def MakeFigure(width):
with style.latex(width, scipy.constants.golden * 2 / 3):
style.pretty()
plot()
with open(filename) as f:
lines = f.readlines()
line_x, line_y = lines
xss = line_x.split()
yss = line_y.split()
xs = map(float, xss)
ys = map(float, yss)
x = np.array(xs)
y = np.array(ys)
order = x.argsort()
x = x[order]
y = y[order]
return lo, x, y
with my_style.latex(my_style.WIDTH_ARTICLE_KOSMA / 2):
my_style.pretty(1)
ax_profile = plt.subplot(1, 1, 1)
los = []
# maxes = []
# noises = []
color_id = 0
# Zoom on the top of the plot.
ax_peak = zoomed_inset_axes(ax_profile, 4, loc=2)
ax_base = zoomed_inset_axes(ax_profile, 4, loc=4)
for filename in filenames:
lo, x, y = load(filename)
to_keep = x < 1042
x = x[to_keep]
y = y[to_keep]
if len(x) <= 1:
def MakeFigure(width):
with style.latex(width):
style.pretty()
plot()
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()