Researchers Design 3D Photonic Crystals for Targeted Photon Density of States

By Dr. Noopur JainReviewed by Susha Cheriyedath, M.Sc.Oct 12 2026

By designing a light pattern that creates the crystal, researchers tackled a long-standing problem: linking complex 3D photonic structures to manufacturable metasurfaces.

Paper: Photon density of states engineering in 3D photonic crystals via generative design of metasurface-enabled holographic lithography. AI-generated abstracted conceptual image created using ChatGPT/OpenAI

In a recent research article in npj Metamaterials, researchers developed an end-to-end inverse design method to engineer the photon density of states in three-dimensional photonic crystals for metasurface-enabled holographic lithography.

Generative 3D pDOS design

The photon density of states (pDOS) governs light-matter interactions and is crucial for technologies such as solar energy harvesting. Photonic crystals can tailor pDOS by modulating the refractive index, creating frequency regions where optical states are increased or suppressed.

Rather than directly designing a 3D crystal's dielectric distribution and then working out how to fabricate it, the researchers design the light interference pattern that creates the crystal. Their method connects target pDOS features to metasurface-enabled holographic lithography, a fabrication approach suited to producing periodic 3D structures over larger areas.

Earlier inverse design methods commonly treat the dielectric distribution as the design variable. Here, the design variables are the intensities and phases of propagating diffraction orders that define the lithographic interference field. This makes fabrication part of the design problem from the start and lets the method search for 3D structures with chosen pDOS characteristics without first specifying an arbitrary morphology.

LSTM prediction and inverse design

The design process began with a forward prediction model based on a Long Short-Term Memory (LSTM) network. The LSTM learned the relationship between metasurface diffraction parameters, the exposure threshold, and the resulting pDOS spectrum.

To generate the dataset, the researchers assumed a metasurface with a 500 nm period illuminated by a 405 nm plane wave, producing five propagating diffraction orders. The orders interfered to form a triply periodic light field with a body-centered-tetragonal (BCT) Bravais lattice.

Applying an intensity threshold to the interference field produced 3D binary structures. The structures were scaled along the propagation direction by a factor of 0.7 to account for volumetric shrinkage during lithography. With a high-contrast material of εr = 13, the pDOS of each reconstructed structure was calculated using an in-house plane-wave expansion method (PWEM).

The dielectric distribution was represented on a 40 × 40 × 40 grid of the primitive cell, and eigenfrequencies were grouped into 80 bins covering normalized frequencies from 0 to 0.8.

The authors generated 22,500 independent samples, then doubled the dataset to 45,000 through symmetry-based augmentation by exchanging two diffraction components that produce identical pDOS responses. Each sample used six inputs describing the diffraction coefficients and exposure threshold, with the corresponding pDOS spectrum as the output.

The LSTM encoder-decoder used an input dimension of 6 and an output sequence length of 80. It was trained to minimize the mean squared error between predicted and ground-truth pDOS sequences. Predictions followed the main spectral trends closely, though errors grew at higher normalized frequencies because some peak heights and positions were harder to reproduce.

The inverse design stage used two steps. First, a conditional generative adversarial network (cGAN) generated candidate diffraction parameters and exposure thresholds from a target frequency and latent random variables. The generator was trained with adversarial, pDOS-target, and energy-conservation loss terms. These terms promoted physically consistent diffraction intensities and pushed generation toward higher pDOS responses.

Next, the generated samples underwent a connectivity test to filter for structurally connected architectures. Valid candidates were then used to reconstruct corresponding metasurface patterns through a coupled finite-difference time-domain (FDTD) and particle swarm optimization (PSO) simulation.

High-pDOS architectures

The cGAN was trained across a normalized frequency range of 0.45 to 0.70. From 10,000 generated samples, the authors selected top-ranked connected candidates for further analysis. For designs targeting higher local pDOS, the authors defined a qualified sample as one with normalized pDOS greater than 2 at the target frequency and reported an average generation fidelity of about 80% across the studied range.

Examples targeting peak normalized pDOS at normalized frequencies of 0.5, 0.6, and 0.7 showed wide variation in both 3D morphology and final metasurface design.

The irregular binary patterns closely matched the target diffraction distributions, with an average deviation below 0.001. Simulations showed that specific metasurface geometries could reproduce the required diffraction patterns, but the study did not report experimental pDOS measurements for the inverse-designed 3D crystals.

The resulting 3D morphologies shared related symmetry characteristics. In the xy plane, they displayed C2 symmetry arising from the symmetric distribution of diffraction coefficients. Along the z direction, the upper and lower halves were approximately 90-degree rotations of each other, producing a characteristic twisted morphology.

Autoencoder analysis followed by principal component analysis identified two main high-pDOS morphological families with similar rotational symmetry but different geometry. Thinner connections were associated with higher pDOS and may be more fragile during fabrication, while calculations indicated that moderate geometric deviations could still preserve relatively high pDOS values.

In a random pairwise comparison, 90.55% of generated structures had higher normalized pDOS than dataset samples. Across the target-frequency range, the best generated designs reached higher peaks than the original dataset. These results came from different structures designed for different target frequencies, rather than from one structure with high pDOS across the full range.

Impact and outlook

The study developed an end-to-end inverse design method to tailor pDOS in 3D photonic crystals for holographic lithography.

The researchers also applied a second cGAN to photonic band-gap design. They found that gap formation depended more strongly on exposure threshold or volume fraction than on fine morphological variation. The structural analysis also clarified a trade-off for high-pDOS designs: thinner connections were associated with stronger pDOS responses but greater fabrication fragility.

The paper describes a process for fabricating dielectric metasurfaces, but it does not report direct optical pDOS measurements of the inverse-designed 3D crystals. The reported pDOS gains come from numerical calculations. The results indicate that metasurface-controlled holographic lithography could target selected photonic responses while accounting for fabrication constraints during the design process.