DDA Core Functionalities

solve_DDA_e(kr,alpha_e_dl;input_field=nothing,solver="CPU",verbose=true)

Builds and solves the DDA equations under a given input field for a group of $N$ only electric dipoles and returns the total incident field on each of the dipoles.

Arguments

• kr: 2D float array of size $N\times 3$ containing the dimensionless position $k\mathbf{r}$ of each dipole.
• alpha_e_dl: complex dimensionless electric polarizability of each dipole. See the Alphas module documentation for accepted formats.
• input_field: 2D complex array of size $N\times 3$ containing the electric input field $\mathbf{E}_0(\mathbf{r}_i)$ at the position of each dipole. It can also be a 3D array of size $N_f\times N\times 3$, allowing to solve the problem for several input fields without re-inverting the matrix. This is a keyword argument. If input_field=nothing, the output of the function will be the inverse of the DDA matrix.
• solver: string that contains the name of the solver to be used. For this, check the DDACore.solve_system function documentation. By default set to "CPU".
• verbose: whether to output informations to the standard output during runtime or not. By default set to true.

Outputs

Depending on the value of input field, it can be:

• e_inc: 2D complex array of size $N\times 3$ containing the incident electric field $\mathbf{E}_{i}$ on each dipole. if input_field is a 2D array.
• e_inc: 3D complex array of size $N_f\times N\times 3$ containing the incident electric field $\mathbf{E}_{i}$ on each dipole for each input field, if input_field is a 3D array.
• Ainv: complex matrix of size $3N\times 3N$, if input_field=nothing.

solve_DDA_e_m(kr,alpha_e_dl,alpha_m_dl;input_field=nothing,solver="CPU",verbose=true)

Builds and solves the CEMD equations with dimensionless inputs under a given input field for a group of $N$ electric and magnetic dipoles and return the total incident field on every dipole.

Arguments

• kr: 2D float array of size $N\times 3$ containing the dimensionless position $k\mathbf{r}$ of each dipole.
• alpha_e_dl: complex dimensionless electric polarizability of each dipole. See the Alphas module documentation for accepted formats.
• alpha_m_dl: complex dimensionless magnetic polarizability of each dipole. See the Alphas module documentation for accepted formats.
• input_field: 2D complex array of size $N\times 6$ containing the electric and magnetic input field $\mathbf{\Phi}_0=(\mathbf{E}_0(\mathbf{r}_i),\mathbf{H}_0(\mathbf{r}_i))$ at the position of each dipole. It can also be a 3D array of size $N_f\times N\times 6$, allowing to solve the problem for several input fields without re-inverting the matrix. This is a keyword argument. If input_field=nothing (default value), the output of the function will be the inverse of the CEMD matrix.
• solver:string that contains the name of the solver to be used. For this, check the DDACore.solve_system function documentation. By default set to "CPU".
• verbose: whether to output pieces of information to the standard output during runtime or not. By default set to true.

Outputs

Depending on the value of input field, it can be:

• phi_inc: 2D complex array of size $N\times 6$ containing the incident electric and magnetic field $\mathbf{\Phi}_i=(\mathbf{E}_i,\mathbf{H}_i)$ on each dipole, if input_field is a 2D array.
• phi_inc: 3D complex array of size $N_f\times N\times 6$ containing the incident electric and magnetic field $\mathbf{\Phi}_i=(\mathbf{E}_i,\mathbf{H}_i)$ on each dipole for each input field, if input_field is a 3D array.
• Ainv: complex matrix of size $6N\times 6N$, if input_field=nothing.

function solve_DDA_e_m(kr,alpha_dl;input_field=nothing,solver="CPU",verbose=true)

Same as solve_DDA_e_m(kr,alpha_e_dl,alpha_m_dl;input_field=nothing,solver="CPU",verbose=true), but the electric and magnetic polarizabilities of each dipole are given by a single 6x6 complex matrix. See the Alphas module documentation for accepted formats.

 solve_system(A,b,solver,verbose)

Solves a system of equations of the type $Ax=b$ using the method solver and returns x. x can be a 1D column vector or a 2D matrix. In this second case, the function is going to solve for each column of the matrix as a different problem (without re-inverting A). The solver flag can be set to

• CPU: In this case, the system is solved using LAPACK on the CPU.
• GPU: In this case, the system is solved using CUSOLVE on the GPU (if available).

 load_dda_matrix_e(kr,alpha_e_dl,verbose)

Builds the electric only DDA matrix $A=[I-G\alpha]$ with dimensionless positions kr (2D array of size $N\times3$) and dimensionless polarizabilities alpha_e_dl (see format rules in the Alphas module documentation). Returns $3N\times 3N$ complex DDA matrix.

 load_dda_matrix_e_m(kr,alpha_e_dl,alpha_m_dl,verbose)

Builds the electric and magnetic CEMD matrix $A=[I-G\alpha]$ with dimensionless positions kr (2D array of size $N\times 3$) and dimensionless electric and magnetic polarizabilities alpha_e_dl and alpha_m_dl (see format rules in the Alphas module documentation). Returns the $6N\times 6N$ complex CEMD matrix.

 load_dda_matrix_e_m(kr,alpha_dl,verbose)

Builds the electric and magnetic CEMD matrix $A=[I-G\alpha]$ with dimensionless positions kr (two dimensional arrays of size $N\times 3$) and dimensionless polarizability alpha_dl (see format rules in the Alphas module documentation). Return $6N\times 6N$ complex DDA matrix