Photonics2D#

Version	0
Design space	`Box(0.0, 1.0, (120, 120), float64)`
Objectives	total_overlap: ↑
Conditions	lambda1: 1.5 lambda2: 1.3 blur_radius: 2
Dataset	IDEALLab/photonics_2d_120_120_v0
Import	`from engibench.problems.photonics2d.v0 import Photonics2D`

Photonic Inverse Design 2D Problem (Wavelength Demultiplexer).

Problem Description#

Optimize a 2D material distribution (rho) to function as a wavelength demultiplexer, routing wave with lambda1 to output 1 and lambda2 to output 2. The design variables represent material density which is converted to permittivity using filtering and projection.

Design space#

2D tensor rho (num_elems_x, num_elems_y) with values in [0, 1], representing material density. Stored as design_space (gymnasium.spaces.Box).

Objectives#

total_overlap: Objective to maximize, defined as overlap1 * overlap2. Higher is better. This is corresponds to the overlap in the target electrical fields with the desired demultiplexing locations. Note that bot simulate and optimize subtract a small material penalty (total_overlap - penalty) to avoid multiple equivalent local optima, but this penalty is small relative to the overlap objective.

Conditions#

These are designed as user-configurable parameters that alter the problem definition. Default problem parameters that can be overridden via the config dict:

lambda1: The first input wavelength in μm (default: 1.5 μm).
lambda2: The first input wavelength in μm (default: 1.3 μm).
blur_radius: Radius for the density blurring filter (default: 2). Higher values correspond to larger elements, which could possibly be more manufacturable.
num_elems_x: Number of grid cells in x (default: 120).
num_elems_y: Number of grid cells in y (default: 120).

In practice, for the dataset loading, we will keep num_elems_x and num_elems_yto set values for each dataset, such that different resolutions correspond to different independent datasets.

Optimization Parameters#

Note: These are advanced parameters that alter the optimization process – we do not recommend changing these if you are only using the library for benchmarking, as it could make results less reproducible across papers using this problem.)

num_optimization_steps: Total number of optimization steps (default: 300).
step_size: Adam optimizer step size (default: 1e-1).
penalty_weight: Weight for the L2 penalty term (default: 1e-2). Larger values reduce unnecessary material, but may lead to worse performance if too large.
eta: Projection center parameter (default: 0.5). There is little reason to change this.
N_proj: Number of projection applications (default: 1). Increasing this can help make the design more binary.
N_blur: Number of blur applications (default: 1). Increasing this smooths the design more.
initial_beta: Initial beta for the optimization continuation scheme (default: 1.0).
save_frame_interval: Interval for saving intermediate design frames during optimization. If > 0, saves a frame every save_frame_interval iterations to the opt_frames/ directory. Default is 0 (disabled).

Internal Constants#

Note: These are not typically changed by users, but provided here for technical reference

dl: Spatial resolution (meters) (default: 40e-9).
Npml: Number of PML cells (default: 20).
epsr_min: Minimum relative permittivity (default: 1.0).
epsr_max: Maximum relative permittivity (default: 12.0).
space_slice: Extra space for source/probe slices (pixels) (default: 8).

Simulator#

The simulation uses the ceviche library’s Finite Difference Frequency Domain (FDFD) solver (fdfd_ez). Optimization uses ceviche.optimizers.adam_optimize with gradients computed via automatic differentiation (autograd).

Dataset#

This problem currently provides one dataset corresponding to resolution of 120x120, are available on the Hugging Face Datasets Hub.

v0#

Fields#

Each dataset contains:

lambda1: The first input wavelength in μm.
lambda2: The second input wavelength in μm.
blur_radius: Radius for the density blurring filter (pixels).
optimal_design: The optimal design density array (shape num_elems_x, num_elems_y).
optimization_history: A list of objective values from the optimization process (field overlap minus penalty, where higher is better) – This is for advanced use.

Creation Method#

To generate a dataset for training, we generate (randomly, uniformly) swept over the following parameters:

\(\lambda_1 \in [0.5\mu m, 1.25\mu m]\) = lambda1 = rng.uniform(low=0.5, high=1.25, size=20) – This corresponds roughly to a portion of the visible spectrum up to near-infrared.
\(\lambda_2 \in [0.75\mu m, 1.5\mu m]\) = lambda2 = rng.uniform(low=0.75, high=1.5, size=20) – This corresponds roughly to a portion of the visible spectrum up to near-infrared.
\(r_{blur}\) = blur_radius = range(0, 5)

Citation#

This problem is directly refactored from the Ceviche Library: https://github.com/fancompute/ceviche and if you use this problem your experiments, you can use the citation below provided by the original library authors:

@article{hughes2019forward,
    title={Forward-Mode Differentiation of Maxwell's Equations},
    author={Hughes, Tyler W and Williamson, Ian AD and Minkov, Momchil and Fan, Shanhui},
    journal={ACS Photonics},
    volume={6},
    number={11},
    pages={3010--3016},
    year={2019},
    publisher={ACS Publications}
}

Lead#

Mark Fuge @markfuge

Photonics2D

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