#!/usr/bin/env python
# coding: utf-8

# # Frequency Domain Solver

# This tutorial demonstrates Meep's frequency-domain solver which is used to compute the fields produced in response to a continuous-wave (CW) source. For a description of its inner workings, see Section 5.3 ("Frequency-domain solver") of Computer Physics Communications, Vol. 181, pp. 687-702, 2010. This example involves using the frequency-domain solver to compute the fields of a ring resonator which is described in Tutorial/Basics. First, we will verify that the error in the fields decreases monotonically with decreasing tolerance of the iterative solver. And then, we will demonstrate qualitative agreement with the frequency-domain fields computed using a different method: Fourier transforming the time-domain fields in response to a narrowband Gaussian-pulse source.
# 
# Usage of the frequency-domain solver involves only two changes to the original simulation: (1) replace the pulse source with a continuous source, and (2) turn on complex fields since real fields are used by default. Everything else remains unchanged.
# 
# Since the frequency-domain solver uses an iterative method, there are a couple of things we can do to improve its convergence properties: (1) use a non-zero smoothing width for the CW source (default is 0) to reduce the high-frequency oscillations produced by its abrupt turn on which have slow group velocities and are absorbed poorly by PML, and (2) increase the L parameter of the BiCGSTAB-L iterative solver from the default of 2 to 10.

# In[2]:


import meep as mp
import numpy as np
from numpy import linalg as LA
import matplotlib.pyplot as plt


# In[5]:


n = 3.4
w = 1
r = 1
pad = 4
dpml = 2

sxy = 2*(r+w+pad+dpml)
cell_size = mp.Vector3(sxy,sxy)

pml_layers = [mp.PML(dpml)]

nonpml_vol = mp.Volume(mp.Vector3(), size=mp.Vector3(sxy-2*dpml,sxy-2*dpml))

geometry = [mp.Cylinder(radius=r+w, material=mp.Medium(index=n)),
            mp.Cylinder(radius=r)]

fcen = 0.118

src = [mp.Source(mp.ContinuousSource(fcen),
                 component=mp.Ez,
                 center=mp.Vector3(r+0.1)),
       mp.Source(mp.ContinuousSource(fcen),
                 component=mp.Ez,
                 center=mp.Vector3(-(r+0.1)),
                 amplitude=-1)]

symmetries = [mp.Mirror(mp.X,phase=-1),
              mp.Mirror(mp.Y,phase=+1)]

sim = mp.Simulation(cell_size=cell_size,
                    geometry=geometry,
                    sources=src,
                    resolution=10,
                    force_complex_fields=True,
                    symmetries=symmetries,
                    boundary_layers=pml_layers)
f = plt.figure(dpi=120)
sim.plot2D(ax=f.gca())
plt.show()


# In[ ]:





# In[ ]:


num_tols = 5
tols = np.power(10, np.arange(-8.0,-8.0-num_tols,-1.0))
ez_dat = np.zeros((122,122,num_tols), dtype=np.complex_)

for i in range(num_tols):
    sim.init_sim()
    sim.solve_cw(tols[i], 10000, 10)
    ez_dat[:,:,i] = sim.get_array(vol=nonpml_vol, component=mp.Ez)


# In[ ]:





# In[2]:


err_dat = np.zeros(num_tols-1)
for i in range(num_tols-1):
    err_dat[i] = LA.norm(ez_dat[:,:,i]-ez_dat[:,:,num_tols-1])

plt.figure(dpi=150)
plt.loglog(tols[:num_tols-1], err_dat, 'bo-');
plt.xlabel("frequency-domain solver tolerance");
plt.ylabel("L2 norm of error in fields");
plt.show()


# In[3]:


eps_data = sim.get_array(vol=nonpml_vol, component=mp.Dielectric)
ez_data = np.real(ez_dat[:,:,num_tols-1])

plt.figure()
plt.imshow(eps_data.transpose(), interpolation='spline36', cmap='binary')
plt.imshow(ez_data.transpose(), interpolation='spline36', cmap='RdBu', alpha=0.9)
plt.axis('off')
plt.show()

if np.all(np.diff(err_dat) < 0):
    print("PASSED solve_cw test: error in the fields is decreasing with increasing resolution")
else:
    print("FAILED solve_cw test: error in the fields is NOT decreasing with increasing resolution")


# In[4]:


sim.reset_meep()

df = 0.08
src = [mp.Source(mp.GaussianSource(fcen,fwidth=df),
                 component=mp.Ez,
                 center=mp.Vector3(r+0.1)),
       mp.Source(mp.GaussianSource(fcen,fwidth=df),
                 component=mp.Ez,
                 center=mp.Vector3(-(r+0.1)),
                 amplitude=-1)]

sim = mp.Simulation(cell_size=mp.Vector3(sxy,sxy),
                    geometry=geometry,
                    sources=src,
                    resolution=10,
                    symmetries=symmetries,
                    boundary_layers=pml_layers)

dft_obj = sim.add_dft_fields([mp.Ez], fcen, 0, 1, where=nonpml_vol)

sim.run(until_after_sources=100)


# In[5]:


eps_data = sim.get_array(vol=nonpml_vol, component=mp.Dielectric)
ez_data = np.real(sim.get_dft_array(dft_obj, mp.Ez, 0))

plt.figure()
plt.imshow(eps_data.transpose(), interpolation='spline36', cmap='binary')
plt.imshow(ez_data.transpose(), interpolation='spline36', cmap='RdBu', alpha=0.9)
plt.axis('off')
plt.show()