xy-periodic lattice Beyn algorithm support in ScatteringSystem
Gives same results as newbeyn_unitcell 26d6e969, making it obsolete. Former-commit-id: b1b1b1e2c11f60948efda237388bfdf9b6d689f5
This commit is contained in:
Marek Nečada
parent
3791db2060
commit
5270430bfd
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@ -0,0 +1,158 @@
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#!/usr/bin/env python3
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import math
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from qpms.argproc import ArgParser
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ap = ArgParser(['rectlattice2d', 'single_particle', 'single_lMax'])
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ap.add_argument("-k", nargs=2, type=float, required=True, help='k vector', metavar=('K_X', 'K_Y'))
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ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
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ap.add_argument("--rank-tol", type=float, required=False)
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ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
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ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
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ap.add_argument("-c", "--min-candidates", type=int, default=1, help='always try at least this many eigenvalue candidates, even if their SVs in the rank tests are lower than rank_tolerance')
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ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
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ap.add_argument("-b", "--band-index", type=int, required=True, help="Argument's absolute value determines the empty lattice band order (counted from 1), -/+ determines whether the eigenvalues are searched below/above that empty lattice band.")
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ap.add_argument("-f", "--interval-factor", type=float, default=0.1)
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ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
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ap.add_argument("-i", "--imaginary-aspect-ratio", type=float, default=1, help="Aspect ratio of the integration contour (Im/Re)")
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ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
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ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
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a=ap.parse_args()
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px, py = a.period
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if a.kpi:
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a.k[0] *= math.pi/px
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a.k[1] *= math.pi/py
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particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
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if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
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defaultprefix = "%s_p%gnmx%gnm_m%s_n%g_b%+d_k(%g_%g)um-1_L%d_cn%d" % (
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particlestr, px*1e9, py*1e9, str(a.material), a.refractive_index, a.band_index, a.k[0]*1e-6, a.k[1]*1e-6, a.lMax, a.N)
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import logging
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logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
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import numpy as np
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import qpms
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from qpms.cybspec import BaseSpec
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from qpms.cytmatrices import CTMatrix
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from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
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from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
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from qpms.constants import eV, hbar
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eh = eV/hbar
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def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
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x = point_xy[0] - centre_xy[0]
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y = point_xy[1] - centre_xy[1]
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ax = halfaxes_xy[0]
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ay = halfaxes_xy[1]
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return ((x/ax)**2 + (y/ay)**2) <= 1
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a1 = ap.direct_basis[0]
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a2 = ap.direct_basis[1]
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#Particle positions
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orig_x = [0]
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orig_y = [0]
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orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)
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if a.material in lorentz_drude:
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emg = EpsMuGenerator(lorentz_drude[a.material])
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else: # constant refractive index
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emg = EpsMuGenerator(EpsMu(a.material**2))
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beta = np.array(a.k)
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empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
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empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])
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# make the frequencies in the list unique
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empty_freqs = list(empty_freqs)
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i = 0
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while i < len(empty_freqs) - 1:
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if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
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del empty_freqs[i+1]
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else:
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i += 1
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logging.info("Empty freqs: %s", str(empty_freqs))
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if a.band_index > 0:
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top = empty_freqs[a.band_index]
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bottom = empty_freqs[a.band_index - 1]
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lebeta_om = bottom
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else: # a.band_index < 0
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top = empty_freqs[abs(a.band_index) - 1]
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bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
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lebeta_om = top
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#print(top,bottom,lebeta_om)
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freqradius = .5 * (top - bottom) * a.interval_factor
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centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius
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bspec = BaseSpec(lMax = a.lMax)
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pp = Particle(orig_xy[0][0], t = ap.tmgen, bspec=bspec)
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ss, ssw = ScatteringSystem.create([pp], ap.background_emg, centfreq, latticebasis = ap.direct_basis)
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if freqradius == 0:
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raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")
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freqradius *= (1-1e-13) # to not totally touch the singularities
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with qpms.pgsl_ignore_error(15):
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res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
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blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
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res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)
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logging.info("Eigenfrequencies found: %s" % str(res['eigval']))
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res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
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(centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))
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res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]
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#del res['omega'] If contour points are not needed...
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#del res['ImTW'] # not if dbg=false anyway
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outfile = defaultprefix + ".npz" if a.output is None else a.output
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np.savez(outfile, meta=vars(a), empty_freqs=np.array(empty_freqs), **res)
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logging.info("Saved to %s" % outfile)
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if a.plot or (a.plot_out is not None):
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imcut = np.linspace(0, -freqradius)
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recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
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recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut
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import matplotlib
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matplotlib.use('pdf')
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from matplotlib import pyplot as plt
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fig = plt.figure()
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ax = fig.add_subplot(111,)
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#ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
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ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
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2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
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ls=':'))
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ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
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)
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ax.plot(recut1/eh, imcut/eh*1e3)
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ax.plot(recut2/eh, imcut/eh*1e3)
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for i,om in enumerate(res['eigval']):
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ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
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xmin = np.amin(res['eigval'].real)/eh
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xmax = np.amax(res['eigval'].real)/eh
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xspan = xmax-xmin
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ymin = np.amin(res['eigval'].imag)/eh*1e3
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ymax = np.amax(res['eigval'].imag)/eh*1e3
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yspan = ymax-ymin
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ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
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ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
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ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
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ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
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plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
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fig.savefig(plotfile)
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exit(0)
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@ -124,9 +124,9 @@ class ArgParser:
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if l != 2: raise ValueError('Two basis vectors must be specified (have %d)' % l)
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from .qpms_c import lll_reduce
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self.direct_basis = lll_reduce(self.args.basis_vector, delta=1.)
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# import numpy as np
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# self.reciprocal_basis1 = np.linalg.inv(self.direct_basis)
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# self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
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import numpy as np
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self.reciprocal_basis1 = np.linalg.inv(self.direct_basis)
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self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
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def _eval_rectlattice2d(self): # feature: rectlattice2d
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a = self.args
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@ -141,4 +141,6 @@ class ArgParser:
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import numpy as np
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a.basis_vectors = [(a.period[0], 0.), (0., a.period[1])]
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self.direct_basis = np.array(a.basis_vectors)
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self.reciprocal_basis1 = np.linalg.inv(self.direct_basis)
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self.reciprocal_basis2pi = 2 * np.pi * self.reciprocal_basis1
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@ -13,7 +13,7 @@ from .cybspec cimport BaseSpec
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from .cycommon cimport make_c_string
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from .cycommon import string_c2py, PointGroupClass
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from .cytmatrices cimport CTMatrix, TMatrixFunction, TMatrixGenerator, TMatrixInterpolator
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from .cymaterials cimport EpsMuGenerator
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from .cymaterials cimport EpsMuGenerator, EpsMu
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from libc.stdlib cimport malloc, free, calloc
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import warnings
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@ -647,16 +647,27 @@ cdef class ScatteringSystem:
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return target_np
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def find_modes(self, cdouble omega_centre, double omega_rr, double omega_ri, iri = None,
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blochvector = None,
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size_t contour_points = 20, double rank_tol = 1e-4, size_t rank_min_sel=1,
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double res_tol = 0):
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"""
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Attempts to find the eigenvalues and eigenvectors using Beyn's algorithm.
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"""
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cdef beyn_result_t *res = qpms_scatsys_finite_find_eigenmodes(self.s,
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self.iri_py2c(iri),
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cdef beyn_result_t *res
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cdef double blochvector_c[3]
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if self.lattice_dimension == 0:
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assert(blochvector is None)
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res = qpms_scatsys_finite_find_eigenmodes(self.s, self.iri_py2c(iri),
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omega_centre, omega_rr, omega_ri, contour_points,
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rank_tol, rank_min_sel, res_tol)
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else:
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if iri is not None: raise NotImplementedError("Irreps decomposition not yet supported for periodic systems")
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blochvector_c[0] = blochvector[0]
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blochvector_c[1] = blochvector[1]
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blochvector_c[2] = blochvector[2] if len(blochvector) > 2 else 0
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res = qpms_scatsys_periodic_find_eigenmodes(self.s, blochvector_c,
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omega_centre, omega_rr, omega_ri, contour_points, rank_tol, rank_min_sel, res_tol)
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if res == NULL: raise RuntimeError
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cdef size_t neig = res[0].neig, i, j
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@ -694,10 +705,40 @@ cdef class ScatteringSystem:
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'eigval_err':eigval_err,
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'ranktest_SV':ranktest_SV,
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'iri': iri,
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'blochvector': blochvector
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}
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return retdict
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def empty_lattice_modes_xy(EpsMu epsmu, reciprocal_basis, wavevector, double maxomega):
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'''Empty (2D, xy-plane) lattice mode (diffraction order) frequencies of a non-dispersive medium.
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reciprocal_basis is of the "mutliplied by 2п" type.
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'''
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cdef double *omegas_c
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cdef size_t n
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cdef cart2_t k_, b1, b2
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k_.x = wavevector[0]
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k_.y = wavevector[1]
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b1.x = reciprocal_basis[0][0]
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b1.y = reciprocal_basis[0][1]
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b2.x = reciprocal_basis[1][0]
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b2.y = reciprocal_basis[1][1]
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if(epsmu.n.imag != 0):
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warnings.warn("Got complex refractive index", epsmu.n, "ignoring the imaginary part")
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refindex = epsmu.n.real
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n = qpms_emptylattice2_modes_maxfreq(&omegas_c, b1, b2, BASIS_RTOL,
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k_, GSL_CONST_MKSA_SPEED_OF_LIGHT / refindex, maxomega)
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cdef np.ndarray[double, ndim=1] omegas = np.empty((n,), dtype=np.double)
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cdef double[::1] omegas_v = omegas
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cdef size_t i
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for i in range(n):
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omegas_v[i] = omegas_c[i]
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free(omegas_c)
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return omegas
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cdef class _ScatteringSystemAtOmegaK:
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'''
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Wrapper over the C qpms_scatsys_at_omega_k_t structure
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@ -10,6 +10,9 @@ cdef extern from "gsl/gsl_errno.h":
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gsl_error_handler_t *gsl_set_error_handler(gsl_error_handler_t *new_handler)
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gsl_error_handler_t *gsl_set_error_handler_off();
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cdef extern from "gsl/gsl_const_mksa.h":
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const double GSL_CONST_MKSA_SPEED_OF_LIGHT
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cdef extern from "qpms_types.h":
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cdef struct cart3_t:
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double x
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@ -2177,7 +2177,7 @@ beyn_result_t *qpms_scatsys_periodic_find_eigenmodes(
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complex double omega_centre, double omega_rr, double omega_ri,
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size_t contour_npoints,
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double rank_tol, size_t rank_sel_min, double res_tol) {
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qpms_ss_ensure_nonperiodic_a(ss, "qpms_scatsys_finite_find_eigenmodes()");
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qpms_ss_ensure_periodic_a(ss, "qpms_scatsys_finite_find_eigenmodes()");
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size_t n = ss->fecv_size; // matrix dimension
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beyn_contour_t *contour = beyn_contour_ellipse(omega_centre,
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