Function build_optimization_problem

python/examples/waveguide_crossing.py:37–212

Build the waveguide-crossing optimization problem. The waveguide crossing is a cononical inverse design problem with both shape- and topology-optimization implementations. The idea is to find the optimal structure that maximizes transmission from one side to the other. It exhibits C

(
    resolution: float,
    beta: float,
    use_smoothed_projection: bool,
    min_length: float = DEFAULT_MIN_LENGTH,
    dx: float = DEFAULT_DESIGN_REGION_WIDTH,
    dy: float = DEFAULT_DESIGN_REGION_HEIGHT,
    waveguide_width: float = DEFAULT_WAVEGUIDE_WIDTH,
    eta: float = DEFAULT_ETA,
    eta_e: float = DEFAULT_ETA_E,
    damping_factor: float = 0.0,
)

def build_optimization_problem(
    resolution: float,
    beta: float,
    use_smoothed_projection: bool,
    min_length: float = DEFAULT_MIN_LENGTH,
    dx: float = DEFAULT_DESIGN_REGION_WIDTH,
    dy: float = DEFAULT_DESIGN_REGION_HEIGHT,
    waveguide_width: float = DEFAULT_WAVEGUIDE_WIDTH,
    eta: float = DEFAULT_ETA,
    eta_e: float = DEFAULT_ETA_E,
    damping_factor: float = 0.0,
) -> Tuple[mpa.OptimizationProblem, Callable]:
    """Build the waveguide-crossing optimization problem.

    The waveguide crossing is a cononical inverse design problem with both
    shape- and topology-optimization implementations. The idea is to find the
    optimal structure that maximizes transmission from one side to the other. It
    exhibits C4 symmetry, and generally resembles the following structure:

         |  |
         |  |
    -----    ------
    -----    ------
         |  |
         |  |

    Args:
        resolution: Simulation resolution in pixels/micron.
        beta: Tanh function projection strength parameter, ranging from [0,∞].
        use_smoothed_projection: Whether or not to use the smoothed projection.
        min_length: Minimum length scale in microns.
        dx: Design region width in microns.
        dy: Design region height in microns.
        waveguide_width: Waveguide width in microns.
        eta: Projection function threshold parameter.
        eta_e: Projection function eroded threshold parameter.
        damping_factor: The material grid damping scalar factor.

    Returns:
        The corresponding optimization problem object and the mapping function
        that applies the linear and nonlinear transformations.
    """
    # Map the design region resolution to the yee grid, which is twice the standard resolution.
    design_region_resolution = int(2 * resolution)

    # pml thickness
    dpml = 1.0

    filter_radius = mpa.get_conic_radius_from_eta_e(min_length, eta_e)

    sxy = dx + 1 + 2 * dpml

    silicon = mp.Medium(epsilon=12)
    cell_size = mp.Vector3(sxy, sxy, 0)
    boundary_layers = [mp.PML(thickness=dpml)]

    eig_parity = mp.EVEN_Y + mp.ODD_Z