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Range Emulator: A Compact Paraxial Optical System to Emulate Long-Distance Monochromatic Laser Propagation

Subaru Shibai, Kiwamu Izumi

Abstract

Emulating long-distance light propagation on a laboratory scale is essential for the ground-based testing of intersatellite optical systems. To address this challenge, we propose and analyze a novel optical system called the Range Emulator (RE) to reproduce the spatial propagation effects of a long-distance beam within a compact apparatus. Our analysis identifies that three lenses are required as the minimum number of lenses to implement the RE. Through a numerical exploration, we quantify the fundamental trade-off between system compactness and manufacturing precision. This work provides a practical framework for designing compact optical testbeds for future multi-satellite laser link technologies.

Range Emulator: A Compact Paraxial Optical System to Emulate Long-Distance Monochromatic Laser Propagation

Abstract

Emulating long-distance light propagation on a laboratory scale is essential for the ground-based testing of intersatellite optical systems. To address this challenge, we propose and analyze a novel optical system called the Range Emulator (RE) to reproduce the spatial propagation effects of a long-distance beam within a compact apparatus. Our analysis identifies that three lenses are required as the minimum number of lenses to implement the RE. Through a numerical exploration, we quantify the fundamental trade-off between system compactness and manufacturing precision. This work provides a practical framework for designing compact optical testbeds for future multi-satellite laser link technologies.
Paper Structure (18 sections, 17 equations, 4 figures)

This paper contains 18 sections, 17 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Range Emulator
  3. The definition
  4. Previous studies on RTM synthesis
  5. Numerical Exploration
  6. Overview
  7. Model and Definition of Primary Cost Function
  8. Global search
  9. Local Solution Sampling
  10. Robustness Analysis
  11. Result
  12. Numerical Exploration Results
  13. Three-Lens Solution of Range Emulator
  14. Discussion
  15. Limits of the Three-Lens RE
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Conceptual image of the Range Emulator (RE). (a) The RE mimics geometric propagation effects, transforming the position and angle of an incoming beam as if it had traveled a long distance. (b) The RE also replicates the evolution of Gaussian beam parameters, such as beam radius and wavefront curvature, corresponding to long-distance propagation.
  • Figure 2: Schematic illustrations of the solution exploration. (a) Genetic Algorithm (GA) explores the solution space to find initial candidates that satisfy the target performance. (b) Hamiltonian Monte Carlo (HMC) samples the parameter space around these candidates, generating a diverse ensemble of solutions. (c) The gradient of the objective function is calculated for each sample, allowing for the evaluation of practical feasibility.
  • Figure 3: (a) Visualization of the HMC sampling results in the parameter space of lens distances $d_1$ and $d_2$. Color indicates the robustness metric $R(\mathbf{p})$. The parameter's range is limited by the maximum size of apparatus $L_{\mathrm{max}}=3m$ and the curvature limitation of the center lens ($R_2$). (b) The calculated robustness metric is plotted against the total system length ($d_1+d_2$). There are inherent trade-offs between compactness and robustness.
  • Figure 4: (a) schematic of the three-lens Range Emulator (RE) configuration. (b) A folded configuration of the RE that reduces the number of alignment parameters by enforcing symmetry, with $d_1=d_2$ and $D_1=D_3$. This design is particularly effective when only one polarization direction is used.