A computer model of a diffractive optical element suggests that a phase-only beam shaper can reproduce a broad, flat-topped light pattern for intersatellite optical links, but the match becomes less reliable as the requested super-Gaussian order rises. The study is therefore best read as a design and sensitivity analysis: it identifies conditions under which the modeled beam remains close to its target, while showing how numerical limits and a finite aperture can erode that agreement.
The work does not report a fabricated optical element, a laboratory beam measurement or an end-to-end communication test. Its results come from numerical phase screens, propagated beam shapes, a model of a fused-silica device and simulated perturbations. Manufacturing and experimental validation are identified as work still to be done, so the calculations do not yet amount to a demonstrated improvement in an operating intersatellite link.
A flatter beam, designed in software
The proposed shaper is intended to generate a super-Gaussian profile: a far-field beam with a relatively even central intensity and a sharper transition at its edges. Here, far-field means the beam pattern after it has propagated away from the shaper. The aim is to examine whether this kind of shaping could reduce sensitivity to transmitter misalignment in an intersatellite optical link.
The starting point is a Gaussian transmitter field. The researchers use Gerchberg–Saxton iteration to calculate a phase-only mask that sends that input toward a prescribed super-Gaussian far-field irradiance. In practical terms, the modeled mask changes the phase of the incoming light while using the resulting propagated pattern to check how closely it follows the requested beam shape.
The analytical part of the study describes an idealized optimum as a flat-top far-field irradiance under two assumptions: the aperture is small enough for the approximation used in the equations, and pointing jitter follows a bivariate Gaussian distribution along the x and y axes. Under those assumptions, the equations associate a higher super-Gaussian order with a wider optimum beam and a lower minimum outage probability, the modeled likelihood of an unfavorable link condition caused by pointing variation.
The numerical examples examine super-Gaussian orders 12 and 20. The lower-order case produced a close match between the computed result and its target. The order-20 case agreed less well, particularly around the target's steep edges, where the desired profile changes quickly.
The sharpest targets were hardest to reproduce
The paper attributes the higher-order mismatch to two features of the model: numerical discretization and the finite aperture. Discretization limits how finely the desired phase pattern can be represented, while the aperture limits the physical area available to realize it. The analysis points to both constraints but does not assign an individual contribution to either one.
The manufacturing-oriented analysis shows that a modeled phase screen can also be sensitive to how it is represented in a device. When the radial cells become thicker, the modeled far-field error increases and fine variations in the phase profile are no longer reproduced as well. The implementation example uses a fused-silica height profile designed for a wavelength of 940 nanometres.
The model also tests phase quantization, meaning the number of discrete phase settings available to approximate a continuous pattern. Error remains comparatively small at 64 levels or more, but rises rapidly in the four- and eight-level cases. The result links coarse phase steps with poorer reproduction of the intended beam in the modeled device.
A separate phase-depth test varies the realized depth of the device profile around its nominal value. The lowest error occurs near the nominal depth, while both under-etching and over-etching correspond to progressive degradation of the generated beam. Phase depth is therefore another modeled source of beam-quality loss when the realized profile departs from its design value.
The incoming wavefront mattered too
The researchers then introduce phase aberrations in the incident beam and test how different wavefront modes alter the shaped far field. The response is not uniform across the individual modes considered: primary spherical aberration produces the largest reported degradation. The supplied analysis does not give mode-specific numerical error values, so this comparison is reported as a relative result rather than a set of precise tolerances.
A Monte Carlo analysis combines the considered Zernike modes at prescribed total root-mean-square wavefront error, a measure of the overall phase departure from an ideal wavefront. Mean normalized intensity RMSE, or root-mean-square error, rises approximately monotonically as total wavefront error increases. The reported interval covering the 5th to 95th percentiles also widens, and the modeled result depends on how the total error is distributed among modes, not only on its overall size.
That finding makes a single wavefront-error budget an incomplete description of modeled performance. Two incident beams could have the same total RMS error yet produce different modeled beam quality if their aberration content differs. The study consequently treats the composition of the aberration as relevant alongside the total amount of wavefront error.
A design lead, not a link demonstration
Taken together, the simulations support a cautious design conclusion. Lower-order super-Gaussian profiles can be generated accurately in the modeled setup, while higher orders face numerical and finite-aperture limits. The authors' interpretation is that fabrication constraints and incident-wavefront errors should be included in manufacturing-aware DOE design, alongside the ideal phase-retrieval calculation.
Several tests remain before the approach can be judged as an optical communications technology. The DOE would need to be fabricated and measured, and the modeled beam shapes would need to be connected to link behavior under receiver angle-of-arrival fluctuations and atmospheric channels. The paper also identifies other optical communication and laser-based applications as possible extensions, but the supplied analysis does not report results for them.
The analytical prediction of lower outage belongs to the stated small-aperture and bivariate-Gaussian-jitter assumptions. It should not be read as a measured outage reduction, because the study's evidence is computational and physical validation remains future work. The strongest result available here is a map of modeled sensitivities that can guide later fabrication and experiments.
The document is an arXiv preprint, arXiv:2608.23532v1 in physics.optics, dated 24 August 2026. The work acknowledges support from the UK Space Agency and the European Space Agency under contract 4000150161 for a project developing a high-speed optical intersatellite-link terminal.
Paper data and sources
Original title: Diffractive optical element for super-Gaussian beam shaping on intersatellite optical communications
Authors: Mario Badás Aldecocea, Ziheng Wang, Mohammad Dabiri, Iman Tavakkolnia
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-24
DOI: Not available
Original paper · Full text