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():
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():
nb_points = 101
f_range = 1000e9
f_start = 0e9
f_stop = f_start + f_range
fs = np.linspace(f_start, f_stop, nb_points)
rAs = np.zeros(nb_points, dtype=complex)
tAs = np.zeros(nb_points, dtype=complex)
rBs = np.zeros(nb_points, dtype=complex)
tBs = np.zeros(nb_points, dtype=complex)
for i, f in enumerate(fs):
rAs[i], tAs[i] = setupA(f)
rBs[i], tBs[i] = setupB(f)
# P = EH and E=ZH => P = E**2 / Z.
yrAs = np.abs(rAs) ** 2 / Z3
ytAs = np.abs(tAs) ** 2 / Z3
yrBs = np.abs(rBs) ** 2 / Z3
ytBs = np.abs(tBs) ** 2 / Z3
xs = fs / 1.e9
plt.subplot(2, 1, 1)
plt.plot(xs, ytAs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film model"))
plt.plot(xs, ytBs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces model"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.annotate(style.latexT("Transmitted"), xy=(150, np.mean(ytAs)), verticalalignment='center', size='x-small')
plt.legend()
plt.subplot(2, 1, 2)
plt.plot(xs, yrAs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film model"))
plt.plot(xs, yrBs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces model"))
plt.xlabel(style.latexT("Frequency [\\si{\\giga\\hertz}]"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.annotate(style.latexT("Reflected"), xy=(150, np.mean(yrAs)), verticalalignment='center', size='x-small')
plt.legend(loc='lower right')
if USE_PDF:
plt.savefig("thin_film_normal_verification.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()
def plot():
nb_points = 11
f_range = 1000e9
f_start = 0e9
f_stop = f_start + f_range
fs = np.linspace(f_start, f_stop, nb_points)
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)
rDhs = np.zeros(nb_points, dtype=complex)
rDvs = np.zeros(nb_points, dtype=complex)
tDhs = np.zeros(nb_points, dtype=complex)
tDvs = np.zeros(nb_points, dtype=complex)
for i, f in enumerate(fs):
# P = EH and E=ZH => P = E**2 / Z.
rah, rav, tah, tav = setupA(f)
rbh, rbv, tbh, tbv = setupB(f)
rAhs[i] = np.linalg.norm(rah) ** 2 / Z1
rAvs[i] = np.linalg.norm(rav) ** 2 / Z1
tAhs[i] = np.linalg.norm(tah) ** 2 / Z1
tAvs[i] = np.linalg.norm(tav) ** 2 / Z1
# rAhs[i] = np.abs(rah[0]) ** 2 / Z1
# rAvs[i] = np.abs(rav[2]) ** 2 / Z1
# tAhs[i] = np.abs(tah[0]) ** 2 / Z1
# tAvs[i] = np.abs(tav[1]) ** 2 / Z1
# rBhs[i] = np.linalg.norm(rbh) ** 2 / Z1
# rBvs[i] = np.linalg.norm(rbv) ** 2 / Z1
# tBhs[i] = np.linalg.norm(tbh) ** 2 / Z1
# tBvs[i] = np.linalg.norm(tbv) ** 2 / Z1
rBhs[i] = np.abs(rbh[0]) ** 2 / Z1
rBvs[i] = np.abs(rbv[2]) ** 2 / Z1
tBhs[i] = np.abs(tbh[0]) ** 2 / Z1
tBvs[i] = np.abs(tbv[1]) ** 2 / Z1
rDhs[i] = np.abs(rbh[0] - rah[0])
rDvs[i] = np.abs(rbv[2] - rav[2])
tDhs[i] = np.abs(tbh[0] - tah[0])
tDvs[i] = np.abs(tbv[0] - tav[0])
xs = fs / 1.e9
plt.subplot(3, 2, 1)
plt.plot(xs, tAhs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film transmission"))
plt.plot(xs, tBhs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces transmission"))
# plt.plot(xs, tDhs)
plt.title(style.latexT("Perpendicular"), fontsize=10)
plt.ylabel(style.latexT("Power coupling [1]"))
plt.ylim((.9, 1.1))
plt.legend(loc='upper left', prop={"size":6})
plt.subplot(3, 2, 2)
plt.plot(xs, tAvs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film transmission"))
plt.plot(xs, tBvs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces transmission"))
plt.plot(xs, tDvs)
plt.title(style.latexT("Parallel"), fontsize=10)
plt.ylim((.99, 1.01))
plt.legend(loc='upper right', prop={"size":6})
plt.subplot(3, 2, 3)
plt.plot(xs, rAhs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film reflection"))
plt.plot(xs, rBhs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces reflection"))
# plt.plot(xs, rDhs)
plt.ylabel(style.latexT("Power coupling [1]"))
plt.ylim((-.1, .1))
plt.legend(loc='lower left', prop={"size":6})
plt.subplot(3, 2, 4)
plt.plot(xs, rAvs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film reflection"))
plt.plot(xs, rBvs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces reflection"))
# plt.plot(xs, rDvs)
plt.ylim((-.01, .01))
plt.legend(loc='lower right', prop={"size":6})
plt.subplot(3, 2, 5)
plt.plot(xs, rAhs + tAhs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film sum"))
plt.plot(xs, rBhs + tBhs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces sum"))
plt.ylim((.99, 1.01))
plt.xlabel(style.latexT("Frequency [\\si{\\giga\\hertz}]"))
plt.ylabel(style.latexT("Power coupling [1]"))
plt.legend(loc='lower left', prop={"size":6})
plt.subplot(3, 2, 6)
plt.plot(xs, rAvs + tAvs, '-', color=style.COLORS_STD[1], label=style.latexT("Thin film sum"))
plt.plot(xs, rBvs + tBvs, '--', color=style.COLORS_STD[2], label=style.latexT("Interfaces sum"))
plt.ylim((.99, 1.01))
plt.xlabel(style.latexT("Frequency [\\si{\\giga\\hertz}]"))
plt.legend(loc='lower right', prop={"size":6})
if USE_PDF:
plt.savefig("thin_film_oblique_verification.pdf", bbox_inches='tight')
else:
plt.show()
# noises.append(np.std(y[continuum_idx]))
ax_profile.plot(x, no_baseline)
ax_peak.plot(x, no_baseline)
ax_base.plot(x, no_baseline)
xmin = 1037.00
xmax = 1037.25
ticks_nb = 6
ticks_pos = np.linspace(xmin, xmax, ticks_nb)
ticks_lbl = ['%07.2f' % tick_pos for tick_pos in ticks_pos]
ticks_lbl = map(my_style.latexM, ticks_lbl)
ax_profile.set_autoscalex_on(False)
ax_profile.set_autoscaley_on(False)
ax_profile.set_xlim(xmin, xmax)
ax_profile.set_xticks(ticks_pos, ticks_lbl)
ax_profile.set_xticklabels(ticks_lbl)
ax_profile.set_xlabel(my_style.latexT("USB Frequency [GHz]"))
ax_profile.set_ylabel(my_style.latexT("Flux [K]"))
x1, x2, y1, y2 = 1037.105, 1037.120, 17.5, 19.5
ax_peak.set_xlim(x1, x2)
ax_peak.set_ylim(y1, y2)
ax_peak.set_xticks([])
ax_peak.set_yticks([])
mark_inset(ax_profile, ax_peak, loc1=2, loc2=4, fc="none", ec="0.5")
x1, x2, y1, y2 = 1037.005, 1037.020, -1.0, 1.0
ax_base.set_xlim(x1, x2)
ax_base.set_ylim(y1, y2)
ax_base.set_xticks([])
ax_base.set_yticks([])
mark_inset(ax_profile, ax_base, loc1=2, loc2=3, fc="none", ec="0.5")
# ax_profile.title(my_style.latexT("Line profile"))
def plot(width, frequencies, b_lo, b_sky):
# Plot unfolded.
lsb = frequencies < lo_freq
usb = frequencies > lo_freq
xs = frequencies / 1e9
def power(field):
return np.abs(field) ** 2 / Z0 / 2
lo_h_f = b_lo[:, 10 * 3 + 0]
lo_v_f = b_lo[:, 10 * 3 + 2]
sky_h_f = b_sky[:, 10 * 3 + 0]
sky_v_f = b_sky[:, 10 * 3 + 2]
lo_h = power(lo_h_f)
lo_v = power(lo_v_f)
sky_h = power(sky_h_f)
sky_v = power(sky_v_f)
with style.latex(width, scipy.constants.golden):
style.pretty()
plt.figure(0)
plt.axvspan(np.max(xs[lsb]),
np.min(xs[usb]),
facecolor='#aaaaaa',
alpha=0.5)
plt.plot(xs[lsb], lo_h[lsb], '-', label=style.latexT("LO H"), color=style.COLORS_STD[1])
plt.plot(xs[lsb], lo_v[lsb], '--', label=style.latexT("LO V"), color=style.COLORS_STD[1])
plt.plot(xs[lsb], sky_h[lsb], '-', label=style.latexT("Sky H"), color=style.COLORS_STD[2])
plt.plot(xs[lsb], sky_v[lsb], '--', label=style.latexT("Sky V"), color=style.COLORS_STD[2])
plt.plot(xs[usb], lo_h[usb], '-', color=style.COLORS_STD[1])
plt.plot(xs[usb], lo_v[usb], '--', color=style.COLORS_STD[1])
plt.plot(xs[usb], sky_h[usb], '-', color=style.COLORS_STD[2])
plt.plot(xs[usb], sky_v[usb], '--', color=style.COLORS_STD[2])
plt.annotate(style.latexT("LSB"),
xy=(np.mean(xs[lsb]), 2),
horizontalalignment='center', verticalalignment='center')
plt.annotate(style.latexT("USB"),
xy=(np.mean(xs[usb]), 2),
horizontalalignment='center', verticalalignment='center')
plt.legend(loc='center', prop={"size":6})
plt.xlabel(style.latexT("Frequency [\\si{\giga\hertz}]"))
plt.ylabel(style.latexT("Flux density [\\si{\watt\per\meter\squared}]"))
if USE_PDF:
plt.savefig("thin_film_beam_splitter_detailed.pdf", bbox_inches='tight')
else:
plt.show()
# Compute folded.
x_folded = xs[usb] - lo_freq / 1.e9
y_folded_h = lo_h[lsb] + sky_h[lsb] + lo_h[usb] + sky_h[usb]
y_folded_v = lo_v[lsb] + sky_v[lsb] + lo_v[usb] + sky_v[usb]
# Plot folded.
# With my previous model, I used to see a beat. The folded signal was not
# at the same period as the original signal. I was saying that this was
# because there were actually two lo-mixer cavities: one using the near
# side, and one using the far side of the beam splitter. Each cavity had
# its own period, and once I was folding it would somehow show drastically.
# This was, I believe, an error on my part. Indeed, I was adding the LSB
# and USB fields, then raising it to a power. I believe now that this is
# wrong: there is no reason for the LSB and USB fields to be phase-locked,
# therefore they do not add coherently. I must raise them to power before
# adding them. When doing that, there is no obvious beat. HOWEVER, when
# using pathological dimensions for the 'thin film' (like, 20 cm thick) and
# a broad enough frequency range, you can see this beat. So my model DOES
# take into account both sides of the thin film, it's just that it does not
# show much. It's almost too bad, it was a neat trick.
with style.latex(width, 1):
style.pretty()
plt.figure(1)
plt.subplot(2, 1, 1)
plt.plot(x_folded, y_folded_h, color=style.COLORS_STD[0], label=style.latexT("H"))
plt.ylim((8.7, 8.9))
plt.title(style.latexT("LO + sky, folded."), fontsize=10)
plt.ylabel(style.latexT("Flux density [\\si{\watt\per\meter\squared}]"))
plt.legend(prop={"size":6})
plt.subplot(2, 1, 2)
plt.plot(x_folded, y_folded_v, color=style.COLORS_STD[0], label=style.latexT("V"))
plt.ylim((2.6, 2.8))
plt.xlabel(style.latexT("Intermediate frequency [\\si{\giga\hertz}]"))
plt.ylabel(style.latexT("Flux density [\\si{\watt\per\meter\squared}]"))
plt.legend(prop={"size":6})
if USE_PDF:
plt.savefig("thin_film_beam_splitter_folded.pdf", bbox_inches='tight')
else:
plt.show()
# Compute FFT.
n = len(x_folded) # Number of samples.
h = np.hanning(n)
y_fft_h = np.abs(np.fft.rfft(y_folded_h * h))
y_fft_v = np.abs(np.fft.rfft(y_folded_v * h))
w = (np.max(x_folded) - np.min(x_folded)) * 1e9 # Width.
# n = len(xs[usb])
# h = np.hanning(n)
# y_fft_h = np.abs(np.fft.rfft(lo_h[usb])) # * h))
# y_fft_v = np.abs(np.fft.rfft(lo_v[usb])) # * h))
# w = (np.max(xs[usb]) - np.min(xs[usb])) * 1e9 # Width.
s = w / n # Sample spacing.
x_fft = np.fft.fftfreq(n, s)[:len(y_fft_h)] # Only positive frequencies.
x_fft = 1 / x_fft / 1e6 # x scale in SW period.
# Plot FFT.
# What would it take to see the 10 micrometer beam splitter?
# d_0 = 1.9999995 m
# d_1 = 1.0000005 m
# T_0 = c / 2d_0 Hz
# T_1 = c / 2d_1 Hz
# F_0 = 2d_0 / c Hz-1 # This is the frequency of the FFT, in Hz-1.
# F_1 = 2d_1 / c Hz-1
# \Delta F = F_1 - F_0 = 2(0.000001)/c Hz-1
# \Delta F = 1 / B # With B the bandwith.
# 1 / B = 0.000002 / c
# B = c / 0.000002 = 1.5e14 Hz
# Well, I will not be having such a bandwidth any time soon so the two peaks
# due to the two distances will not show.
# Our B equals 4 GHz.
# c / B = 0.075 m.
# 2d = 0.075 ; d = 0.0375
# With 4 GHz of bandwidth I should expect to resolve differences of 3.7 mm.
# So if I make the beam splitter 1 cm thick, I should be able to see it on the FFT
# as a second peak.
# Well, it does not work. Even if I use 10 cm. Even if I remove the Hanning window.
# The peak does move to the higher periods, but I do not see a second peak.
# Maybe it is much weaker? Use semilogy. Still not.
# Maybe I should try on the non-folded ? Still not.
# Maybe I am wrong to think that I should see two peaks?
# The thicker the film, the greater the period of the single peak. This
# means that the cavity seems shorter. Is that at least consistent with the
# fact that the speed of light is smaller in the film?
# The spacing between the resonant frequencies is proportional to c:
# f = N c / 2d, with N an integer.
# The period is c / 2d: distance between two resonant frequencies.
# So a slower light should reduce the period, not increase it. Indeed,
# reducing the speed is kinda like increasing the distance. Then why does my
# peak move to higher periods as the thickness of the film increase? Higher
# periods suggests that the distance is reduced.
# Well, there is one distance that is reduced when the thickness increases,
# that is the distance to the near side. Does it match? Standard is a 1 m
# cavity, creating a period of 150 MHz. If I make it a 90 cm cavity I
# should get 166.6667 MHz.
# The film must have a thickness h which, when seen at 45 degrees, appear to
# be l=10 cm long. h and l are linked by a cosine and h is smaller than l,
# so I say h = l cos 45, h = 1/sqrt(2) / 10.
# Once the model ran, I get a peak at 166.6. The resolution is not high, but
# it is high enough to tell me I hit at the right first decimal.
# So what we mostly see is a reflection on the near side. What about the
# far side? How come it has so little effect? Especially because the film
# is mostly transparent, so there should be quite a bit of power hitting the
# far side. Then a bit of that power comes to the near side and is transmitted.
# Because the transmissions are close to 1, I'd expect that the power in the near
# and the far contributions to be very close.
# SOLVED IT ! My problem was that my film had an absorption coefficient.
# That small imaginary component to n2 does not matter much for a 10 micrometer
# film, but it totally killed all transmission in a 10 cm film. As a result, all
# I was seeing was the near side, and 10^-14 of the far side. If I want to see all
# the cavities, I must make n2 a real number. Then I see many peaks, not just 2,
# because each double reflection brings its own cavity length.
with style.latex(width, 1):
style.pretty()
plt.figure(2)
plt.subplot(2, 1, 1)
plt.semilogy(x_fft[10:], y_fft_h[10:], color=style.COLORS_STD[0], label=style.latexT("H"))
plt.title(style.latexT("LO + sky, folded."), fontsize=10)
plt.ylabel(style.latexT("FFT of flux density [arbitrary]"))
# plt.xlim((50, 250))
plt.legend(prop={"size":6})
plt.subplot(2, 1, 2)
plt.semilogy(x_fft[10:], y_fft_v[10:], color=style.COLORS_STD[0], label=style.latexT("V"))
plt.xlabel(style.latexT("Period [\\si{\mega\hertz}]"))
plt.ylabel(style.latexT("FFT of flux density [arbitrary]"))
# plt.xlim((50, 250))
plt.legend(prop={"size":6})
if USE_PDF:
plt.savefig("thin_film_beam_splitter_folded_fft.pdf", bbox_inches='tight')
else:
plt.show()
# Sideband ratio.
sbr_lo_h = lo_h[usb] / (lo_h[usb] + lo_h[lsb])
sbr_lo_v = lo_v[usb] / (lo_v[usb] + lo_v[lsb])
sbr_sky_h = sky_h[usb] / (sky_h[usb] + sky_h[lsb])
sbr_sky_v = sky_v[usb] / (sky_v[usb] + sky_v[lsb])
print "Sky H sbr stddev: %f." % np.std(sbr_sky_h)
print "Sky V sbr stddev: %f." % np.std(sbr_sky_v)
with style.latex(width):
style.pretty()
plt.figure(3)
plt.plot(x_folded, sbr_lo_h, '-', label=style.latexT("LO H"), color=style.COLORS_STD[1])
plt.plot(x_folded, sbr_lo_v, '--', label=style.latexT("LO V"), color=style.COLORS_STD[1])
plt.plot(x_folded, sbr_sky_h, '-', label=style.latexT("Sky H"), color=style.COLORS_STD[2])
plt.plot(x_folded, sbr_sky_v, '--', label=style.latexT("Sky V"), color=style.COLORS_STD[2])
plt.xlabel(style.latexT("Intermediate frequency [\\si{\giga\hertz}]"))
plt.ylabel(style.latexT("USB / (LSB + USB) [1]"))
plt.legend(loc="center right", prop={"size":6})
if USE_PDF:
plt.savefig("thin_film_beam_splitter_sbr.pdf", bbox_inches='tight')
else:
plt.show()
