Photonics Research, Volume. 13, Issue 6, 1600(2025)

Non-symmetrical vortex beam shaping in VECSEL laser arrays

Sopfy Karuseichyk1... Ilan Audoin1, Vishwa Pal2 and Fabien Bretenaker1,* |Show fewer author(s)
Author Affiliations
  • 1Université Paris-Saclay, ENS Paris-Saclay, CNRS, CentraleSupélec, LuMIn, Orsay, France
  • 2Department of Physics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India
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    Figures & Tables(12)
    Scheme of a VECSEL. The 1/2-VCSEL gain chip and amplitude mask are placed at the near-field planes of the intracavity telescope. The telescope is formed by two lenses (L1 and L2 with focal lengths f1 and f2, respectively) in self-imaging positions. OC represents the output coupler.
    Schematic shapes of the different amplitude-mask patterns, called uniform, point defect, gradient, and random. The hole diameters are not to scale.
    Definition of the mask parameters. This example corresponds to n=8 holes. The pink area represents the fraction of the beam coming from one hole injected into its neighbors after reflection on the output coupler (OC).
    (a) Field amplitude |Es,i| calculated from Eq. (1) for z=500 μm,1000μm, and 2000 μm and diameter of the ith hole σi=200 μm. The distance (center-to-center) between two neighboring lasers is equal to d=250 μm. (b) The argument of the normalized overlap coefficient as a function of z.
    (a), (c), (e) Modulus and (b), (d), (f) argument of the coupling coefficients between neighboring lasers for the different masks. (a), (b) Uniform and point defect masks studied with z=500 μm; (c)–(f) gradient and random masks studied both with z=1000 μm and z=1200 μm. Solid lines: κi→i+1; dashed lines: κi→i−1.
    For two different sets of initial conditions, numerically simulated steady-state phase differences between adjacent lasers for different masks, with r=1.2, α=2, τcav=30 ns, and Fsat=1010.
    Intensity (top row) and phase (bottom row) patterns of the phase-locked lasers in a ring array of n=20 lasers with q=1. (a)–(c) Results corresponding to “uniform”, “big” defect, and “small” defect mask profiles with z=500 μm. (d), (f) Results for the gradient mask at z=1000 μm and z=1200 μm. (e), (g) Results for the random mask with z=1000 μm and z=1200 μm. The phase maps display the phase variations from 0 to 2π and the patterns correspond to the solution of the rate equations with coupling parameters shown in Fig. 6.
    (a) Evolution of the limiting values of the Henry factor versus argument of the coupling coefficient for |q|=1 (pink line), |q|=2 (blue line), |q|=3 (orange line), according to Eq. (6). Horizontal dashed lines correspond to a real positive coupling (θ=0). The blue squares are the values predicted by the formula in Ref. [36]. Red circles: values obtained from numerical simulations for |q|=1 and θ=−π/2,−π/10,−π/20, and π/20. (b) Probability to phase-lock the laser array with the value of the topological charge q for the uniform mask at z=500 μm, as a function of α. The coupling argument is taken to be θ=π/10.
    Probabilities for the laser array to exhibit phase-locking with different topological charges q as a function of α, for (a) “big” and (b) “small” defect masks. Coupling coefficients are calculated for z=500 μm, as shown in Figs. 5(a) and 5(b).
    Probabilities for the laser array to exhibit phase-locking with different topological charges q as a function of α, for (a), (c), (e) gradient and (b), (d), (f) random masks. The results are obtained for (a), (b) z=1050 μm, (c), (d) z=1100 μm, and (e), (f) z=1200 μm.
    Probabilities to obtain topological charge with a specially designed mask satisfying the criteria θi→i−1=2π/n and θi→i+1=−2π/n for (a) holes i=20,1,2, (b) holes i=20,1,2,3, (c) half of the array, and (d) the entire array in which each hole satisfies the condition. Zero holes satisfying these criteria correspond to the probability shown in Fig. 9(a).
    • Table 1. Hole Diameters (in µm) in Different Chosen Configurations of 20 Lasersa

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      Table 1. Hole Diameters (in µm) in Different Chosen Configurations of 20 Lasersa

      Hole Index12101920
      “Big” defect202200200200200
      “Small” defect197200200200200
      Gradient197197.25199.25201.5201.75
      Random197.25198.25201199.5200
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    Sopfy Karuseichyk, Ilan Audoin, Vishwa Pal, Fabien Bretenaker, "Non-symmetrical vortex beam shaping in VECSEL laser arrays," Photonics Res. 13, 1600 (2025)

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    Paper Information

    Category: Lasers and Laser Optics

    Received: Sep. 23, 2024

    Accepted: Mar. 26, 2025

    Published Online: May. 26, 2025

    The Author Email: Fabien Bretenaker (fabien.bretenaker@universite-paris-saclay.fr)

    DOI:10.1364/PRJ.542842

    CSTR:32188.14.PRJ.542842

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