al-wassiti, and N.D. Kundikova, Diffraction of a Gaussian beam near the beam waist, J. Eur. Opt. Soc.-Rapid Publ. 15, 17 (2019). https://doi.org/10.1186/s41476-019-0113-4
ISO 11146-1:2021 “Lasers and laser-related equipment: Test methods for laser beam widths, divergence angles and beam propagation ratios Part 1: Stigmatic and simple astigmatic beams”. https://www.iso.org/obp/ui/#iso:std:iso:11146:-1:ed-2:v1:en
ISO 11146-2:2021 “Lasers and laser-related equipment: Test methods for laser beam widths, divergence angles and beam propagation ratios Part 2: General astigmatic beams”. https://www.iso.org/obp/ui/#iso:std:iso:11146:-2:ed-2:v1:en
ISO/TR 11146-3:2004 “Lasers and laser-related equipment: Test methods for laser beam widths, divergence angles and beam propagation ratios Part 3: Intrinsic and geometrical laser beam classification, propagation and details of test methods”. https://www.iso.org/obp/ui/#iso:std:iso:tr:11146:-3:ed-1:v1:en
M.F. Malikov, Fundamentals of metrology, (Kommerpribor Publishing House, Moscow, 1949).
G.A. Zimokosov, and K.I. Muntean, “Method for determining the beam waist coordinate of an optical quantum generator”, USSR Author's Certificate No. 550917 (31 Oct. 1975).
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