2D Finite-Difference Time-Domain (FDTD) simulations of terahertz (THz) wave manipulation using relativistic moving fronts in semiconductor-filled waveguides. This work demonstrates temporal stretching and time-reversal of THz pulses through spatiotemporal control of photoexcited carrier density.
🔬 Overview
This repository contains the FDTD simulation code used to generate Figure 2 in our Nature Communications Physics publication on the SLIPSTREAM (Spacetime Light-Induced Photonic STRucturEs for Advanced Manipulation) platform.
The work explores how moving dielectric perturbations - created by photoexciting mobile charge carriers in a semiconductor waveguide - can manipulate THz light in exotic ways including temporal pulse stretching and time-reversal operations.
Paper: Front-induced transitions control THz waves
A.W. Schiff-Kearn, L. Gingras, S. Bernier, J.-M. Ménard, and D.G. Cooke
Communications Physics 4, 162 (2021)
🎯 Physical Concept
Key Innovation: By tilting the pulse front of a near-infrared pump laser, we create a moving front of photoexcited carriers in a silicon-filled parallel plate waveguide. This front travels at a controllable velocity vf relative to the THz wave velocity c/nSi.
Three Regimes:
- Subluminal (vf < c/nSi) - THz pulse stretching with quasi-static plateaus
- Luminal (vf ≈ c/nSi) - Optimal phase-matched emission
- Superluminal (vf > c/nSi) - Time-reversal via front-induced transitions
Physical Mechanism
- THz Generation: Built-in Schottky fields at metal-semiconductor interfaces
- Pulse Shaping: Spatiotemporal modulation via moving photoexcitation front
- Control Parameter: Front velocity tuned by optical pump tilt angle
- Applications: Sub-cycle THz control, dispersion compensation, pulse engineering
💻 My Contributions - Simulation Work
What I Did (Subluminal Regime Simulations) ✅
I developed and executed 2D-FDTD simulations for the subluminal regime that successfully:
- Modeled the parallel plate waveguide geometry with silicon and conducting boundaries
- Implemented Schottky field emission at top and bottom metal-semiconductor interfaces
- Incorporated Drude dispersion model for photoexcited silicon with realistic carrier densities (~10¹⁷ cm⁻³)
- Simulated moving carrier density fronts with velocity vf = 0.86 c/nSi
- Reproduced experimental THz waveforms showing temporal pulse stretching
- Validated the quasi-static plateau formation mechanism
Key Achievement: The simulations in Figure 2 of the paper quantitatively matched experimental data for various beam clipping configurations, confirming our physical understanding of the subluminal pulse stretching mechanism.
Technical Implementation
FDTD Algorithm Details:
- 2D spatial grid with perfectly conducting boundaries
- Time-stepping with Courant stability condition
- Drude model: carrier scattering time τ = 0.1 ps
- Schottky field depth: ~1 μm (Debye length)
- TEM mode extraction at fixed position
- Post-processing filter for detection response
🚧 Challenges and Limitations
Superluminal Regime - Numerical Difficulties
The Challenge: While the subluminal simulations worked excellently, I encountered significant numerical challenges when attempting to simulate the superluminal regime (vf ≥ c/nSi).
Technical Issues:
- Standard FDTD algorithms become unstable near or beyond the phase velocity
- Numerical dispersion errors accumulate for relativistic front velocities
- Courant condition violations for fast-moving dielectric perturbations
- Difficulty capturing front-induced transitions at phase-matched conditions
What Was Needed:
- Modified FDTD schemes with moving reference frames
- Specialized boundary conditions for superluminal fronts
- Enhanced numerical stability for relativistic regime
- Time-domain formulation of frequency-shifting processes
Personal Context
Unfortunately, I became seriously ill (cancer diagnosis and treatment) before I could develop and implement the modified FDTD algorithm necessary for the superluminal regime simulations. The paper was published during my recovery period.
Impact: The experimental results for time-reversal (superluminal regime) were not independently confirmed numerically in the publication. While the physics is well-supported by theory and experimental data, full numerical validation would have strengthened the complete picture.
📂 Repository Contents
This repository contains the working FDTD code for subluminal simulations that successfully generated Figure 2 of the paper.
Included:
- 2D-FDTD solver for THz propagation
- Moving front carrier density profiles
- Schottky field implementation
- Drude dispersion for photoexcited silicon
- Post-processing and filtering
Not Included:
- Superluminal regime solver (requires algorithmic modifications)
- Time-reversal simulations
- Full 3D field distributions
🔗 Broader Context - Moving Front Research
This experimental work on THz optics connects to my subsequent computational studies on quantum systems:
Common Thread: Spatiotemporal quenches and moving fronts
- This work (2021): THz photonics with moving dielectric fronts
- Long-range paper (2023): Quantum quenches in Ising models with power-law interactions
- 2D paper (2025): Efficient ground state preparation via moving parameter fronts
Insight: The concept of using moving fronts to control systems - whether electromagnetic waves or quantum wavefunctions - proved to be a powerful unifying theme across my research.
📄 Publication
Front-induced transitions control THz waves
A.W. Schiff-Kearn, L. Gingras, S. Bernier, J.-M. Ménard, and D.G. Cooke
Communications Physics 4, 162 (2021)
Open Access - Nature Publishing Group
My Role
Simulation contributor - Developed FDTD simulations for subluminal regime (Figure 2), validating experimental pulse stretching mechanism and demonstrating quantitative agreement between theory and experiment.
Software
- MATLAB implementation (this repository)
- Custom 2D-FDTD solver
- Drude dispersion integration
- Spatiotemporal source modeling
💡 Lessons and Future Work
What I Learned
✓ FDTD is powerful for electromagnetic problems but requires care near phase transitions
✓ Subluminal regime is more numerically stable than superluminal
✓ Good agreement between simulation and experiment validates physical models
✗ Superluminal regime needs specialized numerical methods
✗ Standard FDTD breaks down for relativistic moving boundaries
🔗 Dependencies
- MATLAB (any recent version)
- Standard numerical libraries
- No special toolboxes required
Simon Bernier
📝 Citation
If you use this code or build upon this work, please cite:
@article{schiffkearn2021front,
title={Front-induced transitions control THz waves},
author={Schiff-Kearn, A.W. and Gingras, L. and Bernier, S. and M{\'e}nard, J.-M. and Cooke, D.G.},
journal={Communications Physics},
volume={4},
pages={162},
year={2021},
publisher={Nature Publishing Group},
doi={10.1038/s42005-021-00667-4}
}
🎯 Bottom Line
What worked: FDTD simulations successfully validated the subluminal THz pulse stretching mechanism, providing quantitative agreement with experimental observations.
What didn’t: Superluminal regime simulations required algorithmic modifications I couldn’t complete due to illness.
Why it matters anyway: The successful subluminal simulations confirmed our physical understanding and enabled publication of a complete experimental story. Sometimes research challenges come from unexpected places, but the work that did get done contributed meaningfully to advancing THz photonics.
This project demonstrates: electromagnetic simulation, FDTD methods, ultrafast optics, THz photonics, spatiotemporal control, and the reality that research doesn’t always go according to plan - but valuable contributions can still be made.
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