qpms/misc/infiniterectlat-scatter.py

#!/usr/bin/env python3

import math
pi = math.pi
from qpms.argproc import ArgParser

ap = ArgParser(['rectlattice2d', 'single_particle', 'single_lMax', 'omega_seq_real_ng', 'planewave'])
ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
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")
#ap.add_argument("-g", "--save-gradually", action='store_true', help="saves the partial result after computing each irrep")


a=ap.parse_args()

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

import numpy as np
import qpms
from qpms.qpms_p import cart2sph, sph2cart, sph_loccart2cart, sph_loccart_basis
import warnings
from qpms.cybspec import BaseSpec
from qpms.cytmatrices import CTMatrix, TMatrixGenerator
from qpms.qpms_c import Particle, pgsl_ignore_error
from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
from qpms.cycommon import DebugFlags, dbgmsg_enable
from qpms import FinitePointGroup, ScatteringSystem, BesselType, eV, hbar
eh = eV/hbar

dbgmsg_enable(DebugFlags.INTEGRATION)

px, py = a.period

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_bg%s_φ%g_θ(%g_%g)π_ψ%gπ_χ%gπ_f%s_L%d" % (
    particlestr, px*1e9, py*1e9, str(a.material), str(a.background), a.phi/pi, np.amin(a.theta)/pi, np.amax(a.theta)/pi, a.psi/pi, a.chi/pi, ap.omega_descr, a.lMax)
logging.info("Default file prefix: %s" % defaultprefix)


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)

bspec = BaseSpec(lMax = a.lMax)
# The parameters here should probably be changed (needs a better qpms_c.Particle implementation)
pp = Particle(orig_xy[0][0], ap.tmgen, bspec=bspec)
par = [pp]


ss, ssw = ScatteringSystem.create(par, ap.background_emg, ap.allomegas[0], latticebasis = ap.direct_basis)


## Plane wave data
a.theta = np.array(a.theta)
dir_sph_list = np.stack((np.broadcast_to(1, a.theta.shape), a.theta, np.broadcast_to(a.phi, a.theta.shape)), axis=-1)
sψ, cψ = math.sin(a.psi), math.cos(a.psi)
sχ, cχ = math.sin(a.chi), math.cos(a.chi)
E_sph = (0., cψ*cχ + 1j*sψ*sχ, sψ*cχ + 1j*cψ*sχ)

dir_cart_list = sph2cart(dir_sph_list)
E_cart_list = sph_loccart2cart(E_sph, dir_sph_list)

nfreq = len(ap.allomegas)
ndir = len(dir_sph_list)

k_cart_arr = np.empty((nfreq, ndir, 3), dtype=float)
wavenumbers = np.empty((nfreq,), dtype=float)

σ_ext_arr = np.empty((nfreq,ndir), dtype=float)
σ_scat_arr = np.empty((nfreq,ndir), dtype=float)

with pgsl_ignore_error(15): # avoid gsl crashing on underflow
    for i, omega in enumerate(ap.allomegas):
        if i != 0:
            ssw = ss(omega)
        if ssw.wavenumber.imag != 0:
            warnings.warn("The background medium wavenumber has non-zero imaginary part. Don't expect meaningful results for cross sections.")
        wavenumber = ssw.wavenumber.real
        wavenumbers[i] = wavenumber

        k_sph_list = np.array(dir_sph_list, copy=True)
        k_sph_list[:,0] = wavenumber

        k_cart_arr[i] = sph2cart(k_sph_list)


        for j in range(ndir):
            k_cart = k_cart_arr[i,j]
            blochvector = (k_cart[0], k_cart[1], 0)
            # the following two could be calculated only once, but probably not a big deal
            LU = ssw.scatter_solver(k=blochvector)
            ã = ss.planewave_full(k_cart=k_cart, E_cart=E_cart_list[j])
            Tã = ssw.apply_Tmatrices_full(ã)
            f = LU(Tã)

            σ_ext_arr[i,j] = -np.vdot(ã, f).real/wavenumber**2
            translation_matrix = ssw.translation_matrix_full(blochvector=blochvector) + np.eye(ss.fecv_size)
            σ_scat_arr[i,j] = np.vdot(f,np.dot(translation_matrix, f)).real/wavenumber**2

σ_abs_arr = σ_ext_arr - σ_scat_arr

outfile = defaultprefix + ".npz" if a.output is None else a.output
np.savez(outfile, meta=vars(a), dir_sph=dir_sph_list, k_cart = k_cart_arr, omega = ap.allomegas, E_cart = E_cart_list, wavenumbers= wavenumbers, σ_ext=σ_ext_arr,σ_abs=σ_abs_arr,σ_scat=σ_scat_arr, unitcell_area=ss.unitcell_volume
       )
logging.info("Saved to %s" % outfile)


if a.plot or (a.plot_out is not None):
    import matplotlib
    from matplotlib.backends.backend_pdf import PdfPages
    matplotlib.use('pdf')
    from matplotlib import pyplot as plt
    from scipy.interpolate import griddata

    plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
    with PdfPages(plotfile) as pdf:
        ipm = 'nearest'
        sintheta = np.sin(a.theta)
        if False: #len(ap.omega_ranges) != 0:
            # angle plot ---------------------------------
            fig = plt.figure(figsize=(210/25.4, 297/25.4))
            vmax = max(np.amax(σ_ext_arr), np.amax(σ_scat_arr), np.amax(σ_abs_arr))
            vmin = min(np.amin(σ_ext_arr), np.amin(σ_scat_arr), np.amin(σ_abs_arr))

            ax = fig.add_subplot(311)
            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_ext_arr, vmin=vmin, vmax=vmax)
            ax.set_xlabel('$\\theta$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{ext}$')

            ax = fig.add_subplot(312)
            ax.pcolormesh(a.theta, ap.allomegas/eh, σ_scat_arr, vmin=vmin, vmax=vmax)
            ax.set_xlabel('$\\theta$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{scat}$')

            ax = fig.add_subplot(313)
            im = ax.pcolormesh(a.theta, ap.allomegas/eh, σ_abs_arr, vmin=vmin, vmax=vmax)
            ax.set_xlabel('$\\theta$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{abs}$')
            
            
            fig.subplots_adjust(right=0.8)
            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))

            pdf.savefig(fig)
            plt.close(fig)

        if len(ap.omega_ranges) != 0:
            # "k-space" plot -----------------------------
            domega = np.amin(np.diff(ap.allomegas))
            dsintheta = np.amin(abs(np.diff(sintheta)))
            dk = dsintheta * wavenumbers[0]

            # target image grid
            grid_y, grid_x = np.mgrid[ap.allomegas[0] : ap.allomegas[-1] : domega, np.amin(sintheta) * wavenumbers[-1] : np.amax(sintheta) * wavenumbers[-1] : dk]
            imextent = (np.amin(sintheta) * wavenumbers[-1] / 1e6, np.amax(sintheta) * wavenumbers[-1] / 1e6, ap.allomegas[0] / eh, ap.allomegas[-1] / eh)
            
            # source coordinates for griddata
            ktheta = sintheta[None, :] * wavenumbers[:, None]
            omegapoints = np.broadcast_to(ap.allomegas[:, None], ktheta.shape)
            points = np.stack( (ktheta.flatten(), omegapoints.flatten()), axis = -1)

            fig = plt.figure(figsize=(210/25.4, 297/25.4))
            vmax = np.amax(σ_ext_arr)

            ax = fig.add_subplot(311)
            grid_z = griddata(points, σ_ext_arr.flatten(), (grid_x, grid_y), method = ipm)
            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{ext}$')

            ax = fig.add_subplot(312)
            grid_z = griddata(points, σ_scat_arr.flatten(), (grid_x, grid_y), method = ipm)
            ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{scat}$')

            ax = fig.add_subplot(313)
            grid_z = griddata(points, σ_abs_arr.flatten(), (grid_x, grid_y), method = ipm)
            im = ax.imshow(grid_z, extent = imextent, origin = 'lower', vmin = 0, vmax = vmax, aspect = 'auto', interpolation='none')
            ax.set_xlabel('$k_\\theta / \\mathrm{\\mu m^{-1}}$')
            ax.set_ylabel('$\\hbar\\omega / \\mathrm{eV}$')
            ax.set_title('$\\sigma_\\mathrm{abs}$')

            fig.subplots_adjust(right=0.8)
            fig.colorbar(im, cax = fig.add_axes([0.85, 0.15, 0.05, 0.7]))

            pdf.savefig(fig)
            plt.close(fig)

        for omega in ap.omega_singles:
            i = np.searchsorted(ap.allomegas, omega)

            fig = plt.figure()
            fig.suptitle("%g eV" % (omega / eh))
            ax = fig.add_subplot(111)
            sintheta = np.sin(a.theta)
            ax.plot(sintheta, σ_ext_arr[i]*1e12,label='$\sigma_\mathrm{ext}$')
            ax.plot(sintheta, σ_scat_arr[i]*1e12, label='$\sigma_\mathrm{scat}$')
            ax.plot(sintheta, σ_abs_arr[i]*1e12, label='$\sigma_\mathrm{abs}$')
            ax.legend()
            ax.set_xlabel('$\sin\\theta$')
            ax.set_ylabel('$\sigma/\mathrm{\mu m^2}$')
            
            pdf.savefig(fig)
            plt.close(fig)

exit(0)