qpms/misc/rectlat_simple_modes.py

#!/usr/bin/env python3

import math
from qpms.argproc import ArgParser

ap = ArgParser(['rectlattice2d', 'const_real_background', 'single_particle', 'single_lMax']) # const_real_background needed for calculation of the diffracted orders
ap.add_argument("-k", nargs=2, type=float, required=True, help='k vector', metavar=('K_X', 'K_Y'))
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)")
ap.add_argument("--rank-tol", type=float, required=False)
ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
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')
ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
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.")
ap.add_argument("-f", "--interval-factor", type=float, default=0.1)
ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
ap.add_argument("-i", "--imaginary-aspect-ratio",  type=float, default=1, help="Aspect ratio of the integration contour (Im/Re)")
ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")

a=ap.parse_args()

px, py = a.period

if a.kpi:
    a.k[0] *= math.pi/px
    a.k[1] *= math.pi/py

particlestr = ("sph" if a.height is None else "cyl") + ("_r%gnm" % (a.radius*1e9))
if a.height is not None: particlestr += "_h%gnm" % (a.height * 1e9)
defaultprefix = "%s_p%gnmx%gnm_m%s_n%g_b%+d_k(%g_%g)um-1_L%d_cn%d" % (
    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)

import logging
logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)

import numpy as np
import qpms
from qpms.cybspec import BaseSpec
from qpms.cytmatrices import CTMatrix
from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
from qpms.constants import eV, hbar
eh = eV/hbar

def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
    x = point_xy[0] - centre_xy[0]
    y = point_xy[1] - centre_xy[1]
    ax = halfaxes_xy[0]
    ay = halfaxes_xy[1]
    return ((x/ax)**2 + (y/ay)**2) <= 1

a1 = ap.direct_basis[0]
a2 = ap.direct_basis[1]

#Particle positions
orig_x = [0]                                 
orig_y = [0]            
orig_xy = np.stack(np.meshgrid(orig_x,orig_y),axis=-1)

if a.material in lorentz_drude:
	emg = EpsMuGenerator(lorentz_drude[a.material])
else: # constant refractive index
        emg = EpsMuGenerator(EpsMu(a.material**2))

beta = np.array(a.k)

empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])

# make the frequencies in the list unique
empty_freqs = list(empty_freqs)
i = 0
while i < len(empty_freqs) - 1:
    if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
        del empty_freqs[i+1]
    else:
        i += 1

logging.info("Empty freqs: %s", str(empty_freqs))
if a.band_index > 0:
    top = empty_freqs[a.band_index]
    bottom = empty_freqs[a.band_index - 1]
    lebeta_om = bottom
else: # a.band_index < 0
    top = empty_freqs[abs(a.band_index) - 1]
    bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
    lebeta_om = top
#print(top,bottom,lebeta_om)
freqradius = .5 * (top - bottom) * a.interval_factor

centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius

bspec = BaseSpec(lMax = a.lMax)
pp = Particle(orig_xy[0][0], t = ap.tmgen, bspec=bspec)

ss, ssw = ScatteringSystem.create([pp], ap.background_emg, centfreq, latticebasis = ap.direct_basis)

if freqradius == 0:
    raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")

freqradius *= (1-1e-13) # to not totally touch the singularities

with qpms.pgsl_ignore_error(15):
    res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
            blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
            res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)

logging.info("Eigenfrequencies found: %s" % str(res['eigval']))

res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
         (centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))

res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]

#del res['omega']  If contour points are not needed...
#del res['ImTW'] # not if dbg=false anyway
outfile = defaultprefix + ".npz" if a.output is None else a.output
np.savez(outfile, meta=vars(a), empty_freqs=np.array(empty_freqs), 
        ss_positions=ss.positions, ss_fullvec_poffsets=ss.fullvec_poffsets, 
        ss_fullvec_psizes=ss.fullvec_psizes,
        ss_bspecs_flat = np.concatenate(ss.bspecs),
        ss_lattice_basis=ss.lattice_basis, ss_reciprocal_basis = ss.reciprocal_basis,
        **res)
logging.info("Saved to %s" % outfile)


if a.plot or (a.plot_out is not None):
    imcut = np.linspace(0, -freqradius)
    recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
    recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut

    import matplotlib
    matplotlib.use('pdf')
    from matplotlib import pyplot as plt

    fig = plt.figure()
    ax = fig.add_subplot(111,)
    #ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
    ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
        2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
        ls=':'))
    ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
                      )
    ax.plot(recut1/eh, imcut/eh*1e3)
    ax.plot(recut2/eh, imcut/eh*1e3)
    for i,om in enumerate(res['eigval']):
            ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
    xmin = np.amin(res['eigval'].real)/eh
    xmax = np.amax(res['eigval'].real)/eh
    xspan = xmax-xmin
    ymin = np.amin(res['eigval'].imag)/eh*1e3
    ymax = np.amax(res['eigval'].imag)/eh*1e3
    yspan = ymax-ymin
    ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
    ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
    ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
    ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
    fig.savefig(plotfile)

exit(0)