Fig. 4: Propagation of Hermite-Gaussian modes in a weak gravitational field.

Hermite-Gaussian mode HG_m,n(x⁺, x¹, x²) is not shape invariant under propagation in the Schwarzschild spacetime geometry, and both the intensity and phase profiles modify. a Intensity and phase distributions of the first 9 HG modes m, n ∈ {0, 1, 2} prior to the free-space propagation. b The intensity ∣εψ⁽¹⁾∣² and phase \(\arg \varepsilon {\psi }^{(1)}\) distributions of the corrected term, for the first 9 HG modes m, n ∈ {0, 1, 2}, after the propagation in a weak gravitational field. The rows and columns are associated to m ∈ {0, 1, 2} and n ∈ {0, 1, 2}, respectively. The dimensionless coordinates are used for these plots.