def plot():
nb_points = 4001
f_range = 64e9
f_start = 500e9
f_stop = f_start + f_range
fs = np.linspace(f_start, f_stop, nb_points)
observable = fs <= 504e9
b0s = np.zeros(nb_points, dtype=complex)
b5s = np.zeros(nb_points, dtype=complex)
for i, f in enumerate(fs):
b0s[i], b5s[i] = setup(f)
y0s = np.abs(b0s) ** 2
y5s = np.abs(b5s) ** 2
# Direct.
plt.plot(fs[observable] / 1.e9, y0s[observable], color=style.COLORS_STD[1])
plt.plot(fs[observable] / 1.e9, y5s[observable], color=style.COLORS_STD[2])
plt.xlabel(style.latexT("Frequency [\\si{\\giga\\hertz}]"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.ylim((-.1, 1.1))
if USE_PDF:
plt.savefig("simple_cavity_direct.pdf", bbox_inches='tight')
else:
plt.show()
# FFT.
L = .5
prediction = scipy.constants.speed_of_light / (2 * L) / 1.e6
h = np.hanning(nb_points)
y0s = np.abs(np.fft.rfft(y0s * h))
y5s = np.abs(np.fft.rfft(y5s * h))
cutat = len(y0s)
p = np.fft.fftfreq(nb_points, f_range / (nb_points))[:cutat] # In Hz-1.
p = 1 / p # In Hz.
p /= 1.e6 # In MHz.
# p = p[3:]
# y0s = y0s[3:]
# y5s = y5s[3:]
plt.clf()
# plt.axvline(prediction / 2, linestyle='-', color='#878686', linewidth=1)
# plt.axvline(prediction, linestyle='-', color='#878686', linewidth=1)
plt.plot(p, y0s, '-', color=style.COLORS_STD[1])
plt.plot(p, y5s, '--', color=style.COLORS_STD[2])
plt.xlabel(style.latexT("Period [\\si{\\mega\\hertz}]"))
plt.ylabel(style.latexT("FFT power coupling [arbitrary]"))
plt.annotate(style.latexM("c/2d"),
xy=(prediction, 0),
xytext=(prediction, -5),
horizontalalignment='center',
verticalalignment='center')
plt.annotate(style.latexM("c/4d"),
xy=(prediction / 2, 0),
xytext=(prediction / 2, -5),
horizontalalignment='center',
verticalalignment='center')
plt.xlim((0, 500))
plt.ylim((-10, 70))
if USE_PDF:
plt.savefig("simple_cavity_fft.pdf", bbox_inches='tight')
else:
plt.show()
def plot():
plt.clf()
f = 500e9
omega = 2 * np.pi * f
n = 1
c = scipy.constants.speed_of_light / n
lambda_ = c / f
k = 2 * np.pi / lambda_
phi = 0
x = np.linspace(0, 1e-3, 1000)
ts = np.linspace(0, 1 / f / 2, 5)
legends = []
for i, t in enumerate(ts):
y = np.cos(omega * t - k * x + phi)
j = len(ts) - 1 - i
col = j / (j + 1)
plt.plot(x * 1000, y, color=(col, col, col))
plt.ylim([-1.1, 1.1])
plt.xlabel(style.latexT("Position $z$ [\\si{\\milli\\meter}]"))
plt.ylabel(style.latexT("Amplitude $e(z, t)$ [\\si{\\volt\\per\\meter}]"))
legend = style.latexM("t=\\SI{%04.2f}{\\pico\\second}" % (t * 1e12))
legends.append(legend)
plt.legend(legends, loc="lower right")
if USE_PDF:
plt.savefig("plane_wave_propagation.pdf", bbox_inches='tight')
else:
plt.show()
def plot():
fs_normal = np.linspace(1, 90, 90)
fs_critical = np.linspace(41.8103, 41.8104, 10) # High resolution around critical angle.
fs = np.concatenate((fs_normal, fs_critical))
fs.sort()
fs = np.radians(fs)
nb_points = len(fs)
rAhs = np.zeros(nb_points, dtype=complex)
rAvs = np.zeros(nb_points, dtype=complex)
tAhs = np.zeros(nb_points, dtype=complex)
tAvs = np.zeros(nb_points, dtype=complex)
rBhs = np.zeros(nb_points, dtype=complex)
rBvs = np.zeros(nb_points, dtype=complex)
tBhs = np.zeros(nb_points, dtype=complex)
tBvs = np.zeros(nb_points, dtype=complex)
n1 = 1
n2 = 1.5
Z1 = Z0 / n1 # True for dielectrics only.
Z2 = Z0 / n2 # True for dielectrics only.
for i, f in enumerate(fs):
rh, rv, th, tv = setup(n1, n2, f)
# P = EH and E=ZH => P = E**2 / Z.
rAhs[i] = np.linalg.norm(rh) ** 2 / Z1
rAvs[i] = np.linalg.norm(rv) ** 2 / Z1
tAhs[i] = np.linalg.norm(th) ** 2 / Z2
tAvs[i] = np.linalg.norm(tv) ** 2 / Z2
#
rh, rv, th, tv = setup(n2, n1, f)
rBhs[i] = np.linalg.norm(rh) ** 2 / Z2
rBvs[i] = np.linalg.norm(rv) ** 2 / Z2
tBhs[i] = np.linalg.norm(th) ** 2 / Z1
tBvs[i] = np.linalg.norm(tv) ** 2 / Z1
crit_b = np.degrees(np.arcsin(n1.real / n2.real))
brew_a = np.degrees(np.arctan(n2.real / n1.real))
brew_b = np.degrees(np.arctan(n1.real / n2.real))
xs = np.degrees(fs)
plt.subplot(3, 2, 1)
plt.axvline(brew_a, linestyle=':', color=style.COLORS_STD[0], label=style.latexT("Brewster"))
plt.plot(xs, tAhs, '-', color=style.COLORS_STD[1], label=style.latexM("T_\perp"))
plt.plot(xs, tAvs, '-', color=style.COLORS_STD[2], label=style.latexM("T_\parallel"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.title(style.latexM("n_i=1.0, n_t=1.5"), fontsize=10)
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='center left', prop={"size":6})
plt.subplot(3, 2, 2)
plt.axvline(crit_b, linestyle='--', color=style.COLORS_STD[0], label=style.latexT("Critical"))
plt.axvline(brew_b, linestyle=':', color=style.COLORS_STD[0], label=style.latexT("Brewster"))
plt.plot(xs, tBhs, '-', color=style.COLORS_STD[1], label=style.latexM("T_\perp"))
plt.plot(xs, tBvs, '-', color=style.COLORS_STD[2], label=style.latexM("T_\parallel"))
plt.title(style.latexM("n_i=1.5, n_t=1.0"), fontsize=10)
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='upper right', prop={"size":6})
plt.subplot(3, 2, 3)
plt.axvline(brew_a, linestyle=':', color=style.COLORS_STD[0], label=style.latexT("Brewster"))
plt.plot(xs, rAhs, '-', color=style.COLORS_STD[1], label=style.latexM("R_\perp"))
plt.plot(xs, rAvs, '-', color=style.COLORS_STD[2], label=style.latexM("R_\parallel"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='upper left', prop={"size":6})
plt.subplot(3, 2, 4)
plt.axvline(crit_b, linestyle='--', color=style.COLORS_STD[0], label=style.latexT("Critical"))
plt.axvline(brew_b, linestyle=':', color=style.COLORS_STD[0], label=style.latexT("Brewster"))
plt.plot(xs, rBhs, '-', color=style.COLORS_STD[1], label=style.latexM("R_\perp"))
plt.plot(xs, rBvs, '-', color=style.COLORS_STD[2], label=style.latexM("R_\parallel"))
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='upper right', prop={"size":6})
plt.subplot(3, 2, 5)
plt.plot(xs, tAhs + rAhs, '-', color=style.COLORS_STD[1], label=style.latexT("Sum $\perp$"))
plt.plot(xs, tAvs + rAvs, '--', color=style.COLORS_STD[2], label=style.latexT("Sum $\parallel$"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.xlabel(style.latexT("Incidence angle [\\si{\\degree}]"))
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='center left', prop={"size":6})
plt.subplot(3, 2, 6)
plt.axvline(crit_b, linestyle='--', color=style.COLORS_STD[0], label=style.latexT("Critical"))
plt.plot(xs, tBhs + rBhs, '-', color=style.COLORS_STD[1], label=style.latexT("Sum $\perp$"))
plt.plot(xs, tBvs + rBvs, '--', color=style.COLORS_STD[2], label=style.latexT("Sum $\parallel$"))
plt.xlabel(style.latexT("Incidence angle [\\si{\\degree}]"))
plt.xlim((0, 90))
plt.ylim((-.1, 1.1))
plt.legend(loc='upper right', prop={"size":6})
if USE_PDF:
plt.savefig("interface_oblique_verification.pdf", bbox_inches='tight')
else:
plt.show()
