Inverse Design of Photonic Surfaces via High throughput Femtosecond Laser Processing and Tandem Neural Networks

Abstract

This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one-to-many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root-mean-squared-error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser-matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.

Keywords: deep learning; femtosecond laser processing; inverse design; machine learning; photonic surface; tandem neural network.

Figure 1

High throughput fs laser fabrication and optical property characterization of photonic surfaces for training data. a) Schematic of three laser parameters (scanning speed, spacing, and power) that govern surface morphology and corresponding spectral emissivity during laser fabrication. Laser spot diameter is 30 µm. b) Layout for automated high throughput fs laser fabrication and optical property characterization using FTIR. c) SEM images of two representative surface morphologies, fabricated using the same laser power (0.9 W) and scanning speed (100 mm s⁻¹), but different laser spacings (14 µm left image; 2 µm right image). The black scale bars are 10 µm. d) Example picture of fabricated surfaces on SS. The white scale bar is 10 mm. e) Measured spectral emissivity for all 35280 structures. f) Measured spectral emissivities of 5 different samples independently fabricated using identical laser processing parameters (power: 1.1 W; speed: 152 mm s⁻¹; spacing: 6.5 µm). The maximum standard deviation is 2.1%, demonstrating reproducibility. g) Distribution of unweighted average emissivity for all 35280 structures as a function of laser power, spacing, and speed. h) Example of one‐to‐many mapping; 5‐different laser parameter sets produce similar optical properties.

Figure 2

Architecture and training of the TNN framework. a) Forward DNN training, and b) inverse DNN training integrated with fully trained forward DNN. The laser power parameter is one‐hot encoded to maintain its discreteness. The emissivity values are interpolated across 800 linearly distributed wavelengths, ensuring consistent distribution of the spectral emissivity values. c) Structure of each of the 16 residual hidden layers within both the forward and inverse DNN. The input x is passed through a linear transformation followed by the SELU activation function (both transformations denoted as F). The transformed value, F(x), is then added to the original input x to produce the residual layer's output F(x)+x. d) RMSE for three forward DNNs; 100% model, 90% model, and 70% model. e) Loss functions associated with the TNN training process. The red line shows the validation loss, the blue line represents the average training loss, and the gray band indicates the standard deviation of the training loss oscillations. The graphs are differentiated into three models: 100% model, 90% model, and 70% model, regarding what fraction of total possible data is used for training.

Figure 3

Performance validation for the 100% trained inverse and forward DNNs with the experimental test set. a) The experimental test set's laser parameters (number of test samples N = 3038). b) The inverse DNN‐generated laser parameters that map to the same emissivity curves as those in (a) comprise a compact region of laser parameter space 25 times smaller than the original test set in (a). c) Design novelty (NEPD) versus prediction error (RMSE) generated by the inverse DNN and validated by the forward DNN. NAPD results generated by the 100% inverse DNN for each laser parameter; d) spacing, e) power, and f) speed. g) Representative volume of laser parameter space corresponding to a single measurement (centered on 3.0 µm spacing, 30 mm s⁻¹ speed, and 1.3 W of power) of emissivity at 12 µm wavelength, indicating sparsity of experimental data. h) Corresponding partial dependence plot for the same parameter region in (g) produced by the 100% trained forward DNN. i) Examples of the 100% forward DNN model predicted and experimental spectral emissivity. Corresponding RMSEs are listed as inset numbers.

Figure 4

Experimental TPV emitter design. a) The ideal emissivity for a lead selenide‐based TPV emitter with a bandgap at 4.6 µm wavelength operating at 1400 K. b) The same fully trained inverse DNN, whose characteristics are shown in Figures 2 and 3, predicts laser parameters based on the target emissivity in (a). c) Inverse designed laser fabrication parameters using the 70%, 90%, and 100% models. d) Measured emissivities of substrates fabricated using laser parameters shown in (c). e) SEM image shows representative surface morphologies fabricated under laser parameters predicted by 100% model. The white scale bar is 1 µm. f) Figure of merits and in‐band emission normalized to blackbody for photonic surfaces.