⚡ electrical engineering

Efficient Numerical Modeling of Near-Field Diffraction in ORIS-Assisted Free-Space Optical Links

This paper proposes a computationally efficient FFT-based numerical framework to model near-field diffraction in ORIS-assisted free-space optical links, achieving accuracy comparable to direct Riemann-sum methods while significantly reducing computational complexity.

Original authors: Tuan A. Hoang, Phuc V. Trinh, Shinya Sugiura, Chuyen T. Nguyen, Susumu Ishihara, Thanh V. Pham

Published 2026-06-02

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tuan A. Hoang, Phuc V. Trinh, Shinya Sugiura, Chuyen T. Nguyen, Susumu Ishihara, Thanh V. Pham

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to send a message using a super-bright laser beam, like a high-tech flashlight, from one building to another. Usually, for this to work, you need a perfectly clear, straight line of sight between the sender and the receiver. But what if a big building or a tree blocks the path?

This is where the paper introduces a clever trick: a giant, smart mirror called an ORIS (Optical Reconfigurable Intelligent Surface). Think of this ORIS as a "digital mirror" that can catch the laser beam, bounce it off, and steer it around the obstacle to hit the receiver.

However, there's a catch. When the mirror is relatively close to the sender or receiver (what scientists call the "near-field"), the light doesn't just bounce in a simple, predictable way. Instead, it behaves like water rippling after a stone is thrown, creating complex, messy patterns called diffraction.

The paper tackles a specific problem: How do we calculate exactly where that light will land and how strong it will be, without spending a lifetime waiting for the computer to finish the math?

Here is the breakdown of their solution using simple analogies:

The Problem: The "Pixel-Perfect" Puzzle

To figure out exactly how the light behaves near the mirror, you have to break the mirror's surface down into tiny, tiny squares (like pixels on a screen). Because light waves are so small (thousands of times smaller than a human hair), these squares have to be microscopic to get an accurate answer.

The Old Way (Riemann Sum): Imagine trying to count every single grain of sand on a beach to measure its weight. You have to look at every single grain individually. The paper's authors tried this method first. It works perfectly and gives the right answer, but it is incredibly slow. For a mirror the size of a small room, their computer had to do calculations for about one hour just to get the result. It's like trying to solve a 10-million-piece puzzle by looking at one piece at a time.

The Solution: The "Magic Shortcut" (FFT)

The authors realized that instead of checking every single grain of sand one by one, they could look at the whole beach from a helicopter and see the pattern all at once.

The New Way (FFT-based Method): They used a mathematical tool called the Fast Fourier Transform (FFT). Think of this as a "magic translator."
- Instead of trying to add up the effect of every single tiny square on the mirror (which is hard), the FFT translates the problem into a different language (the "frequency domain").
- In this new language, the complicated math of adding up millions of tiny ripples turns into a simple multiplication problem.
- It's like realizing that instead of adding 1 + 2 + 3 + ... + 1,000,000 one by one, you can just use a formula to get the answer instantly.

The Results: Fast and Accurate

The paper tested both methods:

Accuracy: The "Magic Shortcut" (FFT) gave results that were almost identical to the "Pixel-Perfect" method (Riemann Sum). The light patterns matched up perfectly.
Speed: This is the big win. While the old method took one hour, the new FFT method finished the same job in just 13 seconds. That is a massive speedup, turning a day-long wait into a coffee-break calculation.

Why This Matters (According to the Paper)

The authors aren't saying this will cure diseases or build flying cars. They are strictly focused on communication. By making these calculations fast and accurate, engineers can now design better systems to bounce laser signals around obstacles. This means we could have high-speed internet connections between buildings even if a new skyscraper gets built in the middle of the path, without needing to dig up the ground to lay cables.

In a nutshell: The paper found a way to stop "counting every grain of sand" and start "seeing the whole beach," allowing engineers to design smart laser communication systems much faster than before.

Technical Summary: Efficient Numerical Modeling of Near-Field Diffraction in ORIS-Assisted Free-Space Optical Links

Problem Statement
Free-space optical (FSO) communication systems utilizing Optical Reconfigurable Intelligent Surfaces (ORIS) offer a promising solution for establishing non-line-of-sight (NLoS) links by intelligently manipulating optical wave phases. While existing literature provides tractable analytical models for ORIS-assisted FSO systems in the intermediate-field and far-field regimes, these models rely on linear phase approximations that fail in the near-field regime. In the near-field, higher-order phase terms across the ORIS surface become significant, creating a complex dependency on system parameters such as ORIS size, beam footprint, propagation distance, and misalignment. Consequently, closed-form analytical solutions are unavailable, and conventional far-field approaches are inapplicable. Direct numerical evaluation of the diffraction integral in this regime presents a significant challenge: accurate modeling requires spatial discretization at the scale of the optical wavelength, leading to prohibitively high computational complexity for large ORIS apertures.

Methodology
The paper proposes a numerical framework to evaluate the optical field distribution in ORIS-assisted FSO links operating in the near-field. The study compares two distinct numerical approaches:

Direct Riemann-Sum Evaluation: This method discretizes the ORIS surface into a fine 2D grid and approximates the Huygens-Fresnel diffraction integral by summing contributions from all grid points. To capture rapid phase variations at optical wavelengths (1550 nm), the spatial sampling interval must be extremely small (on the order of micrometers). While this approach serves as a high-accuracy benchmark, it requires $O(N^4)$ operations for an $N \times N$ grid, resulting in excessive computational time.
Fast Fourier Transform (FFT)-Based Method: To improve efficiency, the authors reformulate the propagation process as a convolution between the equivalent aperture field (incident field multiplied by the ORIS phase profile) and the free-space propagation kernel. By applying the angular spectrum formulation, this convolution in the spatial domain is transformed into a multiplication in the spatial-frequency domain. This allows the use of FFT algorithms to compute the propagated field, reducing the computational complexity to $O(N^2 \log N^2)$ .

Key Contributions

Identification of Near-Field Limitations: The work highlights the inadequacy of closed-form analytical models for near-field ORIS-assisted FSO links, where higher-order phase terms cannot be neglected.
Development of a Numerical Framework: The paper establishes a comparative framework using both direct Riemann-sum integration and FFT-based angular spectrum propagation to model near-field diffraction.
Efficiency Optimization: The study demonstrates that reformulating the diffraction integral as a spatial-frequency domain convolution enables the use of FFTs, drastically reducing computational load without sacrificing numerical accuracy.

Results
Simulation results were conducted using an ORIS size of $1\text{m} \times 1\text{m}$ , an optical wavelength of 1550 nm, and specific transmitter/receiver orientations.

Accuracy: The FFT-based method produced electric field amplitude distributions that closely matched those obtained via the Riemann-sum approach. The relative error remained low near the center of the receiver (where optical energy is concentrated) and increased only slightly toward the edges, which has negligible impact on overall propagation characteristics.
Computational Performance: The Riemann-sum approach, requiring a $10^6 \times 10^6$ sampling grid for convergence, took approximately one hour to complete. In contrast, the FFT-based method, utilizing a $1024 \times 1024$ grid on an NVIDIA RTX A4000 GPU, achieved comparable results in an average of 13.1 seconds.
Convergence: The study confirmed that the Riemann-sum approximation converges as spatial resolution increases, validating its use as a reference standard despite its computational cost.

Significance
The paper claims that the proposed FFT-based method provides a practical and efficient solution for analyzing near-field propagation in ORIS-assisted FSO systems. By significantly reducing computational complexity while maintaining accuracy comparable to direct integration, this approach enables the simulation and design of large-scale ORIS systems in the near-field regime, a task that was previously hindered by the intractability of direct numerical methods. The work bridges the gap between theoretical modeling and practical system analysis for next-generation optical communication networks requiring NLoS capabilities.

The Problem: The "Pixel-Perfect" Puzzle

The Solution: The "Magic Shortcut" (FFT)

The Results: Fast and Accurate

Why This Matters (According to the Paper)

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