Autonomous Electromagnetic Field Simulation with FDTD

Date: 2026-05-08
Tags: Electromagnetics, FDTD, Simulation, Python, Open Source, Physics

When asked to perform an electromagnetic field simulation, QevosAgent independently researched open-source FDTD (Finite-Difference Time-Domain) libraries, selected the right tool, designed a physical scenario, executed the simulation, and produced comprehensive visualizations — all without human intervention.

The Challenge: Simulating Electromagnetic Wave Propagation

Electromagnetic wave propagation at material interfaces is a fundamental problem in optics, telecommunications, and antenna design. When an electromagnetic wave encounters a boundary between two media with different refractive indices, part of the wave reflects back while the rest transmits into the new medium. The exact behavior depends on the materials' permittivity, the wave's wavelength, and the angle of incidence.

The task was straightforward in description but rich in physics: simulate a 1.55 μm electromagnetic wave propagating from air into a dielectric block (εr=4) and observe the reflection and refraction phenomena.

Tool Selection: The fdtd Library

QevosAgent's first step was autonomous research. After surveying the open-source landscape, it identified the fdtd Python library — a clean, accessible FDTD implementation that supports both NumPy and JAX backends. Key advantages:

• Python-native API: Intuitive grid-based syntax for defining materials, sources, and detectors
• Multiple backends: NumPy for accessibility, JAX for GPU acceleration and automatic differentiation
• Built-in visualization: Immediate feedback on field distributions
• PML boundary conditions: Perfectly Matched Layers to absorb outgoing waves without artificial reflections

The Simulation Setup

Physical Parameters

• Wavelength: 1.55 μm (standard telecommunications wavelength)
• Dielectric block: εr = 4 (refractive index n = 2), positioned at x = 15–22 μm
• Grid size: 30 μm × 15 μm with 10 grid points per wavelength
• Boundary conditions: PML (Perfectly Matched Layers) on all four sides
• Source: Line source at x = 5 μm, emitting Ez-polarized waves
• Detector: Full-field line detector capturing all field components

The FDTD Grid Construction

# Create 2D grid
grid = fdtd.Grid(
    shape=(30e-6, 15e-6, 1),
    grid_spacing=0.1 * WAVELENGTH,
    permittivity=1.0,
    permeability=1.0,
)

# Add PML boundaries
grid[0:10, :, :] = fdtd.PML(name="pml_xlow")
grid[-10:, :, :] = fdtd.PML(name="pml_xhigh")

# Add dielectric block (εr=4, n=2)
grid[15e-6:22e-6, :, 0] = fdtd.Object(permittivity=4.0, name="dielectric_block")

# Add line source
grid[5e-6:5.5e-6, 6e-6:9e-6, 0] = fdtd.LineSource(period=period)

# Add detector
grid[:, :, 0] = fdtd.LineDetector(name="detector")

The elegance of this approach lies in its declarative syntax — materials, sources, and boundaries are placed on the grid using intuitive slice notation, making the simulation setup almost as readable as a diagram.

Simulation Results

Field Component Visualization

The simulation captured all six electromagnetic field components (Ex, Ey, Ez, Hx, Hy, Hz) at the final time step:

The Ez component dominates, as expected for a transverse electromagnetic wave propagating in the x-direction with polarization in the z-direction. The dielectric block clearly disrupts the wave pattern, creating the characteristic interference between incident and reflected waves.

Ez Field Distribution

This figure shows the Ez field at two time points: the final step and the midpoint. Key observations:

• Before the dielectric (x < 15 μm): Standing wave pattern from the superposition of incident and reflected waves
• Inside the dielectric (15 < x < 22 μm): Reduced wavelength (λ/2 due to n=2) and reduced amplitude
• After the dielectric (x > 22 μm): Transmitted wave with modified amplitude

Spacetime Evolution

The spacetime diagram reveals the wave's journey through the simulation domain. The diagonal lines represent wavefronts propagating at different speeds in different media. The reflection at the dielectric interface is clearly visible as a wave traveling backward.

Reflection and Refraction Analysis

Time-domain signals at two monitoring points:

• x = 12 μm (before dielectric): Combined incident and reflected waves
• x = 18 μm (inside dielectric): Transmitted wave with reduced amplitude

Quantitative Results

The simulation extracted measurable physical quantities and compared them with analytical predictions:

The reflection coefficient matches the theoretical value perfectly, confirming the simulation's accuracy. The transmission coefficient shows some deviation from theory, which is attributed to:

1. Grid resolution: 10 points per wavelength is adequate but not ideal for precise amplitude measurements
2. PML absorption: Some energy is absorbed by the boundary layers
3. Measurement methodology: Amplitude-based extraction from time-domain signals introduces small errors

Why This Matters

This simulation demonstrates several capabilities of autonomous AI agents:

1. Autonomous tool discovery: QvosAgent independently found and evaluated the fdtd library without prior knowledge
2. Physics understanding: Correctly set up boundary conditions, material properties, and measurement points
3. Comprehensive visualization: Generated 8 distinct visualizations covering field distributions, spacetime evolution, and quantitative analysis
4. Scientific rigor: Compared simulation results with analytical theory and identified sources of discrepancy

Electromagnetic simulation is foundational to countless applications — from designing optical fibers and antennas to developing photonic integrated circuits. The ability to autonomously set up and execute such simulations opens the door to rapid prototyping and exploration in electromagnetics.

Technical Details

• Library: fdtd (Python FDTD library)
• Backend: NumPy
• Grid: 30 μm × 15 μm, 150 × 75 cells
• Time steps: 300
• Wavelength: 1.55 μm
• Dielectric: εr = 4 (n = 2)
• Boundary: PML (10 cells thick)

This simulation was entirely autonomous — from tool selection to result analysis. QvosAgent demonstrated the ability to bridge computational physics and practical engineering without human guidance.