misc/rectlat_simple_modes.py

   1 #!/usr/bin/env python3
   2
   3 import math
   4 from qpms.argproc import ArgParser
   5
   6 ap = ArgParser(['rectlattice2d', 'const_real_background', 'single_particle', 'single_lMax']) # const_real_background needed for calculation of the diffracted orders
   7 ap.add_argument("-k", nargs=2, type=float, required=True, help='k vector', metavar=('K_X', 'K_Y'))
   8 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)")
   9 ap.add_argument("--rank-tol", type=float, required=False)
  10 ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
  11 ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
  12 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')
  13 ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
  14 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.")
  15 ap.add_argument("-f", "--interval-factor", type=float, default=0.1)
  16 ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
  17 ap.add_argument("-i", "--imaginary-aspect-ratio",  type=float, default=1, help="Aspect ratio of the integration contour (Im/Re)")
  18 ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
  19 ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
  20
  21 a=ap.parse_args()
  22
  23 px, py = a.period
  24
  25 if a.kpi:
  26     a.k[0] *= math.pi/px
  27     a.k[1] *= math.pi/py
  28
  29 particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
  30 if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
  31 defaultprefix = "%s_p%gnmx%gnm_m%s_n%g_b%+d_k(%g_%g)um-1_L%d_cn%d" % (
  32     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)
  33
  34 import logging
  35 logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
  36
  37 import numpy as np
  38 import qpms
  39 from qpms.cybspec import BaseSpec
  40 from qpms.cytmatrices import CTMatrix
  41 from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
  42 from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
  43 from qpms.constants import eV, hbar
  44 eh = eV/hbar
  45
  46 def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
  47     x = point_xy[0] - centre_xy[0]
  48     y = point_xy[1] - centre_xy[1]
  49     ax = halfaxes_xy[0]
  50     ay = halfaxes_xy[1]
  51     return ((x/ax)**2 + (y/ay)**2) <= 1
  52
  53 a1 = ap.direct_basis[0]
  54 a2 = ap.direct_basis[1]
  55
  56 #Particle positions
  57 orig_x = [0]
  58 orig_y = [0]
  59 orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)
  60
  61 if a.material in lorentz_drude:
  62         emg = EpsMuGenerator(lorentz_drude[a.material])
  63 else: # constant refractive index
  64         emg = EpsMuGenerator(EpsMu(a.material**2))
  65
  66 beta = np.array(a.k)
  67
  68 empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
  69 empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])
  70
  71 # make the frequencies in the list unique
  72 empty_freqs = list(empty_freqs)
  73 i = 0
  74 while i < len(empty_freqs) - 1:
  75     if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
  76         del empty_freqs[i+1]
  77     else:
  78         i += 1
  79
  80 logging.info("Empty freqs: %s", str(empty_freqs))
  81 if a.band_index > 0:
  82     top = empty_freqs[a.band_index]
  83     bottom = empty_freqs[a.band_index - 1]
  84     lebeta_om = bottom
  85 else: # a.band_index < 0
  86     top = empty_freqs[abs(a.band_index) - 1]
  87     bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
  88     lebeta_om = top
  89 #print(top,bottom,lebeta_om)
  90 freqradius = .5 * (top - bottom) * a.interval_factor
  91
  92 centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius
  93
  94 bspec = BaseSpec(lMax = a.lMax)
  95 pp = Particle(orig_xy[0][0], t = ap.tmgen, bspec=bspec)
  96
  97 ss, ssw = ScatteringSystem.create([pp], ap.background_emg, centfreq, latticebasis = ap.direct_basis)
  98
  99 if freqradius == 0:
 100     raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")
 101
 102 freqradius *= (1-1e-13) # to not totally touch the singularities
 103
 104 with qpms.pgsl_ignore_error(15):
 105     res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
 106             blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
 107             res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)
 108
 109 logging.info("Eigenfrequencies found: %s" % str(res['eigval']))
 110
 111 res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
 112          (centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))
 113
 114 res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]
 115
 116 #del res['omega']  If contour points are not needed...
 117 #del res['ImTW'] # not if dbg=false anyway
 118 outfile = defaultprefix + ".npz" if a.output is None else a.output
 119 np.savez(outfile, meta=vars(a), empty_freqs=np.array(empty_freqs),
 120         ss_positions=ss.positions, ss_fullvec_poffsets=ss.fullvec_poffsets,
 121         ss_fullvec_psizes=ss.fullvec_psizes,
 122         ss_bspecs_flat = np.concatenate(ss.bspecs),
 123         ss_lattice_basis=ss.lattice_basis, ss_reciprocal_basis = ss.reciprocal_basis,
 124         **res)
 125 logging.info("Saved to %s" % outfile)
 126
 127
 128 if a.plot or (a.plot_out is not None):
 129     imcut = np.linspace(0, -freqradius)
 130     recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
 131     recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut
 132
 133     import matplotlib
 134     matplotlib.use('pdf')
 135     from matplotlib import pyplot as plt
 136
 137     fig = plt.figure()
 138     ax = fig.add_subplot(111,)
 139     #ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
 140     ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
 141         2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
 142         ls=':'))
 143     ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
 144                       )
 145     ax.plot(recut1/eh, imcut/eh*1e3)
 146     ax.plot(recut2/eh, imcut/eh*1e3)
 147     for i,om in enumerate(res['eigval']):
 148             ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
 149     xmin = np.amin(res['eigval'].real)/eh
 150     xmax = np.amax(res['eigval'].real)/eh
 151     xspan = xmax-xmin
 152     ymin = np.amin(res['eigval'].imag)/eh*1e3
 153     ymax = np.amax(res['eigval'].imag)/eh*1e3
 154     yspan = ymax-ymin
 155     ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
 156     ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
 157     ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
 158     ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
 159     plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
 160     fig.savefig(plotfile)
 161
 162 exit(0)
 163