Scintillation Minimization versus Intensity Maximization in Optimal Beams

TL;DR

The paper addresses reducing scintillation in free-space optical beams by formulating scintillation minimization as a convex optimization over the mutual intensity $J$, revealing that the scintillation-minimizing beam is fully incoherent and yields vanishing receiver power. To make the objective practically useful, the authors introduce a convex trade-off $\mathcal{S}(J)+\mu\mathcal{Q}(J)$ that balances scintillation and received intensity, and solve it using randomized SVD to handle large operators. Analytical results in phase-screen turbulence show that zero scintillation can occur with incoherence but at the cost of very low power, while numerical simulations on phase-screen and PDE models demonstrate how the balance parameter $\mu$ yields beams with substantially reduced scintillation and retained intensity. The work provides a scalable framework for designing optimal beams under turbulence, with broad implications for reliable free-space optical communications and related applications.

Abstract

In free-space optical communications and other applications, it is desirable to design optical beams that have reduced or even minimal scintillation. However, the optimization problem for minimizing scintillation is challenging, and few optimal solutions have been found. Here we investigate the general optimization problem of minimizing scintillation and formulate it as a convex optimization problem. An analytical solution is found and demonstrates that a beam that minimizes scintillation is incoherent light (i.e., spatially uncorrelated). Furthermore, numerical solutions show that beams minimizing scintillation give very low intensity at the receiver. To counteract this effect, we study a new convex cost function that balances both scintillation and intensity. We show through numerical experiments that the minimizers of this cost function reduce scintillation while preserving a significantly higher level of intensity at the receiver.

Figures (4)

• Figure 1: Two illustrations that the scintillation-minimizing $J$ is a Dirac-delta function. (a) Profile of optimal $J$ in the non-parametrized case for PWE model. The optimal $J$ resembles a delta function. (b) Evolution of parameter $\lambda$ for a Gaussian parametrized $J=\exp(-\lambda^2(X_1-X_2)^2/2)$, and the multiple phase screen model. The value of $\lambda$ approaches infinity as the gradient descent progresses, meaning $J$ approaches a delta function.
• Figure 2: Alternative cost function from \ref{['eqn:cost_new']} with $J$ parameterized as $\exp(-\lambda^2(X_1-X_2)^2/2)$. (a) Cost function in \ref{['eqn:cost_new']} as a function of $\lambda$, for different $\mu$. A unique minimum at finite $\lambda$ value is seen for $\mu\neq 0$. (b) Evolution of scintillation $\mathcal{S}$ and intensity quotient $\mathcal{Q}$ at each iteration of gradient descent. Note that the $\mu=0$ case in Panel b has a larger stepsize. The iterations converge if $\mu\neq 0$.
• Figure 3: Profile of optimal $J$ (real part), where $J$ is allowed to be of general form and is non-parameterized. The left panel uses the phase screen model to compute the operator $A$ while the right panel uses PDE simulations.
• Figure 4: Scintillation $\mathcal{S}$ and intensity quotient $\mathcal{Q}$ of optimal $J$. For small $\mu$ values (e.g., $\mu\approx 0.25$ in panel a and $\mu\approx 2$ in panel b), the optimal $J$ provides substantial reduction in scintillation while maintaining adequate intensity. See the zoomed-in version in Supplementary Materials.