def test_dipoleRadiation():
'''
Plots the Electric field in the x,y plane from both a z and y oriented dipole.
Right now, the y-dipole plots |E| -- ultimately this should be a vector plot to highlight
the loop pattern.
'''
wl = 2
#z-oriented dipole
P = np.array([0, 0, 1])
res = 100
x = np.linspace(-5, 5, res)
y = np.linspace(-5, 5, res)
z = 0
X, Y = np.meshgrid(x, y)
Z = X * 0
r = np.array([X, Y, Z])
r = np.swapaxes(r, 0, 2)
E = dipoleRadiation(wl, P, r)
Ez = E[:, :, 2]
vmax = 10 #np.amax(abs(Ez))
vmin = -vmax
plt.imshow(Ez.real,
extent=putil.getExtent(x, y),
cmap='RdBu',
vmax=vmax,
vmin=vmin)
plt.colorbar()
# y-oriented dipole
P = np.array([0, 1, 0])
E = dipoleRadiation(wl, P, r)
Etot = np.array([np.linalg.norm(i)
for i in E.reshape(res**2, 3)]).reshape(res, res)
plt.figure()
plt.imshow(Etot.T,
extent=putil.getExtent(x, y),
cmap='hot',
vmax=vmax,
vmin=0)
# plt.imshow(E[:,:,1].real.T,extent=putil.getExtent(x,y),cmap='RdBu',vmax=vmax,vmin=vmin)
plt.colorbar()
plt.show()
def test_dipoleRadiation():
'''
'''
wl = 2
P = 1
x = np.linspace(-5, 5, 100)
y = np.linspace(-5, 5, 100)
X, Y = np.meshgrid(y, x)
r = sqrt(X**2 + Y**2)
Fz = dipoleRadiation(wl, P, r)
vmax = 1
vmin = -vmax
plt.imshow(Fz.real,
extent=putil.getExtent(x, y),
cmap='RdBu',
vmax=vmax,
vmin=vmin)
plt.colorbar()
plt.show()
def test_addDipoles():
wl = 1
d1 = [-wl / 4., 0, 0]
d2 = [wl / 4., 0, 0]
ds = np.array([d1, d2])
p1 = [0, 0, 1]
p2 = [0, 0, 1]
ps = np.array([p1, p2])
res = 100
xs = np.linspace(-5, 5, res)
ys = np.linspace(-5, 5, res)
targets = np.array([[i, j, 0] for i in xs for j in ys])
E = [addDipoles(wl, ds, ps, t) for t in targets]
E = np.array(E)
Ez = E[:, 2].reshape(res, res)
vmax = 50
vmin = -vmax
plt.imshow(Ez.real.T,
extent=putil.getExtent(xs, ys),
cmap='RdBu',
vmax=vmax,
vmin=vmin)
plt.show()
def plotField(self, xmin, xmax, ymin, ymax, xres=100, yres=100):
xs = np.linspace(xmin, xmax, xres)
ys = np.linspace(ymin, ymax, yres)
X, Y = np.meshgrid(xs, ys)
Fz = np.zeros((len(xs), len(ys)), dtype=complex)
# loop over all dipoles and sum contribution to scattered field
for n in range(self.N):
print 'plotField: processing dipole %u of %u' % (n, self.N)
i = self.x[n]
j = self.y[n]
r = sqrt((X - i)**2 + (Y - j)**2)
Fz += dipoleRadiation(self.wl, self.P[n], r)
Fz_crop = Fz * (
(abs(X) > self.width) +
(abs(Y) > self.height) == 1) # field with resonator removed
vmax = np.amax(abs(Fz_crop)**2)
# vmax = None
plt.figure()
# plt.imshow(Fz.real,cmap='RdBu',vmax=vmax,vmin=-vmax)
plt.imshow(abs(Fz)**2,
extent=putil.getExtent(xs, ys),
cmap='hot',
vmax=vmax,
vmin=0)
# plt.imshow(Fz.real,extent=putil.getExtent(xs,ys),cmap='RdBu',vmax=vmax,vmin=-vmax)
plt.colorbar()
def test_PW():
'''
'''
angle = 25.
wl = 2.
x = np.linspace(-10, 10, 1000)
y = np.linspace(-10, 10, 1000)
X, Y = np.meshgrid(x, y)
pw = PW(X, Y, angle, wl)
plt.imshow(pw.real, extent=putil.getExtent(x, y), cmap='RdBu')
plt.colorbar()
plt.show()
def main():
'''
Simulation Parameters
'''
wl = 4
pol = 'Hz'
# Resonator Properties
AR = 1 # height / width
w = 2.2
h = .36
# h = w * AR
l = 100 * wl
# w *= 1.
# h *= 1.
# Mode indices
m = 4
n = 1
# Simulation Grid
fieldRes = 30
FFres = 200
FFR = 20 * wl
a = wl / 100. # dipole lattice spacing
'''
Get Dipole positions and polarizations
'''
x = np.arange(-w / 2., w / 2., a)
y = np.arange(-h / 2., h / 2., a)
# z = np.arange(-l/2.,l/2.,a)
z = np.array([0])
# center array to ensure symmetry
shift = lambda x: (x % a) / 2.
x += shift(w)
y += shift(h)
z += shift(l)
print 'Number of Dipoles = %u' % (len(x) * len(y) * len(z))
dipoles = [[i, j, k] for i in x for j in y for k in z]
dipoles = np.array(dipoles)
amplitude = sin(m * pi / w *
(dipoles[:, 0] + w / 2.)) * sin(n * pi / h *
(dipoles[:, 1] + h / 2.))
Ps = [np.array([0, 0, a]) for a in amplitude]
'''
FF plot
'''
theta, pwr = FF(wl, dipoles, Ps, R=FFR, res=FFres)
plt.figure()
plt.subplot(111, polar=True)
plt.gca().grid(True)
plt.plot(theta, pwr, color='r', lw=2)
plt.figure()
plt.plot(theta * 180 / pi - 90, pwr, color='r', lw=2)
plt.xlim(0, 90)
'''
Plot Dipole Arrangement
'''
plt.figure()
plt.imshow(amplitude.reshape(len(x), len(y), len(z))[:, :, 0].T,
extent=putil.getExtent(x, y))
plt.show()
return 0
def main():
'''
Complex slab mode solver based on "Exact Solution To Guided Wave Propagation in Lossy Films" by Nagel et al,
Optics Express 2011
Currently supports TE even modes only.
'''
hlam = 0.5
nf = 2 + 0.5j
nc = 1.5
wl = 1
h = hlam * wl
k = 2 * pi / wl
kf = nf * k
kc = nc * k
def f(kx):
return kx * tan(kx * h) - sqrt(kf**2 - kc**2 - kx**2)
f_vector = np.vectorize(f)
def phi(wavevectors):
b, a = wavevectors
kx = b + 1j * a
return np.real(f(kx) * f(kx).conj())
def phiPlotter(kx):
return np.real(10 * sp.log10(f(kx) * f(kx).conj()))
phiPlotter = np.vectorize(phiPlotter)
'''
Find zeros in residue, convert to propagation constants
'''
# Generate residue for complex plane
kmax = abs(kf)
kres = 100
a = np.linspace(0, kmax / 2, kres)
b = np.linspace(0, 2 * kmax, kres)
## Use to match Fig 2 from paper
# a = np.linspace(-1.5,1.5,20)
# b = np.linspace(0,10,20)
B, A = np.meshgrid(b, a)
kx = B + 1j * A
# Look for sign changes in real and imaginary parts of f(kx)
fkx = f_vector(kx)
sign_fr = np.sign(fkx.real)
sign_fi = np.sign(fkx.imag)
diff_fr = np.diff(sign_fr)
diff_fi = np.diff(sign_fi)
# Zeros must occur when both Real and Imag change sign simultaneously
cross = np.abs(diff_fr) + np.abs(diff_fi)
pts = np.where((cross == 4))
guesses = kx[pts]
# Find minimum residual near initial guess. Returns OptimizeResult object
for g in guesses:
res = sp.optimize.minimize(phi, [g.real, g.imag])
if res.success:
bx_min, ax_min = res.x
else:
print 'Minimize fail.'
exit()
kx_min = bx_min + 1j * ax_min
# Find corresponding Beta (from equation A4)
B = sqrt(kf**2 - kx_min**2)
print 'kx: %.3f + %.3fi' % (kx_min.real, kx_min.imag)
print 'Beta: %.3f + %.3fi' % (B.real, B.imag)
'''
# Pretty pictures
'''
ext = np.array(putil.getExtent(b, a))
asp = 'auto'
fig, ax = plt.subplots(2, 2, figsize=(7, 7), sharex=True, sharey=True)
# Residue plot
ax[0, 0].set_title(r'$10\log_{10}(|f|^{2})$')
resIm = ax[0, 0].imshow(phiPlotter(kx),
extent=ext,
vmax=40,
vmin=-20,
aspect=asp)
#Colorbar
# resmag = make_axes_locatable(ax[0])
# cres = resmag.append_axes("right", size="2%", pad=0.05)
# cbarres = plt.colorbar(resIm,cax=cres,format='%u')
ax[0, 1].set_title(r'$\Delta$Sign $Re\{f\}$')
ax[1, 1].set_title(r'$\Delta$Sign $Im\{f\}$')
ax[1, 0].set_title(r'Crossings')
ax[0, 1].imshow(diff_fr, extent=ext, aspect=asp, cmap='coolwarm')
ax[1, 1].imshow(diff_fi, extent=ext, aspect=asp, cmap='coolwarm')
ax[1, 0].imshow(cross, extent=ext, aspect=asp, cmap='afmhot')
ax[1, 0].set_xlabel(r'$\beta_{x} \lambda_{o}$')
ax[1, 1].set_xlabel(r'$\beta_{x} \lambda_{o}$')
ax[0, 0].set_ylabel(r'$\alpha_{x}\lambda_{o}$')
ax[1, 0].set_ylabel(r'$\alpha_{x}\lambda_{o}$')
# Beta(n,d,wl=wl,pol=pol,polarity='even',Nmodes=None,plot=True)
# fig.colorbar(ima)
plt.show()
return
def example():
#--------------------------------#
# Parameters
#--------------------------------#
# Simulation
wl = 400.
k = 2*pi/wl
w = 200
h = 800
m = 1
n = 2
# Plotting
res = 500
xmax = 800
Ro = 1. #distance to measure field (m)
angle_res = 100
#--------------------------------#
# Algorithm
dipoles = getDipoles(m,n,w,h)
xs = ys = np.linspace(-xmax,xmax,res)
X,Y = np.meshgrid(xs,ys)
for di,d in enumerate(dipoles):
R = getR(d[0],d[1],X,Y)
phi = pi*(getPhase(m,n,di))
if di==0: Fz = 1/R*exp(1j*(k*R + phi))
else: Fz += 1/R*exp(1j*(k*R + phi))
# Plot Real Field
fig = plt.figure()
ax = fig.add_subplot(111)
Fz *= -1 #flip values so plot color matches dipole color
Fz /= np.amax(abs(Fz))
scale = 0.01
im = ax.imshow(Fz.real,extent=putil.getExtent(xs,ys),vmax=scale,vmin=-1*scale,cmap='RdBu')
fig.colorbar(im)
drawDipoleBox(m,n,w,h,ax)
for di,d in enumerate(dipoles):
p = getPhase(m,n,di)
ax.add_patch(Circle(d,15,facecolor=colors[p]))
# Power plot
fig = plt.figure()
ax = fig.add_subplot(111)
P = abs(Fz)**2
P /= np.amax(P)
im = ax.imshow(P,extent=putil.getExtent(xs,ys),vmax=sqrt(scale),cmap='hot')
fig.colorbar(im)
# Plot Farfield
ff_fig = plt.figure()
ff_ax = ff_fig.add_subplot(111,polar=True)
ff_ax.grid(True)
FFplot(ff_ax,wl,w,h,m,n,Ro=Ro,angle_res=angle_res)
print getFF(wl,w,h,m,n,0)
plt.show()
return 0
def overlay(modes='horizontal', asym=False, noLines=True):
'''
Display cavity mode map over FDFD results
NOTES:
- There is a reversal in polarization convention between FDFD and waveguides
'''
Q_TE_n4 = 'parameter sweeps/Q_TE_n4_45deg.pickle'
Q_TM_n4 = 'parameter sweeps/Q_TM_n4_45deg.pickle'
Q_TE_n4_0_deg = 'parameter sweeps/Q_TE_n4_0deg.pickle'
Q_TE_n4_lossy = 'parameter sweeps/lossy/Q_TE_n4_k0_1_45deg.pickle'
Qabs_TE_n4_lossy = 'parameter sweeps/lossy/Qabs_TE_n4_k0_1_45deg.pickle'
Q_TE_n4_nsub2 = 'parameter sweeps/w_substrate/Q_TE_n4_nsub2_45deg.pickle'
Q_TE_n4_metalsub = 'parameter sweeps/w_substrate/Q_TE_n4_esub-100_45deg.pickle'
Q_TE_n4_metalsides = 'parameter sweeps/sidewalls/Q_TE_n4_nsides10j_wref_100.pickle'
Q_TM_n4_metalsides = 'parameter sweeps/sidewalls/Q_TM_n4_nsides10j_wref_100.pickle'
# Load FDFD data
with open(PATH + Q_TM_n4, 'rb') as f:
fdfd = pickle.load(f)
ds = np.linspace(0.02, 3., 100)
if not noLines:
# Generate resonance map
ds, ws = rect_cavity_modes(
ncore=4,
nclad=1,
nsub=1,
ms=np.array([3]),
wmodes=7,
pol='TM',
linemap=False,
colormap=False,
usePhase=True #0.5*(pi+phase(ds,pol='TM',mode=0,nsub=1))*pi/180.
)
if asym and not (modes == 'horizontal'
or modes == 'vertical'): #do vertical modes
ds, wsv = rect_cavity_modes(ncore=4,
nclad=1,
nsub=1,
ms=np.array([1]),
wmodes=7,
pol='TM',
linemap=False,
colormap=False,
usePhase=True)
else:
wsv = ws
fig = plt.figure(figsize=(6.5, 5))
ax = fig.add_subplot(111)
ext = putil.getExtent(ds, ds)
vmax = 50
vmin = 0
im = ax.imshow(fdfd, extent=ext, vmin=vmin, vmax=vmax)
fig.colorbar(im)
if noLines:
ax.set_xlabel(r'Width / $\lambda$')
ax.set_ylabel(r'Height / $\lambda$')
ax.set_title('Truncated Dielectric Slab Resonances')
plt.show()
exit()
for i in range(len(ws[0, :, 0, 0])):
for j in range(len(ws[0, 0, :, 0])):
for k in range(5):
if modes == 'horizontal':
if i % 2 == 0:
ax.plot(ws[:, i, j, k], ds, color='w', lw=3, ls='-')
if i % 2 == 1:
ax.plot(ws[:, i, j, k], ds, color='w', lw=3, ls=':')
if modes == 'vertical':
ax.plot(ds, ws[:, i, j, k], color='w', lw=3, ls='-')
if modes == 'both':
ax.plot(ds, wsv[:, i, j, k], color='w', lw=2,
ls='-') #vert
ax.plot(ws[:, i, j, k], ds, color='w', lw=2,
ls='-') #horiz
ax.set_xlim(0.02, 3)
ax.set_ylim(0.02, 3)
ax.set_xlabel(r'Width / $\lambda$')
ax.set_ylabel(r'Height / $\lambda$')
ax.set_title('Truncated Dielectric Slab Resonances')
#ax.set_title(r'$Q_{abs}$',fontsize=18)
plt.show()