Abstract
This paper presents a detailed investigation of the Bessel–Gauss mode in an axicon-based thin-disk resonator utilizing the self-consistency equations. The results show that Bessel–Gauss modes are eigenmodes of it even if the active medium is deformed. Then, both the numerical and the analytical results are consistent. The effects of the active medium deformation and the radius of curvature of the output mirror on the resonator’s behavior have been investigated. In addition, the self-consistency equations have been derived.
Similar content being viewed by others
Data availability
No data were generated or analyzed in the presented research.
References
J. Durnin, J.J. Miceli, J.H. Eberly, Diffraction-free beams. Phys. Rev. Lett. 58, 1499–1501 (1987)
M. Goutsoulas, D. Bongiovanni, D. Li, Z. Chen, N.K. Efremidis, Tunable self-similar Bessel-like beams of arbitrary order. Opt. Lett. 45(7), 1830–1833 (2020)
L. Stoyanov, Y. Zhang, A. Dreischuh, G.G. Paulus, Long-range quasi-non-diffracting Gauss–Bessel beams in a few-cycle laser field. Opt. Express 29(7), 10997–11008 (2021)
V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, K. Dholakia, Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 419(6903), 145–147 (2002)
D.G. Grier, A revolution in optical manipulation. Nature 424(6950), 810–816 (2003)
G. Zhang, R. Stoian, W. Zhao, G. Cheng, Femtosecond laser Bessel beam welding of transparent to non-transparent materials with large focal-position tolerant zone. Opt. Express 26(2), 917–926 (2018)
W. Wang, G. Wang, J. Ma, L. Cheng, B.-O. Guan, Miniature all-fiber axicon probe with extended Bessel focus for optical coherence tomography. Opt. Express 27(2), 358–366 (2019)
N. Mphuthi, L. Gailele, I. Litvin, A. Dudley, R. Botha, A. Forbes, Free-space optical communication link with shape-invariant orbital angular momentum Bessel beams. Appl. Opt. 58(16), 4258–4264 (2019)
T. Auguste, O. Gobert, B. Carré, Numerical study on high-order harmonic generation by a Bessel–Gauss laser beam. Phys. Rev. A 78(3), 033411 (2008)
S. Kumar, A. Parola, P. Di Trapani, O. Jedrkiewicz, Laser plasma wakefield acceleration gain enhancement by means of accelerating Bessel pulses. Appl. Phys. B 123(6), 1–7 (2017)
G. Scott, N. McArdle, Efficient generation of nearly diffraction-free beams using an axicon. Opt. Eng. 31(12), 2640–2643 (1992)
Z.L. Horváth, M. Erdélyi, G. Szabó, Z. Bor, F.K. Tittel, J.R. Cavallaro, Generation of nearly nondiffracting Bessel beams with a Fabry-Perot interferometer. J. Opt. Soc. Am. A 14(11), 3009–3013 (1997)
W.X. Cong, N.X. Chen, B.Y. Gu, Generation of nondiffracting beams by diffractive phase elements. J. Opt. Soc. Am. A 15(9), 2362–2364 (1998)
J. Turunen, A. Vasara, A.T. Friberg, Holographic generation of diffraction-free beams. Appl. Opt. 27(19), 3959–3962 (1988)
A.J. Cox, D.C. Dibble, Holographic reproduction of a diffraction-free beam. Appl. Opt. 30(11), 1330–1332 (1991)
R. Bowman, N. Muller, X. Zambrana-Puyalto, O. Jedrkiewicz, P. Di Trapani, M.J. Padgett, Efficient generation of Bessel beam arrays by means of an SLM. Eur. Phys. J. Spec. Top. 199(1), 159–166 (2011)
P. Boucher, J.D. Hoyo, C. Billet, O. Pinel, G. Labroille, F. Courvoisier, Generation of high conical angle Bessel–Gauss beams with reflective axicons. Appl. Opt. 57(23), 6725–6728 (2018)
N.A. Khilo, E.S. Petrova, A.A. Ryzhevich, Transformation of the order of Bessel beams in uniaxial crystals. Quant. Electron. 31(1), 85–89 (2001)
P. Muys, E. Vandamme, Direct generation of Bessel beams. Appl. Opt. 41(30), 6375–6379 (2002)
D. Naidoo, K. Aït-Ameur, M. Brunel, A. Forbes, Intra-cavity generation of superpositions of Laguerre–Gaussian beams. Appl. Phys. B 106(3), 683–690 (2012)
S. Ngcobo, I. Litvin, L. Burger, A. Forbes, A digital laser for on-demand laser modes. Nat. Commun. 4(1), 2289 (2013)
F. Wu, Y. Chen, D. Guo, Nanosecond pulsed Bessel-gauss beam generated directly from a nd:yag axicon-based resonator. Appl. Opt. 46(22), 4943–4947 (2007)
K. Uehara, H. Kikuchi, Generation of nearly diffraction-free laser beams. Appl. Phys. B 48(2), 125–129 (1989)
D. McGloin, K. Dholakia, Bessel beams: diffraction in a new light. Contemp. Phys. 46(1), 15–28 (2005)
J.K. Jabczynski, A "diffraction-free " resonator. Opt. Commun. 77(4), 292–294 (1990)
P. Pääkkönen, J. Turunen, Resonators with Bessel–Gauss modes. Opt. Commun. 156(4), 359–366 (1998)
J. Rogel-Salazar, G.H.C. New, S. ChÁvez-Cerda, Bessel–Gauss beam optical resonator. Opt. Commun. 190(1), 117–122 (2001)
A. Hakola, T. Hakkarainen, R. Tommila, T. Kajava, Energetic Bessel–Gauss pulses from diode-pumped solid-state lasers. J. Opt. Soc. Am. B 27(11), 2342–2349 (2010)
A.N. Khilo, E.G. Katranji, A.A. Ryzhevich, Axicon-based Bessel resonator: analytical description and experiment. J. Opt. Soc. Am. A 18(8), 1986–1992 (2001)
J.C. Guti’errez-Vega, R. Rodr’iguez-Masegosa, S. Chávez-Cerda, Bessel–Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis. J. Opt. Soc. Am. A 20(11), 2113–2122 (2003). https://doi.org/10.1364/JOSAA.20.002113
C.L. Tsangaris, G.H.C. New, J. Rogel-Salazar, Unstable Bessel beam resonator. Opt. Commun. 223(4), 233–238 (2003)
R.I. Hernández-Aranda, S. Chávez-Cerda, J.C. Gutiérrez-Vega, Theory of the unstable Bessel resonator. J. Opt. Soc. Am. A 22(9), 1909–1917 (2005)
A.S. Rao, G.K. Samanta, On-axis intensity modulation-free, segmented, zero-order Bessel beams with tunable ranges. Opt. Lett. 43(13), 3029–3032 (2018)
B. Singh, V.V. Subramaniam, S.R. Daultabad, A. Chakraborty, Axicon based conical resonators with high power copper vapor laser. Rev. Sci. Instrum. 81(7), 073110 (2010)
A. Giesen, H. Hügel, A. Voss, K. Wittig, U. Brauch, H. Opower, Scalable concept for diode-pumped high-power solid-state lasers. Appl. Phys. B 58(5), 365–372 (1994)
A. Voss, M. Abdou-Ahmed, C. Neugebauer, A. Giesen, T. Graf, in Schuácker, D. (ed.) XVI International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers, vol. 6346 (SPIE, International Society for Optics and Photonics, 2007), pp. 536–547
R. Pereira, B. Weichelt, D. Liang, P.J. Morais, H. Gouveia, M. Abdou-Ahmed, A. Voss, T. Graf, Efficient pump beam shaping for high-power thin-disk laser systems. Appl. Opt. 49(27), 5157–5162 (2010)
Y.H. Peng, Y.X. Lim, J. Cheng, Y. Guo, Y.Y. Cheah, K.S. Lai, Near fundamental mode 1.1 kW Yb:YAG thin-disk laser. Opt. Lett. 38(10), 1709–1711 (2013)
C. Vorholt, U. Wittrock, Intra-cavity pumped Yb:YAG thin-disk laser with 1.74% quantum defect. Opt. Lett. 40(20), 4819–4822 (2015)
S. Nagel, B. Metzger, T. Gottwald, V., Kuhn, A. Killi, S.-S. Schad, in 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference (Optica Publishing Group, 2019), p. 5
S. Nagel, B. Metzger, D. Bauer, J. Dominik, T. Gottwald, V. Kuhn, A. Killi, T. Dekorsy, S.-S. Schad, Thin-disk laser system operating above 10 kw at near fundamental mode beam quality. Opt. Lett. 46(5), 965–968 (2021)
A. Giesen, in CLEO: Science and Innovations (Optica Publishing Group, 2013), p. 1
T. Gottwald, V. Kuhn, S.-S. Schad, C. Stolzenburg, A. Killi, Recent developments in high power thin disk lasers at trumpf laser. Technologies for Optical Countermeasures X; and High-Power Lasers 2013: Technology and Systems vol. 8898 (2013), pp. 187–193
J. Dominik, M. Scharun, B. Dannecker, S. Nagel, T. Dekorsy, D. Bauer, in Advanced Solid State Lasers (Optica Publishing Group, 2021), pp. 2–6
R. Aghbolaghi, S. Batebi, J. Sabaghzadeh, Thin-disk laser with Bessel-like output beam: theory and simulations. Appl. Opt. 52(4), 683–689 (2013)
V. Belyi, A. Forbes, N. Kazak, N. Khilo, P. Ropot, Bessel-like beams with z-dependent cone angles. Opt. Express 18(3), 1966–1973 (2010)
I.A. Litvin, N.A. Khilo, A. Forbes, V.N. Belyi, Intra-cavity generation of Bessel-like beams with longitudinally dependent cone angles. Opt. Express 18(5), 4701–4708 (2010)
J. Li, Y. Wu, Y. Li, in Advances in Imaging and Electron Physics, vol. 164 (Elsevier, 2010), pp. 257–302
P. Nie, D. Jia, C. Du, H. Zhang, T. Xu, T. Liu, Method based on fast fourier transform for calculating conical refraction of beams with noncircular symmetry. IEEE Photon. J. 9(2), 1–7 (2017)
J. Li, J. Zhu, Z. Peng, The s-fft calculation of Collins formula and its application in digital holography. Eur. Phys. J. D 45, 325–330 (2007)
Y. Lou, J. Li, Y. Zhang, J. Gui, C. Li, Z. Fan, in Holography, Diffractive Optics, and Applications IV, vol. 7848 (SPIE, 2010), pp. 346–354
R. Aghbolaghi, H.S. Charehjaloo, V. Fallahi, Simulation of near ideal-Bessel beam generation by a thin-disk laser configuration. JOSA B 39(4), 1186–1194 (2022)
P. Vaity, L. Rusch, Perfect vortex beam: Fourier transformation of a Bessel beam. Opt. Lett. 40(4), 597–600 (2015)
G.B. Arfken, H.J. Weber, Mathematical methods for physicists. Am. Assoc. Phys. Teachers (1999)
J.P. de Leon, Revisiting the orthogonality of Bessel functions of the first kind on an infinite interval. Eur. J. Phys. 36(1), 015016 (2014)
N.M. Temme, Special Functions: An Introduction to the Classical Functions of Mathematical Physics (John Wiley & Sons, New Jersey, 1996)
Author information
Authors and Affiliations
Contributions
HSC wrote the main manuscript text. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Aghbolaghi, R., Sahebghoran Charehjaloo, H. & Fallahi, V. Self-consistency equations in axicon-based thin-disk laser resonators. Appl. Phys. B 129, 131 (2023). https://doi.org/10.1007/s00340-023-08070-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00340-023-08070-3