Solver Comparison & Selection Guide

RCWA vs FDTD Solver Comparison

Compare simulated quantum efficiency (QE) curves from RCWA and FDTD solvers. Adjust pixel pitch and solver parameters to see how results and performance change.

Pixel pitch:

RCWA Fourier order: 9

FDTD grid resolution: 20 nm

RCWA (Fourier order = 9)

FDTD (grid = 20 nm)

RCWA

Time estimate:137 ms

Memory:6 MB

Periodic structures:Yes

Arbitrary geometry:Limited

FDTD

Time estimate:188 ms

Memory:3 MB

Periodic structures:Yes

Arbitrary geometry:Yes

Agreement

Max |Delta QE|:2.2%

Avg |Delta QE|:0.9%

Status:Good agreement

Overview

COMPASS supports multiple electromagnetic solver families for pixel simulation: TMM (Transfer Matrix Method) for fast 1D planar analysis, RCWA (Rigorous Coupled-Wave Analysis) with four implementations (torcwa, grcwa, meent, fmmax) for 2D periodic structures, and FDTD (Finite-Difference Time-Domain) solvers for arbitrary geometries. This guide consolidates benchmark results, cross-solver validation data, and practical selection guidance to help you choose the right solver for your task.

Part 1: RCWA Solver Benchmark

This section compares RCWA solvers (torcwa, grcwa, meent) on the same pixel structure, measuring accuracy and performance.

Goal

Run the same BSI pixel simulation with all available RCWA solvers, then compare QE results and execution times.

Setup

python

import copy
import time
import numpy as np
import matplotlib.pyplot as plt
from compass.runners.single_run import SingleRunner
from compass.analysis.solver_comparison import SolverComparison
from compass.visualization.qe_plot import plot_qe_comparison

pixel_config = {
    "pitch": 1.0,
    "unit_cell": [2, 2],
    "bayer_map": [["R", "G"], ["G", "B"]],
    "layers": {
        "air": {"thickness": 1.0, "material": "air"},
        "microlens": {
            "enabled": True, "height": 0.6,
            "radius_x": 0.48, "radius_y": 0.48,
            "material": "polymer_n1p56",
            "profile": {"type": "superellipse", "n": 2.5, "alpha": 1.0},
            "shift": {"mode": "none"},
        },
        "planarization": {"thickness": 0.3, "material": "sio2"},
        "color_filter": {
            "thickness": 0.6,
            "materials": {"R": "cf_red", "G": "cf_green", "B": "cf_blue"},
            "grid": {"enabled": True, "width": 0.05, "material": "tungsten"},
        },
        "barl": {"layers": [
            {"thickness": 0.010, "material": "sio2"},
            {"thickness": 0.025, "material": "hfo2"},
            {"thickness": 0.015, "material": "sio2"},
            {"thickness": 0.030, "material": "si3n4"},
        ]},
        "silicon": {
            "thickness": 3.0, "material": "silicon",
            "photodiode": {"position": [0, 0, 0.5], "size": [0.7, 0.7, 2.0]},
            "dti": {"enabled": True, "width": 0.1, "material": "sio2"},
        },
    },
}

source_config = {
    "wavelength": {"mode": "sweep", "sweep": {"start": 0.42, "stop": 0.68, "step": 0.02}},
    "polarization": "unpolarized",
}

Run all RCWA solvers

python

solvers = [
    {"name": "torcwa", "type": "rcwa", "params": {"fourier_order": [9, 9]}},
    {"name": "grcwa",  "type": "rcwa", "params": {"fourier_order": [9, 9]}},
    {"name": "meent",  "type": "rcwa", "params": {"fourier_order": [9, 9]}},
]

results = []
labels = []

for solver_cfg in solvers:
    config = {
        "pixel": pixel_config,
        "solver": {
            **solver_cfg,
            "stability": {"precision_strategy": "mixed", "fourier_factorization": "li_inverse"},
        },
        "source": source_config,
        "compute": {"backend": "auto"},
    }

    try:
        result = SingleRunner.run(config)
        results.append(result)
        labels.append(solver_cfg["name"])
        runtime = result.metadata.get("runtime_seconds", 0)
        print(f"{solver_cfg['name']}: {runtime:.2f}s")
    except Exception as e:
        print(f"{solver_cfg['name']}: FAILED - {e}")

Compare QE spectra

python

if len(results) >= 2:
    fig, ax = plt.subplots(figsize=(10, 6))
    plot_qe_comparison(results, labels, ax=ax)
    ax.set_title("RCWA Solver Comparison")
    plt.tight_layout()
    plt.savefig("solver_comparison_qe.png", dpi=150)
    plt.show()

Quantitative comparison

python

if len(results) >= 2:
    comparison = SolverComparison(results, labels)
    summary = comparison.summary()

    print("\n=== Comparison Summary ===")
    print("\nMax QE difference (absolute):")
    for key, val in summary["max_qe_diff"].items():
        print(f"  {key}: {val:.5f}")

    print("\nMax QE relative error (%):")
    for key, val in summary["max_qe_relative_error_pct"].items():
        print(f"  {key}: {val:.2f}%")

    print("\nRuntimes:")
    for solver, runtime in summary["runtimes_seconds"].items():
        print(f"  {solver}: {runtime:.2f}s")

RCWA Convergence Demo

See how increasing the Fourier order N improves the accuracy of permittivity reconstruction and RCWA reflectance/transmittance convergence for a binary grating.

Fourier Order N: 5

Total Harmonics:11

Matrix Size:11×11 = 121

Computational Cost (O(M³)):~1.3K

Gibbs Overshoot:9.4%

Permittivity Profile Reconstruction

R, T Convergence vs Fourier Order

Fourier Order Approximation Demo

See how increasing the number of Fourier harmonics improves the approximation of a square wave (representing a DTI trench or metal grid cross-section). Notice the Gibbs phenomenon ringing at the edges.

Fourier Order N: 5

Duty Cycle: 50%

Total Harmonics:11

Matrix Size (RCWA):11×11

Gibbs Overshoot:18.8%

Gibbs phenomenon: Even with many harmonics, the Fourier series overshoots by ~9% at discontinuities. In RCWA, this affects convergence at sharp material boundaries (e.g., Si/SiO₂ DTI walls). Li's factorization rules mitigate this for TM polarization.

Fourier order convergence comparison

Compare how each solver converges with Fourier order:

python

orders = [5, 7, 9, 11, 13, 15]
convergence_data = {s["name"]: [] for s in solvers}

for order in orders:
    for solver_cfg in solvers:
        config = {
            "pixel": pixel_config,
            "solver": {
                **solver_cfg,
                "params": {"fourier_order": [order, order]},
                "stability": {"precision_strategy": "mixed"},
            },
            "source": {
                "wavelength": {"mode": "single", "value": 0.55},
                "polarization": "unpolarized",
            },
            "compute": {"backend": "auto"},
        }

        try:
            result = SingleRunner.run(config)
            avg_qe = np.mean([qe[0] for qe in result.qe_per_pixel.values()])
            convergence_data[solver_cfg["name"]].append(avg_qe)
        except:
            convergence_data[solver_cfg["name"]].append(np.nan)

    print(f"Order {order}: done")

# Plot convergence
plt.figure(figsize=(8, 5))
for name, qe_values in convergence_data.items():
    plt.plot(orders, qe_values, "o-", label=name, linewidth=2)

plt.xlabel("Fourier Order")
plt.ylabel("Average QE at 550 nm")
plt.title("Convergence: QE vs Fourier Order")
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig("convergence_comparison.png", dpi=150)

Runtime scaling

Measure how runtime scales with Fourier order:

python

orders = [5, 7, 9, 11, 13, 15, 17]
timing_data = {s["name"]: [] for s in solvers}

for order in orders:
    for solver_cfg in solvers:
        config = {
            "pixel": pixel_config,
            "solver": {
                **solver_cfg,
                "params": {"fourier_order": [order, order]},
                "stability": {"precision_strategy": "mixed"},
            },
            "source": {
                "wavelength": {"mode": "single", "value": 0.55},
                "polarization": "TE",  # Single pol for timing
            },
            "compute": {"backend": "auto"},
        }

        try:
            result = SingleRunner.run(config)
            t = result.metadata.get("runtime_seconds", 0)
            timing_data[solver_cfg["name"]].append(t)
        except:
            timing_data[solver_cfg["name"]].append(np.nan)

# Plot
plt.figure(figsize=(8, 5))
for name, times in timing_data.items():
    plt.plot(orders, times, "o-", label=name, linewidth=2)

plt.xlabel("Fourier Order")
plt.ylabel("Runtime (seconds)")
plt.title("Runtime Scaling vs Fourier Order")
plt.legend()
plt.grid(True, alpha=0.3)
plt.yscale("log")
plt.tight_layout()
plt.savefig("runtime_scaling.png", dpi=150)

Expected results

QE agreement: All RCWA solvers should agree within 0.5-1% QE at the same Fourier order.
Convergence: All solvers converge to the same QE as order increases. Convergence rate may differ slightly.
Runtime: torcwa is typically fastest on GPU. grcwa and meent are competitive.
FDTD vs RCWA: Should agree within 1-2% QE. FDTD is significantly slower for single-wavelength runs.

Part 2: TMM vs RCWA

Cross-validation between TMM (1D) and RCWA (2D/3D) solvers confirms that different numerical methods produce physically consistent results and helps identify where 1D approximations break down relative to full 2D electromagnetic solutions.

Overview

Three solvers are compared on the same pixel structure:

TMM (Transfer Matrix Method): 1D analytical solver that treats each layer as an infinite uniform slab. Ignores lateral patterning (microlens shape, Bayer CF pattern, DTI). Extremely fast (~3 ms for a full sweep).
torcwa: PyTorch-based 2D RCWA solver using the S-matrix algorithm. Handles full lateral structure including microlens profile, color filter Bayer pattern, and DTI boundaries.
grcwa: NumPy-based 2D RCWA solver with autograd support. Independent RCWA implementation used to cross-check torcwa results.

Simulation Parameters

Pixel: 1.0 um pitch BSI, 2x2 RGGB Bayer
Stack: 9 layers (air / microlens / planarization / CF / 4-layer BARL / silicon)
RCWA: Fourier order [3,3], 5 microlens slices, 64x64 grid
Source: Normal incidence, unpolarized, 380-780 nm (20 nm step)
Platform: macOS (Apple Silicon), CPU only

Interactive Comparison

Cross-Solver Validation: TMM vs torcwa vs grcwa

Compare absorption, reflection, and transmission spectra from three different electromagnetic solvers. TMM is a fast 1D method, while torcwa and grcwa are full 2D RCWA solvers.

TMM mean Absorption (A):0.6435

torcwa mean Absorption (A):0.9838

grcwa mean Absorption (A):0.9839

Max |torcwa - grcwa|:0.0114

Show numerical data

Wavelength (nm)	TMM	torcwa	grcwa	\|torcwa - grcwa\|
380	0.9081	0.9853	0.9805	0.0048
400	0.8750	0.9761	0.9861	0.0100
420	0.8210	0.9979	0.9869	0.0110
440	0.8566	0.9931	0.9875	0.0056
460	0.7923	0.9982	0.9898	0.0084
480	0.7127	0.9862	0.9881	0.0019
500	0.3990	0.9814	0.9852	0.0038
520	0.0777	0.9742	0.9856	0.0114
540	0.0572	0.9868	0.9879	0.0011
560	0.3528	0.9984	0.9886	0.0098
580	0.6389	0.9971	0.9861	0.0110
600	0.7190	0.9897	0.9824	0.0073
620	0.7349	0.9802	0.9797	0.0005
640	0.7563	0.9684	0.9793	0.0109
660	0.7455	0.9761	0.9807	0.0046
680	0.6935	0.9757	0.9826	0.0069
700	0.6549	0.9777	0.9840	0.0063
720	0.6564	0.9805	0.9837	0.0032
740	0.6815	0.9821	0.9819	0.0002
760	0.6961	0.9813	0.9792	0.0021
780	0.6849	0.9739	0.9765	0.0026

Wavelength Sweep Results

Full Data Table

Complete R, T, A values for all 21 wavelengths across the three solvers. Light propagates from air (top) through the stack into silicon (bottom).

λ (nm)	TMM R	TMM T	TMM A	torcwa R	torcwa T	torcwa A	grcwa R	grcwa T	grcwa A
380	0.0401	0.0517	0.9081	0.0147	0.0000	0.9853	0.0195	0.0000	0.9805
400	0.0529	0.0722	0.8750	0.0239	0.0000	0.9761	0.0139	0.0000	0.9861
420	0.0961	0.0830	0.8210	0.0021	0.0000	0.9979	0.0131	0.0000	0.9869
440	0.0348	0.1085	0.8566	0.0069	0.0000	0.9931	0.0125	0.0000	0.9875
460	0.0633	0.1443	0.7923	0.0018	0.0000	0.9982	0.0102	0.0000	0.9898
480	0.0324	0.2549	0.7127	0.0138	0.0000	0.9862	0.0119	0.0000	0.9881
500	0.1461	0.4549	0.3990	0.0186	0.0000	0.9814	0.0148	0.0000	0.9852
520	0.0088	0.9135	0.0777	0.0258	0.0000	0.9742	0.0144	0.0000	0.9856
540	0.2405	0.7023	0.0572	0.0131	0.0001	0.9868	0.0121	0.0000	0.9879
560	0.1697	0.4775	0.3528	0.0013	0.0003	0.9984	0.0114	0.0000	0.9886
580	0.0280	0.3331	0.6389	0.0021	0.0008	0.9971	0.0139	0.0000	0.9861
600	0.0387	0.2423	0.7190	0.0077	0.0026	0.9897	0.0176	0.0000	0.9824
620	0.0477	0.2175	0.7349	0.0137	0.0061	0.9802	0.0202	0.0000	0.9797
640	0.0180	0.2258	0.7563	0.0223	0.0093	0.9684	0.0206	0.0001	0.9793
660	0.0209	0.2336	0.7455	0.0126	0.0113	0.9761	0.0193	0.0001	0.9807
680	0.0781	0.2284	0.6935	0.0116	0.0126	0.9757	0.0173	0.0001	0.9826
700	0.1199	0.2252	0.6549	0.0093	0.0130	0.9777	0.0159	0.0001	0.9840
720	0.1091	0.2345	0.6564	0.0055	0.0140	0.9805	0.0161	0.0002	0.9837
740	0.0664	0.2522	0.6815	0.0032	0.0147	0.9821	0.0178	0.0003	0.9819
760	0.0372	0.2667	0.6961	0.0045	0.0142	0.9813	0.0205	0.0004	0.9792
780	0.0430	0.2721	0.6849	0.0116	0.0145	0.9739	0.0231	0.0004	0.9765

Key Observations

1D vs 2D Differences

The TMM and RCWA results differ significantly, and understanding why is critical for choosing the right solver for a given task.

1. TMM vs RCWA Absorption

TMM shows absorption ranging from 5% to 91%, while RCWA consistently shows 97-100% absorption across the entire visible spectrum. The 3 um silicon layer absorbs nearly all light that successfully enters it. In TMM (1D), thin-film interference between planar layers creates constructive and destructive patterns that open transmission windows, especially around 500-540 nm where the green color filter becomes transparent. In RCWA (2D), the actual microlens profile focuses light, the Bayer color filter pattern introduces lateral index variation, and DTI boundaries confine light within the pixel. These 2D effects significantly increase the optical path length through silicon and reduce coherent back-reflection.

2. Transmission

TMM predicts substantial transmission (5-91%) through the stack, with a dramatic peak near 520 nm (T=0.91). In contrast, both RCWA solvers show near-zero transmission (T < 0.015 for torcwa, T < 0.0004 for grcwa). The 3 um silicon layer at the Fourier order [3,3] resolution used in RCWA effectively absorbs all power that is not reflected. The S-matrix calculation through thick absorbing layers approaches machine precision limits, and lateral confinement by DTI prevents light from escaping sideways.

3. Reflection

TMM reflectance exhibits strong thin-film oscillations (1-24%), characteristic of coherent interference in a planar multilayer. RCWA reflectance is low and spectrally smooth (0.1-2.6%). The 2D microlens profile acts as a graded-index anti-reflection structure: light incident on a curved surface couples more efficiently into the stack than light hitting a flat interface, reducing specular reflection significantly.

4. torcwa vs grcwa Agreement

Both RCWA solvers agree well with each other, with reflectance differences within 0.5-1.5% absolute and absorption differences within 0.5-2%. This level of agreement between two independent RCWA implementations (PyTorch-based vs NumPy-based) provides strong validation that both solvers are computing the electromagnetic problem correctly. Small residual differences arise from numerical precision in eigendecomposition and S-matrix assembly.

When to Use TMM vs RCWA

TMM: Stack design, BARL thickness optimization, fast parameter sweeps (~3 ms per sweep). Best for thin-film interference analysis where lateral patterning is not the primary concern.
RCWA: Full 2D diffraction effects, absolute QE prediction, cross-pixel crosstalk analysis, microlens design (~15 s per sweep). Required when lateral structure (microlens, Bayer pattern, DTI) significantly affects the result.

Runtime Comparison

Solver	Wavelengths	Runtime	Speedup
TMM	21	2.9 ms	5400x
grcwa	21	0.1 s	157x
torcwa	21	15.7 s	1x

TMM is approximately 5400x faster than torcwa, making it the preferred solver for iterative design loops. grcwa is 157x faster than torcwa for the same RCWA calculation, benefiting from NumPy's optimized linear algebra on CPU. torcwa's PyTorch backend is optimized for GPU acceleration, so the CPU-only comparison understates its performance on CUDA devices.

Solver Compatibility Notes

meent Numerical Stability

meent 0.12.0 has a known numerical instability for multi-layer 2D structures: R+T > 1 occurs for stacks with 2 or more patterned layers. Single-layer simulations are correct. This is under investigation.

FDTD Material Absorption

The flaport fdtd solver uses per-voxel conductivity-based damping to model material absorption (imaginary permittivity). Combined with two-pass reference normalization, this achieves absorption agreement with RCWA within 3% across the visible spectrum.

Energy Conservation

Energy conservation (R + T + A = 1) is a fundamental physical constraint and serves as a self-consistency check for each solver.

Solver	max \|1 - (R+T+A)\|	Notes
TMM	1.11 x 10^-16	Machine precision (analytical transfer matrices)
torcwa	0.0000	S-matrix formulation inherently conserves energy
grcwa	0.0000	S-matrix formulation inherently conserves energy

All three solvers satisfy energy conservation to machine precision, confirming that the numerical implementations are correct regardless of the physical differences in their modeling assumptions.

Execution Environment

Platform    : macOS (Darwin 25.2.0, Apple Silicon)
Python      : 3.11
PyTorch     : 2.5.0 (torcwa backend)
NumPy       : (grcwa backend)
RCWA Order  : [3, 3] (49 harmonics)
Grid        : 64 x 64
Lens Slices : 5

Part 3: RCWA vs FDTD

This section demonstrates how to validate RCWA (grcwa) results against FDTD (flaport) for a BSI CMOS pixel, and compare direct illumination with cone illumination.

Interactive Chart

RCWA vs FDTD Cross-Solver Validation

Compare absorption, reflection, and transmission spectra from RCWA (grcwa) and FDTD (flaport) solvers, plus cone illumination comparison.

grcwa mean Absorption (A):0.9848

fdtd mean Absorption (A):0.9829

Max |grcwa - fdtd|:0.0027

Show numerical data

Wavelength (nm)	grcwa	fdtd	\|grcwa - fdtd\|
400	0.9834	0.9807	0.0027
420	0.9837	0.9821	0.0016
440	0.9915	0.9897	0.0018
460	0.9902	0.9885	0.0017
480	0.9838	0.9825	0.0013
500	0.9835	0.9818	0.0017
520	0.9886	0.9867	0.0019
540	0.9915	0.9902	0.0013
560	0.9881	0.9864	0.0017
580	0.9812	0.9797	0.0015
600	0.9762	0.9745	0.0017
620	0.9758	0.9735	0.0023
640	0.9792	0.9770	0.0022
660	0.9840	0.9821	0.0019
680	0.9876	0.9854	0.0022
700	0.9882	0.9860	0.0022

Why Cross-Solver Validation?

RCWA and FDTD solve Maxwell's equations with fundamentally different approaches:

	RCWA	FDTD
Domain	Frequency domain	Time domain
Periodicity	Inherently periodic	Requires PML boundaries
Strengths	Fast for thin-film stacks	Handles arbitrary geometry
Convergence	Fourier order	Grid spacing + runtime

When both methods agree on absorption/reflection/transmission spectra, it provides strong confidence in the physical validity of the simulation.

Running the Validation

bash

PYTHONPATH=. python3.11 scripts/validate_rcwa_vs_fdtd.py

This script runs three experiments:

Experiment 1: Normal Incidence Sweep

Compares grcwa (fourier_order=[5,5]) vs fdtd_flaport (dx=0.015um, 500fs, pml=20) across 400-700nm. The FDTD solver uses per-voxel absorption damping and two-pass reference normalization for accurate R/T/A extraction.

Acceptance criterion: max |A_grcwa - A_fdtd| < 5%

Experiment 2: Cone Illumination

Compares three illumination conditions using grcwa:

Direct: Normal incidence (θ=0°)
Cone F/2.0 CRA=0°: 19-point Fibonacci sampling, cosine weighting
Cone F/2.0 CRA=15°: Same cone with 15° chief ray angle

Experiment 3: RCWA Cross-Check

Validates grcwa vs torcwa with identical cone illumination to ensure RCWA solver consistency.

Acceptance criterion: max |A_grcwa - A_torcwa| < 5%

Using ConeIlluminationRunner

python

from compass.runners.cone_runner import ConeIlluminationRunner

config = {
    "pixel": { ... },  # pixel stack config
    "solver": {"name": "grcwa", "type": "rcwa", "params": {"fourier_order": [5, 5]}},
    "source": {
        "wavelength": {"mode": "sweep", "sweep": {"start": 0.40, "stop": 0.70, "step": 0.02}},
        "angle": {"theta_deg": 0.0, "phi_deg": 0.0},
        "polarization": "unpolarized",
        "cone": {
            "cra_deg": 0.0,       # Chief ray angle
            "f_number": 2.0,       # Lens F-number
            "sampling": {"type": "fibonacci", "n_points": 19},
            "weighting": "cosine",
        },
    },
    "compute": {"backend": "cpu"},
}

result = ConeIlluminationRunner.run(config)

The runner:

Generates angular sampling points from ConeIllumination
For each angle: sets up source with (θ, φ) and runs the solver
Accumulates weighted R, T, A and per-pixel QE
Returns a single SimulationResult with the weighted average

Convergence Tips

If RCWA and FDTD results diverge:

FDTD: Increase runtime (500→1000fs), decrease grid_spacing (0.015→0.01um), increase pml_layers (20→30)
RCWA: Increase fourier_order ([5,5]→[9,9]→[13,13])

Key FDTD accuracy factors:

Per-voxel absorption damping: The flaport library only supports real-valued permittivity on the grid. COMPASS computes equivalent conductivity from the imaginary permittivity and applies per-voxel E-field damping after each timestep: damping = (1 - α) / (1 + α) where α = σ·dt / (2·ε₀·εᵣ).
Two-pass reference normalization: A vacuum reference simulation establishes incident power (P_inc). The structure run's reflection is computed as excess upward flux relative to the reference, eliminating soft-source artifacts.
Sufficient runtime: At least 500 fs is recommended for the CW source to reach steady state in the 3 um silicon structure.

Part 4: Solver Selection Guide

Use the following decision tree to choose the right solver for your simulation:

1. Do you only have uniform (unpatterned) layers?

Yes → Use TMM

~1000x faster than RCWA, ~5000x faster than FDTD
Ideal for BARL thickness optimization, stack design, fast parameter sweeps
Runtime: ~3 ms for a full wavelength sweep (21 wavelengths)
Limitation: Cannot model microlens focusing, Bayer pattern diffraction, or DTI confinement

2. Do you have periodic 2D patterned layers (microlens, color filter grid, DTI)?

Yes → Use RCWA

Choose the specific RCWA solver based on your needs:

Solver	Backend	Key Strengths	Best For
torcwa	PyTorch	GPU acceleration, S-matrix stability, TF32 disabled for precision	Production GPU runs, large Fourier orders
grcwa	NumPy	Autograd support, fast on CPU, critical for project	Inverse design, CPU-only environments, cross-validation
meent	PyTorch/JAX	Multi-backend flexibility	Experimental, single-layer structures only (see stability note)
fmmax	JAX	4 FMM vector formulations	Research, advanced Fourier factorization studies

3. Do you have non-periodic or complex 3D geometries?

Yes → Use FDTD

Solver	Backend	Key Strengths	Best For
fdtd_flaport	PyTorch	Simple API, differentiable	Quick FDTD prototyping
fdtdz	JAX	Efficient z-propagation	JAX-based workflows
fdtdx	JAX	Multi-GPU, differentiable	Large-scale inverse design
meep	C++/Python	Mature, feature-rich	Complex geometries, reference solutions

Quick Reference

Scenario	Recommended Solver	Approximate Runtime
BARL thickness sweep (1000 configs)	TMM	~3 seconds total
Single wavelength QE (2D pixel)	grcwa or torcwa	0.5-15 seconds
Full wavelength sweep (2D pixel)	grcwa (CPU) / torcwa (GPU)	0.1-16 seconds
Inverse design optimization	grcwa (autograd)	Minutes per iteration
Cross-validation reference	Run TMM + 2 RCWA solvers	Compare results
Non-periodic structure	meep or fdtdx	Minutes to hours

Solver Comparison & Selection Guide ​

RCWA vs FDTD Solver Comparison

Overview ​

Part 1: RCWA Solver Benchmark ​

Goal ​

Setup ​

Run all RCWA solvers ​

Compare QE spectra ​

Quantitative comparison ​

RCWA Convergence Demo

Fourier Order Approximation Demo

Fourier order convergence comparison ​

Runtime scaling ​

Expected results ​

Part 2: TMM vs RCWA ​

Overview ​

Interactive Comparison ​

Cross-Solver Validation: TMM vs torcwa vs grcwa

Wavelength Sweep Results ​

Full Data Table ​

Key Observations ​

1D vs 2D Differences ​

1. TMM vs RCWA Absorption ​

2. Transmission ​

3. Reflection ​

4. torcwa vs grcwa Agreement ​

When to Use TMM vs RCWA ​

Runtime Comparison ​

Solver Compatibility Notes ​

Energy Conservation ​

Execution Environment ​

Part 3: RCWA vs FDTD ​

Interactive Chart ​

RCWA vs FDTD Cross-Solver Validation

Why Cross-Solver Validation? ​

Running the Validation ​

Experiment 1: Normal Incidence Sweep ​

Experiment 2: Cone Illumination ​

Experiment 3: RCWA Cross-Check ​

Using ConeIlluminationRunner ​

Convergence Tips ​

Part 4: Solver Selection Guide ​

1. Do you only have uniform (unpatterned) layers? ​

2. Do you have periodic 2D patterned layers (microlens, color filter grid, DTI)? ​

3. Do you have non-periodic or complex 3D geometries? ​

Quick Reference ​

Solver Comparison & Selection Guide

Overview

Part 1: RCWA Solver Benchmark

Goal

Setup

Run all RCWA solvers

Compare QE spectra

Quantitative comparison

Fourier order convergence comparison

Runtime scaling

Expected results

Part 2: TMM vs RCWA

Overview

Interactive Comparison

Wavelength Sweep Results

Full Data Table

Key Observations

1D vs 2D Differences

1. TMM vs RCWA Absorption

2. Transmission

3. Reflection

4. torcwa vs grcwa Agreement

When to Use TMM vs RCWA

Runtime Comparison

Solver Compatibility Notes

Energy Conservation

Execution Environment

Part 3: RCWA vs FDTD

Interactive Chart

Why Cross-Solver Validation?

Running the Validation

Experiment 1: Normal Incidence Sweep

Experiment 2: Cone Illumination

Experiment 3: RCWA Cross-Check

Using ConeIlluminationRunner

Convergence Tips

Part 4: Solver Selection Guide

1. Do you only have uniform (unpatterned) layers?

2. Do you have periodic 2D patterned layers (microlens, color filter grid, DTI)?

3. Do you have non-periodic or complex 3D geometries?

Quick Reference