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meepgeom.cpp
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/* Copyright (C) 2005-2021 Massachusetts Institute of Technology
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details. %
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software Foundation,
% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <vector>
#include "meepgeom.hpp"
namespace meep_geom {
#define master_printf meep::master_printf
/***************************************************************/
/* global variables for default material */
/***************************************************************/
material_data vacuum_material_data;
material_type vacuum = &vacuum_material_data;
void check_offdiag(medium_struct *m) {
if (m->epsilon_offdiag.x.im != 0 || m->epsilon_offdiag.y.im != 0 ||
m->epsilon_offdiag.z.im != 0 || m->mu_offdiag.x.im != 0 || m->mu_offdiag.y.im != 0 ||
m->mu_offdiag.z.im != 0) {
meep::abort("Found non-zero imaginary part of epsilon or mu offdiag.\n");
}
}
bool susceptibility_equal(const susceptibility &s1, const susceptibility &s2) {
return (vector3_equal(s1.sigma_diag, s2.sigma_diag) &&
vector3_equal(s1.sigma_offdiag, s2.sigma_offdiag) && vector3_equal(s1.bias, s2.bias) &&
s1.frequency == s2.frequency && s1.gamma == s2.gamma && s1.alpha == s2.alpha &&
s1.noise_amp == s2.noise_amp && s1.drude == s2.drude &&
s1.saturated_gyrotropy == s2.saturated_gyrotropy && s1.is_file == s2.is_file);
}
bool susceptibility_list_equal(const susceptibility_list &s1, const susceptibility_list &s2) {
if (s1.num_items != s2.num_items) return false;
for (int i = 0; i < s1.num_items; ++i)
if (!susceptibility_equal(s1.items[i], s2.items[i])) return false;
return true;
}
bool medium_struct_equal(const medium_struct *m1, const medium_struct *m2) {
return (vector3_equal(m1->epsilon_diag, m2->epsilon_diag) &&
cvector3_equal(m1->epsilon_offdiag, m2->epsilon_offdiag) &&
vector3_equal(m1->mu_diag, m2->mu_diag) &&
cvector3_equal(m1->mu_offdiag, m2->mu_offdiag) &&
vector3_equal(m1->E_chi2_diag, m2->E_chi2_diag) &&
vector3_equal(m1->E_chi3_diag, m2->E_chi3_diag) &&
vector3_equal(m1->H_chi2_diag, m2->H_chi2_diag) &&
vector3_equal(m1->D_conductivity_diag, m2->D_conductivity_diag) &&
vector3_equal(m1->B_conductivity_diag, m2->B_conductivity_diag) &&
susceptibility_list_equal(m1->E_susceptibilities, m2->E_susceptibilities) &&
susceptibility_list_equal(m1->H_susceptibilities, m2->H_susceptibilities));
}
bool material_grid_equal(const material_data *m1, const material_data *m2) {
// a rigorous method for comapring material grids
int n1, n2;
n1 = m1->grid_size.x * m1->grid_size.y * m1->grid_size.z;
n2 = m2->grid_size.x * m2->grid_size.y * m2->grid_size.z;
if (n1 != n2) return false;
for (int i = 0; i < n1; i++)
if (m1->epsilon_data[i] != m2->epsilon_data[i]) return false;
return (medium_struct_equal(&(m1->medium), &(m2->medium)) &&
medium_struct_equal(&(m1->medium_1), &(m2->medium_1)) &&
medium_struct_equal(&(m1->medium_2), &(m2->medium_2)));
}
// garbage collection for susceptibility_list structures.
// Assumes that the 'items' field, if non-empty, was allocated using new[];
// this is automatically the case for python code but is not checked
// for c++ code and will yield runtime errors if a user's user_material_func
// uses e.g. malloc() instead.
static void susceptibility_list_gc(susceptibility_list *sl) {
if (!sl || !(sl->num_items)) return;
delete[] sl->items;
sl->items = NULL;
sl->num_items = 0;
}
// garbage collection for material structures: called to deallocate memory
// allocated for susceptibilities in user-defined materials.
// TODO
void material_gc(material_type m) {
if (!m || m->which_subclass != material_data::MATERIAL_USER) return;
susceptibility_list_gc(&(m->medium.E_susceptibilities));
susceptibility_list_gc(&(m->medium.H_susceptibilities));
susceptibility_list_gc(&(m->medium_1.E_susceptibilities));
susceptibility_list_gc(&(m->medium_1.H_susceptibilities));
susceptibility_list_gc(&(m->medium_2.E_susceptibilities));
susceptibility_list_gc(&(m->medium_2.H_susceptibilities));
}
bool material_type_equal(const material_type m1, const material_type m2) {
if (m1 == m2) return true;
if (m1->which_subclass != m2->which_subclass) return false;
switch (m1->which_subclass) {
case material_data::MATERIAL_FILE:
case material_data::PERFECT_METAL: return true;
case material_data::MATERIAL_USER:
return m1->user_func == m2->user_func && m1->user_data == m2->user_data;
case material_data::MATERIAL_GRID:
case material_data::MEDIUM: return medium_struct_equal(&(m1->medium), &(m2->medium));
default: return false;
}
}
/***************************************************************/
/***************************************************************/
/***************************************************************/
typedef struct {
double m00, m01, m02, m11, m12, m22;
} symmetric_matrix;
/* rotate A by a unitary (real) rotation matrix R:
RAR = transpose(R) * A * R
*/
void sym_matrix_rotate(symmetric_matrix *RAR, const symmetric_matrix *A_, const double R[3][3]) {
int i, j;
double A[3][3], AR[3][3];
A[0][0] = A_->m00;
A[1][1] = A_->m11;
A[2][2] = A_->m22;
A[0][1] = A[1][0] = A_->m01;
A[0][2] = A[2][0] = A_->m02;
A[1][2] = A[2][1] = A_->m12;
for (i = 0; i < 3; ++i)
for (j = 0; j < 3; ++j)
AR[i][j] = A[i][0] * R[0][j] + A[i][1] * R[1][j] + A[i][2] * R[2][j];
for (i = 0; i < 3; ++i)
for (j = i; j < 3; ++j)
A[i][j] = R[0][i] * AR[0][j] + R[1][i] * AR[1][j] + R[2][i] * AR[2][j];
RAR->m00 = A[0][0];
RAR->m11 = A[1][1];
RAR->m22 = A[2][2];
RAR->m01 = A[0][1];
RAR->m02 = A[0][2];
RAR->m12 = A[1][2];
}
/* Set Vinv = inverse of V, where both V and Vinv are real-symmetric matrices.*/
void sym_matrix_invert(symmetric_matrix *Vinv, const symmetric_matrix *V) {
double m00 = V->m00, m11 = V->m11, m22 = V->m22;
double m01 = V->m01, m02 = V->m02, m12 = V->m12;
if (m01 == 0.0 && m02 == 0.0 && m12 == 0.0) {
/* optimize common case of a diagonal matrix: */
Vinv->m00 = 1.0 / m00;
Vinv->m11 = 1.0 / m11;
Vinv->m22 = 1.0 / m22;
Vinv->m01 = Vinv->m02 = Vinv->m12 = 0.0;
}
else {
double detinv;
/* compute the determinant: */
detinv = m00 * m11 * m22 - m02 * m11 * m02 + 2.0 * m01 * m12 * m02 - m01 * m01 * m22 -
m12 * m12 * m00;
if (detinv == 0.0) meep::abort("singular 3x3 matrix");
detinv = 1.0 / detinv;
Vinv->m00 = detinv * (m11 * m22 - m12 * m12);
Vinv->m11 = detinv * (m00 * m22 - m02 * m02);
Vinv->m22 = detinv * (m11 * m00 - m01 * m01);
Vinv->m02 = detinv * (m01 * m12 - m11 * m02);
Vinv->m01 = detinv * (m12 * m02 - m01 * m22);
Vinv->m12 = detinv * (m01 * m02 - m00 * m12);
}
}
/* Returns whether or not V is positive-definite. */
int sym_matrix_positive_definite(symmetric_matrix *V) {
double det2, det3;
double m00 = V->m00, m11 = V->m11, m22 = V->m22;
#if defined(WITH_HERMITIAN_EPSILON)
scalar_complex m01 = V->m01, m02 = V->m02, m12 = V->m12;
det2 = m00 * m11 - CSCALAR_NORMSQR(m01);
det3 = det2 * m22 - m11 * CSCALAR_NORMSQR(m02) - CSCALAR_NORMSQR(m12) * m00 +
2.0 * ((m01.re * m12.re - m01.im * m12.im) * m02.re +
(m01.re * m12.im + m01.im * m12.re) * m02.im);
#else /* real matrix */
double m01 = V->m01, m02 = V->m02, m12 = V->m12;
det2 = m00 * m11 - m01 * m01;
det3 = det2 * m22 - m02 * m11 * m02 + 2.0 * m01 * m12 * m02 - m12 * m12 * m00;
#endif /* real matrix */
return (m00 > 0.0 && det2 > 0.0 && det3 > 0.0);
}
/***************************************************************/
/***************************************************************/
/***************************************************************/
static meep::ndim dim = meep::D3;
void set_dimensions(int dims) {
if (dims == CYLINDRICAL) { dim = meep::Dcyl; }
else {
dim = meep::ndim(dims - 1);
}
}
vector3 vec_to_vector3(const meep::vec &pt) {
vector3 v3;
switch (pt.dim) {
case meep::D1:
v3.x = 0;
v3.y = 0;
v3.z = pt.z();
break;
case meep::D2:
v3.x = pt.x();
v3.y = pt.y();
v3.z = 0;
break;
case meep::D3:
v3.x = pt.x();
v3.y = pt.y();
v3.z = pt.z();
break;
case meep::Dcyl:
v3.x = pt.r();
v3.y = 0;
v3.z = pt.z();
break;
}
return v3;
}
meep::vec vector3_to_vec(const vector3 v3) {
switch (dim) {
case meep::D1: return meep::vec(v3.z);
case meep::D2: return meep::vec(v3.x, v3.y);
case meep::D3: return meep::vec(v3.x, v3.y, v3.z);
case meep::Dcyl: return meep::veccyl(v3.x, v3.z);
default: meep::abort("unknown dimensionality in vector3_to_vec");
}
}
geom_box gv2box(const meep::volume &v) {
geom_box box;
box.low = vec_to_vector3(v.get_min_corner());
box.high = vec_to_vector3(v.get_max_corner());
return box;
}
bool is_material_grid(material_type mt) {
return (mt->which_subclass == material_data::MATERIAL_GRID);
}
bool is_material_grid(void *md) { return is_material_grid((material_type)md); }
bool is_variable(material_type mt) {
return (mt->which_subclass == material_data::MATERIAL_USER) ||
(mt->which_subclass == material_data::MATERIAL_GRID);
}
bool is_variable(void *md) { return is_variable((material_type)md); }
bool is_file(material_type md) { return (md->which_subclass == material_data::MATERIAL_FILE); }
bool is_file(void *md) { return is_file((material_type)md); }
bool is_medium(material_type md, medium_struct **m) {
if (md->which_subclass == material_data::MEDIUM) {
*m = &(md->medium);
return true;
};
return false;
}
bool is_medium(void *md, medium_struct **m) { return is_medium((material_type)md, m); }
bool is_metal(meep::field_type ft, const material_type *material) {
material_data *md = *material;
if (ft == meep::E_stuff) switch (md->which_subclass) {
case material_data::MEDIUM:
case material_data::MATERIAL_GRID:
return (md->medium.epsilon_diag.x < 0 || md->medium.epsilon_diag.y < 0 ||
md->medium.epsilon_diag.z < 0);
case material_data::PERFECT_METAL: return true;
default: meep::abort("unknown material type"); return false;
}
else
switch (md->which_subclass) {
case material_data::MEDIUM:
case material_data::MATERIAL_GRID:
return (md->medium.mu_diag.x < 0 || md->medium.mu_diag.y < 0 || md->medium.mu_diag.z < 0);
case material_data::PERFECT_METAL:
return false; // is an electric conductor, but not a magnetic conductor
default: meep::abort("unknown material type"); return false;
}
}
meep::realnum material_grid_val(vector3 p, material_data *md) {
// given the relative location, p, interpolate the material grid point.
if (!is_material_grid(md)) { meep::abort("Invalid material grid detected.\n"); }
meep::realnum u;
u = meep::linear_interpolate(p.x, p.y, p.z, md->design_parameters, md->grid_size.x,
md->grid_size.y, md->grid_size.z, 1);
return u;
}
meep::realnum matgrid_val(vector3 p, geom_box_tree tp, int oi, material_data *md) {
meep::realnum uprod = 1.0, umin = 1.0, usum = 0.0, udefault = 0.0, u;
int matgrid_val_count = 0;
// iterate through object tree at current point
if (tp) {
do {
u = material_grid_val(to_geom_box_coords(p, &tp->objects[oi]),
(material_data *)tp->objects[oi].o->material);
if (matgrid_val_count == 0) udefault = u;
if (u < umin) umin = u;
uprod *= u;
usum += u;
++matgrid_val_count;
tp = geom_tree_search_next(p, tp, &oi);
} while (tp && is_material_grid((material_data *)tp->objects[oi].o->material));
}
// perhaps there is not object tree and the default material is a material grid
if (!tp && is_material_grid(&default_material)) {
p.x = geometry_lattice.size.x == 0 ? 0
: 0.5 + (p.x - geometry_center.x) / geometry_lattice.size.x;
p.y = geometry_lattice.size.y == 0 ? 0
: 0.5 + (p.y - geometry_center.y) / geometry_lattice.size.y;
p.z = geometry_lattice.size.z == 0 ? 0
: 0.5 + (p.z - geometry_center.z) / geometry_lattice.size.z;
u = material_grid_val(p, (material_data *)default_material);
if (matgrid_val_count == 0) udefault = u;
if (u < umin) umin = u;
uprod *= u;
usum += u;
++matgrid_val_count;
}
return (md->material_grid_kinds == material_data::U_MIN
? umin
: (md->material_grid_kinds == material_data::U_PROD
? uprod
: (md->material_grid_kinds == material_data::U_SUM ? usum / matgrid_val_count
: udefault)));
}
static void cinterp_tensors(vector3 diag_in_1, cvector3 offdiag_in_1, vector3 diag_in_2,
cvector3 offdiag_in_2, vector3 *diag_out, cvector3 *offdiag_out,
double u) {
/* convenience routine to interpolate material tensors with real and imaginary components */
diag_out->x = diag_in_1.x + u * (diag_in_2.x - diag_in_1.x);
diag_out->y = diag_in_1.y + u * (diag_in_2.y - diag_in_1.y);
diag_out->z = diag_in_1.z + u * (diag_in_2.z - diag_in_1.z);
offdiag_out->x.re = offdiag_in_1.x.re + u * (offdiag_in_2.x.re - offdiag_in_1.x.re);
offdiag_out->x.im = offdiag_in_1.x.im + u * (offdiag_in_2.x.im - offdiag_in_1.x.im);
offdiag_out->y.re = offdiag_in_1.y.re + u * (offdiag_in_2.y.re - offdiag_in_1.y.re);
offdiag_out->y.im = offdiag_in_1.y.im + u * (offdiag_in_2.y.im - offdiag_in_1.y.im);
offdiag_out->z.re = offdiag_in_1.z.re + u * (offdiag_in_2.z.re - offdiag_in_1.z.re);
offdiag_out->z.im = offdiag_in_1.z.im + u * (offdiag_in_2.z.im - offdiag_in_1.z.im);
}
static void interp_tensors(vector3 diag_in_1, vector3 offdiag_in_1, vector3 diag_in_2,
vector3 offdiag_in_2, vector3 *diag_out, vector3 *offdiag_out,
double u) {
/* convenience routine to interpolate material tensors with all real components */
diag_out->x = diag_in_1.x + u * (diag_in_2.x - diag_in_1.x);
diag_out->y = diag_in_1.y + u * (diag_in_2.y - diag_in_1.y);
diag_out->z = diag_in_1.z + u * (diag_in_2.z - diag_in_1.z);
offdiag_out->x = offdiag_in_1.x + u * (offdiag_in_2.x - offdiag_in_1.x);
offdiag_out->y = offdiag_in_1.y + u * (offdiag_in_2.y - offdiag_in_1.y);
offdiag_out->z = offdiag_in_1.z + u * (offdiag_in_2.z - offdiag_in_1.z);
}
// return material of the point p from the material grid
void epsilon_material_grid(material_data *md, meep::realnum u) {
// NOTE: assume p lies on normalized grid within (0,1)
if (!(md->design_parameters)) meep::abort("material params were not initialized!");
medium_struct *mm = &(md->medium);
medium_struct *m1 = &(md->medium_1);
medium_struct *m2 = &(md->medium_2);
// Linearly interpolate dc epsilon values
cinterp_tensors(m1->epsilon_diag, m1->epsilon_offdiag, m2->epsilon_diag, m2->epsilon_offdiag,
&mm->epsilon_diag, &mm->epsilon_offdiag, u);
// Interpolate resonant strength from d.p.
vector3 zero_vec;
zero_vec.x = zero_vec.y = zero_vec.z = 0;
for (int i = 0; i < m1->E_susceptibilities.num_items; i++) {
// iterate through medium1 sus list first
interp_tensors(zero_vec, zero_vec, m1->E_susceptibilities.items[i].sigma_diag,
m1->E_susceptibilities.items[i].sigma_offdiag,
&mm->E_susceptibilities.items[i].sigma_diag,
&mm->E_susceptibilities.items[i].sigma_offdiag, (1 - u));
}
for (int i = 0; i < m2->E_susceptibilities.num_items; i++) {
// iterate through medium2 sus list next
int j = i + m1->E_susceptibilities.num_items;
interp_tensors(zero_vec, zero_vec, m2->E_susceptibilities.items[i].sigma_diag,
m2->E_susceptibilities.items[i].sigma_offdiag,
&mm->E_susceptibilities.items[j].sigma_diag,
&mm->E_susceptibilities.items[j].sigma_offdiag, u);
}
// Linearly interpolate electric conductivity
vector3 zero_offdiag;
interp_tensors(m1->D_conductivity_diag, zero_vec, m2->D_conductivity_diag, zero_vec,
&mm->D_conductivity_diag, &zero_offdiag, u);
// Add damping factor if we have dispersion.
// This prevents instabilities when interpolating between sus. profiles.
if ((m1->E_susceptibilities.num_items + m2->E_susceptibilities.num_items) > 0.0) {
// calculate mean harmonic frequency
double omega_mean = 0;
for (int i = 0; i < m1->E_susceptibilities.num_items; i++) {
omega_mean += m1->E_susceptibilities.items[i].frequency;
}
for (int i = 0; i < m2->E_susceptibilities.num_items; i++) {
omega_mean += m2->E_susceptibilities.items[i].frequency;
}
omega_mean = omega_mean / (m1->E_susceptibilities.num_items + m2->E_susceptibilities.num_items);
// assign interpolated, nondimensionalized conductivity term
// TODO: dampen the lorentzians to improve stability
// mm->D_conductivity_diag.x = mm->D_conductivity_diag.y = mm->D_conductivity_diag.z = u*(1-u) *
// omega_mean;
}
}
// return material of the point p from the file (assumed already read)
void epsilon_file_material(material_data *md, vector3 p) {
default_material = (void *)md;
if (md->which_subclass != material_data::MATERIAL_FILE)
meep::abort("epsilon-input-file only works with a type=file default-material");
if (!(md->epsilon_data)) return;
medium_struct *mm = &(md->medium);
double rx =
geometry_lattice.size.x == 0 ? 0 : 0.5 + (p.x - geometry_center.x) / geometry_lattice.size.x;
double ry =
geometry_lattice.size.y == 0 ? 0 : 0.5 + (p.y - geometry_center.y) / geometry_lattice.size.y;
double rz =
geometry_lattice.size.z == 0 ? 0 : 0.5 + (p.z - geometry_center.z) / geometry_lattice.size.z;
mm->epsilon_diag.x = mm->epsilon_diag.y = mm->epsilon_diag.z =
meep::linear_interpolate(rx, ry, rz, md->epsilon_data, md->epsilon_dims[0],
md->epsilon_dims[1], md->epsilon_dims[2], 1);
mm->epsilon_offdiag.x.re = mm->epsilon_offdiag.y.re = mm->epsilon_offdiag.z.re = 0;
}
struct pol {
susceptibility user_s;
struct pol *next;
};
// structure to hold a conductivity profile (for scalar absorbing layers)
struct cond_profile {
double L; // thickness
int N; // number of points prof[n] from 0..N corresponding to 0..L
double *prof; // (NULL if none)
};
class geom_epsilon : public meep::material_function {
geometric_object_list geometry;
geom_box_tree geometry_tree;
geom_box_tree restricted_tree;
cond_profile cond[5][2]; // [direction][side]
public:
geom_epsilon(geometric_object_list g, material_type_list mlist, const meep::volume &v);
virtual ~geom_epsilon();
virtual void set_cond_profile(meep::direction, meep::boundary_side, double L, double dx,
double (*prof)(int, double *, void *), void *, double R);
virtual void set_volume(const meep::volume &v);
virtual void unset_volume(void);
bool has_chi(meep::component c, int p);
virtual bool has_chi3(meep::component c);
virtual bool has_chi2(meep::component c);
double chi(meep::component c, const meep::vec &r, int p);
virtual double chi3(meep::component c, const meep::vec &r);
virtual double chi2(meep::component c, const meep::vec &r);
virtual bool has_mu();
virtual bool has_conductivity(meep::component c);
virtual double conductivity(meep::component c, const meep::vec &r);
virtual double chi1p1(meep::field_type ft, const meep::vec &r);
virtual void eff_chi1inv_row(meep::component c, double chi1inv_row[3], const meep::volume &v,
double tol, int maxeval);
void eff_chi1inv_matrix(meep::component c, symmetric_matrix *chi1inv_matrix,
const meep::volume &v, double tol, int maxeval, bool &fallback);
void fallback_chi1inv_row(meep::component c, double chi1inv_row[3], const meep::volume &v,
double tol, int maxeval);
virtual void sigma_row(meep::component c, double sigrow[3], const meep::vec &r);
void add_susceptibilities(meep::structure *s);
void add_susceptibilities(meep::field_type ft, meep::structure *s);
private:
void get_material_pt(material_type &material, const meep::vec &r);
material_type_list extra_materials;
pol *current_pol;
};
/***********************************************************************/
geom_epsilon::geom_epsilon(geometric_object_list g, material_type_list mlist,
const meep::volume &v) {
geometry = g; // don't bother making a copy, only used in one place
extra_materials = mlist;
current_pol = NULL;
FOR_DIRECTIONS(d) FOR_SIDES(b) { cond[d][b].prof = NULL; }
if (meep::am_master()) {
int num_print = meep::verbosity > 2
? geometry.num_items
: std::min(geometry.num_items, meep::verbosity > 0 ? 10 : 0);
for (int i = 0; i < geometry.num_items; ++i) {
if (i < num_print) display_geometric_object_info(5, geometry.items[i]);
medium_struct *mm;
if (is_medium(geometry.items[i].material, &mm)) {
check_offdiag(mm);
if (i < num_print)
master_printf("%*sdielectric constant epsilon diagonal "
"= (%g,%g,%g)\n",
5 + 5, "", mm->epsilon_diag.x, mm->epsilon_diag.y, mm->epsilon_diag.z);
}
}
if (num_print < geometry.num_items && meep::verbosity > 0)
master_printf("%*s...(+ %d objects not shown)...\n", 5, "", geometry.num_items - num_print);
}
geom_fix_object_list(geometry);
geom_box box = gv2box(v);
geometry_tree = create_geom_box_tree0(geometry, box);
if (meep::verbosity > 2 && meep::am_master()) {
master_printf("Geometric-object bounding-box tree:\n");
display_geom_box_tree(5, geometry_tree);
int tree_depth, tree_nobjects;
geom_box_tree_stats(geometry_tree, &tree_depth, &tree_nobjects);
master_printf("Geometric object tree has depth %d "
"and %d object nodes (vs. %d actual objects)\n",
tree_depth, tree_nobjects, geometry.num_items);
}
restricted_tree = geometry_tree;
}
geom_epsilon::~geom_epsilon() {
unset_volume();
destroy_geom_box_tree(geometry_tree);
FOR_DIRECTIONS(d) FOR_SIDES(b) {
if (cond[d][b].prof) delete[] cond[d][b].prof;
}
}
void geom_epsilon::set_cond_profile(meep::direction dir, meep::boundary_side side, double L,
double dx, double (*P)(int, double *, void *), void *data,
double R) {
if (cond[dir][side].prof) delete[] cond[dir][side].prof;
int N = int(L / dx + 0.5);
cond[dir][side].L = L;
cond[dir][side].N = N;
double *prof = cond[dir][side].prof = new double[N + 1];
double umin = 0, umax = 1, esterr;
int errflag;
double prof_int =
adaptive_integration(P, &umin, &umax, 1, data, 1e-9, 1e-4, 50000, &esterr, &errflag);
double prefac = (-log(R)) / (4 * L * prof_int);
for (int i = 0; i <= N; ++i) {
double u = double(i) / N;
prof[i] = prefac * P(1, &u, data);
}
}
void geom_epsilon::unset_volume(void) {
if (restricted_tree != geometry_tree) {
destroy_geom_box_tree(restricted_tree);
restricted_tree = geometry_tree;
}
}
void geom_epsilon::set_volume(const meep::volume &v) {
unset_volume();
geom_box box = gv2box(v);
restricted_tree = create_geom_box_tree0(geometry, box);
}
static void material_epsmu(meep::field_type ft, material_type material, symmetric_matrix *epsmu,
symmetric_matrix *epsmu_inv) {
material_data *md = material;
if (ft == meep::E_stuff) switch (md->which_subclass) {
case material_data::MEDIUM:
case material_data::MATERIAL_FILE:
case material_data::MATERIAL_USER:
case material_data::MATERIAL_GRID:
epsmu->m00 = md->medium.epsilon_diag.x;
epsmu->m11 = md->medium.epsilon_diag.y;
epsmu->m22 = md->medium.epsilon_diag.z;
epsmu->m01 = md->medium.epsilon_offdiag.x.re;
epsmu->m02 = md->medium.epsilon_offdiag.y.re;
epsmu->m12 = md->medium.epsilon_offdiag.z.re;
sym_matrix_invert(epsmu_inv, epsmu);
break;
case material_data::PERFECT_METAL:
epsmu->m00 = -meep::infinity;
epsmu->m11 = -meep::infinity;
epsmu->m22 = -meep::infinity;
epsmu_inv->m00 = -0.0;
epsmu_inv->m11 = -0.0;
epsmu_inv->m22 = -0.0;
epsmu->m01 = epsmu->m02 = epsmu->m12 = 0.0;
epsmu_inv->m01 = epsmu_inv->m02 = epsmu_inv->m12 = 0.0;
break;
default: meep::abort("unknown material type");
}
else
switch (md->which_subclass) {
case material_data::MEDIUM:
case material_data::MATERIAL_FILE:
case material_data::MATERIAL_USER:
case material_data::MATERIAL_GRID:
epsmu->m00 = md->medium.mu_diag.x;
epsmu->m11 = md->medium.mu_diag.y;
epsmu->m22 = md->medium.mu_diag.z;
epsmu->m01 = md->medium.mu_offdiag.x.re;
epsmu->m02 = md->medium.mu_offdiag.y.re;
epsmu->m12 = md->medium.mu_offdiag.z.re;
sym_matrix_invert(epsmu_inv, epsmu);
break;
case material_data::PERFECT_METAL:
epsmu->m00 = 1.0;
epsmu->m11 = 1.0;
epsmu->m22 = 1.0;
epsmu_inv->m00 = 1.0;
epsmu_inv->m11 = 1.0;
epsmu_inv->m22 = 1.0;
epsmu->m01 = epsmu->m02 = epsmu->m12 = 0.0;
epsmu_inv->m01 = epsmu_inv->m02 = epsmu_inv->m12 = 0.0;
break;
default: meep::abort("unknown material type");
}
}
// the goal of this routine is to fill in the 'medium' field
// within the material structure as appropriate for the
// material properties at r.
void geom_epsilon::get_material_pt(material_type &material, const meep::vec &r) {
vector3 p = vec_to_vector3(r);
boolean inobject;
material =
(material_type)material_of_unshifted_point_in_tree_inobject(p, restricted_tree, &inobject);
material_data *md = material;
switch (md->which_subclass) {
// material grid: interpolate onto user specified material grid to get properties at r
case material_data::MATERIAL_GRID:
meep::realnum u;
int oi;
geom_box_tree tp;
tp = geom_tree_search(p, restricted_tree, &oi);
u = matgrid_val(p, tp, oi, md); // interpolate onto material grid
epsilon_material_grid(md, u); // interpolate material from material grid point
return;
// material read from file: interpolate to get properties at r
case material_data::MATERIAL_FILE:
if (md->epsilon_data)
epsilon_file_material(md, p);
else
material = (material_type)default_material;
return;
// material specified by user-supplied function: call user
// function to get properties at r.
// Note that we initialize the medium to vacuum, so that
// the user's function only needs to fill in whatever is
// different from vacuum.
case material_data::MATERIAL_USER:
md->medium = medium_struct();
md->user_func(p, md->user_data, &(md->medium));
check_offdiag(&md->medium);
return;
// position-independent material or metal: there is nothing to do
case material_data::MEDIUM:
case material_data::PERFECT_METAL: return;
default: meep::abort("unknown material type");
};
}
// returns trace of the tensor diagonal
double geom_epsilon::chi1p1(meep::field_type ft, const meep::vec &r) {
symmetric_matrix chi1p1, chi1p1_inv;
#ifdef DEBUG
vector3 p = vec_to_vector3(r);
if (p.x < restricted_tree->b.low.x || p.y < restricted_tree->b.low.y ||
p.z < restricted_tree->b.low.z || p.x > restricted_tree->b.high.x ||
p.y > restricted_tree->b.high.y || p.z > restricted_tree->b.high.z)
meep::abort("invalid point (%g,%g,%g)\n", p.x, p.y, p.z);
#endif
material_type material;
get_material_pt(material, r);
material_epsmu(ft, material, &chi1p1, &chi1p1_inv);
material_gc(material);
return (chi1p1.m00 + chi1p1.m11 + chi1p1.m22) / 3;
}
/* Find frontmost object in v, along with the constant material behind it.
Returns false if material behind the object is not constant.
Requires moderately horrifying logic to figure things out properly,
stolen from MPB. */
static bool get_front_object(const meep::volume &v, geom_box_tree geometry_tree, vector3 &pcenter,
const geometric_object **o_front, vector3 &shiftby_front,
material_type &mat_front, material_type &mat_behind) {
vector3 p;
const geometric_object *o1 = 0, *o2 = 0;
vector3 shiftby1 = {0, 0, 0}, shiftby2 = {0, 0, 0};
geom_box pixel;
material_type mat1 = vacuum, mat2 = vacuum;
int id1 = -1, id2 = -1;
const int num_neighbors[3] = {3, 5, 9};
const int neighbors[3][9][3] = {{{0, 0, 0},
{0, 0, -1},
{0, 0, 1},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0}},
{{0, 0, 0},
{-1, -1, 0},
{1, 1, 0},
{-1, 1, 0},
{1, -1, 0},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0},
{0, 0, 0}},
{{0, 0, 0},
{1, 1, 1},
{1, 1, -1},
{1, -1, 1},
{1, -1, -1},
{-1, 1, 1},
{-1, 1, -1},
{-1, -1, 1},
{-1, -1, -1}}};
pixel = gv2box(v);
pcenter = p = vec_to_vector3(v.center());
double d1, d2, d3;
d1 = (pixel.high.x - pixel.low.x) * 0.5;
d2 = (pixel.high.y - pixel.low.y) * 0.5;
d3 = (pixel.high.z - pixel.low.z) * 0.5;
int dimension_index = meep::number_of_directions(dim) - 1;
for (int i = 0; i < num_neighbors[dimension_index]; ++i) {
const geometric_object *o;
material_type mat;
vector3 q, shiftby;
int id;
q.x = p.x + neighbors[dimension_index][i][0] * d1;
q.y = p.y + neighbors[dimension_index][i][1] * d2;
q.z = p.z + neighbors[dimension_index][i][2] * d3;
o = object_of_point_in_tree(q, geometry_tree, &shiftby, &id);
if ((id == id1 && vector3_equal(shiftby, shiftby1)) ||
(id == id2 && vector3_equal(shiftby, shiftby2)))
continue;
mat = (material_type)default_material;
if (o) {
material_data *md = (material_data *)o->material;
if (md->which_subclass != material_data::MATERIAL_FILE) mat = md;
}
if (id1 == -1) {
o1 = o;
shiftby1 = shiftby;
id1 = id;
mat1 = mat;
}
else if (id2 == -1 ||
((id >= id1 && id >= id2) && (id1 == id2 || material_type_equal(mat1, mat2)))) {
o2 = o;
shiftby2 = shiftby;
id2 = id;
mat2 = mat;
}
else if (!(id1 < id2 && (id1 == id || material_type_equal(mat1, mat))) &&
!(id2 < id1 && (id2 == id || material_type_equal(mat2, mat))))
return false;
}
// CHECK(id1 > -1, "bug in object_of_point_in_tree?");
if (id2 == -1) { /* only one nearby object/material */
id2 = id1;
o2 = o1;
mat2 = mat1;
shiftby2 = shiftby1;
}
if ((o1 && is_variable(o1->material)) || (o2 && is_variable(o2->material)) ||
((is_variable(default_material) || is_file(default_material)) &&
(!o1 || is_file(o1->material) || !o2 || is_file(o2->material))))
return false;
if (id1 >= id2) {
*o_front = o1;
shiftby_front = shiftby1;
mat_front = mat1;
if (id1 == id2)
mat_behind = mat1;
else
mat_behind = mat2;
}
if (id2 > id1) {
*o_front = o2;
shiftby_front = shiftby2;
mat_front = mat2;
mat_behind = mat1;
}
return true;
}
void geom_epsilon::eff_chi1inv_row(meep::component c, double chi1inv_row[3], const meep::volume &v,
double tol, int maxeval) {
symmetric_matrix meps_inv;
bool fallback;
eff_chi1inv_matrix(c, &meps_inv, v, tol, maxeval, fallback);
;
if (fallback) { fallback_chi1inv_row(c, chi1inv_row, v, tol, maxeval); }
else {
switch (component_direction(c)) {
case meep::X:
case meep::R:
chi1inv_row[0] = meps_inv.m00;
chi1inv_row[1] = meps_inv.m01;
chi1inv_row[2] = meps_inv.m02;
break;
case meep::Y:
case meep::P:
chi1inv_row[0] = meps_inv.m01;
chi1inv_row[1] = meps_inv.m11;
chi1inv_row[2] = meps_inv.m12;
break;
case meep::Z:
chi1inv_row[0] = meps_inv.m02;
chi1inv_row[1] = meps_inv.m12;
chi1inv_row[2] = meps_inv.m22;
break;
case meep::NO_DIRECTION: chi1inv_row[0] = chi1inv_row[1] = chi1inv_row[2] = 0; break;
}
}
}
void geom_epsilon::eff_chi1inv_matrix(meep::component c, symmetric_matrix *chi1inv_matrix,
const meep::volume &v, double tol, int maxeval,
bool &fallback) {
const geometric_object *o;
material_type mat, mat_behind;
symmetric_matrix meps;
vector3 p, shiftby, normal;
fallback = false;
if (maxeval == 0) {
noavg:
get_material_pt(mat, v.center());
trivial:
material_epsmu(meep::type(c), mat, &meps, chi1inv_matrix);
material_gc(mat);
return;
}
if (!get_front_object(v, geometry_tree, p, &o, shiftby, mat, mat_behind)) {
get_material_pt(mat, v.center());
if (mat && mat->which_subclass == material_data::MATERIAL_USER && mat->do_averaging) {
fallback = true;
return;
}
else {
goto trivial;
}
}
/* check for trivial case of only one object/material */
if (material_type_equal(mat, mat_behind)) goto trivial;
// it doesn't make sense to average metals (electric or magnetic)
if (is_metal(meep::type(c), &mat) || is_metal(meep::type(c), &mat_behind)) goto noavg;
normal = unit_vector3(normal_to_fixed_object(vector3_minus(p, shiftby), *o));
if (normal.x == 0 && normal.y == 0 && normal.z == 0)
goto noavg; // couldn't get normal vector for this point, punt
geom_box pixel = gv2box(v);
pixel.low = vector3_minus(pixel.low, shiftby);
pixel.high = vector3_minus(pixel.high, shiftby);
double fill = box_overlap_with_object(pixel, *o, tol, maxeval);
material_epsmu(meep::type(c), mat, &meps, chi1inv_matrix);
symmetric_matrix eps2, epsinv2;
symmetric_matrix eps1, delta;
double Rot[3][3];
material_epsmu(meep::type(c), mat_behind, &eps2, &epsinv2);
eps1 = meps;
Rot[0][0] = normal.x;
Rot[1][0] = normal.y;
Rot[2][0] = normal.z;
if (fabs(normal.x) > 1e-2 || fabs(normal.y) > 1e-2) {
Rot[0][2] = normal.y;
Rot[1][2] = -normal.x;
Rot[2][2] = 0;
}
else { /* n is not parallel to z direction, use (x x n) instead */
Rot[0][2] = 0;
Rot[1][2] = -normal.z;
Rot[2][2] = normal.y;
}
{ /* normalize second column */
double s = Rot[0][2] * Rot[0][2] + Rot[1][2] * Rot[1][2] + Rot[2][2] * Rot[2][2];
s = 1.0 / sqrt(s);
Rot[0][2] *= s;
Rot[1][2] *= s;
Rot[2][2] *= s;
}
/* 1st column is 2nd column x 0th column */
Rot[0][1] = Rot[1][2] * Rot[2][0] - Rot[2][2] * Rot[1][0];
Rot[1][1] = Rot[2][2] * Rot[0][0] - Rot[0][2] * Rot[2][0];
Rot[2][1] = Rot[0][2] * Rot[1][0] - Rot[1][2] * Rot[0][0];
/* rotate epsilon tensors to surface parallel/perpendicular axes */
sym_matrix_rotate(&eps1, &eps1, Rot);
sym_matrix_rotate(&eps2, &eps2, Rot);
#define AVG (fill * (EXPR(eps1)) + (1 - fill) * (EXPR(eps2)))
#define SQR(x) ((x) * (x))
#define EXPR(eps) (-1 / eps.m00)
delta.m00 = AVG;
#undef EXPR
#define EXPR(eps) (eps.m11 - SQR(eps.m01) / eps.m00)
delta.m11 = AVG;
#undef EXPR
#define EXPR(eps) (eps.m22 - SQR(eps.m02) / eps.m00)
delta.m22 = AVG;
#undef EXPR
#define EXPR(eps) (eps.m01 / eps.m00)
delta.m01 = AVG;
#undef EXPR
#define EXPR(eps) (eps.m02 / eps.m00)
delta.m02 = AVG;
#undef EXPR
#define EXPR(eps) (eps.m12 - eps.m02 * eps.m01 / eps.m00)
delta.m12 = AVG;
#undef EXPR