Navette - Weaving the mathematics of light in thin film systems

Navette is a high-performance, physically rigorous 1D optical engine designed for the simulation of light propagation in stratified media. Built on a modern Scattering Matrix (S-matrix) architecture, it offers a numerically stable and vectorized alternative to traditional Transfer Matrix Methods (TMM).

1. Unconditional Numerical Stability

Traditional TMM suffers from numerical divergence (exponentially growing evanescent waves) when dealing with thick layers or highly absorbing materials. Navette utilizes the Redheffer Star Product to propagate scattering matrices, ensuring that all matrix elements remain bounded and physically meaningful, regardless of layer thickness.

2. High-Concurrency Performance

As a Principal Performance Engineer, you need tools that scale. Navette is built for speed:

• Parallel Execution: Utilizes Numba’s @njit(parallel=True) to saturate all available CPU cores.

• Vectorized Engine: Operations are performed across the entire (wavelength × angle) coordinate space in a single pass, eliminating Python's loop overhead.

• Memory Efficiency: Collapses multi-layer stacks into a compact global S-matrix to minimize cache misses.

3. Partial Coherence Support

Real-world systems often involve thick substrates (like a 1mm glass slide) where phase information is lost. Navette features a Hybrid Coherence Engine:

• Coherent Blocks: Preserves phase for thin-film interference.

• Incoherent Interfaces: Switches to intensity-based propagation for thick layers, preventing the "unphysical ringing" caused by assuming perfect coherence across a macroscopic substrate.

4. Advanced Physics Modeling

Navette goes beyond simple Fresnel equations to provide research-grade accuracy:

• Interface Roughness: Implements the Névot-Croce model, providing superior accuracy for high-frequency or X-ray reflectometry compared to standard Gaussian approximations.

• Ellipsometric Rigor: Outputs (Ψ,Δ) parameters that strictly follow the Azzam & Bashara convention, ensuring direct compatibility with commercial ellipsometers (e.g., Woollam, Horiba).

Technical Specifications

Feature	Implementation & Engineering Benefit
Core Algorithm	1D Scattering Matrix ($S$-matrix): Utilizes the Redheffer Star Product to eliminate numerical divergence and precision loss in thick or highly absorbing layers.
Propagation Logic	Hybrid Mixed Coherence: Sophisticated dual-stage engine supporting phase-accurate (coherent) and intensity-only (incoherent) layers within a single pass.
Coherent Blocks	$2 \times 2$ Complex Field Matrices: Maintains full phase and amplitude information, ensuring rigorous calculation of thin-film interference and ellipsometric parameters.
Incoherent Blocks	Stokes-Mueller / Intensity Redheffer: Prevents unphysical interference artifacts in macroscopic substrates by utilizing intensity-based propagation.
Roughness Model	Névot-Croce (Exact Wavevector): Achieves research-grade accuracy for X-ray and UV interfaces by modeling exact wavevector correlations across boundaries.
Optimization	Numba-JIT / Parallelized prange: Delivers near-native C performance with Pythonic flexibility, optimized for high-concurrency simulation and real-time GUI responsiveness.
Polarization	Full $s$ and $p$ Support: Comprehensive Jones and Stokes calculus integration, following standard commercial ellipsometry conventions (Azzam & Bashara).
Complexity	$O(N)$ Scaling: Optimized linear time complexity relative to the number of layers, ensuring stable performance for complex multi-stack architectures.