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 projection function to the design parameters before obtaining the permittivity values.

from tidy3d.plugins.adjoint.utils.filter import ConicFilter, BinaryProjector

conic_filter = ConicFilter(radius=filter_radius, design_region_dl=dr_grid_size)

def tanh_projection(x, beta, eta=0.5):
    tanhbn = jnp.tanh(beta * eta)
    num = tanhbn + jnp.tanh(beta * (x - eta))
    den = tanhbn + jnp.tanh(beta * (1 - eta))
    return num / den

def filter_project(x, beta, eta=0.5):
    x = conic_filter.evaluate(x)
    return tanh_projection(x, beta=beta, eta=eta)

def get_eps_values(params, beta):
    params = filter_project(params, beta=beta)
    eps_values = eps_min + (eps_max - eps_min) * params
    return eps_values