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nmie-nearfield.hpp
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nmie-nearfield.hpp
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#ifndef SRC_NMIE_NEARFIELD_HPP_
#define SRC_NMIE_NEARFIELD_HPP_
//**********************************************************************************//
// Copyright (C) 2009-2021 Ovidio Pena <ovidio@bytesfall.com> //
// Copyright (C) 2013-2021 Konstantin Ladutenko <kostyfisik@gmail.com> //
// //
// This file is part of scattnlay //
// //
// This program is free software: you can redistribute it and/or modify //
// it under the terms of the GNU General Public License as published by //
// the Free Software Foundation, either version 3 of the License, or //
// (at your option) any later version. //
// //
// This program is distributed in the hope that it will be useful, //
// but WITHOUT ANY WARRANTY; without even the implied warranty of //
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
// GNU General Public License for more details. //
// //
// The only additional remark is that we expect that all publications //
// describing work using this software, or all commercial products //
// using it, cite at least one of the following references: //
// [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
// a multilayered sphere," Computer Physics Communications, //
// vol. 180, Nov. 2009, pp. 2348-2354. //
// [2] K. Ladutenko, U. Pal, A. Rivera, and O. Pena-Rodriguez, "Mie //
// calculation of electromagnetic near-field for a multilayered //
// sphere," Computer Physics Communications, vol. 214, May 2017, //
// pp. 225-230. //
// //
// You should have received a copy of the GNU General Public License //
// along with this program. If not, see <http://www.gnu.org/licenses/>. //
//**********************************************************************************//
//**********************************************************************************//
// This class implements the algorithm for a multilayered sphere described by: //
// [1] W. Yang, "Improved recursive algorithm for light scattering by a //
// multilayered sphere,” Applied Optics, vol. 42, Mar. 2003, pp. 1710-1720. //
// //
// You can find the description of all the used equations in: //
// [2] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
// a multilayered sphere," Computer Physics Communications, //
// vol. 180, Nov. 2009, pp. 2348-2354. //
// [3] K. Ladutenko, U. Pal, A. Rivera, and O. Pena-Rodriguez, "Mie //
// calculation of electromagnetic near-field for a multilayered //
// sphere," Computer Physics Communications, vol. 214, May 2017, //
// pp. 225-230. //
// //
// Hereinafter all equations numbers refer to [2] //
//**********************************************************************************//
#include <iostream>
#include <iomanip>
#include <stdexcept>
#include <vector>
//#include "nmie.hpp"
namespace nmie {
//class implementation
//**********************************************************************************//
// This function calculates the expansion coefficients inside the particle, //
// required to calculate the near-field parameters. //
// //
// Input parameters: //
// L: Number of layers //
// pl: Index of PEC layer. If there is none just send -1 //
// x: Array containing the size parameters of the layers [0..L-1] //
// m: Array containing the relative refractive indexes of the layers [0..L-1] //
// nmax: Maximum number of multipolar expansion terms to be used for the //
// calculations. Only use it if you know what you are doing, otherwise //
// set this parameter to -1 and the function will calculate it. //
// //
// Output parameters: //
// aln, bln, cln, dln: Complex scattering amplitudes inside the particle //
// //
// Return value: //
// Number of multipolar expansion terms used for the calculations //
//**********************************************************************************//
template <typename FloatType>
void MultiLayerMie<FloatType>::calcExpanCoeffs() {
if (!isScaCoeffsCalc_)
throw std::invalid_argument("(calcExpanCoeffs) You should calculate external coefficients first!");
isExpCoeffsCalc_ = false;
aln_.clear(); bln_.clear(); cln_.clear(); dln_.clear();
std::complex<FloatType> c_one(1.0, 0.0), c_zero(0.0, 0.0);
const int L = refractive_index_.size();
aln_.resize(L + 1);
bln_.resize(L + 1);
cln_.resize(L + 1);
dln_.resize(L + 1);
for (int l = 0; l <= L; l++) {
aln_[l].resize(nmax_, static_cast<FloatType>(0.0));
bln_[l].resize(nmax_, static_cast<FloatType>(0.0));
cln_[l].resize(nmax_, static_cast<FloatType>(0.0));
dln_[l].resize(nmax_, static_cast<FloatType>(0.0));
}
// Yang, paragraph under eq. A3
// a^(L + 1)_n = a_n, d^(L + 1) = 1 ...
for (int n = 0; n < nmax_; n++) {
aln_[L][n] = an_[n];
bln_[L][n] = bn_[n];
cln_[L][n] = c_one;
dln_[L][n] = c_one;
}
std::vector<std::complex<FloatType> > D1z(nmax_ + 1), D1z1(nmax_ + 1), D3z(nmax_ + 1), D3z1(nmax_ + 1);
std::vector<std::complex<FloatType> > Psiz(nmax_ + 1), Psiz1(nmax_ + 1), Zetaz(nmax_ + 1), Zetaz1(nmax_ + 1);
std::complex<FloatType> denomZeta, denomPsi, T1, T2, T3, T4;
auto &m = refractive_index_;
std::vector< std::complex<FloatType> > m1(L);
for (int l = 0; l < L - 1; l++) m1[l] = m[l + 1];
m1[L - 1] = std::complex<FloatType> (1.0, 0.0);
std::complex<FloatType> z, z1;
for (int l = L - 1; l >= 0; l--) {
if (l <= PEC_layer_position_) { // We are inside a PEC. All coefficients must be zero!!!
for (int n = 0; n < nmax_; n++) {
// aln
aln_[l][n] = c_zero;
// bln
bln_[l][n] = c_zero;
// cln
cln_[l][n] = c_zero;
// dln
dln_[l][n] = c_zero;
}
} else { // Regular material, just do the calculation
z = size_param_[l]*m[l];
z1 = size_param_[l]*m1[l];
calcD1D3(z, D1z, D3z);
calcD1D3(z1, D1z1, D3z1);
calcPsiZeta(z, Psiz, Zetaz);
calcPsiZeta(z1, Psiz1, Zetaz1);
for (int n = 0; n < nmax_; n++) {
int n1 = n + 1;
denomZeta = Zetaz[n1]*(D1z[n1] - D3z[n1]);
denomPsi = Psiz[n1]*(D1z[n1] - D3z[n1]);
T1 = aln_[l + 1][n]*Zetaz1[n1] - dln_[l + 1][n]*Psiz1[n1];
T2 = (bln_[l + 1][n]*Zetaz1[n1] - cln_[l + 1][n]*Psiz1[n1])*m[l]/m1[l];
T3 = (dln_[l + 1][n]*D1z1[n1]*Psiz1[n1] - aln_[l + 1][n]*D3z1[n1]*Zetaz1[n1])*m[l]/m1[l];
T4 = cln_[l + 1][n]*D1z1[n1]*Psiz1[n1] - bln_[l + 1][n]*D3z1[n1]*Zetaz1[n1];
// aln
aln_[l][n] = (D1z[n1]*T1 + T3)/denomZeta;
// bln
bln_[l][n] = (D1z[n1]*T2 + T4)/denomZeta;
// cln
cln_[l][n] = (D3z[n1]*T2 + T4)/denomPsi;
// dln
dln_[l][n] = (D3z[n1]*T1 + T3)/denomPsi;
} // end of all n
} // end PEC condition
} // end of all l
int print_precision = 16;
#ifdef MULTI_PRECISION
print_precision = MULTI_PRECISION;
#endif
// Check the result and change aln_[0][n] and aln_[0][n] for exact zero
int print_count = 0;
for (int n = 0; n < nmax_; ++n) {
if (cabs(aln_[0][n]) > 1e-10 && print_count < 2) {
print_count++;
std::cout<< std::setprecision(print_precision)
<< "Warning: Potentially unstable calculation of aln[0]["
<< n << "] = "<< aln_[0][n] << " which is expected to be exact zero!"<<std::endl;
}
if (cabs(bln_[0][n]) > 1e-10 && print_count < 2) {
print_count++;
std::cout<< std::setprecision(print_precision)
<< "Warning: Potentially unstable calculation of bln[0]["
<< n << "] = "<< bln_[0][n] << " which is expected to be exact zero!" <<std::endl;
}
aln_[0][n] = 0.0;
bln_[0][n] = 0.0;
}
isExpCoeffsCalc_ = true;
} // end of void MultiLayerMie::calcExpanCoeffs()
template <typename FloatType>
void MultiLayerMie<FloatType>::convertFieldsFromSphericalToCartesian() {
long total_points = coords_polar_.size();
E_.clear(); H_.clear();
Eabs_.clear(); Habs_.clear();
for (int point=0; point < total_points; point++) {
auto Theta = coords_polar_[point][1];
auto Phi = coords_polar_[point][2];
auto Es = Es_[point];
auto Hs = Hs_[point];
using nmm::sin;
using nmm::cos;
E_.push_back({ sin(Theta)*cos(Phi)*Es[0] + cos(Theta)*cos(Phi)*Es[1] - sin(Phi)*Es[2],
sin(Theta)*sin(Phi)*Es[0] + cos(Theta)*sin(Phi)*Es[1] + cos(Phi)*Es[2],
cos(Theta)*Es[0] - sin(Theta)*Es[1]});
H_.push_back({ sin(Theta)*cos(Phi)*Hs[0] + cos(Theta)*cos(Phi)*Hs[1] - sin(Phi)*Hs[2],
sin(Theta)*sin(Phi)*Hs[0] + cos(Theta)*sin(Phi)*Hs[1] + cos(Phi)*Hs[2],
cos(Theta)*Hs[0] - sin(Theta)*Hs[1]});
Eabs_.push_back(vabs(E_.back()));
Habs_.push_back(vabs(H_.back()));
}
} // end of void MultiLayerMie::convertFieldsFromSphericalToCartesian()
//**********************************************************************************//
// This function calculates the electric (E) and magnetic (H) fields inside and //
// around the particle. //
//
// Main trouble of near-field evaluations is supposed to originate from special functions
// evaluation, so we expect that nmax needed for the convergence is the size
// of Psi vector.
// //
// Input parameters (coordinates of the point): //
// Rho: Radial distance //
// Phi: Azimuthal angle //
// Theta: Polar angle //
// mode_n: mode order. //
// -1 - use all modes (all_) //
// 1 - use dipole mode only //
// 2 - use quadrupole mode only //
// ... //
// mode_type: only used when mode_n != -1 //
// 0 - electric only //
// 1 - magnetic only //
// //
// //
// Output parameters: //
// E, H: Complex electric and magnetic fields //
//**********************************************************************************//
template <typename FloatType> template <typename evalType>
void MultiLayerMie<FloatType>::calcFieldByComponents(const evalType Rho,
const evalType Theta, const evalType Phi,
const std::vector<std::complex<evalType> > &Psi,
const std::vector<std::complex<evalType> > &D1n,
const std::vector<std::complex<evalType> > &Zeta,
const std::vector<std::complex<evalType> > &D3n,
const std::vector<evalType> &Pi,
const std::vector<evalType> &Tau,
std::vector<std::complex<evalType> > &E,
std::vector<std::complex<evalType> > &H,
std::vector<bool> &isConvergedE,
std::vector<bool> &isConvergedH,
bool isMarkUnconverged) {
auto nmax = Psi.size() - 1;
std::complex<evalType> c_zero(0.0, 0.0), c_i(0.0, 1.0), c_one(1.0, 0.0);
// auto c_nan = ConvertComplex<FloatType>(std::complex<double>(std::nan(""), std::nan("")));
// Vector containing precomputed integer powers of i to avoid computation
std::vector<std::complex<evalType> > ipow = {c_one, c_i, -c_one, -c_i};
std::vector<std::complex<evalType> > M3o1n(3), M3e1n(3), N3o1n(3), N3e1n(3);
std::vector<std::complex<evalType> > M1o1n(3), M1e1n(3), N1o1n(3), N1e1n(3);
std::complex<evalType> ml;
// Initialize E and H
for (int i = 0; i < 3; i++) {
E[i] = c_zero;
H[i] = c_zero;
}
const unsigned L = refractive_index_.size();
for (int n = 0; n < nmax_; n++) {
cln_[L][n] = c_zero;
dln_[L][n] = c_zero;
}
unsigned int l;
GetIndexAtRadius(Rho, ml, l);
isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
// evalType E0 = 0, H0=0;
std::vector< std::complex<evalType> > Ediff_prev = {{0.,0.},{0.,0.},{0.,0.}},
Hdiff_prev = {{0.,0.},{0.,0.},{0.,0.}};
for (unsigned int n = 0; n < nmax; n++) {
if ( isConvergedE[0] && isConvergedE[1] && isConvergedE[2]
&& isConvergedH[0] && isConvergedH[1] && isConvergedH[2]) {
std::cout<<"Near-field early convergence at nmax = "<<n+1<<std::endl;
break;
}
int n1 = n + 1;
auto rn = static_cast<evalType>(n1);
// using BH 4.12 and 4.50
calcSpherHarm(Rho*ml, Theta, Phi, Psi[n1], D1n[n1], Pi[n], Tau[n], rn, M1o1n, M1e1n, N1o1n, N1e1n);
calcSpherHarm(Rho*ml, Theta, Phi, Zeta[n1], D3n[n1], Pi[n], Tau[n], rn, M3o1n, M3e1n, N3o1n, N3e1n);
// Total field in the lth layer: eqs. (1) and (2) in Yang, Appl. Opt., 42 (2003) 1710-1720
std::complex<evalType> En = ipow[n1 % 4]
*static_cast<evalType>((rn + rn + 1.0)/(rn*rn + rn));
std::complex<evalType> Ediff, Hdiff;
std::complex<FloatType> Ediff_ft, Hdiff_ft;
auto aln = ConvertComplex<evalType>(aln_[l][n]);
auto bln = ConvertComplex<evalType>(bln_[l][n]);
auto cln = ConvertComplex<evalType>(cln_[l][n]);
auto dln = ConvertComplex<evalType>(dln_[l][n]);
for (int i = 0; i < 3; i++) {
if (isConvergedE[i] && isConvergedH[i]) continue; // TODO is it safe?
Ediff = En*( cln*M1o1n[i] - c_i*dln*N1e1n[i]
+ c_i*aln*N3e1n[i] - bln*M3o1n[i]);
Hdiff = En*( -dln*M1e1n[i] - c_i*cln*N1o1n[i]
+ c_i*bln*N3o1n[i] + aln*M3e1n[i]);
Ediff_ft = ConvertComplex<FloatType>(Ediff);
Hdiff_ft = ConvertComplex<FloatType>(Hdiff);
if ( nmm::isnan(Ediff_ft.real()) || nmm::isnan(Ediff_ft.imag()) ||
nmm::isnan(Hdiff_ft.real()) || nmm::isnan(Hdiff_ft.imag()) ) {
std::cout << "Unexpected truncation during near-field evaluation at n = "<< n
<< " (of total nmax = "<<nmax<<")!!!"<<std::endl;
break;
}
if (n>0) {
if (
(cabs(Ediff_prev[i]) <= cabs(E[i]) * nearfield_convergence_threshold_)
&& (cabs(Ediff) <= cabs(E[i]) * nearfield_convergence_threshold_)
) isConvergedE[i] = true;
if (
(cabs(Hdiff_prev[i]) <= cabs(H[i]) * nearfield_convergence_threshold_)
&& (cabs(Hdiff) <= cabs(H[i]) * nearfield_convergence_threshold_)
) isConvergedH[i] = true;
}
Ediff_prev[i] = Ediff;
Hdiff_prev[i] = Hdiff;
if ((!isConvergedH[i] || !isConvergedE[i]) && n==nmax-1 && GetFieldConvergence()) {
std::cout<<"Econv:"<<cabs(Ediff)/cabs(E[i])<<" Hconv:"<<cabs(Hdiff)/cabs(H[i])<<std::endl;
}
if (mode_n_ == Modes::kAll) {
// electric field E [V m - 1] = EF*E0
E[i] += Ediff;
H[i] += Hdiff;
continue;
}
if (n == 0) {
}
if (n1 == mode_n_) {
if (mode_type_ == Modes::kElectric || mode_type_ == Modes::kAll) {
E[i] += En*( -c_i*dln*N1e1n[i]
+ c_i*aln*N3e1n[i]);
H[i] += En*(-dln*M1e1n[i]
+aln*M3e1n[i]);
//std::cout << mode_n_;
}
if (mode_type_ == Modes::kMagnetic || mode_type_ == Modes::kAll) {
E[i] += En*( cln*M1o1n[i]
- bln*M3o1n[i]);
H[i] += En*( -c_i*cln*N1o1n[i]
+ c_i*bln*N3o1n[i]);
//std::cout << mode_n_;
}
//std::cout << std::endl;
}
//throw std::invalid_argument("Error! Unexpected mode for field evaluation!\n mode_n="+std::to_string(mode_n)+", mode_type="+std::to_string(mode_type)+"\n=====*****=====");
}
if (nmm::isnan(Ediff_ft.real()) || nmm::isnan(Ediff_ft.imag()) ||
nmm::isnan(Hdiff_ft.real()) || nmm::isnan(Hdiff_ft.imag())
) break;
} // end of for all n
// Add the incident field
if(l==L) {
const auto z = Rho*cos_t(Theta);
const auto Ex = std::complex<evalType>(cos_t(z), sin_t(z));
E[0] += Ex*cos_t(Phi)*sin_t(Theta);
E[1] += Ex*cos_t(Phi)*cos_t(Theta);
E[2] += -Ex*sin_t(Phi);
const auto Hy = Ex;
H[0] += Hy*sin_t(Theta)*sin_t(Phi);
H[1] += Hy*cos_t(Theta)*sin_t(Phi);
H[2] += Hy*cos_t(Phi);
}
if( (!isConvergedE[0] || !isConvergedE[1] ||!isConvergedE[2] ||
!isConvergedH[0] || !isConvergedH[1] ||!isConvergedH[2] ) && GetFieldConvergence()) {
std::cout << "Field evaluation failed to converge an nmax = "<< nmax << std::endl;
std::cout << "Near-field convergence threshold: "<<nearfield_convergence_threshold_<<std::endl;
if (isMarkUnconverged) { //mark as NaN
for(auto &ee :E) ee /= c_zero;
for(auto &ee :H) ee /= c_zero;
}
}
// magnetic field
std::complex<evalType> hffact = ml/static_cast<evalType>(nmie::cc_*nmie::mu_);
for (int i = 0; i < 3; i++) {
H[i] = hffact*H[i];
}
} // end of MultiLayerMie::calcFieldByComponents(...)
//**********************************************************************************//
// This function calculates complex electric and magnetic field in the surroundings //
// and inside the particle. //
// //
// Input parameters: //
// L: Number of layers //
// pl: Index of PEC layer. If there is none just send 0 (zero) //
// x: Array containing the size parameters of the layers [0..L-1] //
// m: Array containing the relative refractive indexes of the layers [0..L-1] //
// nmax: Maximum number of multipolar expansion terms to be used for the //
// calculations. Only use it if you know what you are doing, otherwise //
// set this parameter to 0 (zero) and the function will calculate it. //
// ncoord: Number of coordinate points //
// Coords: Array containing all coordinates where the complex electric and //
// magnetic fields will be calculated //
// mode_n: mode order. //
// -1 - use all modes (all_) //
// 1 - use dipole mode only //
// 2 - use quadrupole mode only //
// ... //
// mode_type: only used when mode_n != -1 //
// 0 - electric only //
// 1 - magnetic only //
// //
// Output parameters: //
// E, H: Complex electric and magnetic field at the provided coordinates //
// //
// Return value: //
// Number of multipolar expansion terms used for the calculations //
//**********************************************************************************//
template <typename FloatType>
void MultiLayerMie<FloatType>::RunFieldCalculation(bool isMarkUnconverged) {
// Calculate scattering coefficients an_ and bn_
calcScattCoeffs();
// Calculate expansion coefficients aln_, bln_, cln_, and dln_
calcExpanCoeffs();
std::vector<bool> isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
isConvergedE_ = {true, true, true}, isConvergedH_ = {true, true, true};
Es_.clear(); Hs_.clear(); coords_polar_.clear();
long total_points = coords_[0].size();
for (int point = 0; point < total_points; point++) {
const FloatType &Xp = coords_[0][point];
const FloatType &Yp = coords_[1][point];
const FloatType &Zp = coords_[2][point];
// Convert to spherical coordinates
auto Rho = nmm::sqrt(pow2(Xp) + pow2(Yp) + pow2(Zp));
// If Rho=0 then Theta is undefined. Just set it to zero to avoid problems
auto Theta = (Rho > 0.0) ? nmm::acos(Zp/Rho) : 0.0;
// std::atan2 should take care of any special cases, e.g. Xp=Yp=0, etc.
auto Phi = nmm::atan2(Yp,Xp);
coords_polar_.push_back({Rho, Theta, Phi});
// Avoid convergence problems due to Rho too small
if (Rho < 1e-5) Rho = 1e-5;
//*******************************************************//
// external scattering field = incident + scattered //
// BH p.92 (4.37), 94 (4.45), 95 (4.50) //
// assume: medium is non-absorbing; refim = 0; Uabs = 0 //
//*******************************************************//
// This array contains the fields in spherical coordinates
std::vector<std::complex<FloatType> > Es(3), Hs(3);
// Do the actual calculation of electric and magnetic field
std::vector<std::complex<FloatType> > Psi(nmax_ + 1), D1n(nmax_ + 1), Zeta(nmax_ + 1), D3n(nmax_ + 1);
std::vector<FloatType> Pi(nmax_), Tau(nmax_);
std::complex<FloatType> ml;
GetIndexAtRadius(Rho, ml);
// Calculate logarithmic derivative of the Ricatti-Bessel functions
calcD1D3(Rho*ml, D1n, D3n);
// Calculate Ricatti-Bessel functions
calcPsiZeta(Rho*ml, Psi, Zeta);
// Calculate angular functions Pi and Tau
calcPiTau(nmm::cos(Theta), Pi, Tau);
calcFieldByComponents(Rho, Theta, Phi, Psi, D1n, Zeta, D3n, Pi, Tau, Es, Hs,
isConvergedE, isConvergedH, isMarkUnconverged);
UpdateConvergenceStatus(isConvergedE, isConvergedH);
Es_.push_back(Es);
Hs_.push_back(Hs);
} // end of for all field coordinates
convertFieldsFromSphericalToCartesian();
} // end of MultiLayerMie::RunFieldCalculation()
// TODO do we really need this eval_delta()?
template <typename FloatType>
double eval_delta(const unsigned int steps, const double from_value, const double to_value) {
auto delta = std::abs(from_value - to_value);
if (steps < 2) return delta;
delta /= static_cast<double>(steps-1);
// We have a limited double precision evaluation of special functions, typically it is 1e-10.
if ( (2.*delta)/std::abs(from_value+to_value) < 1e-9)
throw std::invalid_argument("Error! The step is too fine, not supported!");
return delta;
}
// ml - refractive index
// l - Layer number
template <typename FloatType> template <typename evalType>
void MultiLayerMie<FloatType>::GetIndexAtRadius(const evalType Rho,
std::complex<evalType> &ml,
unsigned int &l) {
l = 0;
if (Rho > size_param_.back()) {
l = size_param_.size();
ml = std::complex<evalType>(1.0, 0.0);
} else {
for (int i = size_param_.size() - 1; i >= 0 ; i--) {
if (Rho <= size_param_[i]) {
l = i;
}
}
ml = ConvertComplex<evalType>(refractive_index_[l]);
}
}
template <typename FloatType> template <typename evalType>
void MultiLayerMie<FloatType>::GetIndexAtRadius(const evalType Rho,
std::complex<evalType> &ml) {
unsigned int l;
GetIndexAtRadius(Rho, ml, l);
}
template <typename FloatType>
void MultiLayerMie<FloatType>::calcMieSeriesNeededToConverge(const FloatType Rho, int nmax_in) {
if (nmax_in < 1) {
auto required_near_field_nmax = calcNmax(Rho);
SetMaxTerms(required_near_field_nmax);
} else {
SetMaxTerms(nmax_in);
}
// Calculate scattering coefficients an_ and bn_
calcScattCoeffs();
// We might be limited with available machine precision
available_maximal_nmax_ = nmax_;
// Calculate expansion coefficients aln_, bln_, cln_, and dln_
calcExpanCoeffs();
}
template <typename FloatType>
void MultiLayerMie<FloatType>::calcRadialOnlyDependantFunctions(const double from_Rho, const double to_Rho,
std::vector<std::vector<std::complex<FloatType> > > &Psi,
std::vector<std::vector<std::complex<FloatType> > > &D1n,
std::vector<std::vector<std::complex<FloatType> > > &Zeta,
std::vector<std::vector<std::complex<FloatType> > > &D3n,
int nmax_in) {
auto radius_points = Psi.size();
std::vector<std::vector<std::complex<FloatType> > > PsiZeta(radius_points);
double delta_Rho = eval_delta<double>(radius_points, from_Rho, to_Rho);
for (unsigned int j=0; j < radius_points; j++) {
auto Rho = static_cast<FloatType>(from_Rho + j*delta_Rho);
// if (Rho < 1e-5) Rho = 1e-5; // TODO do we need this?.
int near_field_nmax = nmax_in;
if (nmax_in < 1) near_field_nmax = calcNmax(Rho);
// Skip if not enough terms in Mie series (i.e. required near field nmax > available terms )
if (near_field_nmax > available_maximal_nmax_) near_field_nmax = available_maximal_nmax_;
Psi[j].resize(near_field_nmax + 1, static_cast<FloatType>(0.0)); D1n[j].resize(near_field_nmax + 1, static_cast<FloatType>(0.0));
Zeta[j].resize(near_field_nmax + 1, static_cast<FloatType>(0.0)); D3n[j].resize(near_field_nmax + 1, static_cast<FloatType>(0.0));
PsiZeta[j].resize(near_field_nmax + 1, static_cast<FloatType>(0.0));
std::complex<FloatType> ml;
GetIndexAtRadius(Rho, ml);
auto z = Rho*ml;
evalDownwardD1(z, D1n[j]);
evalUpwardPsi(z, D1n[j], Psi[j]);
evalUpwardD3 (z, D1n[j], D3n[j], PsiZeta[j]);
for (unsigned int k = 0; k < Zeta[j].size(); k++) {
Zeta[j][k] = PsiZeta[j][k]/Psi[j][k];
}
}
}
// input parameters:
// outer_arc_points: will be increased to the nearest power of 2.
template <typename FloatType>
void MultiLayerMie<FloatType>::RunFieldCalculationPolar(const int outer_arc_points,
const int radius_points,
const double from_Rho, const double to_Rho,
const double from_Theta, const double to_Theta,
const double from_Phi, const double to_Phi,
const bool isMarkUnconverged,
int nmax_in) {
if (from_Rho > to_Rho || from_Theta > to_Theta || from_Phi > to_Phi
|| outer_arc_points < 1 || radius_points < 1
|| from_Rho < 0.)
throw std::invalid_argument("Error! Invalid argument for RunFieldCalculationPolar() !");
// auto nmax_old = nmax_;
int theta_points = 0, phi_points = 0;
if (to_Theta-from_Theta > to_Phi-from_Phi) {
theta_points = outer_arc_points;
phi_points = static_cast<int>((to_Phi-from_Phi)/(to_Theta-from_Theta) * outer_arc_points);
} else {
phi_points = outer_arc_points;
theta_points = static_cast<int>((to_Theta-from_Theta)/(to_Phi-from_Phi) * outer_arc_points);
}
if (theta_points == 0) theta_points = 1;
if (phi_points == 0) phi_points = 1;
calcMieSeriesNeededToConverge(to_Rho, nmax_in);
std::vector<std::vector<FloatType> > Pi(theta_points), Tau(theta_points);
calcPiTauAllTheta(from_Theta, to_Theta, Pi, Tau);
std::vector<std::vector<std::complex<FloatType> > > Psi(radius_points), D1n(radius_points),
Zeta(radius_points), D3n(radius_points), PsiZeta(radius_points);
calcRadialOnlyDependantFunctions(from_Rho, to_Rho,
Psi, D1n, Zeta, D3n,
nmax_in);
// std::cout<<"Done evaluation of special functions."<<std::endl;
double delta_Rho = eval_delta<double>(radius_points, from_Rho, to_Rho);
double delta_Theta = eval_delta<double>(theta_points, from_Theta, to_Theta);
double delta_Phi = eval_delta<double>(phi_points, from_Phi, to_Phi);
Es_.clear(); Hs_.clear(); coords_polar_.clear();
std::vector<bool> isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
isConvergedE_ = {true, true, true}, isConvergedH_ = {true, true, true};
for (int j=0; j < radius_points; j++) {
auto Rho = from_Rho + j * delta_Rho;
std::vector< std::complex<double> > Psi_dp = ConvertComplexVector<double>(Psi[j]);
std::vector< std::complex<double> > Zeta_dp = ConvertComplexVector<double>(Zeta[j]);
std::vector< std::complex<double> > D1n_dp = ConvertComplexVector<double>(D1n[j]);
std::vector< std::complex<double> > D3n_dp = ConvertComplexVector<double>(D3n[j]);
for (int i = 0; i < theta_points; i++) {
auto Theta = from_Theta + i * delta_Theta;
std::vector<double> Pi_dp = ConvertVector<double>(Pi[i]);
std::vector<double> Tau_dp = ConvertVector<double>(Tau[i]);
for (int k = 0; k < phi_points; k++) {
auto Phi = from_Phi + k * delta_Phi;
coords_polar_.push_back({Rho, Theta, Phi});
std::vector<std::complex<double> > Es(3), Hs(3);
calcFieldByComponents( Rho, Theta, Phi,
Psi_dp, D1n_dp, Zeta_dp, D3n_dp, Pi_dp, Tau_dp,
Es, Hs, isConvergedE, isConvergedH,
isMarkUnconverged);
UpdateConvergenceStatus(isConvergedE, isConvergedH);
Es_.push_back(ConvertComplexVector<FloatType>(Es));
Hs_.push_back(ConvertComplexVector<FloatType>(Hs));
}
}
}
convertFieldsFromSphericalToCartesian();
}
template <typename FloatType>
void MultiLayerMie<FloatType>::UpdateConvergenceStatus(std::vector<bool> isConvergedE, std::vector<bool> isConvergedH) {
for (int i = 0; i< 3; i++) isConvergedE_[i] = isConvergedE_[i] && isConvergedE[i];
for (int i = 0; i< 3; i++) isConvergedH_[i] = isConvergedH_[i] && isConvergedH[i];
}
template <typename FloatType>
bool MultiLayerMie<FloatType>::GetFieldConvergence () {
bool convergence = true;
for (auto conv:isConvergedE_) convergence = convergence && conv;
for (auto conv:isConvergedH_) convergence = convergence && conv;
return convergence;
}
template <typename FloatType>
void MultiLayerMie<FloatType>::RunFieldCalculationCartesian(const int first_side_points,
const int second_side_points,
const double relative_side_length,
const int plane_selected,
const double at_x, const double at_y,
const double at_z,
const bool isMarkUnconverged,
const int nmax_in) {
SetMaxTerms(nmax_in);
std::vector<FloatType> Xp(0), Yp(0), Zp(0);
if (size_param_.size()<1) throw "Expect size_param_ to have at least one element before running a simulation";
const FloatType total_R = size_param_.back();
const FloatType second_side_max_coord_value = total_R * relative_side_length;
// TODO add test if side_1_points <= 1 or side_2_points <= 1
const FloatType space_step = second_side_max_coord_value*2/( (second_side_points<2 ? 2 : second_side_points) - 1.0);
auto push_coords = [&](const int nx, const int ny, const int nz) {
const FloatType xi = at_x*total_R - space_step*(nx-1)/2;
const FloatType yi = at_y*total_R - space_step*(ny-1)/2;
const FloatType zi = at_z*total_R - space_step*(nz-1)/2;
for (int i = 0; i < nx; i++) {
for (int j = 0; j < ny; j++) {
for (int k = 0; k < nz; k++) {
Xp.push_back(xi + static_cast<FloatType>(i) * space_step);
Yp.push_back(yi + static_cast<FloatType>(j) * space_step);
Zp.push_back(zi + static_cast<FloatType>(k) * space_step);
}
}
}
};
// TODO add test to check that side_2_points is for z-axis
if (plane_selected == Planes::kEk) push_coords(first_side_points, 1, second_side_points);
if (plane_selected == Planes::kHk) push_coords(1, first_side_points, second_side_points);
if (plane_selected == Planes::kEH) push_coords(first_side_points, second_side_points, 1);
const unsigned int total_size = first_side_points*second_side_points;
if (Xp.size() != total_size || Yp.size() != total_size || Zp.size() != total_size)
throw std::invalid_argument("Error! Wrong dimension of field monitor points for cartesian grid!");
SetFieldCoords({Xp, Yp, Zp});
RunFieldCalculation(isMarkUnconverged);
} // end of void MultiLayerMie<FloatType>::RunFieldCalculationCartesian(...)
} // end of namespace nmie
#endif // SRC_NMIE_NEARFIELD_HPP_