C Mie T-matrices but demand yet Bessel functions of complex arguments.
Former-commit-id: 101201f5d72ab0f45eefc09c860b65b6841460bf
This commit is contained in:
Marek Nečada
parent
2af9b83e35
commit
4475cffeba
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@ -6,6 +6,7 @@
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#include "kahansum.h"
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#include <gsl/gsl_sf_bessel.h>
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#include <complex.h>
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#include "qpms_error.h"
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#ifndef M_LN2
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#define M_LN2 0.69314718055994530942 /* log_e 2 */
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@ -16,7 +17,7 @@ static inline complex double ipow(int x) {
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}
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// There is a big issue with gsl's precision of spherical bessel function; these have to be implemented differently
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qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array) {
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qpms_errno_t qpms_sph_bessel_realx_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array) {
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int retval;
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double tmparr[lmax+1];
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switch(typ) {
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@ -49,6 +50,14 @@ qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, co
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assert(0);
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}
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qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *result_array) {
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int retval = qpms_sph_bessel_realx_fill(typ, lmax, creal(x), result_array);
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if(!cimag(x))
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return retval;
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else
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QPMS_NOT_IMPLEMENTED("complex argument of Bessel function.");
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}
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static inline ptrdiff_t akn_index(qpms_l_t n, qpms_l_t k) {
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assert(k <= n);
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return ((ptrdiff_t) n + 1) * n / 2 + k;
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@ -1131,8 +1131,11 @@ cdef class CTMatrix: # N.B. there is another type called TMatrix in tmatrices.py
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def __cinit__(CTMatrix self, BaseSpec spec, matrix):
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self.spec = spec
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self.t.spec = self.spec.rawpointer();
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# The following will raise an exception if shape is wrong
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self.m = np.array(matrix, dtype=complex, copy=True, order='C').reshape((len(spec), len(spec)))
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if matrix is None or matrix == 0:
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self.m = np.zeros((len(spec),len(spec)), dtype=complex, order='C')
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else:
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# The following will raise an exception if shape is wrong
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self.m = np.array(matrix, dtype=complex, copy=True, order='C').reshape((len(spec), len(spec)))
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#self.m.setflags(write=False) # checkme
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cdef cdouble[:,:] m_memview = self.m
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self.t.m = &(m_memview[0,0])
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@ -1158,6 +1161,19 @@ cdef class CTMatrix: # N.B. there is another type called TMatrix in tmatrices.py
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# Maybe not totally needed after all, as np.array(T[...]) should be equivalent and not longer
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return np.array(self.m, copy=True)
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def spherical_fill(CTMatrix self, double radius, cdouble k_int,
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cdouble k_ext, cdouble mu_int = 1, cdouble mu_ext = 1):
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''' Replaces the contents of the T-matrix with those of a spherical particle. '''
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qpms_tmatrix_spherical_fill(&self.t, radius, k_int, k_ext, mu_int, mu_ext)
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@staticmethod
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def spherical(BaseSpec spec, double radius, cdouble k_int, cdouble k_ext,
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cdouble mu_int = 1, cdouble mu_ext = 1):
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''' Creates a T-matrix of a spherical nanoparticle. '''
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tm = CTMatrix(spec, 0)
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tm.spherical_fill(radius, k_int, k_ext, mu_int, mu_ext)
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return tm
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cdef char *make_c_string(pythonstring):
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'''
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Copies contents of a python string into a char[]
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@ -38,6 +38,12 @@ cdef extern from "qpms_types.h":
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QPMS_NORMALISATION_SPHARM
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QPMS_NORMALISATION_SPHARM_CS
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QPMS_NORMALISATION_UNDEF
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ctypedef enum qpms_bessel_t:
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QPMS_BESSEL_REGULAR
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QPMS_BESSEL_SINGULAR
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QPMS_HANKEL_PLUS
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QPMS_HANKEL_MINUS
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QPMS_HANKEL_UNDEF
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ctypedef int qpms_lm_t
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ctypedef int qpms_l_t
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ctypedef int qpms_m_t
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@ -258,6 +264,12 @@ cdef extern from "tmatrices.h":
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qpms_errno_t qpms_load_scuff_tmatrix(const char *path, const qpms_vswf_set_spec_t *bspec,
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size_t *n, double **freqs, double **freqs_su, qpms_tmatrix_t **tmatrices_array,
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cdouble **tmdata)
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cdouble *qpms_mie_coefficients_reflection(cdouble *target, const qpms_vswf_set_spec_t *bspec,
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double a, cdouble k_i, cdouble k_e, cdouble mu_i, cdouble mu_e, qpms_bessel_t J_ext, qpms_bessel_t J_scat)
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qpms_errno_t qpms_tmatrix_spherical_fill(qpms_tmatrix_t *t, double a,
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cdouble k_i, cdouble k_e, cdouble mu_i, cdouble mu_e)
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qpms_tmatrix_t *qpms_tmatrix_spherical(const qpms_vswf_set_spec_t *bspec,
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double a, cdouble k_i, cdouble k_e, cdouble mu_i, cdouble mu_e)
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cdef extern from "scatsystem.h":
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struct qpms_particle_t:
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@ -29,4 +29,7 @@ void qpms_pr_debug_at_flf(const char *filename, unsigned int linenum,
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#define QPMS_ENSURE(x, msg, ...) {if(!(x)) qpms_pr_error_at_flf(__FILE__,__LINE__,__func__,msg, ##__VA_ARGS__); }
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#define QPMS_NOT_IMPLEMENTED(msg, ...) qpms_pr_error_at_flf(__FILE__,__LINE__,__func__, \
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"Not implemented:" msg, ##__VA_ARGS__)
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#endif
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@ -8,7 +8,7 @@
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******************************************************************************/
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// TODO unify types
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qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, double x, complex double *result_array);
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qpms_errno_t qpms_sph_bessel_fill(qpms_bessel_t typ, qpms_l_t lmax, complex double x, complex double *result_array);
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@ -16,6 +16,7 @@
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#include <string.h>
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#include "qpms_error.h"
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#include "tmatrices.h"
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#include "qpms_specfunc.h"
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#define HBAR (1.05457162825e-34)
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#define ELECTRONVOLT (1.602176487e-19)
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@ -314,16 +315,21 @@ void qpms_tmatrix_interpolator_free(qpms_tmatrix_interpolator_t *ip) {
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qpms_tmatrix_t *qpms_tmatrix_interpolator_eval(const qpms_tmatrix_interpolator_t *ip, double freq) {
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qpms_tmatrix_t *t = qpms_tmatrix_init(ip->bspec);
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QPMS_ENSURE_SUCCESS(qpms_tmatrix_interpolator_eval_fill(t, ip, freq));
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return t;
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}
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qpms_errno_t qpms_tmatrix_interpolator_eval_fill(qpms_tmatrix_t *t,
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const qpms_tmatrix_interpolator_t *ip, double freq) {
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QPMS_ENSURE(qpms_vswf_set_spec_isidentical(t->spec, ip->bspec), "Tried to fill a T-matrix with an incompatible interpolator!");
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const size_t n = ip->bspec->n;
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for (size_t i = 0; i < n*n; ++i){
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if (ip->splines_real[i]) t->m[i] = gsl_spline_eval(ip->splines_real[i], freq, NULL /*does this work?*/);
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if (ip->splines_imag[i]) t->m[i] += I* gsl_spline_eval(ip->splines_imag[i], freq, NULL /*does this work?*/);
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}
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return t;
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return QPMS_SUCCESS;
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}
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double qpms_SU2eV(double e_SU) {
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return e_SU * SCUFF_OMEGAUNIT / (ELECTRONVOLT / HBAR);
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}
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@ -454,3 +460,82 @@ qpms_errno_t qpms_load_scuff_tmatrix(
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return retval;
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}
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complex double *qpms_mie_coefficients_reflection(
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complex double *target, ///< Target array of length bspec->n. If NULL, a new one will be allocated.
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const qpms_vswf_set_spec_t *bspec, ///< Defines which of the coefficients are calculated.
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double a, ///< Radius of the sphere.
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complex double k_i, ///< Wave number of the internal material of the sphere.
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complex double k_e, ///< Wave number of the surrounding medium.
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complex double mu_i, ///< Relative permeability of the sphere material.
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complex double mu_e, ///< Relative permeability of the surrounding medium.
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qpms_bessel_t J_ext,
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qpms_bessel_t J_scat
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// TODO J_ext, J_scat?
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) {
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/*
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* This implementation pretty much copies mie_coefficients() from qpms_p.py, so
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* any bugs there should affect this function as well and perhaps vice versa.
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*/
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QPMS_ENSURE(J_ext != J_scat, "J_ext and J_scat must not be equal. Perhaps you want J_ext = 1 and J_scat = 3 anyways.");
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if (!target) QPMS_CRASHING_MALLOC(target, bspec->n * sizeof(complex double));
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qpms_l_t lMax = bspec->lMax;
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complex double x_i = k_i * a;
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complex double x_e = k_e * a;
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complex double m = k_i / k_e;
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complex double eta_inv_i = k_i / mu_i;
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complex double eta_inv_e = k_e / mu_e;
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complex double zi[lMax + 2];
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complex double ze[lMax + 2];
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complex double zs[lMax + 2];
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complex double RH[lMax + 1] /* MAGNETIC */, RV[lMax+1] /* ELECTRIC */;
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QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(QPMS_BESSEL_REGULAR, lMax+1, x_i, zi));
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QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J_ext, lMax+1, x_e, ze));
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QPMS_ENSURE_SUCCESS(qpms_sph_bessel_fill(J_scat, lMax+1, x_e, zs));
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for (qpms_l_t l = 0; l <= lMax; ++l) {
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// Bessel function derivatives as in DLMF 10.51.2
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complex double dzi = -zi[l+1] + l/x_i*zi[l];
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complex double dze = -ze[l+1] + l/x_e*ze[l];
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complex double dzs = -zs[l+1] + l/x_e*zs[l];
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complex double fi = zi[l]/x_i+dzi;
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complex double fs = zs[l]/x_e+dzs;
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complex double fe = ze[l]/x_e+dze;
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RV[l] = -((-eta_inv_i * fe * zi[l] + eta_inv_e * ze[l] * fi)/(-eta_inv_e * fi * zs[l] + eta_inv_i * zi[l] * fs));
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RH[l] = -((-eta_inv_e * fe * zi[l] + eta_inv_i * ze[l] * fi)/(-eta_inv_i * fi * zs[l] + eta_inv_e * zi[l] * fs));
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}
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for (size_t i = 0; i < bspec->n; ++i) {
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qpms_l_t l; qpms_m_t m; qpms_vswf_type_t t;
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QPMS_ENSURE_SUCCESS(qpms_uvswfi2tmn(bspec->ilist[i], &t, &m, &l));
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assert(l <= lMax);
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switch(t) {
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case QPMS_VSWF_ELECTRIC:
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target[i] = RV[l];
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break;
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case QPMS_VSWF_MAGNETIC:
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target[i] = RH[l];
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break;
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default: QPMS_WTF;
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}
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}
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return target;
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}
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/// Replaces the contents of an existing T-matrix with that of a spherical nanoparticle calculated using the Lorentz-mie theory.
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qpms_errno_t qpms_tmatrix_spherical_fill(qpms_tmatrix_t *t, ///< T-matrix whose contents are to be replaced. Not NULL.
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double a, ///< Radius of the sphere.
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complex double k_i, ///< Wave number of the internal material of the sphere.
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complex double k_e, ///< Wave number of the surrounding medium.
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complex double mu_i, ///< Relative permeability of the sphere material.
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complex double mu_e ///< Relative permeability of the surrounding medium.
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) {
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qpms_l_t lMax = t->spec->lMax;
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complex double *miecoeffs = qpms_mie_coefficients_reflection(NULL, t->spec, a, k_i, k_e, mu_i, mu_e,
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QPMS_BESSEL_REGULAR, QPMS_HANKEL_PLUS);
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memset(t->m, 0, SQ(t->spec->n));
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for(size_t i = 0; i < t->spec->n; ++i)
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t->m[t->spec->n*i + i] = miecoeffs[i];
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free(miecoeffs);
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return QPMS_SUCCESS;
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}
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@ -233,6 +233,10 @@ typedef struct qpms_tmatrix_interpolator_t {
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/// Free a T-matrix interpolator.
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void qpms_tmatrix_interpolator_free(qpms_tmatrix_interpolator_t *interp);
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/// Fills an existing T-matrix with new interpolated values.
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qpms_errno_t qpms_tmatrix_interpolator_eval_fill(qpms_tmatrix_t *target, ///< T-matrix to be updated, not NULL.
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const qpms_tmatrix_interpolator_t *interp, double freq);
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/// Evaluate a T-matrix interpolated value.
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/** The result is to be freed using qpms_tmatrix_free().*/
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qpms_tmatrix_t *qpms_tmatrix_interpolator_eval(const qpms_tmatrix_interpolator_t *interp, double freq);
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@ -244,6 +248,63 @@ qpms_tmatrix_interpolator_t *qpms_tmatrix_interpolator_create(size_t n, ///< Num
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//, bool copy_bspec ///< if true, copies its own copy of basis spec from the first T-matrix.
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/*, ...? */);
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/// Calculates the reflection Mie-Lorentz coefficients for a spherical particle.
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/**
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* This function is based on the previous python implementation mie_coefficients() from qpms_p.py,
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* so any bugs therein should affect this function as well and perhaps vice versa.
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*
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* Most importantly, the case of magnetic material, \a mu_i != 0 or \a mu_e != 0 has never been tested
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* and might give wrong results.
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*
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* \return Array with the Mie-Lorentz reflection coefficients in the order determined by bspec.
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* If \a target was not NULL, this is target, otherwise a newly allocated array.
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*
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* TODO better doc.
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*/
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complex double *qpms_mie_coefficients_reflection(
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complex double *target, ///< Target array of length bspec->n. If NULL, a new one will be allocated.
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const qpms_vswf_set_spec_t *bspec, ///< Defines which of the coefficients are calculated.
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double a, ///< Radius of the sphere.
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complex double k_i, ///< Wave number of the internal material of the sphere.
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complex double k_e, ///< Wave number of the surrounding medium.
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complex double mu_i, ///< Relative permeability of the sphere material.
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complex double mu_e, ///< Relative permeability of the surrounding medium.
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qpms_bessel_t J_ext, ///< Kind of the "incoming" waves. Most likely QPMS_BESSEL_REGULAR.
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qpms_bessel_t J_scat ///< Kind of the "scattered" waves. Most likely QPMS_HANKEL_PLUS.
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);
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/// Replaces the contents of an existing T-matrix with that of a spherical nanoparticle calculated using the Lorentz-mie theory.
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qpms_errno_t qpms_tmatrix_spherical_fill(qpms_tmatrix_t *t, ///< T-matrix whose contents are to be replaced. Not NULL.
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double a, ///< Radius of the sphere.
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complex double k_i, ///< Wave number of the internal material of the sphere.
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complex double k_e, ///< Wave number of the surrounding medium.
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complex double mu_i, ///< Relative permeability of the sphere material.
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complex double mu_e ///< Relative permeability of the surrounding medium.
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);
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/// Creates a new T-matrix of a spherical particle using the Lorentz-Mie theory.
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static inline qpms_tmatrix_t *qpms_tmatrix_spherical(
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const qpms_vswf_set_spec_t *bspec,
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double a, ///< Radius of the sphere.
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complex double k_i, ///< Wave number of the internal material of the sphere.
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complex double k_e, ///< Wave number of the surrounding medium.
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complex double mu_i, ///< Relative permeability of the sphere material.
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complex double mu_e ///< Relative permeability of the surrounding medium.
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) {
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qpms_tmatrix_t *t = qpms_tmatrix_init(bspec);
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qpms_tmatrix_spherical_fill(t, a, k_i, k_e, mu_i, mu_e);
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return t;
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}
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/// Relative permittivity from the Drude model.
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static inline complex double qpms_drude_epsilon(
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complex double eps_inf, ///< Permittivity at
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complex double omega_p, ///< Plasma frequency \f$ \omega_p \f$ of the material.
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complex double gamma_p, ///< Decay constant \f$ \gamma_p \f$ of the material.
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complex double omega ///< Frequency \f$ \omega \f$ at which the permittivity is evaluated.
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) {
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return eps_inf - omega_p*omega_p/(omega*(omega+I*gamma_p));
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}
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#if 0
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// Abstract types that describe T-matrix/particle/scatsystem symmetries
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@ -0,0 +1,61 @@
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#!/usr/bin/env python
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# coding: utf-8
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# In[1]:
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from qpms import *
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# In[6]:
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R = 40e-9
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ω_p = 9*eV/ℏ #9*eV/ℏ
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ε_inf = 4.6
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γ_p = 0.1*eV/ℏ
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ε_b = 2.13
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lMax = 3
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ω = 1.5*eV/ℏ
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# In[7]:
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ε_m = ε_drude(ε_inf, ω_p, γ_p, ω)
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# In[9]:
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k_i = cmath.sqrt(ε_m)*ω/c
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k_e = cmath.sqrt(ε_b)*ω/c
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RH, RV, TH, TV = mie_coefficients(a=R, nmax=lMax, k_i=k_i, k_e=k_e, J_ext=1, J_scat=3)
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# In[11]:
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spec = BaseSpec(lMax=lMax)
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cT = CTMatrix.spherical(spec, R, k_i, k_e, 1, 1)
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# In[16]:
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print(np.diag(cT[...]))
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|
||||
# In[18]:
|
||||
|
||||
|
||||
print(RV)
|
||||
print(RH)
|
||||
|
||||
|
||||
# In[ ]:
|
||||
|
||||
|
||||
|
||||
|
||||
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Reference in New Issue