def get_toymodel_data():
wg_kwargs = dict(N=2.6,
L=25.0,
W=1.0,
x_R0=0.16,
y_R0=2.5,
init_phase=-0.55,
switch_losses_on_off=True,
eta=1.0,
eta0=1.0,
loop_type='Bell')
D = DirichletPositionDependentLossReduced(**wg_kwargs)
_, b1, b2 = D.solve_ODE()
eps, delta = D.get_cycle_parameters()
v1, v2 = [D.eVecs_r[:, :, m] for m in (0, 1)]
return eps, delta, v1, v2
def plot_spectrum(fig=None, ax1=None, ax2=None, pos_dep=False,
eps_min=None, eps_max=None, eps_N=None, delta_N=None,
interpolate=False, p_space=False):
wg_kwargs = dict(N=2.05,
x_R0=0.1,
y_R0=0.85,
switch_losses_on_off=True,
loop_type='Bell')
if pos_dep:
wg_kwargs.update(dict(init_phase=0.0,
eta=1.0,
eta0=1.0))
D = DirichletPositionDependentLossReduced(**wg_kwargs)
delta_min, delta_max = -1.1, 1.1
else:
wg_kwargs.update(dict(init_phase=0.3,
eta=0.6))
D = DirichletReduced(**wg_kwargs)
delta_min, delta_max = -0.65, 1.25
eps, delta = D.get_cycle_parameters()
limits = (eps_min, eps_max, eps_N,
delta_min, delta_max, delta_N)
x, y, z = D.sample_H(*limits)
z_diff = z[..., 0] - z[..., 1]
Z0 = np.sqrt(z_diff.real**2 + (z_diff.imag)**2)
if pos_dep:
vmax_real = 2.0
vmax_imag = 8.0
else:
vmax_real = 2.0
vmax_imag = 1.0
Z1 = np.abs(z_diff.real)
Z2 = np.abs(z_diff.imag)
if p_space:
phi = lambda e, d: np.arctan2((d - D.init_phase)/D.y_R0, e/D.x_R0)
R = lambda e, d: np.hypot(e/D.x_R0, (d - D.init_phase)/D.y_R0)
get_p1 = lambda e, d: R(e, d)*np.sin(2*phi(e, d))
get_p2 = lambda e, d: R(e, d)*np.cos(2*phi(e, d))
pp1 = get_p1(x, y)
pp2 = get_p2(x, y)
x, y = pp2, pp1
p1 = ax1.pcolormesh(y, x, Z1, cmap=cmap,
vmin=0.0, vmax=vmax_real)
p2 = ax2.pcolormesh(y, x, Z2, cmap=cmap,
vmin=0.0, vmax=vmax_imag)
ax1.plot(get_p1(eps, delta), get_p2(eps, delta), "k-")
ax2.plot(get_p1(eps, delta), get_p2(eps, delta), "k-")
plt.show()
else:
p1 = ax1.imshow(Z1, cmap=cmap, aspect='auto', origin='lower',
extent=[y.min(), y.max(), x.min(), x.max()],
vmin=0.0, vmax=vmax_real)
p2 = ax2.imshow(Z2, cmap=cmap, aspect='auto', origin='lower',
extent=[y.min(), y.max(), x.min(), x.max()],
vmin=0.0, vmax=vmax_imag)
for (p, ax) in zip((p1, p2), (ax1, ax2)):
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.15)
if ax == ax1:
loc = MultipleLocator(vmax_real/2.)
else:
loc = MultipleLocator(vmax_imag/2.)
cb = plt.colorbar(p, cax=cax, ticks=loc, format="%.1f")
cb.ax.tick_params(labelsize=10)
cb.solids.set_edgecolor('face')
idx = np.argmin(Z0)
x_EP, y_EP = [u.ravel()[idx] for u in (x, y)]
print "x_EP", x_EP
print "y_EP", y_EP
dot_kwargs = dict(ms=6.0, mec='w', clip_on=False, zorder=10)
for ax in (ax1, ax2):
ax.plot(delta, eps, "w-", zorder=10)
ax.plot(delta[0], eps[0], "wo", **dot_kwargs)
ax.plot(delta[-1], eps[-1], "wo", **dot_kwargs)
ax.set_ylim(eps_min, eps_max)
ax.set_xlim(delta_min, delta_max)
if pos_dep:
ax.scatter(y_EP, x_EP, color="w")
ax.xaxis.set_major_locator(MultipleLocator(1.00))
# eps^1 scaling
# ax.annotate('EP', (-0.35, 0.005), textcoords='data',
# weight='bold', size=14, color='white')
# eps^2 scaling
ax.annotate('EP', (-0.325, 0.0175), textcoords='data',
weight='bold', size=14, color='white')
else:
ax.scatter(D.y_EP, D.x_EP, color="w")
ax.xaxis.set_major_locator(MultipleLocator(0.50))
ax.annotate('EP', (0.1, 0.04), textcoords='data',
weight='bold', size=14, color='white')
ax.get_xaxis().set_tick_params(direction='out')
ax.get_yaxis().set_tick_params(direction='out')
ax.yaxis.set_major_locator(MultipleLocator(0.05))
ax.yaxis.set_major_formatter(FormatStrFormatter("%.2f"))
ax.xaxis.set_major_formatter(FormatStrFormatter("%.1f"))
if pos_dep:
# eps^1 scaling
# datay = [y_EP, -0.278, -0.234, -0.188, -0.140, -0.072, -0.048, -0.024, -0.007, 0.000, 0.0]
# datax = [x_EP, 0.033, 0.034, 0.034, 0.033, 0.028, 0.025, 0.021, 0.015, 0.008, -0.1]
# eps^2 scaling
data = np.asarray([
[-0.242, 0.046],
[-0.175, 0.049],
[-0.121, 0.049],
[-0.070, 0.047],
[-0.035, 0.041],
[-0.016, 0.032],
[-0.010, 0.021],
[-0.003, 0.001],
[0.000, -0.009],
])
datay, datax = data.T
if interpolate:
tck, _ = splprep([datay, datax], s=0.0001, k=3)
datay, datax = splev(np.linspace(0, 1, 10), tck)
np.savetxt("interpolate_coordinates.dat", np.vstack([datay, datax]).T,
fmt="[%.3f,%.3f],", delimiter=",", header="[", footer="]",
comments='')
ax1.plot(datay, datax, "w--", ms=1, lw=0.5, dashes=[4, 3])
# eps^1 scaling
# datay = [y_EP, -0.352, -0.416, -0.506, -0.596, -0.650, -0.684, -0.736, -0.791, -0.827, -0.901, -0.972, -1.058, -1.145]
# datax = [x_EP, 0.030, 0.026, 0.018, 0.011, 0.007, 0.005, 0.002, 0.000, 0.000, 0.000, 0.003, 0.008, 0.015]
# eps^2 scaling
data = np.asarray([
[-0.240, 0.046],
[-0.390, 0.032],
[-0.513, 0.021],
[-0.603, 0.013],
[-0.675, 0.007],
[-0.766, 0.002],
[-0.853, -0.001],
[-0.954, 0.003],
[-1.024, 0.006],
[-1.096, 0.011],
]).T
datay, datax = data
ax2.plot(datay, datax, "w--", ms=1, lw=0.5, dashes=[4, 3])
else:
ax1.plot([0, D.y_EP], [-10, D.x_EP], "w--", lw=0.5, dashes=[4, 3])
ax2.plot([0, D.y_EP], [10, D.x_EP], "w--", lw=0.5, dashes=[4, 3])
ax1.set_ylabel(r'Amplitude $\sigma$')
fig.text(0.45, 0.0, r'Detuning $\delta$', va='center')
fig.text(-0.00, 0.92, 'a', weight='bold', size=14, color='black')
fig.text(-0.00, 0.45, 'b', weight='bold', size=14, color='black')
# for (ax, text) in zip((ax1, ax2), ('a', 'b')):
# ax.annotate(text, (-0.90, 0.08), textcoords='data',
# weight='bold', size=14, color='white')
return ax1, ax2