Inverse Design Solutions

Core Theory: Gradient Optimization & Adjoint Method #

In inverse design, faced with tens of thousands of design variables, traditional finite difference gradient calculation (which involves perturbing each variable and repeating simulations) generates enormous computational overhead. SimWorks adopts the advanced Adjoint Method, achieving a quantum leap in computational efficiency.

Adjoint-based Gradient Calculation #

The Adjoint Method transforms the original differential equations into a dual-space form, ensuring that the cost of gradient calculation no longer increases linearly with the number of design variables $n$. Regardless of the number of design variables, the full gradient information can be obtained through only two simulations (one forward simulation and one adjoint simulation).

In the FDTD algorithm framework, if the gradient of the objective function $F$ with respect to the design parameter $p$ is represented as $\nabla F = (\frac{\partial F}{\partial p_1}, \dots, \frac{\partial F}{\partial p_n})$, the calculation logic is as follows:

1. Forward Simulation: Under the action of a specific source $\mathbf{b}$, the electromagnetic field components $\mathbf{x}$ within the simulation region are solved.
2. Adjoint Simulation: By introducing the adjoint source (defined by the target field $\frac{\partial F}{\partial \mathbf{x}}$), the adjoint field $\mathbf{V}$ is solved.

Through these two simulations, the gradient can be efficiently obtained via the following equation:

$\frac{\partial F}{\partial p} = \mathbf{V} \left( \frac{\partial \mathbf{b}}{\partial p} - \frac{\partial A}{\partial p}\mathbf{x} \right)$

Intelligent Module: simopt #

To further improve script-writing efficiency, SimWorks features the built-in simopt module. This module encapsulates complex optimization logic into standardized Python objects, allowing users to construct complete optimization tasks through simple scripting commands.
Taking the ModeMatch design case as an example, users can implement the full automatic process from "Light Source Injection" to "Target Performance Optimization" by configuring the following objects via Python scripts:

Typical Python Script Logic Example
import simworks.simopt as simopt
1. Define Design Domain & Optimization Object (e.g., 2D or 3D topology domain)
geometry = simopt.TopologyOptimization2D(params=params, ...)
2. Configure simopt Core Components
source = simopt.ModeSource(type='gaussian', wavelength=0.155)     # Mode Source
opt_fields = simopt.FDFP_Monitor(type='field_gradient')          # Field Monitor
fom_monitor = simopt.FDFP_Monitor(type='power_coupling')         # FOM Monitor
3. Set Objective Function (FOM) and Start Iteration
optimizer = simopt.ScipyOptimizers(method='L-BFGS-B', max_iter=50)
opt = simopt.Optimization(geometry=geometry, fom=fom_monitor, optimizer=optimizer)
opt.run()

Component Logical Relationship:

graph LR
subgraph "Python Script Control"
direction LR
S[Source] --> |Excitation| P[Design Domain]
P --> |Field Generation| OF[Opt_fields Monitor]
P --> |Target Response| F[FOM Monitor]
OF --> |Gradient Feedback| Opt[Optimizer]
F --> |Performance Feedback| Opt
Opt --> |Parameter Update| P
end

Main Applications #

Leveraging precise electromagnetic solving capabilities and powerful automated optimization logic, the SimWorks Inverse Design solution is widely applicable to various cutting-edge research fields in micro-nano photonics:

• Photonic Integrated Circuits (PICs): High-efficiency optimization of silicon waveguides, couplers, micro-ring resonators, and optical switches.
• Metasurfaces & Metamaterials: Design of meta-atoms with specific phase, amplitude, or polarization control.
• Nano-photonics Research: Exploration of non-linear and non-reciprocal devices with unique physical effects.
• Beam Shaping: Design of high-performance micro-nano structures for diffractive optics and beam shaping.