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mpb.cpp
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mpb.cpp
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/* Copyright (C) 2005-2022 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 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* 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 <stdarg.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include "meep.hpp"
#include "config.h"
#ifdef HAVE_MPB
#include <mpb.h>
#include "adjust_verbosity.hpp"
#ifndef SCALAR_COMPLEX
#error Meep requires complex version of MPB
#endif
#endif
using namespace std;
namespace meep {
#ifdef HAVE_MPB
typedef struct {
const double *s, *o;
double frequency;
ndim dim;
const fields *f;
/* for parallel efficiency, we first cache the epsinv data from each process, then
sum_to_all to synchonize, and then re-run set_maxwell_dielectric with the cached data */
double *cache; // array of 6*ncache eps_inv matrix entries in the order that they are needed
size_t ncache; // allocated size of the cache
size_t icache; // current position in the cache
bool use_cache; // whether we are using the cache
} meep_mpb_eps_data;
static int meep_mpb_eps(symmetric_matrix *eps, symmetric_matrix *eps_inv, mpb_real n[3],
mpb_real d1, mpb_real d2, mpb_real d3, mpb_real tol, const mpb_real r[3],
void *eps_data_) {
adjust_mpb_verbosity amv;
meep_mpb_eps_data *eps_data = (meep_mpb_eps_data *)eps_data_;
size_t i = eps_data->icache;
(void)n;
(void)d1;
(void)d2;
(void)d3;
(void)tol; // unused
if (eps_data->use_cache) {
const double *cache = eps_data->cache;
eps_inv->m00 = cache[6 * i];
eps_inv->m11 = cache[6 * i + 1];
eps_inv->m22 = cache[6 * i + 2];
ASSIGN_ESCALAR(eps_inv->m01, cache[6 * i + 3], 0);
ASSIGN_ESCALAR(eps_inv->m02, cache[6 * i + 4], 0);
ASSIGN_ESCALAR(eps_inv->m12, cache[6 * i + 5], 0);
maxwell_sym_matrix_invert(eps, eps_inv);
}
else {
// get cache pointer, doubling cache size as needed:
double *cache = i < eps_data->ncache
? eps_data->cache
: (eps_data->cache = (double *)realloc(
eps_data->cache, sizeof(double) * 6 * (eps_data->ncache *= 2)));
const double *s = eps_data->s;
const double *o = eps_data->o;
double frequency = eps_data->frequency;
vec p(eps_data->dim == D3 ? vec(o[0] + r[0] * s[0], o[1] + r[1] * s[1], o[2] + r[2] * s[2])
: (eps_data->dim == D2 ? vec(o[0] + r[0] * s[0], o[1] + r[1] * s[1]) :
/* D1 */ vec(o[2] + r[2] * s[2])));
const fields *f = eps_data->f;
// call get_chi1inv with parallel=false to get only local epsilon data
cache[6 * i] = real(f->get_chi1inv(Ex, X, p, frequency, false));
cache[6 * i + 1] = real(f->get_chi1inv(Ey, Y, p, frequency, false));
cache[6 * i + 2] = real(f->get_chi1inv(Ez, Z, p, frequency, false));
cache[6 * i + 3] = real(f->get_chi1inv(Ex, Y, p, frequency, false));
cache[6 * i + 4] = real(f->get_chi1inv(Ex, Z, p, frequency, false));
cache[6 * i + 5] = real(f->get_chi1inv(Ey, Z, p, frequency, false));
// return a dummy value epsilon = 1 while we are building up the cache
eps->m00 = eps->m11 = eps->m22 = eps_inv->m00 = eps_inv->m11 = eps_inv->m22 = 1;
ASSIGN_ESCALAR(eps->m01, 0, 0);
eps->m02 = eps->m12 = eps_inv->m01 = eps_inv->m02 = eps_inv->m12 = eps->m01;
}
eps_data->icache += 1; // next call will use the subsequent cache element
return 1; // tells MPB not to do its own subpixel averaging
}
/**************************************************************/
/* prototype for position-dependent amplitude function passed */
/* to add_volume_source */
/**************************************************************/
typedef complex<double> (*amplitude_function)(const vec &);
// default implementation of amplitude_function
static complex<double> default_amp_func(const vec &pt) {
(void)pt;
return 1.0;
}
/*******************************************************************/
/* structure storing all data needed to compute position-dependent */
/* amplitude for eigenmode source (the fields of this structure */
/* were formerly global variables) */
/* Note: 'Gk' is the k-point in real space, i.e. G*k where */
/* G = matrix of reciprocal-lattice basis vectors */
/* k = k vector in reciprocal-lattice basis */
/*******************************************************************/
typedef struct eigenmode_data {
maxwell_data *mdata;
scalar_complex *fft_data_H, *fft_data_E;
evectmatrix H;
int n[3];
double s[3];
double Gk[3];
vec center;
amplitude_function amp_func;
int band_num;
double frequency;
double group_velocity;
} eigenmode_data;
#define TWOPI 6.2831853071795864769252867665590057683943388
// utility routine for modular arithmetic that always returns a nonnegative integer
static int pmod(int n, int modulus) {
n = n % modulus;
if (n < 0) n += modulus;
return n;
}
/*******************************************************************/
/* compute position-dependent amplitude for eigenmode source */
/* (similar to the routine formerly called meep_mpb_A) */
/*******************************************************************/
complex<double> eigenmode_amplitude(void *vedata, const vec &p, component c) {
eigenmode_data *edata = (eigenmode_data *)vedata;
if (!edata || !(edata->mdata)) meep::abort("%s:%i: internal error", __FILE__, __LINE__);
int *n = edata->n;
double *s = edata->s;
vec center = edata->center;
amplitude_function amp_func = edata->amp_func;
complex<mpb_real> *cdata =
(complex<mpb_real> *)((c >= Hx) ? edata->fft_data_H : edata->fft_data_E);
const complex<mpb_real> *data;
switch (c) {
case Ex:
cdata = (complex<mpb_real> *)edata->fft_data_E;
data = cdata + 0;
break;
case Ey:
cdata = (complex<mpb_real> *)edata->fft_data_E;
data = cdata + 1;
break;
case Ez:
cdata = (complex<mpb_real> *)edata->fft_data_E;
data = cdata + 2;
break;
case Hx:
cdata = (complex<mpb_real> *)edata->fft_data_H;
data = cdata + 0;
break;
case Hy:
cdata = (complex<mpb_real> *)edata->fft_data_H;
data = cdata + 1;
break;
case Hz:
cdata = (complex<mpb_real> *)edata->fft_data_H;
data = cdata + 2;
break;
default: meep::abort("invalid component in eigenmode_amplitude");
};
int nx = n[0];
int ny = n[1];
int nz = n[2];
double r[3] = {0, 0, 0};
vec p0(p - center);
double phase = 0;
LOOP_OVER_DIRECTIONS(p.dim, d) {
double pd = p0.in_direction(d);
int i = d % 3;
phase += edata->Gk[i] * pd; // k dot p
r[i] = pd / s[i] + 0.5;
}
double rx = r[0], ry = r[1], rz = r[2];
/* linearly interpolate the amplitude from MPB at point p */
int x, y, z, x2, y2, z2;
double dx, dy, dz;
/* get the point corresponding to r in the epsilon array grid: */
x = int(rx * nx);
y = int(ry * ny);
z = int(rz * nz);
/* get the difference between (x,y,z) and the actual point */
dx = rx * nx - x;
dy = ry * ny - y;
dz = rz * nz - z;
/* wrap around to 0..n-1, assuming periodic boundaries */
x = pmod(x, nx);
y = pmod(y, ny);
z = pmod(z, nz);
/* get the other closest point in the grid, with periodic boundaries: */
x2 = pmod((dx >= 0.0 ? x + 1 : x - 1), nx);
y2 = pmod((dy >= 0.0 ? y + 1 : y - 1), ny);
z2 = pmod((dz >= 0.0 ? z + 1 : z - 1), nz);
x = x % nx;
y = y % ny;
z = z % nz;
/* take abs(d{xyz}) to get weights for {xyz} and {xyz}2: */
dx = fabs(dx);
dy = fabs(dy);
dz = fabs(dz);
/* define a macro to give us data(x,y,z) on the grid,
in row-major order (the order used by MPB): */
#define D(x, y, z) (data[(((x)*ny + (y)) * nz + (z)) * 3])
complex<mpb_real> ret;
ret = (((D(x, y, z) * (1.0 - dx) + D(x2, y, z) * dx) * (1.0 - dy) +
(D(x, y2, z) * (1.0 - dx) + D(x2, y2, z) * dx) * dy) *
(1.0 - dz) +
((D(x, y, z2) * (1.0 - dx) + D(x2, y, z2) * dx) * (1.0 - dy) +
(D(x, y2, z2) * (1.0 - dx) + D(x2, y2, z2) * dx) * dy) *
dz);
#undef D
return (complex<double>(double(real(ret)), double(imag(ret))) * amp_func(p)) *
std::polar(1.0, TWOPI * phase);
}
/***************************************************************/
/* entry point to eigenmode_amplitude with the right prototype */
/* for passage as the A parameter to add_volume_source */
/***************************************************************/
static eigenmode_data *global_eigenmode_data = 0;
static component global_eigenmode_component;
static complex<double> meep_mpb_A(const vec &p) {
return eigenmode_amplitude((void *)global_eigenmode_data, p, global_eigenmode_component);
}
// compute axb = a cross b
static void cross_product(mpb_real axb[3], const mpb_real a[3], const mpb_real b[3]) {
axb[0] = a[1] * b[2] - a[2] * b[1];
axb[1] = a[2] * b[0] - a[0] * b[2];
axb[2] = a[0] * b[1] - a[1] * b[0];
}
static double dot_product(const mpb_real a[3], const mpb_real b[3]) {
return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
// return the next number factorizable into powers of 2,3,5,7
// for efficient FFTs, similar to optimize-grid-size! in MPB:
static int nextpow2357(int n) {
while (1) {
int m = n;
while (m % 3 == 0)
m /= 3;
while (m % 5 == 0)
m /= 5;
while (m % 7 == 0)
m /= 7;
if ((m & (m - 1)) == 0) // if m is a power of 2
return n;
n += 1;
}
}
void special_kz_phasefix(eigenmode_data *edata, bool phase_flip) {
size_t n = edata->n[0] * edata->n[1] * edata->n[2];
complex<mpb_real> *E = (complex<mpb_real> *)edata->fft_data_E;
complex<mpb_real> *H = (complex<mpb_real> *)edata->fft_data_H;
complex<mpb_real> im(0, phase_flip ? -1 : 1);
for (size_t i = 0; i < n; ++i) {
E[3 * i + 2] *= im; // Ez
H[3 * i + 0] *= im; // Hx
H[3 * i + 1] *= im; // Hy
}
}
/****************************************************************/
/* call MPB to get the band_numth eigenmode at freq frequency. */
/* */
/* this routine constitutes the first 75% of what was formerly */
/* add_eigenmode_source; it has been split off as a separate */
/* routine to allow it to be followed either by */
/* (a) add_eigenmode_src() */
/* or */
/* (b) get_eigenmode_coefficients() */
/* */
/* the return value is an opaque pointer to an eigenmode_data */
/* structure (needs to be opaque to allow compilation without */
/* MPB, in which case maxwell_data and other types aren't */
/* defined). this structure may then be passed to */
/* eigenmode_amplitude (above) to compute eigenmode E and H */
/* field components at arbitrary points in space. */
/* call destroy_eigenmode_data() to deallocate when finished. */
/****************************************************************/
void *fields::get_eigenmode(double frequency, direction d, const volume where, const volume eig_vol,
int band_num, const vec &_kpoint, bool match_frequency, int parity,
double resolution, double eigensolver_tol, double *kdom,
void **user_mdata, diffractedplanewave *dp) {
/*--------------------------------------------------------------*/
/*- part 1: preliminary setup for calling MPB -----------------*/
/*--------------------------------------------------------------*/
adjust_mpb_verbosity amv;
// if the mode region extends over the full computational grid and we are bloch-periodic
// in any direction, set the corresponding component of the eigenmode initial-guess
// k-vector to be the (real part of the) bloch vector in that direction.
grid_volume eig_gv;
if (eig_vol.dim == D1)
eig_gv = vol1d(eig_vol.in_direction(Z), a);
else if (eig_vol.dim == D2)
eig_gv = vol2d(eig_vol.in_direction(X), eig_vol.in_direction(Y), a);
else
eig_gv = vol3d(eig_vol.in_direction(X), eig_vol.in_direction(Y), eig_vol.in_direction(Z), a);
vec kpoint(_kpoint);
LOOP_OVER_DIRECTIONS(v.dim, dd) {
if (dd != d && eig_gv.num_direction(dd) == user_volume.num_direction(dd))
if (boundaries[High][dd] == Periodic && boundaries[Low][dd] == Periodic)
kpoint.set_direction(dd, real(k[dd]));
}
bool empty_dim[3] = {false, false, false};
// special case: 2d cell in x and y with non-zero kz
if ((v.dim == D3) && (float(v.in_direction(Z)) == float(1 / a)) &&
(boundaries[High][Z] == Periodic && boundaries[Low][Z] == Periodic) && (real(k[Z]) != 0))
empty_dim[2] = true;
if (resolution <= 0.0) resolution = 2 * gv.a; // default to twice resolution
int n[3], local_N, N_start, alloc_N, mesh_size[3] = {1, 1, 1};
mpb_real k[3] = {0, 0, 0}, kcart[3] = {0, 0, 0};
double s[3] = {0, 0, 0}, o[3] = {0, 0, 0};
mpb_real R[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
mpb_real G[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
mpb_real kdir[3] = {0, 0, 0};
double match_tol = eigensolver_tol * 10;
if ((d == NO_DIRECTION && abs(_kpoint) == 0) || coordinate_mismatch(gv.dim, d))
meep::abort("invalid direction in add_eigenmode_source");
if (where.dim != gv.dim || eig_vol.dim != gv.dim)
meep::abort("invalid volume dimensionality in add_eigenmode_source");
if (!eig_vol.contains(where))
meep::abort("invalid grid_volume in add_eigenmode_source (WHERE must be in EIG_VOL)");
switch (gv.dim) {
case D3:
o[0] = eig_vol.in_direction_min(X);
o[1] = eig_vol.in_direction_min(Y);
o[2] = eig_vol.in_direction_min(Z);
s[0] = eig_vol.in_direction(X);
s[1] = eig_vol.in_direction(Y);
s[2] = eig_vol.in_direction(Z);
kcart[0] = kpoint.in_direction(X);
kcart[1] = kpoint.in_direction(Y);
kcart[2] = kpoint.in_direction(Z);
break;
case D2:
o[0] = eig_vol.in_direction_min(X);
o[1] = eig_vol.in_direction_min(Y);
s[0] = eig_vol.in_direction(X);
s[1] = eig_vol.in_direction(Y);
kcart[0] = kpoint.in_direction(X);
kcart[1] = kpoint.in_direction(Y);
kcart[2] = beta; // special_kz feature
empty_dim[2] = true;
break;
case D1:
o[2] = eig_vol.in_direction_min(Z);
s[2] = eig_vol.in_direction(Z);
kcart[2] = kpoint.in_direction(Z);
empty_dim[0] = empty_dim[1] = true;
break;
default: meep::abort("unsupported dimensionality in add_eigenmode_source");
}
double kcart_len = sqrt(dot_product(kcart, kcart));
for (int i = 0; i < 3; ++i) {
n[i] = int(resolution * s[i] + 0.5);
if (n[i] == 0) n[i] = 1;
n[i] = nextpow2357(n[i]);
if (s[i] != 0)
R[i][i] = s[i];
else {
if (d != NO_DIRECTION || empty_dim[i])
R[i][i] = 1;
else { // get lattice vector from kpoint
for (int j = 0; j < 3; ++j)
R[i][j] = kcart[j] / kcart_len;
}
s[i] = 1;
}
}
for (int i = 0; i < 3; ++i) {
k[i] = dot_product(R[i], kcart); // convert k to reciprocal basis
// G = inverse of R transpose, via cross-product formula
cross_product(G[i], R[(i + 1) % 3], R[(i + 2) % 3]);
double GdotR = dot_product(G[i], R[i]);
for (int j = 0; j < 3; ++j)
G[i][j] /= GdotR;
}
if (verbosity > 1) master_printf("KPOINT: %g, %g, %g\n", k[0], k[1], k[2]);
maxwell_data *mdata;
if (!user_mdata || *user_mdata == NULL) {
mdata = create_maxwell_data(n[0], n[1], n[2], &local_N, &N_start, &alloc_N, band_num, band_num);
if (local_N != n[0] * n[1] * n[2]) meep::abort("MPI version of MPB library not supported");
meep_mpb_eps_data eps_data;
eps_data.s = s;
eps_data.o = o;
eps_data.dim = gv.dim;
eps_data.f = this;
eps_data.frequency = frequency;
eps_data.cache = (double *)malloc(sizeof(double) * 6 * (eps_data.ncache = 512));
// first, build up a cache of the local epsilon data (while returning dummy values to MPB)
eps_data.use_cache = false;
eps_data.icache = 0;
set_maxwell_dielectric(mdata, mesh_size, R, G, NULL, meep_mpb_eps, &eps_data);
// then, synchronize the data
eps_data.ncache = eps_data.icache; // actual amount of cached data
double *summed_cache = (double *)malloc(sizeof(double) * 6 * eps_data.ncache);
am_now_working_on(MpiAllTime);
sum_to_all(eps_data.cache, summed_cache, eps_data.ncache * 6);
finished_working();
free(eps_data.cache);
eps_data.cache = summed_cache;
// finally, send MPB the real epsilon data using the synchronized cache
eps_data.use_cache = true;
eps_data.icache = 0;
set_maxwell_dielectric(mdata, mesh_size, R, G, NULL, meep_mpb_eps, &eps_data);
assert(eps_data.icache == eps_data.ncache);
free(eps_data.cache);
if (user_mdata) *user_mdata = (void *)mdata;
}
else {
mdata = (maxwell_data *)(*user_mdata);
maxwell_set_num_bands(mdata, band_num);
N_start = mdata->N_start;
local_N = mdata->local_N;
alloc_N = mdata->alloc_N;
}
if (check_maxwell_dielectric(mdata, 0)) meep::abort("invalid dielectric function for MPB");
double kmatch;
if (d == NO_DIRECTION) {
for (int i = 0; i < 3; ++i)
kdir[i] = kcart[i] / kcart_len;
if (gv.dim == D2) {
kdir[2] = 0; // beta is fixed
kmatch = sqrt(kcart[0] * kcart[0] + kcart[1] * kcart[1]);
}
else
kmatch = kcart_len;
}
else {
kmatch = G[d - X][d - X] * k[d - X]; // k[d] in cartesian
kdir[d - X] = 1; // kdir = unit vector in d direction
}
// if match_frequency is true, we need at least a crude guess for kmatch;
// which we automatically pick if kmatch == 0.
if (match_frequency && kmatch == 0) {
vec cen = eig_vol.center();
kmatch = frequency * sqrt(real(get_eps(cen, frequency)) * real(get_mu(cen, frequency)));
if (d == NO_DIRECTION) {
for (int i = 0; i < 3; ++i)
k[i] = dot_product(R[i], kdir) * kmatch; // kdir*kmatch in reciprocal basis
if (gv.dim == D2) k[2] = beta;
}
else {
k[d - X] = kmatch * R[d - X][d - X]; // convert to reciprocal basis
if (eig_vol.in_direction(d) > 0 &&
fabs(k[d - X]) > 0.4) // ensure k is well inside the Brillouin zone
k[d - X] = k[d - X] > 0 ? 0.4 : -0.4;
}
if (verbosity > 1) master_printf("NEW KPOINT: %g, %g, %g\n", k[0], k[1], k[2]);
}
set_maxwell_data_parity(mdata, parity);
update_maxwell_data_k(mdata, k, G[0], G[1], G[2]);
if (k[0] == 0 && k[1] == 0 && k[2] == 0) {
evectmatrix H;
H.p = band_num;
H.c = 2;
band_num -= maxwell_zero_k_num_const_bands(H, mdata);
if (band_num == 0) meep::abort("zero-frequency bands at k=0 are ill-defined");
}
evectmatrix H = create_evectmatrix(n[0] * n[1] * n[2], 2, band_num, local_N, N_start, alloc_N);
/* initialize H to pseudorandom values on the master process; on other
processes we get the value via broadcast() below */
if (am_master()) {
set_random_seed(314159);
for (int i = 0; i < H.n * H.p; ++i) {
ASSIGN_SCALAR(H.data[i], uniform_random(-1, 1), uniform_random(-1, 1));
}
restore_random_seed();
}
mpb_real *eigvals = new mpb_real[band_num];
int num_iters;
evectmatrix W[3];
for (int i = 0; i < 3; ++i)
W[i] = create_evectmatrix(n[0] * n[1] * n[2], 2, band_num, local_N, N_start, alloc_N);
evectconstraint_chain *constraints = NULL;
constraints = evect_add_constraint(constraints, maxwell_parity_constraint, (void *)mdata);
if (k[0] == 0 && k[1] == 0 && k[2] == 0)
constraints = evect_add_constraint(constraints, maxwell_zero_k_constraint, (void *)mdata);
mpb_real vgrp; // Re( W[0]* (dTheta/dk) W[0] ) = group velocity
// track #times change in kmatch increases to detect non-convergence
double dkmatch_prev = kmatch;
int count_dkmatch_increase = 0;
/*--------------------------------------------------------------*/
/*- part 2: newton iteration loop with call to MPB on each step */
/*- until eigenmode converged to requested tolerance */
/*--------------------------------------------------------------*/
if (am_master() && !dp) do {
eigensolver(H, eigvals, maxwell_operator, (void *)mdata,
#if MPB_VERSION_MAJOR > 1 || (MPB_VERSION_MAJOR == 1 && MPB_VERSION_MINOR >= 6)
NULL, NULL, /* eventually, we can support mu here */
#endif
maxwell_preconditioner2, (void *)mdata, evectconstraint_chain_func,
(void *)constraints, W, 3, eigensolver_tol, &num_iters,
EIGS_DEFAULT_FLAGS | (am_master() && verbosity > 1 ? EIGS_VERBOSE : 0));
if (verbosity > 0)
master_printf("MPB solved for frequency_%d(%g,%g,%g) = %g after %d iters\n", band_num,
G[0][0] * k[0], G[1][1] * k[1], G[2][2] * k[2], sqrt(eigvals[band_num - 1]),
num_iters);
// copy desired single eigenvector into scratch arrays
evectmatrix_resize(&W[0], 1, 0);
evectmatrix_resize(&W[1], 1, 0);
for (int i = 0; i < H.n; ++i)
W[0].data[i] = H.data[H.p - 1 + i * H.p];
// compute the group velocity in the kdir direction
maxwell_ucross_op(W[0], W[1], mdata, kdir); // W[1] = (dTheta/dk) W[0]
mpb_real vscratch;
evectmatrix_XtY_diag_real(W[0], W[1], &vgrp, &vscratch);
vgrp /= sqrt(eigvals[band_num - 1]);
// return to original size
evectmatrix_resize(&W[0], band_num, 0);
evectmatrix_resize(&W[1], band_num, 0);
if (match_frequency) {
// update k via Newton step
double dkmatch = (sqrt(eigvals[band_num - 1]) - frequency) / vgrp;
kmatch = kmatch - dkmatch;
if (verbosity > 1)
master_printf("Newton step: group velocity v=%g, kmatch=%g\n", vgrp, kmatch);
count_dkmatch_increase += fabs(dkmatch) > fabs(dkmatch_prev);
if (count_dkmatch_increase > 4) {
eigvals[band_num - 1] = -1;
break;
}
if (d == NO_DIRECTION) {
for (int i = 0; i < 3; ++i)
k[i] = dot_product(R[i], kdir) * kmatch; // kdir*kmatch in reciprocal basis
if (gv.dim == D2) k[2] = beta;
}
else { k[d - X] = kmatch * R[d - X][d - X]; }
update_maxwell_data_k(mdata, k, G[0], G[1], G[2]);
}
} while (match_frequency &&
fabs(sqrt(eigvals[band_num - 1]) - frequency) > frequency * match_tol);
if (dp) {
scalar_complex s = {real(dp->get_s()), imag(dp->get_s())};
scalar_complex p = {real(dp->get_p()), imag(dp->get_p())};
// compute sum of (kparallel+G)^2 in all the periodic directions
double k2sum = 0, ktmp = 0;
int m = 0;
LOOP_OVER_DIRECTIONS(v.dim, dd) {
m = dp->get_g()[dd - X];
if (eig_vol.in_direction(dd) != 0) {
ktmp = kpoint.in_direction(dd) + m / eig_vol.in_direction(dd);
k2sum += ktmp * ktmp;
}
}
if (((v.dim == D3) && (float(v.in_direction(Z)) == float(1 / a)) &&
(boundaries[High][Z] == Periodic && boundaries[Low][Z] == Periodic) &&
(real(k[Z]) != 0)) ||
((v.dim == D2) && (real(k[Z]) != 0))) {
k2sum += k[Z] * k[Z];
}
// compute kperp (if it is non evanescent) OR
// frequency from kperp^2 and sum of (kparallel+G)^2
{
direction dd = eig_vol.normal_direction();
if (eig_vol.dim == D3 && empty_dim[2]) {
volume eig_vol_2d(D2);
eig_vol_2d.set_direction_min(X, eig_vol.in_direction_min(X));
eig_vol_2d.set_direction_min(Y, eig_vol.in_direction_min(Y));
eig_vol_2d.set_direction_max(X, eig_vol.in_direction_max(X));
eig_vol_2d.set_direction_max(Y, eig_vol.in_direction_max(Y));
dd = eig_vol_2d.normal_direction();
}
if (match_frequency) {
vec cen = eig_vol.center();
double nn = sqrt(real(get_eps(cen, frequency)) * real(get_mu(cen, frequency)));
double k2 = frequency * frequency * nn * nn - k2sum;
if (k2 < 0) {
master_printf("WARNING: diffraction order for g=(%d,%d,%d) is evanescent!\n",
dp->get_g()[0], dp->get_g()[1], dp->get_g()[2]);
return NULL;
}
else if (k2 > 0)
k[dd - X] = sqrt(k2);
}
else
frequency = sqrt(kpoint.in_direction(dd) * kpoint.in_direction(dd) + k2sum);
}
if (am_master()) {
update_maxwell_data_k(mdata, k, G[0], G[1], G[2]);
maxwell_set_planewave(mdata, H, band_num, dp->get_g(), s, p, dp->get_axis());
eigvals[band_num - 1] = frequency * frequency;
evectmatrix_resize(&W[0], 1, 0);
evectmatrix_resize(&W[1], 1, 0);
for (int i = 0; i < H.n; ++i)
W[0].data[i] = H.data[H.p - 1 + i * H.p];
maxwell_ucross_op(W[0], W[1], mdata, kdir); // W[1] = (dTheta/dk) W[0]
mpb_real vscratch;
evectmatrix_XtY_diag_real(W[0], W[1], &vgrp, &vscratch);
vgrp /= sqrt(eigvals[band_num - 1]);
}
}
double eigval = eigvals[band_num - 1];
// cleanup temporary storage
delete[] eigvals;
evect_destroy_constraints(constraints);
for (int i = 0; i < 3; ++i)
destroy_evectmatrix(W[i]);
am_now_working_on(MpiAllTime);
/* We only run MPB eigensolver on the master process to avoid
any possibility of inconsistent mode solutions (#568) */
eigval = broadcast(0, eigval);
broadcast(0, k, 3);
vgrp = broadcast(0, vgrp);
if (eigval < 0) { // no mode found
destroy_evectmatrix(H);
if (!user_mdata) destroy_maxwell_data(mdata);
return NULL;
}
if (!am_master()) update_maxwell_data_k(mdata, k, G[0], G[1], G[2]);
broadcast(0, (double *)H.data, 2 * H.n * H.p);
finished_working();
if (!match_frequency) frequency = sqrt(eigval);
/*--------------------------------------------------------------*/
/*- part 3: do one stage of postprocessing to tabulate H-field */
/*- components on the internal storage buffer in mdata */
/*--------------------------------------------------------------*/
complex<mpb_real> *cdata = (complex<mpb_real> *)mdata->fft_data;
maxwell_compute_h_from_H(mdata, H, (scalar_complex *)cdata, band_num - 1, 1);
/* choose deterministic phase, maximizing power in real part;
see fix_field_phase routine in MPB.*/
{
int i, N = mdata->fft_output_size * 3;
double sq_sum0 = 0, sq_sum1 = 0, maxabs = 0.0;
double theta;
for (i = 0; i < N; ++i) {
double a = real(cdata[i]), b = imag(cdata[i]);
sq_sum0 += a * a - b * b;
sq_sum1 += 2 * a * b;
}
theta = 0.5 * atan2(-sq_sum1, sq_sum0);
complex<mpb_real> phase(cos(theta), sin(theta));
phase /= sqrt(fabs(R[0][0] * R[1][1] * R[2][2]));
for (i = 0; i < N; ++i) {
double r = fabs(real(cdata[i] * phase));
if (r > maxabs) maxabs = r;
}
for (i = N - 1; i >= 0 && fabs(real(cdata[i] * phase)) < 0.5 * maxabs; --i)
;
if (real(cdata[i] * phase) < 0) phase = -phase;
for (i = 0; i < N; ++i)
cdata[i] *= phase;
complex<mpb_real> *hdata = (complex<mpb_real> *)H.data;
for (i = 0; i < H.n; ++i)
hdata[i * H.p + (band_num - 1)] *= phase;
}
/*--------------------------------------------------------------*/
/* do a second round of post-processing to tabulate E-fields -*/
/* on a (separate) internal storage buffer. (Previously -*/
/* there was only one internal buffer which held either E-field */
/* or H-field data, but this is inconvenient for cases in which */
/* you want the E and H fields of an eigenmode simultaneously.) */
/*--------------------------------------------------------------*/
int NFFT = 3 * mdata->fft_output_size;
scalar_complex *fft_data_E = (scalar_complex *)malloc(NFFT * sizeof(scalar_complex));
maxwell_compute_d_from_H(mdata, H, fft_data_E, band_num - 1, 1);
// d_from_H actually computes -frequency*D (see mpb/src/maxwell/maxwell_op.c),
// so we need to divide the E-field amplitudes by -frequency; we also take this
// opportunity to rescale the overall E and H amplitudes to yield unit power flux.
double scale = -1.0 / frequency, factor = 2.0 / sqrt(fabs(vgrp));
complex<double> *efield = (complex<double> *)fft_data_E,
*hfield = (complex<double> *)(mdata->fft_data);
for (int n = 0; n < NFFT; ++n) {
efield[n] *= factor * scale;
hfield[n] *= factor;
}
maxwell_compute_e_from_d(mdata, fft_data_E, 1);
/*--------------------------------------------------------------*/
/*- part 4: initialize and return output data structures. */
/*--------------------------------------------------------------*/
eigenmode_data *edata = new eigenmode_data;
edata->mdata = mdata;
edata->fft_data_H = mdata->fft_data;
edata->fft_data_E = fft_data_E;
edata->H = H;
edata->n[0] = n[0];
edata->n[1] = n[1];
edata->n[2] = n[2];
edata->s[0] = s[0];
edata->s[1] = s[1];
edata->s[2] = s[2];
edata->Gk[0] = G[0][0] * k[0] + G[1][0] * k[1] + G[2][0] * k[2];
edata->Gk[1] = G[0][1] * k[0] + G[1][1] * k[1] + G[2][1] * k[2];
edata->Gk[2] = G[0][2] * k[0] + G[1][2] * k[1] + G[2][2] * k[2];
edata->center = eig_vol.center();
edata->amp_func = default_amp_func;
edata->band_num = band_num;
edata->frequency = frequency;
edata->group_velocity = (double)vgrp;
if (kdom) {
#if MPB_VERSION_MAJOR > 1 || (MPB_VERSION_MAJOR == 1 && MPB_VERSION_MINOR >= 7)
maxwell_dominant_planewave(mdata, H, band_num, kdom);
if (verbosity > 0)
master_printf("Dominant planewave for band %d: (%f,%f,%f)\n", band_num, kdom[0], kdom[1],
kdom[2]);
#else
kdom[0] = kdom[1] = kdom[2] = 0;
#endif
}
return (void *)edata;
}
void destroy_eigenmode_data(void *vedata, bool destroy_mdata) {
adjust_mpb_verbosity amv;
eigenmode_data *edata = (eigenmode_data *)vedata;
destroy_evectmatrix(edata->H);
if (destroy_mdata) destroy_maxwell_data(edata->mdata);
free(edata->fft_data_E);
delete edata;
}
double get_group_velocity(void *vedata) {
eigenmode_data *edata = (eigenmode_data *)vedata;
return edata->group_velocity;
}
vec get_k(void *vedata) {
eigenmode_data *edata = (eigenmode_data *)vedata;
return vec(edata->Gk[0], edata->Gk[1], edata->Gk[2]);
}
/***************************************************************/
/* call get_eigenmode() to solve for the specified eigenmode, */
/* then call add_volume_source() to add current sources whose */
/* radiated fields reproduce the eigenmode fields */
/***************************************************************/
void fields::add_eigenmode_source(component c0, const src_time &src, direction d,
const volume &where, const volume &eig_vol, int band_num,
const vec &kpoint, bool match_frequency, int parity,
double resolution, double eigensolver_tol, complex<double> amp,
complex<double> A(const vec &), diffractedplanewave *dp) {
/*--------------------------------------------------------------*/
/* step 1: call MPB to compute the eigenmode */
/*--------------------------------------------------------------*/
adjust_mpb_verbosity amv;
double frequency = real(src.frequency());
am_now_working_on(MPBTime);
global_eigenmode_data = (eigenmode_data *)get_eigenmode(
frequency, d, where, eig_vol, band_num, kpoint, match_frequency, parity, resolution,
eigensolver_tol, NULL, NULL, dp);
finished_working();
if (is_real && beta != 0) special_kz_phasefix(global_eigenmode_data, true /* phase_flip */);
if (global_eigenmode_data == NULL) meep::abort("MPB could not find the eigenmode");
/* add_volume_source amp_fun coordinates are relative to where.center();
this is not the default in get_eigenmode because where-relative coordinates
are not used elsewhere, e.g. in getting mode coefficients in dft.cpp. */
global_eigenmode_data->center -= where.center();
if (!global_eigenmode_data)
meep::abort(
"eigenmode solver failed to find the requested mode; you may need to supply a better "
"guess for k");
global_eigenmode_data->amp_func = A ? A : default_amp_func;
src_time *src_mpb = src.clone();
if (!match_frequency) src_mpb->set_frequency(global_eigenmode_data->frequency);
/*--------------------------------------------------------------*/
// step 2: add sources whose radiated field reproduces the */
// the eigenmode */
// electric current K = nHat \times H */
// magnetic current N = -nHat \times E */
/*--------------------------------------------------------------*/
if (is_D(c0)) c0 = direction_component(Ex, component_direction(c0));
if (is_B(c0)) c0 = direction_component(Hx, component_direction(c0));
component cE[3] = {Ex, Ey, Ez}, cH[3] = {Hx, Hy, Hz};
int n = (d == X ? 0 : (d == Y ? 1 : 2));
if (d == NO_DIRECTION) {
n = where.in_direction(X) == 0 ? 0
: where.in_direction(Y) == 0 ? 1
: where.in_direction(Z) == 0 ? 2
: -1;
if (n == -1)
meep::abort(
"can't determine source direction for non-empty source volume with NO_DIRECTION source");
}
int np1 = (n + 1) % 3;
int np2 = (n + 2) % 3;
// Kx = -Hy, Ky = Hx (for d==Z)
global_eigenmode_component = cH[np1];
add_volume_source_check(cE[np2], *src_mpb, where, meep_mpb_A, +1.0 * amp, c0, d,
parity & ODD_Z_PARITY, parity & EVEN_Z_PARITY);
global_eigenmode_component = cH[np2];
add_volume_source_check(cE[np1], *src_mpb, where, meep_mpb_A, -1.0 * amp, c0, d,
parity & ODD_Z_PARITY, parity & EVEN_Z_PARITY);
// Nx = +Ey, Ny = -Ex (for d==Z)
global_eigenmode_component = cE[np1];
add_volume_source_check(cH[np2], *src_mpb, where, meep_mpb_A, -1.0 * amp, c0, d,
parity & ODD_Z_PARITY, parity & EVEN_Z_PARITY);
global_eigenmode_component = cE[np2];
add_volume_source_check(cH[np1], *src_mpb, where, meep_mpb_A, +1.0 * amp, c0, d,
parity & ODD_Z_PARITY, parity & EVEN_Z_PARITY);
delete src_mpb;
destroy_eigenmode_data((void *)global_eigenmode_data);
}
/***************************************************************/
/* get eigenmode coefficients for all frequencies in flux */
/* and all band indices in the caller-populated bands array. */
/* */
/* on input, coeffs must point to a user-allocated array of */
/* length 2*num_freqs*num_bands (where num_freqs=flux.Nfreq). */
/* on return, the coefficients of the forward/backward traveling*/
/* eigenmodes for frequency #nf and band index bands[nb] are */
/* coeffs[ 2*nb*num_freqs + 2*nf + 0/1 ]. */
/* */
/* if vgrp is non-null, it should point to a caller-allocated */
/* array of size num_bands*num_freqs. then on return the group */
/* velocity for the mode with frequency #nf and band index */
/* bands[nb] is stored in vgrp[nb*num_freqs + nf]. */
/* */
/* similarly, if kpoints is non-null it should point to a */
/* caller-allocated array of size num_bands*num_freqs, which on*/
/* return will be populated by the k-vectors for the modes. */
/***************************************************************/
void fields::get_eigenmode_coefficients(dft_flux flux, const volume &eig_vol, int *bands,
int num_bands, int parity, double eig_resolution,
double eigensolver_tol, std::complex<double> *coeffs,
double *vgrp, kpoint_func user_kpoint_func,
void *user_kpoint_data, vec *kpoints, vec *kdom_list,
double *cscale, direction d, diffractedplanewave *dp) {
adjust_mpb_verbosity amv;
int num_freqs = flux.freq.size();
bool match_frequency = true;
if (flux.use_symmetry && S.multiplicity() > 1 && parity == 0)
meep::abort("flux regions for eigenmode projection with symmetry should be created by "
"add_mode_monitor()");
vec kpoint(0.0, 0.0, 0.0); // default guess
// get_eigenmode will create mdata only once and then reuse it on each iteration of the loop
maxwell_data *mdata = NULL;
// loop over all bands and all frequencies
for (int nb = 0; nb < num_bands; nb++) {
for (int nf = 0; nf < num_freqs; nf++) {
/*--------------------------------------------------------------*/
/*- call mpb to compute the eigenmode --------------------------*/
/*--------------------------------------------------------------*/
int band_num = bands ? bands[nb] : 1;
double kdom[3];
if (user_kpoint_func) kpoint = user_kpoint_func(flux.freq[nf], band_num, user_kpoint_data);
am_now_working_on(MPBTime);
void *mode_data =
get_eigenmode(flux.freq[nf], d, flux.where, eig_vol, band_num, kpoint, match_frequency,
parity, eig_resolution, eigensolver_tol, kdom, (void **)&mdata, dp);
finished_working();
if (!mode_data) { // mode not found, assume evanescent
coeffs[2 * nb * num_freqs + 2 * nf] = coeffs[2 * nb * num_freqs + 2 * nf + 1] = 0;
if (vgrp) vgrp[nb * num_freqs + nf] = 0;
if (kpoints) kpoints[nb * num_freqs + nf] = vec(0.0, 0.0, 0.0);
if (kdom_list) kdom_list[nb * num_freqs + nf] = vec(0.0, 0.0, 0.0);
continue;
}
if (is_real && beta != 0)
special_kz_phasefix((eigenmode_data *)mode_data, false /* phase_flip */);
double vg = get_group_velocity(mode_data);
vec kfound = get_k(mode_data);
if (vgrp) vgrp[nb * num_freqs + nf] = vg;
if (kpoints) kpoints[nb * num_freqs + nf] = kfound;
if (kdom_list) kdom_list[nb * num_freqs + nf] = vec(kdom[0], kdom[1], kdom[2]);
/* in the common case of k aligned along a cartesian direction, update
our k-point guess based on the current k point plus a correction from the group velocity */
if (match_frequency && nf + 1 < num_freqs && abs(kfound) > 0 &&
((kfound.x() == 0 && (kfound.y() == 0 || kfound.z() == 0)) ||
(kfound.y() == 0 && kfound.z() == 0)))
kpoint = kfound + kfound * ((flux.freq[nf + 1] - flux.freq[nf]) / (vg * abs(kfound)));
/*--------------------------------------------------------------*/
/*--------------------------------------------------------------*/
/*--------------------------------------------------------------*/
complex<double> mode_flux[2], mode_mode[2];
get_mode_flux_overlap(mode_data, flux, nf, mode_flux);
get_mode_mode_overlap(mode_data, mode_data, flux, mode_mode);
complex<double> cplus = 0.5 * (mode_flux[0] + mode_flux[1]);
complex<double> cminus = 0.5 * (mode_flux[0] - mode_flux[1]);
/* MPB modes are normalized to unit power above, but we need to re-normalize here to have
unit power as integrated on Meep's Yee grid and not on MPB's grid. Thus, normfac differs
from a constant factor only because of discretization effects. */
complex<double> normfac = 0.5 * (mode_mode[0] + mode_mode[1]);
if (normfac == 0.0) normfac = 1.0;
double csc = sqrt((flux.use_symmetry ? S.multiplicity() : 1.0) / abs(normfac));
if (cscale)
cscale[nb * num_freqs + nf] =
csc; // return real part of coefficient scalar for adjoint calculations
coeffs[2 * nb * num_freqs + 2 * nf + (vg > 0.0 ? 0 : 1)] = cplus * csc;
coeffs[2 * nb * num_freqs + 2 * nf + (vg > 0.0 ? 1 : 0)] = cminus * csc;
destroy_eigenmode_data((void *)mode_data, false);
}
}
destroy_maxwell_data(mdata);
}
/**************************************************************/
/* dummy versions of class methods for compiling without MPB */
/**************************************************************/