Physics-augmented deep learning for high-speed electromagnetic simulation and optimization
M. Chen, R. Lupoiu, C. Mao, D.-H. Huang, J. Jiang, P. Lalanne, and J. A. Fan
The dataset used in the original WaveY-Net study
to collect performance statistics and to perform local and global device optimization is composed of 27,000 training examples and 3,000 testing examples. These are available for download below. The WaveY-Net code is available on GitHub.
Both the training and test datasets are composed of dielectric device structures with varying permittivity of the dielectric metagrating, a variable number of nanoridges per unit cell, and a varying ridge height. The refractive index of the dielectric material of each device in the dataset is one of eleven values, ranging from that of anatase titanium dioxide to that of polycrystal silicon, with the in-between values incremented by a constant step-size in dielectric constant. The proportion of devices generated with each of the eleven possible refractive index values was sampled in a manner that is directly proportional to the permittivity constant. The number of nanoridges within the metagrating unit cell is 1, 2, 3, and 4, and the number of devices generated with each of these four values scales with the exponential increase in geometrical complexity with increasing nanoridge number. As such, \(50\), \(2,800\), \(10,150\), and \(17,000\) devices were generated for 1, 2, 3, and 4 nanoridges, respectively. The ten ridge heights are uniformly sampled from 293.75 nm to 350 nm with a step size of 6.25 nm.
The \(H_y^{fwd}\) field responses of the dielectric metagrating unit cells were generated using the FDFD-based electromagnetic simulator Ceviche. Perfectly matched layers (PMLs) are utilized in the vertical \(z\) direction and periodic boundary conditions are adopted in the horizontal \(x\) direction. The metagrating device is placed at the center of the simulation domain, leaving at least a wavelength of space from the PML to ensure the integrity of its high absorbing performance. The lower half of the simulation domain is set as silicon dioxide, and the upper half is set as air. An infinitely large magnetic current sheet is used for field radiation to simulate a plane wave source. Only the fields and grating pattern within the immediate vicinity of the dielectric structure are saved to generate the labels for WaveY-Net training. The window is of size \([256, 64]\) and contains five rows of substrate pixels at the bottom of the window and seven rows of pixels of air at the top. The simulation is set such that the phase of the x component of the incident electric field is zero at the lower edge of the window in forward simulation. A more detailed discussion regarding the training set generation and Ceviche setup is in Supplementary Section 1 of the study.
The data is available for download as NumpPy zipped archive (.npz) format. The train file contains 27,000 examples and is composed of the three arrays used for training in the paper: structures, Hy_fields, and dielectric_permittivities. The latter-most array contains the dielectric permittivity of the dielectric structure in the structures array at the corresponding index. The field arrays contain two channels: the first corresponds to the real component of \(H_y^{fwd}\) and the second to the imaginary component of \(H_y^{fwd}\). The test file contains 3,000 examples and is composed of the six arrays necessary to test the performance of the surrogate model: structures, Hy_fields, Ex_fields, Ez_fields, efficiencies, and dielectric_permittivities.
Loading the data from the Metanet URL using a Python script is demonstrated below.
Alternatively, the files can be downloaded locally using the buttons below and then loaded as demonstrated.
Both the training and test datasets are composed of dielectric device structures with varying permittivity of the dielectric metagrating, a variable number of nanoridges per unit cell, and a varying ridge height. The refractive index of the dielectric material of each device in the dataset is one of eleven values, ranging from that of anatase titanium dioxide to that of polycrystal silicon, with the in-between values incremented by a constant step-size in dielectric constant. The proportion of devices generated with each of the eleven possible refractive index values was sampled in a manner that is directly proportional to the permittivity constant. The number of nanoridges within the metagrating unit cell is 1, 2, 3, and 4, and the number of devices generated with each of these four values scales with the exponential increase in geometrical complexity with increasing nanoridge number. As such, \(50\), \(2,800\), \(10,150\), and \(17,000\) devices were generated for 1, 2, 3, and 4 nanoridges, respectively. The ten ridge heights are uniformly sampled from 293.75 nm to 350 nm with a step size of 6.25 nm.
The \(H_y^{fwd}\) field responses of the dielectric metagrating unit cells were generated using the FDFD-based electromagnetic simulator Ceviche. Perfectly matched layers (PMLs) are utilized in the vertical \(z\) direction and periodic boundary conditions are adopted in the horizontal \(x\) direction. The metagrating device is placed at the center of the simulation domain, leaving at least a wavelength of space from the PML to ensure the integrity of its high absorbing performance. The lower half of the simulation domain is set as silicon dioxide, and the upper half is set as air. An infinitely large magnetic current sheet is used for field radiation to simulate a plane wave source. Only the fields and grating pattern within the immediate vicinity of the dielectric structure are saved to generate the labels for WaveY-Net training. The window is of size \([256, 64]\) and contains five rows of substrate pixels at the bottom of the window and seven rows of pixels of air at the top. The simulation is set such that the phase of the x component of the incident electric field is zero at the lower edge of the window in forward simulation. A more detailed discussion regarding the training set generation and Ceviche setup is in Supplementary Section 1 of the study.
The data is available for download as NumpPy zipped archive (.npz) format. The train file contains 27,000 examples and is composed of the three arrays used for training in the paper: structures, Hy_fields, and dielectric_permittivities. The latter-most array contains the dielectric permittivity of the dielectric structure in the structures array at the corresponding index. The field arrays contain two channels: the first corresponds to the real component of \(H_y^{fwd}\) and the second to the imaginary component of \(H_y^{fwd}\). The test file contains 3,000 examples and is composed of the six arrays necessary to test the performance of the surrogate model: structures, Hy_fields, Ex_fields, Ez_fields, efficiencies, and dielectric_permittivities.
Loading the data from the Metanet URL using a Python script is demonstrated below.
Alternatively, the files can be downloaded locally using the buttons below and then loaded as demonstrated.
If you use this code or data in your research, please cite: