DiffSMat

DiffSMat provides the code for the paper

Ziwei Zhu, and Changxi Zheng. Differentiable Scattering Matrix for Optimization of Photonic Structures. Optics Express 28.25 (2020).

A PyTorch version is here.

Compile

The C++ program is currently built on Ubuntu 18.04. The lastest C++ version (C++17) is recommended.

We use CMake (3.10 or newer) and Make to build the program.

It depends on the following libraries:

• Eigen 3 (3.3.9 or newer, earlier version like 3.3.7 may be not compatible due to API change)
• Intel® oneAPI Threading Building Blocks (2021.5 or newer)
• Intel® oneAPI Math Kernel Library

After the installation of Intel® oneAPI, please remember to go to the main directory (like /opt/intel/oneapi, dependent on where you install the library) and try source setvars.sh to set the environment variables that cmake will need.

Please make sure you have the above libraries correctly installed to proceed. Once all dependencies are solved, you can do the following steps to build the program.

Firstly, go to the main directory of this respository (where CMakeLists.txt is).

cmake .

You should see Makefile is generated in the main folder. Then,

make

Once Make is done, you should see a new folder tests/ is created. These are all the testing programs for our code.

Usage

The code provides the derivatives for a single z-invariant device such as meta-atom. You could refer to all the files in src/tests/ for usage.

For example, in test5() of test_smat_deriv.cpp you will find the following code.

const int N = 23;

This line specifies the number of harmonics per dimension in xy-plane. Therefore. Specifying an odd number of the harmonics ensures the existence of central harmonic.

const scalar lambda = 1.55;
const scalar wx = 1.0;
const scalar wy = 0.22;
const scalar wz = 0.31;

The above lines specifies the wavelength and the dimensions of the meta-atom along three axes.

Eigen::MatrixXcs P, Q, dP, dQ;
WaveEquationCoeff coeff(N, N, 5., 5.);
coeff.solve(lambda, wx, wy, P, Q, &dP, nullptr, &dQ, nullptr);

The aboves lines solve for the P and Q matrices (assuming the period for xy-plane is 5 microns x 5 microns) and the derivative dP of P with respect to wx, and the derivative dQ of Q with respect to wx.

dtmm::RCWAScatterMatrix rcwa(N, N, 5., 5.);
rcwa.compute(lambda, wz, P, Q);

The above lines calculate the scattering matrix using P and Q.

Now you can call rcwa.Tuu() to get the scattering matrix.

dtmm::ScatterMatrixDerivative<dtmm::RCWAScatterMatrix> deriv;
deriv.compute(rcwa, P, Q, dP, dQ);

The above lines use the precomputed rcwa, P, Q, dP, and dQ to calculate the derivatives of the scattering matrices with respect to wx.

Now you can call deriv.dTuu() to get the derivative of scattering matrix.

We also provide codes for more general grid-based and star-convex-shape-based configuration. Please refer to the code for more details.

An example code is made available here