Optical Downlink Modeling for LEO and MEO Satellites under Atmospheric Turbulence with a Quantum State Tomography Use Case

This paper presents a comprehensive analysis of the link budget for free-space optical systems involving Low Earth Orbit (LEO) and Medium Earth Orbit (MEO) satellites. We develop a detailed model of the satellite-to-ground channel that accounts for the primary physical processes affecting transmittance: atmospheric absorption and scattering, free-space diffraction, and turbulence-induced fluctuations. The study introduces a general method for computing transmittance along a slant path between a satellite and an optical ground station, incorporating zenith angle, slant range, and altitude-dependent attenuation. The proposed framework is intended to support the design and evaluation of space-based optical links and serves as a critical tool for defining technical specifications in satellite communication demonstrators and simulations. Numerical estimates are provided to illustrate the magnitude of losses under typical operational conditions, including the role of aperture averaging. In addition to the link budget analysis, we introduce a satellite-based quantum use case. We propose a scheme for quantum state tomography performed on states generated by an onboard photon source on an LEO or MEO satellite and transmitted to the optical ground station. This approach enables continuous verification of the quality of quantum resources that can be used to perform quantum protocols within quantum information networks.

💡 Research Summary

This paper presents a comprehensive framework for modeling and analyzing the performance of free-space optical (FSO) downlinks from Low Earth Orbit (LEO) and Medium Earth Orbit (MEO) satellites to optical ground stations (OGS). The primary objective is to develop a generalized method for accurately predicting the total link budget, which quantifies the signal loss experienced during transmission.

The overall transmittance (η) is modeled as the product of four statistically independent factors: internal detection loss (η_int), atmospheric attenuation (η_atm), diffraction-induced loss (η_d), and turbulence-induced intensity fluctuation (I). Atmospheric attenuation, caused by absorption and scattering, is calculated by integrating an altitude-dependent attenuation coefficient along the slant path defined by the satellite altitude (H) and zenith angle (ζ). A simplified approximation (η_zen_atm)^(sec ζ) is also provided. Diffraction loss is derived from a Gaussian beam model, describing the geometric loss due to the mismatch between the expanding beam spot and the finite receiver aperture size as propagation distance increases.

A central focus of the study is the impact of atmospheric turbulence. Turbulence strength is characterized by the altitude-dependent refractive index structure parameter (C_n²), modeled using the Hufnagel-Valley (H-V) profile. The effect of turbulence is quantified by the Intensity Scintillation Index (ISI, σ_I²), which measures the normalized variance of received optical power. The paper provides a detailed examination of “aperture averaging,” a key technique for mitigating turbulence effects. Using a larger receiver aperture averages out rapid spatial intensity fluctuations, resulting in a reduced effective signal variance described by the Power Scintillation Index (PSI).

The authors conduct extensive numerical simulations comparing link performance for LEO (~500 km altitude) and MEO (~20,000 km altitude) satellites. They evaluate photon loss as a function of zenith angle (from 0 to 80 degrees) and receiver telescope diameter (from 0.1 m to 1.0 m) under both the ISI (no averaging) and PSI (with averaging) models. The results demonstrate that while MEO links suffer significantly higher diffraction losses due to the longer propagation distance, they also benefit more substantially from aperture averaging. This highlights the critical importance of selecting an appropriate receiver aperture size to counteract turbulence-induced degradation, especially for higher-altitude satellites.

Beyond classical link budget analysis, the paper introduces an innovative quantum use case. It proposes a scheme for satellite-based Quantum State Tomography (QST). In this scheme, polarization-encoded quantum states (e.g., single photons) are generated by an onboard source on the satellite and transmitted down to the OGS. The received states are then continuously characterized via QST on the ground. This approach allows for real-time verification of the quality (fidelity) of the quantum resources distributed through the turbulent atmospheric channel. It serves as a practical method to assess the feasibility and reliability of using LEO/MEO satellites as nodes in future quantum communication networks or for quantum key distribution (QKD).

In summary, this work delivers a robust and generalizable analytical framework for modeling optical satellite downlinks, with particular emphasis on quantifying and mitigating atmospheric turbulence effects through aperture averaging. Furthermore, it successfully bridges the gap between classical optical communication modeling and cutting-edge quantum information science by proposing a concrete application for monitoring quantum resource quality in space-to-ground links.