Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Curving Beam Reflections: Model and Experimental Validation

Caroline Jane Spindel, Edward Knightly

TL;DR

This paper tackles the challenge of predicting reflections of convex curving beams in sub-THz wireless scenarios, where conventional ray-mirror thinking fails for finite or nonplanar reflectors. It introduces a geometric framework that represents the incident beam as a family of tangents and applies the law of reflection to each tangent, leveraging a Legendre transform to reconstruct the reflected envelope. The authors validate the approach with FEM simulations across planar and convex reflectors and with over-the-air THz experiments, achieving millimeter-scale accuracy in predicting reflected trajectories. The framework enables accurate design of reflected curved links and curving radar paths, offering a foundation for robust sub-THz sensing and communication in complex environments.

Abstract

Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately, attempting to "mirror" the incident beam trajectory across the normal of the reflector, as in ray optics, fails in general. Thus, we introduce the first geometric framework capable of modeling the reflections of arbitrary convex sub-THz curving beams from general reflectors with experimental verification. Rather than "mirroring" the trajectory, we decompose the beam into a family of tangents and demonstrate that this process is equivalent to the Legendre transform. This approach allows us to accurately account for reflectors of any shape, size, and position while preserving the underlying physics of wave propagation. Our model is validated through finite element method simulations and over-the-air experiments, demonstrating millimeter-scale accuracy in predicting reflections. Our model provides a foundation for future curving beam communication and sensing systems, enabling the design of reflected curved links and curving radar paths.

Curving Beam Reflections: Model and Experimental Validation

TL;DR

This paper tackles the challenge of predicting reflections of convex curving beams in sub-THz wireless scenarios, where conventional ray-mirror thinking fails for finite or nonplanar reflectors. It introduces a geometric framework that represents the incident beam as a family of tangents and applies the law of reflection to each tangent, leveraging a Legendre transform to reconstruct the reflected envelope. The authors validate the approach with FEM simulations across planar and convex reflectors and with over-the-air THz experiments, achieving millimeter-scale accuracy in predicting reflected trajectories. The framework enables accurate design of reflected curved links and curving radar paths, offering a foundation for robust sub-THz sensing and communication in complex environments.

Abstract

Curving beams are a promising new method for bypassing obstacles in future millimeter-wave to sub-terahertz (sub-THz) networks but lack a general predictive model for their reflections from arbitrary surfaces. We show that, unfortunately, attempting to "mirror" the incident beam trajectory across the normal of the reflector, as in ray optics, fails in general. Thus, we introduce the first geometric framework capable of modeling the reflections of arbitrary convex sub-THz curving beams from general reflectors with experimental verification. Rather than "mirroring" the trajectory, we decompose the beam into a family of tangents and demonstrate that this process is equivalent to the Legendre transform. This approach allows us to accurately account for reflectors of any shape, size, and position while preserving the underlying physics of wave propagation. Our model is validated through finite element method simulations and over-the-air experiments, demonstrating millimeter-scale accuracy in predicting reflections. Our model provides a foundation for future curving beam communication and sensing systems, enabling the design of reflected curved links and curving radar paths.
Paper Structure (23 sections, 11 equations, 12 figures)

This paper contains 23 sections, 11 equations, 12 figures.

Table of Contents

  1. Introduction
  2. BACKGROUND
  3. Modeling Curving Beam Reflections
  4. Model Overview
  5. Model Inputs
  6. Decomposing the Trajectory into Tangents
  7. Reflecting the Tangents
  8. Reconstructing the Reflection
  9. Computational Complexity
  10. MODEL EVALUATION WITH FEM SIMULATIONS
  11. Scenario and Performance Metrics
  12. Single-Trajectory Input with Large Planar Reflector
  13. Multiple-Trajectory Input with Large Reflector
  14. Single-Trajectory Input with Small Planar Reflector
  15. Multiple-Trajectory Input with Convex Reflector
  16. ...and 8 more sections

Figures (12)

  • Figure 1: Electric field distribution of a truncated Airy beam at 150 GHz.
  • Figure 2: Characterizing the trajectory of an Airy beam.
  • Figure 3: An illustration of the model's inputs and outputs.
  • Figure 4: Predicting the reflection off (a) a large planar reflector and (b) a small planar reflector.
  • Figure 5: Prediction accounting for the beamwidth and three lobes (tangents not shown).
  • ...and 7 more figures