La guia recta – Jesus Manzanares Martinez

# From the Meep tutorial: plotting permittivity and fields of a straight waveguide
import meep as mp

cell = mp.Vector3(16, 8, 0)

geometry = [
    mp.Block(
        mp.Vector3(mp.inf, 1, mp.inf),
        center=mp.Vector3(),
        material=mp.Medium(epsilon=12),
    )
]

sources = [
    mp.Source(
        mp.ContinuousSource(frequency=0.15), component=mp.Ez, center=mp.Vector3(-7, 0)
    )
]

pml_layers = [mp.PML(1.0)]

resolution = 10

sim = mp.Simulation(
    cell_size=cell,
    boundary_layers=pml_layers,
    geometry=geometry,
    sources=sources,
    resolution=resolution,
)

sim.run(until=200)

Ahi el programa corre, para visualizar tenemos

import matplotlib.pyplot as plt
import numpy as np

eps_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Dielectric)
plt.figure()
plt.imshow(eps_data.transpose(), interpolation="spline36", cmap="binary")
plt.axis("off")
plt.show()

ez_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Ez)
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()

Es muy interesante darse cuenta de que ya tenemos los datos de la funcion dielectrica en python y los podemos visualizar haciendo

plt.imshow(eps_data)

plt.imshow(ez_data)

plt.plot(ez_data[:,40])

Vamos a entender la relacion de dispersion

Este paper esta enhttps://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://journals.riverpublishers.com/index.php/ACES/article/download/10289/8605/32011&ved=2ahUKEwjx0ZuEy8WLAxWjEEQIHdd_HiIQFnoECBIQAQ&usg=AOvVaw2g6KH89R-yyESrphePaN3H

Esta es una guia de $n_h=2$ en aire ( $n_l=1$ ).

import meep as mp
cell = mp.Vector3(16, 8, 0)
geometry = [mp.Block(mp.Vector3(mp.inf, 1, mp.inf),center=mp.Vector3(),material=mp.Medium(epsilon=4),)]
sources = [mp.Source(mp.ContinuousSource(frequency=0.2), component=mp.Ez, center=mp.Vector3(-7, 0))]
pml_layers = [mp.PML(1.0)]
resolution = 10
sim = mp.Simulation(cell_size=cell,boundary_layers=pml_layers,geometry=geometry,sources=sources,resolution=resolution,)
sim.run(until=200)

import matplotlib.pyplot as plt
import numpy as np

eps_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Dielectric)
plt.figure()
plt.imshow(eps_data.transpose(), interpolation="spline36", cmap="binary")
plt.axis("off")
plt.show()

ez_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Ez)
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()

plt.plot(ez_data[:,40])

Para el modo en $|Omega=0.2$ tenemos que $Q_y=0.32$ , considerando que

$Q_y=\frac{k_yd}{2\pi}$

$Q_y=\frac{d}{\lambda_m}$

$\lambda_m = \frac{Q_y}{d}$

Para el caso de $Q_y=0.32$ tenemos $\lambda_m=(1/0.32)d=3.125 d$

Para poder medir la distancia entre valle y valle (o cresta y cresta), hacemos

f = open("python.dat","w")
for i in range(ez_data.shape[0]):
 print(i,ez_data[i,40])
 f.write(str(i/10.0)+" "+str(ez_data[i,40])+"\n")
f.close()

El siguiente codigo se llama lee.py y se corre en el sistema operativo para que se genere una grafica en donde con el mouse, se pueda medir las distancias

import numpy  as np
import matplotlib.pyplot as plt
data = np.loadtxt('python.dat')
x = data[:, 0]
y = data[:, 1]
plt.plot(x, y,'r--')
plt.show()

Cuando $\Omega=0.4$ , tenemos $Q_y=0.72$ , nos sale $\lambda = 1.38$ la longitud de onda, que e slo que vemos

Podemos generar el segundo modo

# From the Meep tutorial: plotting permittivity and fields of a straight waveguide
import meep as mp
cell = mp.Vector3(16, 8, 0)
geometry = [mp.Block(mp.Vector3(mp.inf, 1, mp.inf),center=mp.Vector3(),material=mp.Medium(epsilon=4),)]
sources = [mp.Source(mp.ContinuousSource(frequency=0.4), component=mp.Ez, center=mp.Vector3(-7,  0.4),amplitude=+1.0),
           mp.Source(mp.ContinuousSource(frequency=0.4), component=mp.Ez, center=mp.Vector3(-7, -0.4),amplitude=-1.0)]
pml_layers = [mp.PML(1.0)]
resolution = 10
sim = mp.Simulation(cell_size=cell,boundary_layers=pml_layers,geometry=geometry,sources=sources,resolution=resolution,)
sim.run(until=200)

import matplotlib.pyplot as plt
import numpy as np

eps_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Dielectric)
plt.figure()
plt.imshow(eps_data.transpose(), interpolation="spline36", cmap="binary")
plt.axis("off")
plt.show()

ez_data = sim.get_array(center=mp.Vector3(), size=cell, component=mp.Ez)
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()

Podemos checar que la maxima amplitud NO esta en el centro