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+//**********************************************************************************//
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+// Copyright (C) 2009-2015 Ovidio Pena <ovidio@bytesfall.com> //
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+// //
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+// This file is part of scattnlay //
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+// //
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+// This program is free software: you can redistribute it and/or modify //
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+// it under the terms of the GNU General Public License as published by //
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+// the Free Software Foundation, either version 3 of the License, or //
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+// (at your option) any later version. //
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+// //
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+// This program is distributed in the hope that it will be useful, //
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+// but WITHOUT ANY WARRANTY; without even the implied warranty of //
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+// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
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+// GNU General Public License for more details. //
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+// //
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+// The only additional remark is that we expect that all publications //
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+// describing work using this software, or all commercial products //
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+// using it, cite the following reference: //
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+// [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
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+// a multilayered sphere," Computer Physics Communications, //
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+// vol. 180, Nov. 2009, pp. 2348-2354. //
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+// //
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+// You should have received a copy of the GNU General Public License //
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+// along with this program. If not, see <http://www.gnu.org/licenses/>. //
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+//**********************************************************************************//
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+
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+//**********************************************************************************//
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+// This class implements the algorithm for a multilayered sphere described by: //
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+// [1] W. Yang, "Improved recursive algorithm for light scattering by a //
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+// multilayered sphere,” Applied Optics, vol. 42, Mar. 2003, pp. 1710-1720. //
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+// //
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+// You can find the description of all the used equations in: //
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+// [2] O. Pena and U. Pal, "Scattering of electromagnetic radiation by //
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+// a multilayered sphere," Computer Physics Communications, //
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+// vol. 180, Nov. 2009, pp. 2348-2354. //
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+// //
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+// Hereinafter all equations numbers refer to [2] //
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+//**********************************************************************************//
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+#include "nmie-core.h"
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+#include <array>
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+#include <algorithm>
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+#include <cstdio>
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+#include <cstdlib>
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+#include <stdexcept>
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+#include <vector>
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+
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+namespace nmie {
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+ //helpers
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+ template<class T> inline T pow2(const T value) {return value*value;}
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+
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+ int round(double x) {
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+ return x >= 0 ? (int)(x + 0.5):(int)(x - 0.5);
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+ }
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+
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+
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+//**********************************************************************************//
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+// This function emulates a C call to calculate the actual scattering parameters //
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+// and amplitudes. //
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+// //
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+// Input parameters: //
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+// L: Number of layers //
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+// pl: Index of PEC layer. If there is none just send -1 //
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+// x: Array containing the size parameters of the layers [0..L-1] //
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+// m: Array containing the relative refractive indexes of the layers [0..L-1] //
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+// nTheta: Number of scattering angles //
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+// Theta: Array containing all the scattering angles where the scattering //
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+// amplitudes will be calculated //
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+// nmax: Maximum number of multipolar expansion terms to be used for the //
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+// calculations. Only use it if you know what you are doing, otherwise //
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+// set this parameter to -1 and the function will calculate it //
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+// //
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+// Output parameters: //
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+// Qext: Efficiency factor for extinction //
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+// Qsca: Efficiency factor for scattering //
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+// Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca) //
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+// Qbk: Efficiency factor for backscattering //
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+// Qpr: Efficiency factor for the radiation pressure //
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+// g: Asymmetry factor (g = (Qext-Qpr)/Qsca) //
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+// Albedo: Single scattering albedo (Albedo = Qsca/Qext) //
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+// S1, S2: Complex scattering amplitudes //
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+// //
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+// Return value: //
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+// Number of multipolar expansion terms used for the calculations //
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+//**********************************************************************************//
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+ int nMie(int L, std::vector<double>& x, std::vector<std::complex<double> >& m, int nTheta, std::vector<double>& Theta, double *Qext, double *Qsca, double *Qabs, double *Qbk, double *Qpr, double *g, double *Albedo, std::vector<std::complex<double> >& S1, std::vector<std::complex<double> >& S2) {
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+
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+ if (x.size() != L || m.size() != L)
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+ throw std::invalid_argument("Declared number of layers do not fit x and m!");
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+ if (Theta.size() != nTheta)
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+ throw std::invalid_argument("Declared number of sample for Theta is not correct!");
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+ try {
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+ MultiLayerMie multi_layer_mie;
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+ multi_layer_mie.SetLayersWidth(x);
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+ multi_layer_mie.SetLayersIndex(m);
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+ multi_layer_mie.SetAngles(Theta);
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+
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+ multi_layer_mie.RunMieCalculations();
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+
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+ *Qext = multi_layer_mie.GetQext();
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+ *Qsca = multi_layer_mie.GetQsca();
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+ *Qabs = multi_layer_mie.GetQabs();
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+ *Qbk = multi_layer_mie.GetQbk();
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+ *Qpr = multi_layer_mie.GetQpr();
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+ *g = multi_layer_mie.GetAsymmetryFactor();
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+ *Albedo = multi_layer_mie.GetAlbedo();
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+ S1 = multi_layer_mie.GetS1();
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+ S2 = multi_layer_mie.GetS2();
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+ } catch(const std::invalid_argument& ia) {
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+ // Will catch if multi_layer_mie fails or other errors.
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+ std::cerr << "Invalid argument: " << ia.what() << std::endl;
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+ throw std::invalid_argument(ia);
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+ return -1;
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+ }
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+
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+ return 0;
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+ }
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+
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+
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+//**********************************************************************************//
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+// This function emulates a C call to calculate complex electric and magnetic field //
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+// in the surroundings and inside (TODO) the particle. //
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+// //
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+// Input parameters: //
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+// L: Number of layers //
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+// pl: Index of PEC layer. If there is none just send 0 (zero) //
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+// x: Array containing the size parameters of the layers [0..L-1] //
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+// m: Array containing the relative refractive indexes of the layers [0..L-1] //
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+// nmax: Maximum number of multipolar expansion terms to be used for the //
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+// calculations. Only use it if you know what you are doing, otherwise //
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+// set this parameter to 0 (zero) and the function will calculate it. //
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+// ncoord: Number of coordinate points //
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+// Coords: Array containing all coordinates where the complex electric and //
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+// magnetic fields will be calculated //
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+// //
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+// Output parameters: //
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+// E, H: Complex electric and magnetic field at the provided coordinates //
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+// //
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+// Return value: //
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+// Number of multipolar expansion terms used for the calculations //
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+//**********************************************************************************//
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+
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+ int nField(const int L, const int pl, const std::vector<double>& x, const std::vector<std::complex<double> >& m, const int nmax, const int ncoord, const std::vector<double>& Xp_vec, const std::vector<double>& Yp_vec, const std::vector<double>& Zp_vec, std::vector<std::vector<std::complex<double> > >& E, std::vector<std::vector<std::complex<double> > >& H) {
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+ if (x.size() != L || m.size() != L)
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+ throw std::invalid_argument("Declared number of layers do not fit x and m!");
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+ if (Xp_vec.size() != ncoord || Yp_vec.size() != ncoord || Zp_vec.size() != ncoord
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+ || E.size() != ncoord || H.size() != ncoord)
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+ throw std::invalid_argument("Declared number of coords do not fit Xp, Yp, Zp, E, or H!");
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+ for (auto f:E)
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+ if (f.size() != 3)
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+ throw std::invalid_argument("Field E is not 3D!");
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+ for (auto f:H)
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+ if (f.size() != 3)
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+ throw std::invalid_argument("Field H is not 3D!");
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+ try {
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+ MultiLayerMie multi_layer_mie;
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+ //multi_layer_mie.SetPEC(pl);
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+ multi_layer_mie.SetLayersWidth(x);
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+ multi_layer_mie.SetLayersIndex(m);
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+ multi_layer_mie.SetFieldCoords({Xp_vec, Yp_vec, Zp_vec});
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+ multi_layer_mie.RunFieldCalculations();
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+ E = multi_layer_mie.GetFieldE();
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+ H = multi_layer_mie.GetFieldH();
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+ //multi_layer_mie.GetFailed();
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+ } catch(const std::invalid_argument& ia) {
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+ // Will catch if multi_layer_mie fails or other errors.
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+ std::cerr << "Invalid argument: " << ia.what() << std::endl;
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+ throw std::invalid_argument(ia);
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+ return - 1;
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+ }
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+
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+ return 0;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Qext //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetQext() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return Qext_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Qabs //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetQabs() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return Qabs_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Qsca //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetQsca() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return Qsca_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Qbk //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetQbk() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return Qbk_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Qpr //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetQpr() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return Qpr_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated assymetry factor //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetAsymmetryFactor() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return asymmetry_factor_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated Albedo //
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+ // ********************************************************************** //
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+
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+ double MultiLayerMie::GetAlbedo() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return albedo_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated S1 //
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+ // ********************************************************************** //
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+
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+ std::vector<std::complex<double> > MultiLayerMie::GetS1() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return S1_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Returns previously calculated S2 //
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+ // ********************************************************************** //
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+
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+ std::vector<std::complex<double> > MultiLayerMie::GetS2() {
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+ if (!isMieCalculated_)
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+ throw std::invalid_argument("You should run calculations before result request!");
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+ return S2_;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::AddTargetLayer(double width, std::complex<double> layer_index) {
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+ isMieCalculated_ = false;
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+ if (width <= 0)
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+ throw std::invalid_argument("Layer width should be positive!");
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+ target_width_.push_back(width);
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+ target_index_.push_back(layer_index);
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+ } // end of void MultiLayerMie::AddTargetLayer(...)
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetTargetPEC(double radius) {
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+ isMieCalculated_ = false;
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+ if (target_width_.size() != 0 || target_index_.size() != 0)
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+ throw std::invalid_argument("Error! Define PEC target radius before any other layers!");
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+ // Add layer of any index...
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+ AddTargetLayer(radius, std::complex<double>(0.0, 0.0));
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+ // ... and mark it as PEC
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+ SetPEC(0.0);
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+ }
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetCoatingIndex(std::vector<std::complex<double> > index) {
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+ isMieCalculated_ = false;
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+ index_.clear();
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+ for (auto value : index) index_.push_back(value);
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+ } // end of void MultiLayerMie::SetCoatingIndex(std::vector<complex> index);
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetAngles(const std::vector<double>& angles) {
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+ isMieCalculated_ = false;
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+ theta_ = angles;
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+ // theta_.clear();
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+ // for (auto value : angles) theta_.push_back(value);
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+ } // end of SetAngles()
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetCoatingWidth(std::vector<double> width) {
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+ isMieCalculated_ = false;
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+ width_.clear();
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+ for (auto w : width)
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+ if (w <= 0)
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+ throw std::invalid_argument("Coating width should be positive!");
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+ else width_.push_back(w);
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+ }
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+ // end of void MultiLayerMie::SetCoatingWidth(...);
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetLayersWidth(const std::vector<double>& size_parameter) {
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+ isMieCalculated_ = false;
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+ size_parameter_.clear();
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+ double prev_size_parameter = 0.0;
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+ for (auto layer_size_parameter : size_parameter) {
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+ if (layer_size_parameter <= 0.0)
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+ throw std::invalid_argument("Size parameter should be positive!");
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+ if (prev_size_parameter > layer_size_parameter)
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+ throw std::invalid_argument
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+ ("Size parameter for next layer should be larger than the previous one!");
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+ prev_size_parameter = layer_size_parameter;
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+ size_parameter_.push_back(layer_size_parameter);
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+ }
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+ }
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+ // end of void MultiLayerMie::SetLayersWidth(...);
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetLayersIndex(const std::vector< std::complex<double> >& index) {
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+ isMieCalculated_ = false;
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+ //index_.clear();
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+ index_ = index;
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+ // for (auto value : index) index_.push_back(value);
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+ } // end of void MultiLayerMie::SetLayersIndex(...);
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetFieldCoords(const std::vector< std::vector<double> >& coords_sp) {
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+ if (coords_sp.size() != 3)
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+ throw std::invalid_argument("Error! Wrong dimension of field monitor points!");
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+ if (coords_sp[0].size() != coords_sp[1].size() || coords_sp[0].size() != coords_sp[2].size())
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+ throw std::invalid_argument("Error! Missing coordinates for field monitor points!");
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+ coords_sp_ = coords_sp;
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+ // for (int i = 0; i < coords_sp_[0].size(); ++i) {
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+ // printf("%g, %g, %g\n", coords_sp_[0][i], coords_sp_[1][i], coords_sp_[2][i]);
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+ // }
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+ } // end of void MultiLayerMie::SetFieldCoords(...)
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ // ********************************************************************** //
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+ void MultiLayerMie::SetPEC(int layer_position) {
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+ isMieCalculated_ = false;
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+ if (layer_position < 0)
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+ throw std::invalid_argument("Error! Layers are numbered from 0!");
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+ PEC_layer_position_ = layer_position;
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+ }
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+
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+
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+ // ********************************************************************** //
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+ // Set maximun number of terms to be used //
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+ // ********************************************************************** //
|
|
|
+
|
|
|
+ void MultiLayerMie::SetMaxTerms(int nmax) {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ nmax_preset_ = nmax;
|
|
|
+ //debug
|
|
|
+ printf("Setting max terms: %d\n", nmax_preset_);
|
|
|
+ }
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::GenerateIndex() {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ index_.clear();
|
|
|
+ for (auto index : target_index_) index_.push_back(index);
|
|
|
+ for (auto index : index_) index_.push_back(index);
|
|
|
+ } // end of void MultiLayerMie::GenerateIndex();
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ double MultiLayerMie::GetTotalRadius() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("You should run calculations before result request!");
|
|
|
+ if (total_radius_ == 0) GenerateSizeParameter();
|
|
|
+ return total_radius_;
|
|
|
+ } // end of double MultiLayerMie::GetTotalRadius();
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Clear layer information //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ void MultiLayerMie::ClearLayers() {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ width_.clear();
|
|
|
+ index_.clear();
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Computational core
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate Nstop - equation (17) //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ void MultiLayerMie::Nstop() {
|
|
|
+ const double& xL = size_parameter_.back();
|
|
|
+ if (xL <= 8) {
|
|
|
+ nmax_ = round(xL + 4.0*pow(xL, 1.0/3.0) + 1);
|
|
|
+ } else if (xL <= 4200) {
|
|
|
+ nmax_ = round(xL + 4.05*pow(xL, 1.0/3.0) + 2);
|
|
|
+ } else {
|
|
|
+ nmax_ = round(xL + 4.0*pow(xL, 1.0/3.0) + 2);
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Maximum number of terms required for the calculation //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ void MultiLayerMie::Nmax(int first_layer) {
|
|
|
+ int ri, riM1;
|
|
|
+ const std::vector<double>& x = size_parameter_;
|
|
|
+ const std::vector<std::complex<double> >& m = index_;
|
|
|
+ Nstop(); // Set initial nmax_ value
|
|
|
+ for (int i = first_layer; i < x.size(); i++) {
|
|
|
+ if (i > PEC_layer_position_)
|
|
|
+ ri = round(std::abs(x[i]*m[i]));
|
|
|
+ else
|
|
|
+ ri = 0;
|
|
|
+ nmax_ = std::max(nmax_, ri);
|
|
|
+ // first layer is pec, if pec is present
|
|
|
+ if ((i > first_layer) && ((i - 1) > PEC_layer_position_))
|
|
|
+ riM1 = round(std::abs(x[i - 1]* m[i]));
|
|
|
+ else
|
|
|
+ riM1 = 0;
|
|
|
+ nmax_ = std::max(nmax_, riM1);
|
|
|
+ }
|
|
|
+ nmax_ += 15; // Final nmax_ value
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the spherical Bessel (jn) and Hankel (h1n) functions //
|
|
|
+ // and their derivatives for a given complex value z. See pag. 87 B&H. //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // z: Real argument to evaluate jn and h1n //
|
|
|
+ // nmax_: Maximum number of terms to calculate jn and h1n //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // jn, h1n: Spherical Bessel and Hankel functions //
|
|
|
+ // jnp, h1np: Derivatives of the spherical Bessel and Hankel functions //
|
|
|
+ // //
|
|
|
+ // The implementation follows the algorithm by I.J. Thompson and A.R. Barnett, //
|
|
|
+ // Comp. Phys. Comm. 47 (1987) 245-257. //
|
|
|
+ // //
|
|
|
+ // Complex spherical Bessel functions from n=0..nmax_-1 for z in the upper half //
|
|
|
+ // plane (Im(z) > -3). //
|
|
|
+ // //
|
|
|
+ // j[n] = j/n(z) Regular solution: j[0]=sin(z)/z //
|
|
|
+ // j'[n] = d[j/n(z)]/dz //
|
|
|
+ // h1[n] = h[0]/n(z) Irregular Hankel function: //
|
|
|
+ // h1'[n] = d[h[0]/n(z)]/dz h1[0] = j0(z) + i*y0(z) //
|
|
|
+ // = (sin(z)-i*cos(z))/z //
|
|
|
+ // = -i*exp(i*z)/z //
|
|
|
+ // Using complex CF1, and trigonometric forms for n=0 solutions. //
|
|
|
+ //**********************************************************************************//
|
|
|
+
|
|
|
+ void MultiLayerMie::sbesjh(std::complex<double> z,
|
|
|
+ std::vector<std::complex<double> >& jn,
|
|
|
+ std::vector<std::complex<double> >& jnp,
|
|
|
+ std::vector<std::complex<double> >& h1n,
|
|
|
+ std::vector<std::complex<double> >& h1np) {
|
|
|
+ const int limit = 20000;
|
|
|
+ const double accur = 1.0e-12;
|
|
|
+ const double tm30 = 1e-30;
|
|
|
+
|
|
|
+ double absc;
|
|
|
+ std::complex<double> zi, w;
|
|
|
+ std::complex<double> pl, f, b, d, c, del, jn0, jndb, h1nldb, h1nbdb;
|
|
|
+
|
|
|
+ absc = std::abs(std::real(z)) + std::abs(std::imag(z));
|
|
|
+ if ((absc < accur) || (std::imag(z) < -3.0)) {
|
|
|
+ throw std::invalid_argument("TODO add error description for condition if ((absc < accur) || (std::imag(z) < -3.0))");
|
|
|
+ }
|
|
|
+
|
|
|
+ zi = 1.0/z;
|
|
|
+ w = zi + zi;
|
|
|
+
|
|
|
+ pl = double(nmax_)*zi;
|
|
|
+
|
|
|
+ f = pl + zi;
|
|
|
+ b = f + f + zi;
|
|
|
+ d = 0.0;
|
|
|
+ c = f;
|
|
|
+ for (int n = 0; n < limit; n++) {
|
|
|
+ d = b - d;
|
|
|
+ c = b - 1.0/c;
|
|
|
+
|
|
|
+ absc = std::abs(std::real(d)) + std::abs(std::imag(d));
|
|
|
+ if (absc < tm30) {
|
|
|
+ d = tm30;
|
|
|
+ }
|
|
|
+
|
|
|
+ absc = std::abs(std::real(c)) + std::abs(std::imag(c));
|
|
|
+ if (absc < tm30) {
|
|
|
+ c = tm30;
|
|
|
+ }
|
|
|
+
|
|
|
+ d = 1.0/d;
|
|
|
+ del = d*c;
|
|
|
+ f = f*del;
|
|
|
+ b += w;
|
|
|
+
|
|
|
+ absc = std::abs(std::real(del - 1.0)) + std::abs(std::imag(del - 1.0));
|
|
|
+
|
|
|
+ if (absc < accur) {
|
|
|
+ // We have obtained the desired accuracy
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ if (absc > accur) {
|
|
|
+ throw std::invalid_argument("We were not able to obtain the desired accuracy");
|
|
|
+ }
|
|
|
+
|
|
|
+ jn[nmax_ - 1] = tm30;
|
|
|
+ jnp[nmax_ - 1] = f*jn[nmax_ - 1];
|
|
|
+
|
|
|
+ // Downward recursion to n=0 (N.B. Coulomb Functions)
|
|
|
+ for (int n = nmax_ - 2; n >= 0; n--) {
|
|
|
+ jn[n] = pl*jn[n + 1] + jnp[n + 1];
|
|
|
+ jnp[n] = pl*jn[n] - jn[n + 1];
|
|
|
+ pl = pl - zi;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Calculate the n=0 Bessel Functions
|
|
|
+ jn0 = zi*std::sin(z);
|
|
|
+ h1n[0] = std::exp(std::complex<double>(0.0, 1.0)*z)*zi*(-std::complex<double>(0.0, 1.0));
|
|
|
+ h1np[0] = h1n[0]*(std::complex<double>(0.0, 1.0) - zi);
|
|
|
+
|
|
|
+ // Rescale j[n], j'[n], converting to spherical Bessel functions.
|
|
|
+ // Recur h1[n], h1'[n] as spherical Bessel functions.
|
|
|
+ w = 1.0/jn[0];
|
|
|
+ pl = zi;
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ jn[n] = jn0*(w*jn[n]);
|
|
|
+ jnp[n] = jn0*(w*jnp[n]) - zi*jn[n];
|
|
|
+ if (n != 0) {
|
|
|
+ h1n[n] = (pl - zi)*h1n[n - 1] - h1np[n - 1];
|
|
|
+
|
|
|
+ // check if hankel is increasing (upward stable)
|
|
|
+ if (std::abs(h1n[n]) < std::abs(h1n[n - 1])) {
|
|
|
+ jndb = z;
|
|
|
+ h1nldb = h1n[n];
|
|
|
+ h1nbdb = h1n[n - 1];
|
|
|
+ }
|
|
|
+
|
|
|
+ pl += zi;
|
|
|
+
|
|
|
+ h1np[n] = -(pl*h1n[n]) + h1n[n - 1];
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the spherical Bessel functions (bj and by) and the //
|
|
|
+ // logarithmic derivative (bd) for a given complex value z. See pag. 87 B&H. //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // z: Complex argument to evaluate bj, by and bd //
|
|
|
+ // nmax_: Maximum number of terms to calculate bj, by and bd //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // bj, by: Spherical Bessel functions //
|
|
|
+ // bd: Logarithmic derivative //
|
|
|
+ //**********************************************************************************//
|
|
|
+
|
|
|
+ void MultiLayerMie::sphericalBessel(std::complex<double> z,
|
|
|
+ std::vector<std::complex<double> >& bj,
|
|
|
+ std::vector<std::complex<double> >& by,
|
|
|
+ std::vector<std::complex<double> >& bd) {
|
|
|
+ std::vector<std::complex<double> > jn(nmax_), jnp(nmax_), h1n(nmax_), h1np(nmax_);
|
|
|
+ sbesjh(z, jn, jnp, h1n, h1np);
|
|
|
+
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ bj[n] = jn[n];
|
|
|
+ by[n] = (h1n[n] - jn[n])/std::complex<double>(0.0, 1.0);
|
|
|
+ bd[n] = jnp[n]/jn[n] + 1.0/z;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate an - equation (5) //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ std::complex<double> MultiLayerMie::calc_an(int n, double XL, std::complex<double> Ha, std::complex<double> mL,
|
|
|
+ std::complex<double> PsiXL, std::complex<double> ZetaXL,
|
|
|
+ std::complex<double> PsiXLM1, std::complex<double> ZetaXLM1) {
|
|
|
+
|
|
|
+ std::complex<double> Num = (Ha/mL + n/XL)*PsiXL - PsiXLM1;
|
|
|
+ std::complex<double> Denom = (Ha/mL + n/XL)*ZetaXL - ZetaXLM1;
|
|
|
+
|
|
|
+ return Num/Denom;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculate bn - equation (6) //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ std::complex<double> MultiLayerMie::calc_bn(int n, double XL, std::complex<double> Hb, std::complex<double> mL,
|
|
|
+ std::complex<double> PsiXL, std::complex<double> ZetaXL,
|
|
|
+ std::complex<double> PsiXLM1, std::complex<double> ZetaXLM1) {
|
|
|
+
|
|
|
+ std::complex<double> Num = (mL*Hb + n/XL)*PsiXL - PsiXLM1;
|
|
|
+ std::complex<double> Denom = (mL*Hb + n/XL)*ZetaXL - ZetaXLM1;
|
|
|
+
|
|
|
+ return Num/Denom;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculates S1 - equation (25a) //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ std::complex<double> MultiLayerMie::calc_S1(int n, std::complex<double> an, std::complex<double> bn,
|
|
|
+ double Pi, double Tau) {
|
|
|
+ return double(n + n + 1)*(Pi*an + Tau*bn)/double(n*n + n);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // Calculates S2 - equation (25b) (it's the same as (25a), just switches //
|
|
|
+ // Pi and Tau) //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ std::complex<double> MultiLayerMie::calc_S2(int n, std::complex<double> an, std::complex<double> bn,
|
|
|
+ double Pi, double Tau) {
|
|
|
+ return calc_S1(n, an, bn, Tau, Pi);
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the Riccati-Bessel functions (Psi and Zeta) for a //
|
|
|
+ // real argument (x). //
|
|
|
+ // Equations (20a) - (21b) //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // x: Real argument to evaluate Psi and Zeta //
|
|
|
+ // nmax: Maximum number of terms to calculate Psi and Zeta //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // Psi, Zeta: Riccati-Bessel functions //
|
|
|
+ //**********************************************************************************//
|
|
|
+
|
|
|
+ void MultiLayerMie::calcPsiZeta(std::complex<double> z,
|
|
|
+ std::vector<std::complex<double> > D1,
|
|
|
+ std::vector<std::complex<double> > D3,
|
|
|
+ std::vector<std::complex<double> >& Psi,
|
|
|
+ std::vector<std::complex<double> >& Zeta) {
|
|
|
+
|
|
|
+ //Upward recurrence for Psi and Zeta - equations (20a) - (21b)
|
|
|
+ std::complex<double> c_i(0.0, 1.0);
|
|
|
+ Psi[0] = std::sin(z);
|
|
|
+ Zeta[0] = std::sin(z) - c_i*std::cos(z);
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ Psi[n] = Psi[n - 1]*(static_cast<double>(n)/z - D1[n - 1]);
|
|
|
+ Zeta[n] = Zeta[n - 1]*(static_cast<double>(n)/z - D3[n - 1]);
|
|
|
+ }
|
|
|
+
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the logarithmic derivatives of the Riccati-Bessel //
|
|
|
+ // functions (D1 and D3) for a complex argument (z). //
|
|
|
+ // Equations (16a), (16b) and (18a) - (18d) //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // z: Complex argument to evaluate D1 and D3 //
|
|
|
+ // nmax_: Maximum number of terms to calculate D1 and D3 //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // D1, D3: Logarithmic derivatives of the Riccati-Bessel functions //
|
|
|
+ //**********************************************************************************//
|
|
|
+
|
|
|
+ void MultiLayerMie::calcD1D3(const std::complex<double> z,
|
|
|
+ std::vector<std::complex<double> >& D1,
|
|
|
+ std::vector<std::complex<double> >& D3) {
|
|
|
+
|
|
|
+ // Downward recurrence for D1 - equations (16a) and (16b)
|
|
|
+ D1[nmax_] = std::complex<double>(0.0, 0.0);
|
|
|
+ const std::complex<double> zinv = std::complex<double>(1.0, 0.0)/z;
|
|
|
+
|
|
|
+ for (int n = nmax_; n > 0; n--) {
|
|
|
+ D1[n - 1] = double(n)*zinv - 1.0/(D1[n] + double(n)*zinv);
|
|
|
+ }
|
|
|
+
|
|
|
+ if (std::abs(D1[0]) > 100000.0)
|
|
|
+ throw std::invalid_argument("Unstable D1! Please, try to change input parameters!\n");
|
|
|
+
|
|
|
+ // Upward recurrence for PsiZeta and D3 - equations (18a) - (18d)
|
|
|
+ PsiZeta_[0] = 0.5*(1.0 - std::complex<double>(std::cos(2.0*z.real()), std::sin(2.0*z.real()))
|
|
|
+ *std::exp(-2.0*z.imag()));
|
|
|
+ D3[0] = std::complex<double>(0.0, 1.0);
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ PsiZeta_[n] = PsiZeta_[n - 1]*(static_cast<double>(n)*zinv - D1[n - 1])
|
|
|
+ *(static_cast<double>(n)*zinv- D3[n - 1]);
|
|
|
+ D3[n] = D1[n] + std::complex<double>(0.0, 1.0)/PsiZeta_[n];
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates Pi and Tau for all values of Theta. //
|
|
|
+ // Equations (26a) - (26c) //
|
|
|
+ // //
|
|
|
+ // Input parameters: //
|
|
|
+ // nmax_: Maximum number of terms to calculate Pi and Tau //
|
|
|
+ // nTheta: Number of scattering angles //
|
|
|
+ // Theta: Array containing all the scattering angles where the scattering //
|
|
|
+ // amplitudes will be calculated //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // Pi, Tau: Angular functions Pi and Tau, as defined in equations (26a) - (26c) //
|
|
|
+ //**********************************************************************************//
|
|
|
+
|
|
|
+ void MultiLayerMie::calcSinglePiTau(const double& costheta, std::vector<double>& Pi,
|
|
|
+ std::vector<double>& Tau) {
|
|
|
+
|
|
|
+ //****************************************************//
|
|
|
+ // Equations (26a) - (26c) //
|
|
|
+ //****************************************************//
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ if (n == 0) {
|
|
|
+ // Initialize Pi and Tau
|
|
|
+ Pi[n] = 1.0;
|
|
|
+ Tau[n] = (n + 1)*costheta;
|
|
|
+ } else {
|
|
|
+ // Calculate the actual values
|
|
|
+ Pi[n] = ((n == 1) ? ((n + n + 1)*costheta*Pi[n - 1]/n)
|
|
|
+ : (((n + n + 1)*costheta*Pi[n - 1]
|
|
|
+ - (n + 1)*Pi[n - 2])/n));
|
|
|
+ Tau[n] = (n + 1)*costheta*Pi[n] - (n + 2)*Pi[n - 1];
|
|
|
+ }
|
|
|
+ }
|
|
|
+ } // end of void MultiLayerMie::calcPiTau(...)
|
|
|
+
|
|
|
+
|
|
|
+ void MultiLayerMie::calcAllPiTau(std::vector< std::vector<double> >& Pi,
|
|
|
+ std::vector< std::vector<double> >& Tau) {
|
|
|
+ std::vector<double> costheta(theta_.size(), 0.0);
|
|
|
+ for (int t = 0; t < theta_.size(); t++) {
|
|
|
+ costheta[t] = std::cos(theta_[t]);
|
|
|
+ }
|
|
|
+ // Do not join upper and lower 'for' to a single one! It will slow
|
|
|
+ // down the code!!! (For about 0.5-2.0% of runtime, it is probably
|
|
|
+ // due to increased cache missing rate originated from the
|
|
|
+ // recurrence in calcPiTau...)
|
|
|
+ for (int t = 0; t < theta_.size(); t++) {
|
|
|
+ calcSinglePiTau(costheta[t], Pi[t], Tau[t]);
|
|
|
+ //calcSinglePiTau(std::cos(theta_[t]), Pi[t], Tau[t]); // It is slow!!
|
|
|
+ }
|
|
|
+ } // end of void MultiLayerMie::calcAllPiTau(...)
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the scattering coefficients required to calculate //
|
|
|
+ // both the near- and far-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: //
|
|
|
+ // an, bn: Complex scattering amplitudes //
|
|
|
+ // //
|
|
|
+ // Return value: //
|
|
|
+ // Number of multipolar expansion terms used for the calculations //
|
|
|
+ //**********************************************************************************//
|
|
|
+ void MultiLayerMie::ExtScattCoeffs(std::vector<std::complex<double> >& an,
|
|
|
+ std::vector<std::complex<double> >& bn) {
|
|
|
+ const std::vector<double>& x = size_parameter_;
|
|
|
+ const std::vector<std::complex<double> >& m = index_;
|
|
|
+ const int& pl = PEC_layer_position_;
|
|
|
+ const int L = index_.size();
|
|
|
+ //************************************************************************//
|
|
|
+ // Calculate the index of the first layer. It can be either 0 (default) //
|
|
|
+ // or the index of the outermost PEC layer. In the latter case all layers //
|
|
|
+ // below the PEC are discarded. //
|
|
|
+ // ***********************************************************************//
|
|
|
+ // TODO, is it possible for PEC to have a zero index? If yes than
|
|
|
+ // is should be:
|
|
|
+ // int fl = (pl > - 1) ? pl : 0;
|
|
|
+ // This will give the same result, however, it corresponds the
|
|
|
+ // logic - if there is PEC, than first layer is PEC.
|
|
|
+ // Well, I followed the logic: First layer is always zero unless it has
|
|
|
+ // an upper PEC layer.
|
|
|
+ int fl = (pl > 0) ? pl : 0;
|
|
|
+ if (nmax_ <= 0) Nmax(fl);
|
|
|
+
|
|
|
+ std::complex<double> z1, z2;
|
|
|
+ //**************************************************************************//
|
|
|
+ // Note that since Fri, Nov 14, 2014 all arrays start from 0 (zero), which //
|
|
|
+ // means that index = layer number - 1 or index = n - 1. The only exception //
|
|
|
+ // are the arrays for representing D1, D3 and Q because they need a value //
|
|
|
+ // for the index 0 (zero), hence it is important to consider this shift //
|
|
|
+ // between different arrays. The change was done to optimize memory usage. //
|
|
|
+ //**************************************************************************//
|
|
|
+ // Allocate memory to the arrays
|
|
|
+ std::vector<std::complex<double> > D1_mlxl(nmax_ + 1), D1_mlxlM1(nmax_ + 1),
|
|
|
+ D3_mlxl(nmax_ + 1), D3_mlxlM1(nmax_ + 1);
|
|
|
+
|
|
|
+ std::vector<std::vector<std::complex<double> > > Q(L), Ha(L), Hb(L);
|
|
|
+
|
|
|
+ for (int l = 0; l < L; l++) {
|
|
|
+ Q[l].resize(nmax_ + 1);
|
|
|
+ Ha[l].resize(nmax_);
|
|
|
+ Hb[l].resize(nmax_);
|
|
|
+ }
|
|
|
+
|
|
|
+ an.resize(nmax_);
|
|
|
+ bn.resize(nmax_);
|
|
|
+ PsiZeta_.resize(nmax_ + 1);
|
|
|
+
|
|
|
+ std::vector<std::complex<double> > D1XL(nmax_ + 1), D3XL(nmax_ + 1),
|
|
|
+ PsiXL(nmax_ + 1), ZetaXL(nmax_ + 1);
|
|
|
+
|
|
|
+ //*************************************************//
|
|
|
+ // Calculate D1 and D3 for z1 in the first layer //
|
|
|
+ //*************************************************//
|
|
|
+ if (fl == pl) { // PEC layer
|
|
|
+ for (int n = 0; n <= nmax_; n++) {
|
|
|
+ D1_mlxl[n] = std::complex<double>(0.0, - 1.0);
|
|
|
+ D3_mlxl[n] = std::complex<double>(0.0, 1.0);
|
|
|
+ }
|
|
|
+ } else { // Regular layer
|
|
|
+ z1 = x[fl]* m[fl];
|
|
|
+ // Calculate D1 and D3
|
|
|
+ calcD1D3(z1, D1_mlxl, D3_mlxl);
|
|
|
+ }
|
|
|
+ // do { \
|
|
|
+ // ++iformat;\
|
|
|
+ // if (iformat%5 == 0) printf("%24.16e",z1.real());
|
|
|
+ // } while (false);
|
|
|
+ //******************************************************************//
|
|
|
+ // Calculate Ha and Hb in the first layer - equations (7a) and (8a) //
|
|
|
+ //******************************************************************//
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ Ha[fl][n] = D1_mlxl[n + 1];
|
|
|
+ Hb[fl][n] = D1_mlxl[n + 1];
|
|
|
+ }
|
|
|
+ //*****************************************************//
|
|
|
+ // Iteration from the second layer to the last one (L) //
|
|
|
+ //*****************************************************//
|
|
|
+ std::complex<double> Temp, Num, Denom;
|
|
|
+ std::complex<double> G1, G2;
|
|
|
+ for (int l = fl + 1; l < L; l++) {
|
|
|
+ //************************************************************//
|
|
|
+ //Calculate D1 and D3 for z1 and z2 in the layers fl + 1..L //
|
|
|
+ //************************************************************//
|
|
|
+ z1 = x[l]*m[l];
|
|
|
+ z2 = x[l - 1]*m[l];
|
|
|
+ //Calculate D1 and D3 for z1
|
|
|
+ calcD1D3(z1, D1_mlxl, D3_mlxl);
|
|
|
+ //Calculate D1 and D3 for z2
|
|
|
+ calcD1D3(z2, D1_mlxlM1, D3_mlxlM1);
|
|
|
+ // prn(z1.real());
|
|
|
+ // for (auto i : D1_mlxl) { prn(i.real());
|
|
|
+ // // prn(i.imag());
|
|
|
+ // } printf("\n");
|
|
|
+
|
|
|
+ //*********************************************//
|
|
|
+ //Calculate Q, Ha and Hb in the layers fl + 1..L //
|
|
|
+ //*********************************************//
|
|
|
+ // Upward recurrence for Q - equations (19a) and (19b)
|
|
|
+ Num = std::exp(-2.0*(z1.imag() - z2.imag()))
|
|
|
+ *std::complex<double>(std::cos(-2.0*z2.real()) - std::exp(-2.0*z2.imag()), std::sin(-2.0*z2.real()));
|
|
|
+ Denom = std::complex<double>(std::cos(-2.0*z1.real()) - std::exp(-2.0*z1.imag()), std::sin(-2.0*z1.real()));
|
|
|
+ Q[l][0] = Num/Denom;
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ Num = (z1*D1_mlxl[n] + double(n))*(double(n) - z1*D3_mlxl[n - 1]);
|
|
|
+ Denom = (z2*D1_mlxlM1[n] + double(n))*(double(n) - z2*D3_mlxlM1[n - 1]);
|
|
|
+ Q[l][n] = ((pow2(x[l - 1]/x[l])* Q[l][n - 1])*Num)/Denom;
|
|
|
+ }
|
|
|
+ // Upward recurrence for Ha and Hb - equations (7b), (8b) and (12) - (15)
|
|
|
+ for (int n = 1; n <= nmax_; n++) {
|
|
|
+ //Ha
|
|
|
+ if ((l - 1) == pl) { // The layer below the current one is a PEC layer
|
|
|
+ G1 = -D1_mlxlM1[n];
|
|
|
+ G2 = -D3_mlxlM1[n];
|
|
|
+ } else {
|
|
|
+ G1 = (m[l]*Ha[l - 1][n - 1]) - (m[l - 1]*D1_mlxlM1[n]);
|
|
|
+ G2 = (m[l]*Ha[l - 1][n - 1]) - (m[l - 1]*D3_mlxlM1[n]);
|
|
|
+ } // end of if PEC
|
|
|
+ Temp = Q[l][n]*G1;
|
|
|
+ Num = (G2*D1_mlxl[n]) - (Temp*D3_mlxl[n]);
|
|
|
+ Denom = G2 - Temp;
|
|
|
+ Ha[l][n - 1] = Num/Denom;
|
|
|
+ //Hb
|
|
|
+ if ((l - 1) == pl) { // The layer below the current one is a PEC layer
|
|
|
+ G1 = Hb[l - 1][n - 1];
|
|
|
+ G2 = Hb[l - 1][n - 1];
|
|
|
+ } else {
|
|
|
+ G1 = (m[l - 1]*Hb[l - 1][n - 1]) - (m[l]*D1_mlxlM1[n]);
|
|
|
+ G2 = (m[l - 1]*Hb[l - 1][n - 1]) - (m[l]*D3_mlxlM1[n]);
|
|
|
+ } // end of if PEC
|
|
|
+
|
|
|
+ Temp = Q[l][n]*G1;
|
|
|
+ Num = (G2*D1_mlxl[n]) - (Temp* D3_mlxl[n]);
|
|
|
+ Denom = (G2- Temp);
|
|
|
+ Hb[l][n - 1] = (Num/ Denom);
|
|
|
+ } // end of for Ha and Hb terms
|
|
|
+ } // end of for layers iteration
|
|
|
+ //**************************************//
|
|
|
+ //Calculate D1, D3, Psi and Zeta for XL //
|
|
|
+ //**************************************//
|
|
|
+ // Calculate D1XL and D3XL
|
|
|
+ calcD1D3(x[L - 1], D1XL, D3XL);
|
|
|
+ //printf("%5.20f\n",Ha[L - 1][0].real());
|
|
|
+ // Calculate PsiXL and ZetaXL
|
|
|
+ calcPsiZeta(x[L - 1], D1XL, D3XL, PsiXL, ZetaXL);
|
|
|
+ //*********************************************************************//
|
|
|
+ // Finally, we calculate the scattering coefficients (an and bn) and //
|
|
|
+ // the angular functions (Pi and Tau). Note that for these arrays the //
|
|
|
+ // first layer is 0 (zero), in future versions all arrays will follow //
|
|
|
+ // this convention to save memory. (13 Nov, 2014) //
|
|
|
+ //*********************************************************************//
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ //********************************************************************//
|
|
|
+ //Expressions for calculating an and bn coefficients are not valid if //
|
|
|
+ //there is only one PEC layer (ie, for a simple PEC sphere). //
|
|
|
+ //********************************************************************//
|
|
|
+ if (pl < (L - 1)) {
|
|
|
+ an[n] = calc_an(n + 1, x[L - 1], Ha[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
|
|
|
+ bn[n] = calc_bn(n + 1, x[L - 1], Hb[L - 1][n], m[L - 1], PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
|
|
|
+ } else {
|
|
|
+ an[n] = calc_an(n + 1, x[L - 1], std::complex<double>(0.0, 0.0), std::complex<double>(1.0, 0.0), PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
|
|
|
+ bn[n] = PsiXL[n + 1]/ZetaXL[n + 1];
|
|
|
+ }
|
|
|
+ } // end of for an and bn terms
|
|
|
+ } // end of void MultiLayerMie::ExtScattCoeffs(...)
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::InitMieCalculations() {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ // Initialize the scattering parameters
|
|
|
+ Qext_ = 0;
|
|
|
+ Qsca_ = 0;
|
|
|
+ Qabs_ = 0;
|
|
|
+ Qbk_ = 0;
|
|
|
+ Qpr_ = 0;
|
|
|
+ asymmetry_factor_ = 0;
|
|
|
+ albedo_ = 0;
|
|
|
+ Qsca_ch_.clear();
|
|
|
+ Qext_ch_.clear();
|
|
|
+ Qabs_ch_.clear();
|
|
|
+ Qbk_ch_.clear();
|
|
|
+ Qpr_ch_.clear();
|
|
|
+ Qsca_ch_.resize(nmax_ - 1);
|
|
|
+ Qext_ch_.resize(nmax_ - 1);
|
|
|
+ Qabs_ch_.resize(nmax_ - 1);
|
|
|
+ Qbk_ch_.resize(nmax_ - 1);
|
|
|
+ Qpr_ch_.resize(nmax_ - 1);
|
|
|
+ Qsca_ch_norm_.resize(nmax_ - 1);
|
|
|
+ Qext_ch_norm_.resize(nmax_ - 1);
|
|
|
+ Qabs_ch_norm_.resize(nmax_ - 1);
|
|
|
+ Qbk_ch_norm_.resize(nmax_ - 1);
|
|
|
+ Qpr_ch_norm_.resize(nmax_ - 1);
|
|
|
+ // Initialize the scattering amplitudes
|
|
|
+ std::vector<std::complex<double> > tmp1(theta_.size(),std::complex<double>(0.0, 0.0));
|
|
|
+ S1_.swap(tmp1);
|
|
|
+ S2_ = S1_;
|
|
|
+ }
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::ConvertToSP() {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ if (target_width_.size() + width_.size() == 0)
|
|
|
+ return; // Nothing to convert, we suppose that SP was set directly
|
|
|
+ GenerateSizeParameter();
|
|
|
+ GenerateIndex();
|
|
|
+ if (size_parameter_.size() != index_.size())
|
|
|
+ throw std::invalid_argument("Ivalid conversion of width to size parameter units!/n");
|
|
|
+ }
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates the actual scattering parameters and amplitudes //
|
|
|
+ // //
|
|
|
+ // 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] //
|
|
|
+ // nTheta: Number of scattering angles //
|
|
|
+ // Theta: Array containing all the scattering angles where the scattering //
|
|
|
+ // amplitudes will be calculated //
|
|
|
+ // 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: //
|
|
|
+ // Qext: Efficiency factor for extinction //
|
|
|
+ // Qsca: Efficiency factor for scattering //
|
|
|
+ // Qabs: Efficiency factor for absorption (Qabs = Qext - Qsca) //
|
|
|
+ // Qbk: Efficiency factor for backscattering //
|
|
|
+ // Qpr: Efficiency factor for the radiation pressure //
|
|
|
+ // g: Asymmetry factor (g = (Qext-Qpr)/Qsca) //
|
|
|
+ // Albedo: Single scattering albedo (Albedo = Qsca/Qext) //
|
|
|
+ // S1, S2: Complex scattering amplitudes //
|
|
|
+ // //
|
|
|
+ // Return value: //
|
|
|
+ // Number of multipolar expansion terms used for the calculations //
|
|
|
+ //**********************************************************************************//
|
|
|
+ void MultiLayerMie::RunMieCalculations() {
|
|
|
+ isMieCalculated_ = false;
|
|
|
+ ConvertToSP();
|
|
|
+ nmax_ = nmax_preset_;
|
|
|
+ if (size_parameter_.size() != index_.size())
|
|
|
+ throw std::invalid_argument("Each size parameter should have only one index!");
|
|
|
+ if (size_parameter_.size() == 0)
|
|
|
+ throw std::invalid_argument("Initialize model first!");
|
|
|
+ const std::vector<double>& x = size_parameter_;
|
|
|
+ // Calculate scattering coefficients
|
|
|
+ ExtScattCoeffs(an_, bn_);
|
|
|
+
|
|
|
+ // std::vector< std::vector<double> > Pi(nmax_), Tau(nmax_);
|
|
|
+ std::vector< std::vector<double> > Pi, Tau;
|
|
|
+ Pi.resize(theta_.size());
|
|
|
+ Tau.resize(theta_.size());
|
|
|
+ for (int i =0; i< theta_.size(); ++i) {
|
|
|
+ Pi[i].resize(nmax_);
|
|
|
+ Tau[i].resize(nmax_);
|
|
|
+ }
|
|
|
+ calcAllPiTau(Pi, Tau);
|
|
|
+ InitMieCalculations(); //
|
|
|
+ std::complex<double> Qbktmp(0.0, 0.0);
|
|
|
+ std::vector< std::complex<double> > Qbktmp_ch(nmax_ - 1, Qbktmp);
|
|
|
+ // By using downward recurrence we avoid loss of precision due to float rounding errors
|
|
|
+ // See: https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html
|
|
|
+ // http://en.wikipedia.org/wiki/Loss_of_significance
|
|
|
+ for (int i = nmax_ - 2; i >= 0; i--) {
|
|
|
+ const int n = i + 1;
|
|
|
+ // Equation (27)
|
|
|
+ Qext_ch_norm_[i] = (an_[i].real() + bn_[i].real());
|
|
|
+ Qext_ch_[i] = (n + n + 1.0)*Qext_ch_norm_[i];
|
|
|
+ //Qext_ch_[i] = (n + n + 1)*(an_[i].real() + bn_[i].real());
|
|
|
+ Qext_ += Qext_ch_[i];
|
|
|
+ // Equation (28)
|
|
|
+ Qsca_ch_norm_[i] = (an_[i].real()*an_[i].real() + an_[i].imag()*an_[i].imag()
|
|
|
+ + bn_[i].real()*bn_[i].real() + bn_[i].imag()*bn_[i].imag());
|
|
|
+ Qsca_ch_[i] = (n + n + 1.0)*Qsca_ch_norm_[i];
|
|
|
+ Qsca_ += Qsca_ch_[i];
|
|
|
+ // Qsca_ch_[i] += (n + n + 1)*(an_[i].real()*an_[i].real() + an_[i].imag()*an_[i].imag()
|
|
|
+ // + bn_[i].real()*bn_[i].real() + bn_[i].imag()*bn_[i].imag());
|
|
|
+
|
|
|
+ // Equation (29) TODO We must check carefully this equation. If we
|
|
|
+ // remove the typecast to double then the result changes. Which is
|
|
|
+ // the correct one??? Ovidio (2014/12/10) With cast ratio will
|
|
|
+ // give double, without cast (n + n + 1)/(n*(n + 1)) will be
|
|
|
+ // rounded to integer. Tig (2015/02/24)
|
|
|
+ Qpr_ch_[i]=((n*(n + 2)/(n + 1))*((an_[i]*std::conj(an_[n]) + bn_[i]*std::conj(bn_[n])).real())
|
|
|
+ + ((double)(n + n + 1)/(n*(n + 1)))*(an_[i]*std::conj(bn_[i])).real());
|
|
|
+ Qpr_ += Qpr_ch_[i];
|
|
|
+ // Equation (33)
|
|
|
+ Qbktmp_ch[i] = (double)(n + n + 1)*(1 - 2*(n % 2))*(an_[i]- bn_[i]);
|
|
|
+ Qbktmp += Qbktmp_ch[i];
|
|
|
+ // Calculate the scattering amplitudes (S1 and S2) //
|
|
|
+ // Equations (25a) - (25b) //
|
|
|
+ for (int t = 0; t < theta_.size(); t++) {
|
|
|
+ S1_[t] += calc_S1(n, an_[i], bn_[i], Pi[t][i], Tau[t][i]);
|
|
|
+ S2_[t] += calc_S2(n, an_[i], bn_[i], Pi[t][i], Tau[t][i]);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ double x2 = pow2(x.back());
|
|
|
+ Qext_ = 2.0*(Qext_)/x2; // Equation (27)
|
|
|
+ for (double& Q : Qext_ch_) Q = 2.0*Q/x2;
|
|
|
+ Qsca_ = 2.0*(Qsca_)/x2; // Equation (28)
|
|
|
+ for (double& Q : Qsca_ch_) Q = 2.0*Q/x2;
|
|
|
+ //for (double& Q : Qsca_ch_norm_) Q = 2.0*Q/x2;
|
|
|
+ Qpr_ = Qext_ - 4.0*(Qpr_)/x2; // Equation (29)
|
|
|
+ for (int i = 0; i < nmax_ - 1; ++i) Qpr_ch_[i] = Qext_ch_[i] - 4.0*Qpr_ch_[i]/x2;
|
|
|
+
|
|
|
+ Qabs_ = Qext_ - Qsca_; // Equation (30)
|
|
|
+ for (int i = 0; i < nmax_ - 1; ++i) {
|
|
|
+ Qabs_ch_[i] = Qext_ch_[i] - Qsca_ch_[i];
|
|
|
+ Qabs_ch_norm_[i] = Qext_ch_norm_[i] - Qsca_ch_norm_[i];
|
|
|
+ }
|
|
|
+
|
|
|
+ albedo_ = Qsca_/Qext_; // Equation (31)
|
|
|
+ asymmetry_factor_ = (Qext_ - Qpr_)/Qsca_; // Equation (32)
|
|
|
+
|
|
|
+ Qbk_ = (Qbktmp.real()*Qbktmp.real() + Qbktmp.imag()*Qbktmp.imag())/x2; // Equation (33)
|
|
|
+
|
|
|
+ isMieCalculated_ = true;
|
|
|
+ nmax_used_ = nmax_;
|
|
|
+ // printf("Run Mie result: Qext = %g, Qsca = %g, Qabs = %g, Qbk = %g \n",
|
|
|
+ // GetQext(), GetQsca(), GetQabs(), GetQbk());
|
|
|
+ //return nmax;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::IntScattCoeffsInit() {
|
|
|
+ const int L = index_.size();
|
|
|
+ // we need to fill
|
|
|
+ // std::vector< std::vector<std::complex<double> > > al_n_, bl_n_, cl_n_, dl_n_;
|
|
|
+ // for n = [0..nmax_) and for l=[L..0)
|
|
|
+ // TODO: to decrease cache miss outer loop is with n and inner with reversed l
|
|
|
+ // at the moment outer is forward l and inner in n
|
|
|
+ al_n_.resize(L + 1);
|
|
|
+ bl_n_.resize(L + 1);
|
|
|
+ cl_n_.resize(L + 1);
|
|
|
+ dl_n_.resize(L + 1);
|
|
|
+ for (auto& element:al_n_) element.resize(nmax_);
|
|
|
+ for (auto& element:bl_n_) element.resize(nmax_);
|
|
|
+ for (auto& element:cl_n_) element.resize(nmax_);
|
|
|
+ for (auto& element:dl_n_) element.resize(nmax_);
|
|
|
+ std::complex<double> c_one(1.0, 0.0);
|
|
|
+ std::complex<double> c_zero(0.0, 0.0);
|
|
|
+ // Yang, paragraph under eq. A3
|
|
|
+ // a^(L + 1)_n = a_n, d^(L + 1) = 1 ...
|
|
|
+ for (int i = 0; i < nmax_; ++i) {
|
|
|
+ al_n_[L][i] = an_[i];
|
|
|
+ bl_n_[L][i] = bn_[i];
|
|
|
+ cl_n_[L][i] = c_one;
|
|
|
+ dl_n_[L][i] = c_one;
|
|
|
+ if (i < 3) printf(" (%g) ", std::abs(an_[i]));
|
|
|
+ }
|
|
|
+
|
|
|
+ }
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::IntScattCoeffs() {
|
|
|
+ if (!isMieCalculated_)
|
|
|
+ throw std::invalid_argument("(IntScattCoeffs) You should run calculations first!");
|
|
|
+ IntScattCoeffsInit();
|
|
|
+ const int L = index_.size();
|
|
|
+ std::vector<std::complex<double> > z(L), z1(L);
|
|
|
+ for (int i = 0; i < L - 1; ++i) {
|
|
|
+ z[i] =size_parameter_[i]*index_[i];
|
|
|
+ z1[i]=size_parameter_[i]*index_[i + 1];
|
|
|
+ }
|
|
|
+ z[L - 1] = size_parameter_[L - 1]*index_[L - 1];
|
|
|
+ z1[L - 1] = size_parameter_[L - 1];
|
|
|
+ std::vector< std::vector<std::complex<double> > > D1z(L), D1z1(L), D3z(L), D3z1(L);
|
|
|
+ std::vector< std::vector<std::complex<double> > > Psiz(L), Psiz1(L), Zetaz(L), Zetaz1(L);
|
|
|
+ for (int l = 0; l < L; ++l) {
|
|
|
+ D1z[l].resize(nmax_ + 1);
|
|
|
+ D1z1[l].resize(nmax_ + 1);
|
|
|
+ D3z[l].resize(nmax_ + 1);
|
|
|
+ D3z1[l].resize(nmax_ + 1);
|
|
|
+ Psiz[l].resize(nmax_ + 1);
|
|
|
+ Psiz1[l].resize(nmax_ + 1);
|
|
|
+ Zetaz[l].resize(nmax_ + 1);
|
|
|
+ Zetaz1[l].resize(nmax_ + 1);
|
|
|
+ }
|
|
|
+ for (int l = 0; l < L; ++l) {
|
|
|
+ calcD1D3(z[l],D1z[l],D3z[l]);
|
|
|
+ calcD1D3(z1[l],D1z1[l],D3z1[l]);
|
|
|
+ calcPsiZeta(z[l],D1z[l],D3z[l], Psiz[l],Zetaz[l]);
|
|
|
+ calcPsiZeta(z1[l],D1z1[l],D3z1[l], Psiz1[l],Zetaz1[l]);
|
|
|
+ }
|
|
|
+ auto& m = index_;
|
|
|
+ std::vector< std::complex<double> > m1(L);
|
|
|
+ for (int l = 0; l < L - 1; ++l) m1[l] = m[l + 1];
|
|
|
+ m1[L - 1] = std::complex<double> (1.0, 0.0);
|
|
|
+ // for (auto zz : m) printf ("m[i]=%g \n\n ", zz.real());
|
|
|
+ for (int l = L - 1; l >= 0; --l) {
|
|
|
+ for (int n = 0; n < nmax_; ++n) {
|
|
|
+ // al_n
|
|
|
+ auto denom = m1[l]*Zetaz[l][n + 1]*(D1z[l][n + 1] - D3z[l][n + 1]);
|
|
|
+ al_n_[l][n] = D1z[l][n + 1]*m1[l]*(al_n_[l + 1][n]*Zetaz1[l][n + 1] - dl_n_[l + 1][n]*Psiz1[l][n + 1])
|
|
|
+ - m[l]*(-D1z1[l][n + 1]*dl_n_[l + 1][n]*Psiz1[l][n + 1] + D3z1[l][n + 1]*al_n_[l + 1][n]*Zetaz1[l][n + 1]);
|
|
|
+ al_n_[l][n] /= denom;
|
|
|
+
|
|
|
+ // dl_n
|
|
|
+ denom = m1[l]*Psiz[l][n + 1]*(D1z[l][n + 1] - D3z[l][n + 1]);
|
|
|
+ dl_n_[l][n] = D3z[l][n + 1]*m1[l]*(al_n_[l + 1][n]*Zetaz1[l][n + 1] - dl_n_[l + 1][n]*Psiz1[l][n + 1])
|
|
|
+ - m[l]*(-D1z1[l][n + 1]*dl_n_[l + 1][n]*Psiz1[l][n + 1] + D3z1[l][n + 1]*al_n_[l + 1][n]*Zetaz1[l][n + 1]);
|
|
|
+ dl_n_[l][n] /= denom;
|
|
|
+
|
|
|
+ // bl_n
|
|
|
+ denom = m1[l]*Zetaz[l][n + 1]*(D1z[l][n + 1] - D3z[l][n + 1]);
|
|
|
+ bl_n_[l][n] = D1z[l][n + 1]*m[l]*(bl_n_[l + 1][n]*Zetaz1[l][n + 1] - cl_n_[l + 1][n]*Psiz1[l][n + 1])
|
|
|
+ - m1[l]*(-D1z1[l][n + 1]*cl_n_[l + 1][n]*Psiz1[l][n + 1] + D3z1[l][n + 1]*bl_n_[l + 1][n]*Zetaz1[l][n + 1]);
|
|
|
+ bl_n_[l][n] /= denom;
|
|
|
+
|
|
|
+ // cl_n
|
|
|
+ denom = m1[l]*Psiz[l][n + 1]*(D1z[l][n + 1] - D3z[l][n + 1]);
|
|
|
+ cl_n_[l][n] = D3z[l][n + 1]*m[l]*(bl_n_[l + 1][n]*Zetaz1[l][n + 1] - cl_n_[l + 1][n]*Psiz1[l][n + 1])
|
|
|
+ - m1[l]*(-D1z1[l][n + 1]*cl_n_[l + 1][n]*Psiz1[l][n + 1] + D3z1[l][n + 1]*bl_n_[l + 1][n]*Zetaz1[l][n + 1]);
|
|
|
+ cl_n_[l][n] /= denom;
|
|
|
+ } // end of all n
|
|
|
+ } // end of for all l
|
|
|
+
|
|
|
+ // Check the result and change an__0 and bn__0 for exact zero
|
|
|
+ for (int n = 0; n < nmax_; ++n) {
|
|
|
+ if (std::abs(al_n_[0][n]) < 1e-10) al_n_[0][n] = 0.0;
|
|
|
+ else throw std::invalid_argument("Unstable calculation of a__0_n!");
|
|
|
+ if (std::abs(bl_n_[0][n]) < 1e-10) bl_n_[0][n] = 0.0;
|
|
|
+ else throw std::invalid_argument("Unstable calculation of b__0_n!");
|
|
|
+ }
|
|
|
+
|
|
|
+ // for (int l = 0; l < L; ++l) {
|
|
|
+ // printf("l=%d --> ", l);
|
|
|
+ // for (int n = 0; n < nmax_ + 1; ++n) {
|
|
|
+ // if (n < 20) continue;
|
|
|
+ // printf("n=%d --> D1zn=%g, D3zn=%g, D1zn=%g, D3zn=%g || ",
|
|
|
+ // n,
|
|
|
+ // D1z[l][n].real(), D3z[l][n].real(),
|
|
|
+ // D1z1[l][n].real(), D3z1[l][n].real());
|
|
|
+ // }
|
|
|
+ // printf("\n\n");
|
|
|
+ // }
|
|
|
+ // for (int l = 0; l < L; ++l) {
|
|
|
+ // printf("l=%d --> ", l);
|
|
|
+ // for (int n = 0; n < nmax_ + 1; ++n) {
|
|
|
+ // printf("n=%d --> D1zn=%g, D3zn=%g, D1zn=%g, D3zn=%g || ",
|
|
|
+ // n,
|
|
|
+ // D1z[l][n].real(), D3z[l][n].real(),
|
|
|
+ // D1z1[l][n].real(), D3z1[l][n].real());
|
|
|
+ // }
|
|
|
+ // printf("\n\n");
|
|
|
+ // }
|
|
|
+ for (int i = 0; i < L + 1; ++i) {
|
|
|
+ printf("Layer =%d ---> ", i);
|
|
|
+ for (int n = 0; n < nmax_; ++n) {
|
|
|
+ // if (n < 20) continue;
|
|
|
+ printf(" || n=%d --> a=%g,%g b=%g,%g c=%g,%g d=%g,%g",
|
|
|
+ n,
|
|
|
+ al_n_[i][n].real(), al_n_[i][n].imag(),
|
|
|
+ bl_n_[i][n].real(), bl_n_[i][n].imag(),
|
|
|
+ cl_n_[i][n].real(), cl_n_[i][n].imag(),
|
|
|
+ dl_n_[i][n].real(), dl_n_[i][n].imag());
|
|
|
+ }
|
|
|
+ printf("\n\n");
|
|
|
+ }
|
|
|
+ }
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // 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
|
|
|
+
|
|
|
+ void MultiLayerMie::fieldExt(const double Rho, const double Phi, const double Theta, const std::vector<double>& Pi, const std::vector<double>& Tau, std::vector<std::complex<double> >& E, std::vector<std::complex<double> >& H) {
|
|
|
+
|
|
|
+ std::complex<double> c_zero(0.0, 0.0), c_i(0.0, 1.0);
|
|
|
+ std::vector<std::complex<double> > vm3o1n(3), vm3e1n(3), vn3o1n(3), vn3e1n(3);
|
|
|
+ std::vector<std::complex<double> > Ei(3,c_zero), Hi(3,c_zero), Es(3,c_zero), Hs(3,c_zero);
|
|
|
+ std::vector<std::complex<double> > bj(nmax_ + 1), by(nmax_ + 1), bd(nmax_ + 1);
|
|
|
+ // Calculate spherical Bessel and Hankel functions
|
|
|
+ printf("########## layer OUT ############\n");
|
|
|
+ sphericalBessel(Rho,bj, by, bd);
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ double rn = static_cast<double>(n + 1);
|
|
|
+ std::complex<double> zn = bj[n + 1] + c_i*by[n + 1];
|
|
|
+ // using BH 4.12 and 4.50
|
|
|
+ std::complex<double> xxip = Rho*(bj[n] + c_i*by[n]) - rn*zn;
|
|
|
+
|
|
|
+ using std::sin;
|
|
|
+ using std::cos;
|
|
|
+ vm3o1n[0] = c_zero;
|
|
|
+ vm3o1n[1] = cos(Phi)*Pi[n]*zn;
|
|
|
+ vm3o1n[2] = -sin(Phi)*Tau[n]*zn;
|
|
|
+ vm3e1n[0] = c_zero;
|
|
|
+ vm3e1n[1] = -sin(Phi)*Pi[n]*zn;
|
|
|
+ vm3e1n[2] = -cos(Phi)*Tau[n]*zn;
|
|
|
+ vn3o1n[0] = sin(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn3o1n[1] = sin(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn3o1n[2] = cos(Phi)*Pi[n]*xxip/Rho;
|
|
|
+ vn3e1n[0] = cos(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn3e1n[1] = cos(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn3e1n[2] = -sin(Phi)*Pi[n]*xxip/Rho;
|
|
|
+
|
|
|
+ // scattered field: BH p.94 (4.45)
|
|
|
+ std::complex<double> encap = std::pow(c_i, rn)*(2.0*rn + 1.0)/(rn*rn + rn);
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ Es[i] = Es[i] + encap*(c_i*an_[n]*vn3e1n[i] - bn_[n]*vm3o1n[i]);
|
|
|
+ Hs[i] = Hs[i] + encap*(c_i*bn_[n]*vn3o1n[i] + an_[n]*vm3e1n[i]);
|
|
|
+ //if (n<3) printf(" E[%d]=%g ", i,std::abs(Es[i]));
|
|
|
+ if (n<3) printf(" !!=%d=== %g ", i,std::abs(Es[i]));
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ // incident E field: BH p.89 (4.21); cf. p.92 (4.37), p.93 (4.38)
|
|
|
+ // basis unit vectors = er, etheta, ephi
|
|
|
+ std::complex<double> eifac = std::exp(std::complex<double>(0.0, Rho*std::cos(Theta)));
|
|
|
+ {
|
|
|
+ using std::sin;
|
|
|
+ using std::cos;
|
|
|
+ Ei[0] = eifac*sin(Theta)*cos(Phi);
|
|
|
+ Ei[1] = eifac*cos(Theta)*cos(Phi);
|
|
|
+ Ei[2] = -eifac*sin(Phi);
|
|
|
+ }
|
|
|
+
|
|
|
+ // magnetic field
|
|
|
+ double hffact = 1.0/(cc_*mu_);
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ Hs[i] = hffact*Hs[i];
|
|
|
+ }
|
|
|
+
|
|
|
+ // incident H field: BH p.26 (2.43), p.89 (4.21)
|
|
|
+ std::complex<double> hffacta = hffact;
|
|
|
+ std::complex<double> hifac = eifac*hffacta;
|
|
|
+ {
|
|
|
+ using std::sin;
|
|
|
+ using std::cos;
|
|
|
+ Hi[0] = hifac*sin(Theta)*sin(Phi);
|
|
|
+ Hi[1] = hifac*cos(Theta)*sin(Phi);
|
|
|
+ Hi[2] = hifac*cos(Phi);
|
|
|
+ }
|
|
|
+
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ // electric field E [V m - 1] = EF*E0
|
|
|
+ E[i] = Ei[i] + Es[i];
|
|
|
+ H[i] = Hi[i] + Hs[i];
|
|
|
+ // printf("ext E[%d]=%g",i,std::abs(E[i]));
|
|
|
+ }
|
|
|
+ } // end of void fieldExt(...)
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ void MultiLayerMie::fieldInt(const double Rho, const double Phi, const double Theta, const std::vector<double>& Pi, const std::vector<double>& Tau, std::vector<std::complex<double> >& E, std::vector<std::complex<double> >& H) {
|
|
|
+ // printf("field int Qext = %g, Qsca = %g, Qabs = %g, Qbk = %g, \n",
|
|
|
+ // GetQext(), GetQsca(), GetQabs(), GetQbk());
|
|
|
+
|
|
|
+ std::complex<double> c_zero(0.0, 0.0), c_i(0.0, 1.0), c_one(1.0, 0.0);
|
|
|
+ std::vector<std::complex<double> > vm3o1n(3), vm3e1n(3), vn3o1n(3), vn3e1n(3);
|
|
|
+ std::vector<std::complex<double> > vm1o1n(3), vm1e1n(3), vn1o1n(3), vn1e1n(3);
|
|
|
+ std::vector<std::complex<double> > El(3,c_zero),Ei(3,c_zero), Hl(3,c_zero);
|
|
|
+ std::vector<std::complex<double> > bj(nmax_ + 1), by(nmax_ + 1), bd(nmax_ + 1);
|
|
|
+ int layer=0; // layer number
|
|
|
+ std::complex<double> index_l;
|
|
|
+ for (int i = 0; i < size_parameter_.size() - 1; ++i) {
|
|
|
+ if (size_parameter_[i] < Rho && Rho <= size_parameter_[i + 1]) {
|
|
|
+ layer=i;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ if (Rho > size_parameter_.back()) {
|
|
|
+ layer = size_parameter_.size();
|
|
|
+ index_l = c_one;
|
|
|
+ } else {
|
|
|
+ index_l = index_[layer];
|
|
|
+ }
|
|
|
+
|
|
|
+ std::complex<double> bessel_arg = Rho*index_l;
|
|
|
+ std::complex<double>& rh = bessel_arg;
|
|
|
+ std::complex<double> besselj_1 = std::sin(rh)/pow2(rh)-std::cos(rh)/rh;
|
|
|
+ printf("bessel arg = %g,%g index=%g,%g besselj[1]=%g,%g\n", bessel_arg.real(), bessel_arg.imag(), index_l.real(), index_l.imag(), besselj_1.real(), besselj_1.imag());
|
|
|
+ const int& l = layer;
|
|
|
+ printf("########## layer %d ############\n",l);
|
|
|
+ // Calculate spherical Bessel and Hankel functions
|
|
|
+ sphericalBessel(bessel_arg,bj, by, bd);
|
|
|
+ printf("besselj[1]=%g,%g\n", bj[1].real(), bj[1].imag());
|
|
|
+ printf("bessely[1]=%g,%g\n", by[1].real(), by[1].imag());
|
|
|
+ for (int n = 0; n < nmax_; n++) {
|
|
|
+ double rn = static_cast<double>(n + 1);
|
|
|
+ std::complex<double> znm1 = bj[n] + c_i*by[n];
|
|
|
+ std::complex<double> zn = bj[n + 1] + c_i*by[n + 1];
|
|
|
+ //if (n<3) printf("\nbesselh = %g,%g", zn.real(), zn.imag()); //!
|
|
|
+ // using BH 4.12 and 4.50
|
|
|
+ std::complex<double> xxip = Rho*(bj[n] + c_i*by[n]) - rn*zn;
|
|
|
+ //if (n<3) printf("\nxxip = %g,%g", xxip.real(), xxip.imag()); //!
|
|
|
+
|
|
|
+ using std::sin;
|
|
|
+ using std::cos;
|
|
|
+ vm3o1n[0] = c_zero;
|
|
|
+ vm3o1n[1] = cos(Phi)*Pi[n]*zn;
|
|
|
+ vm3o1n[2] = -sin(Phi)*Tau[n]*zn;
|
|
|
+ // if (n<3) printf("\nRE vm3o1n[0]%g vm3o1n[1]%g vm3o1n[2]%g \nIM vm3o1n[0]%g vm3o1n[1]%g vm3o1n[2]%g",
|
|
|
+ // vm3o1n[0].real(), vm3o1n[1].real(), vm3o1n[2].real(),
|
|
|
+ // vm3o1n[0].imag(), vm3o1n[1].imag(), vm3o1n[2].imag());
|
|
|
+ vm3e1n[0] = c_zero;
|
|
|
+ vm3e1n[1] = -sin(Phi)*Pi[n]*zn;
|
|
|
+ vm3e1n[2] = -cos(Phi)*Tau[n]*zn;
|
|
|
+ vn3o1n[0] = sin(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn3o1n[1] = sin(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn3o1n[2] = cos(Phi)*Pi[n]*xxip/Rho;
|
|
|
+ vn3e1n[0] = cos(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn3e1n[1] = cos(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn3e1n[2] = -sin(Phi)*Pi[n]*xxip/Rho;
|
|
|
+ // if (n<3) printf("\nRE vn3e1n[0]%g vn3e1n[1]%g vn3e1n[2]%g \nIM vn3e1n[0]%g vn3e1n[1]%g vn3e1n[2]%g",
|
|
|
+ // vn3e1n[0].real(), vn3e1n[1].real(), vn3e1n[2].real(),
|
|
|
+ // vn3e1n[0].imag(), vn3e1n[1].imag(), vn3e1n[2].imag());
|
|
|
+
|
|
|
+ znm1 = bj[n];
|
|
|
+ zn = bj[n + 1];
|
|
|
+ // znm1 = (bj[n] + c_i*by[n]).real();
|
|
|
+ // zn = (bj[n + 1] + c_i*by[n + 1]).real();
|
|
|
+ xxip = Rho*(bj[n]) - rn*zn;
|
|
|
+ if (n<3)printf("\nbesselj = %g,%g", zn.real(), zn.imag()); //!
|
|
|
+ vm1o1n[0] = c_zero;
|
|
|
+ vm1o1n[1] = cos(Phi)*Pi[n]*zn;
|
|
|
+ vm1o1n[2] = -sin(Phi)*Tau[n]*zn;
|
|
|
+ vm1e1n[0] = c_zero;
|
|
|
+ vm1e1n[1] = -sin(Phi)*Pi[n]*zn;
|
|
|
+ vm1e1n[2] = -cos(Phi)*Tau[n]*zn;
|
|
|
+ vn1o1n[0] = sin(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn1o1n[1] = sin(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn1o1n[2] = cos(Phi)*Pi[n]*xxip/Rho;
|
|
|
+ // if (n<3) printf("\nvn1o1n[2](%g) = cos(Phi)(%g)*Pi[n](%g)*xxip(%g)/Rho(%g)",
|
|
|
+ // std::abs(vn1o1n[2]), cos(Phi),Pi[n],std::abs(xxip),Rho);
|
|
|
+ vn1e1n[0] = cos(Phi)*rn*(rn + 1.0)*sin(Theta)*Pi[n]*zn/Rho;
|
|
|
+ vn1e1n[1] = cos(Phi)*Tau[n]*xxip/Rho;
|
|
|
+ vn1e1n[2] = -sin(Phi)*Pi[n]*xxip/Rho;
|
|
|
+ // if (n<3) printf("\nRE vm3o1n[0]%g vm3o1n[1]%g vm3o1n[2]%g \nIM vm3o1n[0]%g vm3o1n[1]%g vm3o1n[2]%g",
|
|
|
+ // vm3o1n[0].real(), vm3o1n[1].real(), vm3o1n[2].real(),
|
|
|
+ // vm3o1n[0].imag(), vm3o1n[1].imag(), vm3o1n[2].imag());
|
|
|
+
|
|
|
+ // scattered field: BH p.94 (4.45)
|
|
|
+ std::complex<double> encap = std::pow(c_i, rn)*(2.0*rn + 1.0)/(rn*rn + rn);
|
|
|
+ // if (n<3) printf("\n===== n=%d ======\n",n);
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ // if (n<3 && i==0) printf("\nn=%d",n);
|
|
|
+ // if (n<3) printf("\nbefore !El[%d]=%g,%g! ", i, El[i].real(), El[i].imag());
|
|
|
+ Ei[i] = encap*(cl_n_[l][n]*vm1o1n[i] - c_i*dl_n_[l][n]*vn1e1n[i]
|
|
|
+ + c_i*al_n_[l][n]*vn3e1n[i] - bl_n_[l][n]*vm3o1n[i]);
|
|
|
+ El[i] = El[i] + encap*(cl_n_[l][n]*vm1o1n[i] - c_i*dl_n_[l][n]*vn1e1n[i]
|
|
|
+ + c_i*al_n_[l][n]*vn3e1n[i] - bl_n_[l][n]*vm3o1n[i]);
|
|
|
+ Hl[i] = Hl[i] + encap*(-dl_n_[l][n]*vm1e1n[i] - c_i*cl_n_[l][n]*vn1o1n[i]
|
|
|
+ + c_i*bl_n_[l][n]*vn3o1n[i] + al_n_[l][n]*vm3e1n[i]);
|
|
|
+ // printf("\n !Ei[%d]=%g,%g! ", i, Ei[i].real(), Ei[i].imag());
|
|
|
+ // if (n<3) printf("\n !El[%d]=%g,%g! ", i, El[i].real(), El[i].imag());
|
|
|
+ // //printf(" ===%d=== %g ", i,std::abs(cl_n_[l][n]*vm1o1n[i] - c_i*dl_n_[l][n]*vn1e1n[i]));
|
|
|
+ // if (n<3) printf(" ===%d=== %g ", i,std::abs(//-dl_n_[l][n]*vm1e1n[i]
|
|
|
+ // //- c_i*cl_n_[l][n]*
|
|
|
+ // vn1o1n[i]
|
|
|
+ // // + c_i*bl_n_[l][n]*vn3o1n[i]
|
|
|
+ // // + al_n_[l][n]*vm3e1n[i]
|
|
|
+ // ));
|
|
|
+ // if (n<3) printf(" --- Ei[%d]=%g! ", i,std::abs(encap*(vm1o1n[i] - c_i*vn1e1n[i])));
|
|
|
+
|
|
|
+ }
|
|
|
+ //if (n<3) printf(" bj=%g \n", std::abs(bj[n]));
|
|
|
+ } // end of for all n
|
|
|
+
|
|
|
+ // magnetic field
|
|
|
+ double hffact = 1.0/(cc_*mu_);
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ Hl[i] = hffact*Hl[i];
|
|
|
+ }
|
|
|
+
|
|
|
+ for (int i = 0; i < 3; i++) {
|
|
|
+ // electric field E [V m - 1] = EF*E0
|
|
|
+ E[i] = El[i];
|
|
|
+ H[i] = Hl[i];
|
|
|
+ printf("\n !El[%d]=%g,%g! ", i, El[i].real(), El[i].imag());
|
|
|
+ //printf(" E[%d]=%g",i,std::abs(El[i]));
|
|
|
+ }
|
|
|
+ } // end of void fieldExt(...)
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+ // ********************************************************************** //
|
|
|
+
|
|
|
+ //**********************************************************************************//
|
|
|
+ // This function calculates complex electric and magnetic field in the surroundings //
|
|
|
+ // and inside (TODO) 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 //
|
|
|
+ // //
|
|
|
+ // Output parameters: //
|
|
|
+ // E, H: Complex electric and magnetic field at the provided coordinates //
|
|
|
+ // //
|
|
|
+ // Return value: //
|
|
|
+ // Number of multipolar expansion terms used for the calculations //
|
|
|
+ //**********************************************************************************//
|
|
|
+ void MultiLayerMie::RunFieldCalculations() {
|
|
|
+ // Calculate scattering coefficients an_ and bn_
|
|
|
+ RunMieCalculations();
|
|
|
+ //nmax_=10;
|
|
|
+ IntScattCoeffs();
|
|
|
+
|
|
|
+ std::vector<double> Pi(nmax_), Tau(nmax_);
|
|
|
+ long total_points = coords_sp_[0].size();
|
|
|
+ E_field_.resize(total_points);
|
|
|
+ H_field_.resize(total_points);
|
|
|
+ for (auto& f:E_field_) f.resize(3);
|
|
|
+ for (auto& f:H_field_) f.resize(3);
|
|
|
+
|
|
|
+ for (int point = 0; point < total_points; ++point) {
|
|
|
+ const double& Xp = coords_sp_[0][point];
|
|
|
+ const double& Yp = coords_sp_[1][point];
|
|
|
+ const double& Zp = coords_sp_[2][point];
|
|
|
+ printf("X=%g, Y=%g, Z=%g\n", Xp, Yp, Zp);
|
|
|
+ // Convert to spherical coordinates
|
|
|
+ double Rho, Phi, Theta;
|
|
|
+ Rho = std::sqrt(pow2(Xp) + pow2(Yp) + pow2(Zp));
|
|
|
+ // printf("Rho=%g\n", Rho);
|
|
|
+ // Avoid convergence problems due to Rho too small
|
|
|
+ if (Rho < 1e-10) Rho = 1e-10;
|
|
|
+ // If Rho=0 then Theta is undefined. Just set it to zero to avoid problems
|
|
|
+ if (Rho == 0.0) Theta = 0.0;
|
|
|
+ else Theta = std::acos(Zp/Rho);
|
|
|
+ // printf("Theta=%g\n", Theta);
|
|
|
+ // If Xp=Yp=0 then Phi is undefined. Just set it to zero to zero to avoid problems
|
|
|
+ if (Xp == 0.0 && Yp == 0.0) Phi = 0.0;
|
|
|
+ else Phi = std::acos(Xp/std::sqrt(pow2(Xp) + pow2(Yp)));
|
|
|
+ // printf("Phi=%g\n", Phi);
|
|
|
+
|
|
|
+ calcSinglePiTau(std::cos(Theta), Pi, Tau);
|
|
|
+ //*******************************************************//
|
|
|
+ // 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<double> > Es(3), Hs(3);
|
|
|
+ const double outer_size = size_parameter_.back();
|
|
|
+ // Firstly the easiest case: the field outside the particle
|
|
|
+ printf("rho=%g, outer=%g ", Rho, outer_size);
|
|
|
+ if (Rho >= outer_size) {
|
|
|
+ fieldExt(Rho, Phi, Theta, Pi, Tau, Es, Hs);
|
|
|
+ printf("\nFin E ext: %g,%g,%g Rho=%g\n", std::abs(Es[0]), std::abs(Es[1]),std::abs(Es[2]), Rho);
|
|
|
+ } else {
|
|
|
+ fieldInt(Rho, Phi, Theta, Pi, Tau, Es, Hs);
|
|
|
+ printf("\nFin E int: %g,%g,%g Rho=%g\n", std::abs(Es[0]), std::abs(Es[1]),std::abs(Es[2]), Rho);
|
|
|
+ }
|
|
|
+ std::complex<double>& Ex = E_field_[point][0];
|
|
|
+ std::complex<double>& Ey = E_field_[point][1];
|
|
|
+ std::complex<double>& Ez = E_field_[point][2];
|
|
|
+ std::complex<double>& Hx = H_field_[point][0];
|
|
|
+ std::complex<double>& Hy = H_field_[point][1];
|
|
|
+ std::complex<double>& Hz = H_field_[point][2];
|
|
|
+ //Now, convert the fields back to cartesian coordinates
|
|
|
+ {
|
|
|
+ using std::sin;
|
|
|
+ using std::cos;
|
|
|
+ Ex = sin(Theta)*cos(Phi)*Es[0] + cos(Theta)*cos(Phi)*Es[1] - sin(Phi)*Es[2];
|
|
|
+ Ey = sin(Theta)*sin(Phi)*Es[0] + cos(Theta)*sin(Phi)*Es[1] + cos(Phi)*Es[2];
|
|
|
+ Ez = cos(Theta)*Es[0] - sin(Theta)*Es[1];
|
|
|
+
|
|
|
+ Hx = sin(Theta)*cos(Phi)*Hs[0] + cos(Theta)*cos(Phi)*Hs[1] - sin(Phi)*Hs[2];
|
|
|
+ Hy = sin(Theta)*sin(Phi)*Hs[0] + cos(Theta)*sin(Phi)*Hs[1] + cos(Phi)*Hs[2];
|
|
|
+ Hz = cos(Theta)*Hs[0] - sin(Theta)*Hs[1];
|
|
|
+ }
|
|
|
+ printf("Cart E: %g,%g,%g Rho=%g\n", std::abs(Ex), std::abs(Ey),std::abs(Ez),
|
|
|
+ Rho);
|
|
|
+ } // end of for all field coordinates
|
|
|
+
|
|
|
+ } // end of void MultiLayerMie::RunFieldCalculations()
|
|
|
+
|
|
|
+} // end of namespace nmie
|
Ovidio Peña Rodríguez