How do I include fabrication constraints in adjoint topology optimization?

Date	Category
2023-12-21 23:00:02	Inverse Design

To ensure reliable fabrication of a device, it is crucial to avoid using feature sizes below a certain radius of curvature when performing inverse design. To achieve this in topology (density-based) optimization, you can use a conic density filter, which is popular in topology optimization problems, to enforce a minimum feature size specified by the filter_radius variable. Next, a hyperbolic tangent projection function can be applied to eliminate grayscale and obtain a binarized permittivity pattern. The code example below demonstrates how to apply the conic filter and the tanh projection to the design parameters before obtaining the permittivity values.

from tidy3d.plugins.autograd import make_filter_and_project, rescale

# radius of the circular filter (um) and the threshold strength
radius = 0.120
beta = 50

filter_project = make_filter_and_project(radius, lx / nx)


def get_eps(params, beta):
    """Get the permittivity values (1, eps_wg) array as a function of the parameters (0, 1)"""
    processed_params = filter_project(params, beta)
    eps = rescale(processed_params, 1, eps_wg)
    return eps


def make_input_structures(params, beta) -> List[td.Structure]:
    box = td.Box(center=(0, 0, 0), size=(lx, ly, lz))
    eps_data = get_eps(params, beta=beta).reshape((nx, ny, 1))
    custom_structure = td.Structure.from_permittivity_array(geometry=box, eps_data=eps_data)

    return [custom_structure]