Fig. 7: Discovery of a previously unreported experimental blueprint within a highly parameterized optical setup.

The parameter space comprises 6 × (824 × 824) pixel phases, 6 extra optical modulation parameters corresponding to the wave plates, and 8 distances (a total of ∼4 million optical parameters). a Discovered optical topology. The minimum value of the loss is demonstrated in detector #2. The setup topology is easily retrieved from detector #2 following the identified beam splitter ratios across the system. The identified optical parameters correspond to: the beam splitter ratios, in [Transmittance, Reflectance] pairs: BS#1: [0.000, 0.999], BS#2: [0.338, 0.662], BS#5: [0.000, 0.999], and BS#6: [0.999, 0.000]. The wave plates, in radians (1): η = 1.09, θ = 0.28, and (2): η = 0.19, θ = − 3.16. The propagation distances (in cm) are z₁ = 29.98, z₂ = 56.91, z₃ = 58.28, z₄ = 99.91, z₅ = 42.89, z₆= 53.96, and z₇ = 50.96. b Discovered phase masks corresponding to the super-SLM (sSLM) in (1) and (2). The speckle-like patterns of SLMs' phase masks are not detrimental to robustness. c Total intensity (∣E_x∣² + ∣E_y∣² + ∣E_z∣²) horizontal cross-section of the detected light beams of 650 nm (orange), 532 nm (green), and effective beam emulating stimulated emission (dashed blue). d Horizontal cross-section of the normalized total intensity (∣E_x∣² + ∣E_y∣² + ∣E_z∣²) of the effective beam from the discovered solution (blue), the simulated STED reference (dashed red), and the simulated reference (dotted black) using 532 nm wavelength. The spot size is computed as ϕ = (π/4)FWHM_x FWHM_y, where FWHM denotes Full Width Half Maximum. We use a fluorophore emission wavelength of 560 nm. The discovered solution outperforms both simulated references for STED microscopy¹⁰ and the sharp focus from Dorn, Quabis, and Leuchs (2003)⁵¹, demonstrating a spot size of 9.45% smaller than both references.