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Added functionality to compute potential due to a Gaussian beam with astigmatism, plotting of ideal potential along with affected potential to show deviation.

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Karthik 2023-01-12 19:16:52 +01:00
parent 30e6a8b7a4
commit 60b9def24e
1 changed files with 45 additions and 17 deletions
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60
calculateDipoleTrapPotential.py
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@ -33,7 +33,7 @@ def z_R(w_0:np.ndarray, lamb:float)->np.ndarray:
# Beam Radius # Beam Radius
def w(pos, w_0, lamb): def w(pos, w_0, lamb):
return w_0*np.sqrt(1+(pos*lamb/(np.pi*w_0**2))**2) return w_0*np.sqrt(1+(pos / z_R(w_0, lamb))**2)
def trap_depth(w_1:"float|u.quantity.Quantity", w_2:"float|u.quantity.Quantity", P:"float|u.quantity.Quantity", alpha:float)->"float|u.quantity.Quantity": def trap_depth(w_1:"float|u.quantity.Quantity", w_2:"float|u.quantity.Quantity", P:"float|u.quantity.Quantity", alpha:float)->"float|u.quantity.Quantity":
return 2*P/(np.pi*w_1*w_2) * (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3) return 2*P/(np.pi*w_1*w_2) * (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
@ -47,6 +47,12 @@ def single_gaussian_beam_potential(positions: "np.ndarray|u.quantity.Quantity",
U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:], waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:], waists[1], wavelength))**2)) U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:], waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:], waists[1], wavelength))**2))
return U return U
def astigmatic_single_gaussian_beam_potential(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", del_y:"float|u.quantity.Quantity", alpha:"float|u.quantity.Quantity", P:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um)->np.ndarray:
A = 2*P/(np.pi*w(positions[1,:] - (del_y/2), waists[0], wavelength)*w(positions[1,:] + (del_y/2), waists[1], wavelength))
U_tilde = (1 / (2 * ac.eps0 * ac.c)) * alpha * (4 * np.pi * ac.eps0 * ac.a0**3)
U = - U_tilde * A * np.exp(-2 * ((positions[0,:]/w(positions[1,:] - (del_y/2), waists[0], wavelength))**2 + (positions[2,:]/w(positions[1,:] + (del_y/2), waists[1], wavelength))**2))
return U
def single_gaussian_beam_potential_harmonic_approximation(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", depth:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um)->np.ndarray: def single_gaussian_beam_potential_harmonic_approximation(positions: "np.ndarray|u.quantity.Quantity", waists: "np.ndarray|u.quantity.Quantity", depth:"float|u.quantity.Quantity"=1, wavelength:"float|u.quantity.Quantity"=1.064*u.um)->np.ndarray:
U = - depth * (1 - (2 * (positions[0,:]/waists[0])**2) - (2 * (positions[2,:]/waists[1])**2) - (0.5 * positions[1,:]**2 * np.sum(np.reciprocal(z_R(waists, wavelength)))**2)) U = - depth * (1 - (2 * (positions[0,:]/waists[0])**2) - (2 * (positions[2,:]/waists[1])**2) - (0.5 * positions[1,:]**2 * np.sum(np.reciprocal(z_R(waists, wavelength)))**2))
return U return U
@ -88,19 +94,24 @@ def plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels):
## plot of the measured parameter vs. scan parameter ## plot of the measured parameter vs. scan parameter
plt.figure(figsize=(9, 7)) plt.figure(figsize=(9, 7))
j = 0
for i in range(np.size(ComputedPotentials, 0)): for i in range(np.size(ComputedPotentials, 0)):
v, dv, popt, pcov = extractTrapFrequency(Positions, ComputedPotentials[i], TrapDepthInKelvin, axis) v, dv, popt, pcov = extractTrapFrequency(Positions, ComputedPotentials[i], TrapDepthInKelvin, axis)
unit = 'Hz' unit = 'Hz'
if v <= 0: if v <= 0.0:
v = np.nan v = np.nan
dv = np.nan dv = np.nan
unit = 'Hz' unit = 'Hz'
elif v > 0 and orderOfMagnitude(v) > 2: elif v > 0.0 and orderOfMagnitude(v) > 2:
v = v / 1e3 # in kHz v = v / 1e3 # in kHz
dv = dv / 1e3 # in kHz dv = dv / 1e3 # in kHz
unit = 'kHz' unit = 'kHz'
tf_label = '\u03BD = %.1f \u00B1 %.2f %s'% tuple([v,dv,unit]) tf_label = '\u03BD = %.1f \u00B1 %.2f %s'% tuple([v,dv,unit])
plt.plot(Positions[axis], ComputedPotentials[i][axis], label = 'P = ' + str(Powers[i]) + ' W; ' + TrapDepthLabels[i] + '; ' + tf_label) if i % 2 == 0 and j < len(Powers):
plt.plot(Positions[axis], ComputedPotentials[i][axis], '--',label = 'P = ' + str(Powers[j]) + ' W; ' + TrapDepthLabels[j] + '; ' + tf_label)
elif i % 2 != 0 and j < len(Powers):
plt.plot(Positions[axis], ComputedPotentials[i][axis], label = 'P = ' + str(Powers[j]) + ' W; ' + tf_label)
j = j + 1
if axis == 0: if axis == 0:
dir = 'X' dir = 'X'
elif axis == 1: elif axis == 1:
@ -111,7 +122,7 @@ def plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels):
plt.ylabel('Trap Potential (uK)', fontsize= 12, fontweight='bold') plt.ylabel('Trap Potential (uK)', fontsize= 12, fontweight='bold')
plt.tight_layout() plt.tight_layout()
plt.grid(visible=1) plt.grid(visible=1)
plt.legend(prop={'size': 12, 'weight': 'bold'}) plt.legend(loc=3, prop={'size': 12, 'weight': 'bold'})
plt.show() plt.show()
# plt.savefig('pot_' + dir + '.png') # plt.savefig('pot_' + dir + '.png')
@ -122,7 +133,7 @@ if __name__ == '__main__':
Powers = [40] Powers = [40]
Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability Polarizability = 184.4 # in a.u, most precise measured value of Dy polarizability
w_x, w_z = 34*u.um, 27.5*u.um # Beam Waists in the x and y directions w_x, w_z = 34*u.um, 27.5*u.um # Beam Waists in the x and y directions
# w_x, w_z = 70*u.um, 70*u.um # Beam Waists in the x and y directions # w_x, w_z = 30*u.um, 30*u.um # Beam Waists in the x and y directions
# w_x, w_z = 20.5*u.um, 20.5*u.um # w_x, w_z = 20.5*u.um, 20.5*u.um
axis = 1 # axis referenced to the beam along which you want the dipole trap potential axis = 1 # axis referenced to the beam along which you want the dipole trap potential
@ -132,13 +143,15 @@ if __name__ == '__main__':
ComputedPotentials = [] ComputedPotentials = []
TrapDepthLabels = [] TrapDepthLabels = []
gravity = True gravity = False
astigmatism = False astigmatism = True
tilt_gravity = True tilt_gravity = True
theta = 1 # in degrees theta = 1 # in degrees
tilt_axis = [1, 0, 0] # lab space coordinates are rotated about x-axis in reference frame of beam tilt_axis = [1, 0, 0] # lab space coordinates are rotated about x-axis in reference frame of beam
disp_foci = 1.5 * z_R(w_0 = np.asarray([30]), lamb = 1.064)[0]*u.um # difference in position of the foci along the propagation direction (Astigmatism)
for p in Powers: for p in Powers:
Power = p*u.W # Single Beam Power Power = p*u.W # Single Beam Power
@ -163,12 +176,12 @@ if __name__ == '__main__':
z_Positions = np.arange(-extent, extent, 1)*u.um z_Positions = np.arange(-extent, extent, 1)*u.um
Positions = np.vstack((x_Positions, y_Positions, z_Positions)) * projection_axis[:, np.newaxis] Positions = np.vstack((x_Positions, y_Positions, z_Positions)) * projection_axis[:, np.newaxis]
if not gravity and not astigmatism: IdealTrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability)
TrappingPotential = single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, alpha = Polarizability) IdealTrappingPotential = IdealTrappingPotential + np.zeros((3, len(IdealTrappingPotential))) * IdealTrappingPotential.unit
TrappingPotential = TrappingPotential + np.zeros((3, len(TrappingPotential))) * TrappingPotential.unit IdealTrappingPotential = (IdealTrappingPotential/ac.k_B).to(u.uK)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif gravity and not astigmatism: if gravity and not astigmatism:
ComputedPotentials.append(IdealTrappingPotential)
# Influence of Gravity # Influence of Gravity
m = 164*u.u m = 164*u.u
gravity_axis = np.array([0, 0, 1]) gravity_axis = np.array([0, 0, 1])
@ -180,17 +193,32 @@ if __name__ == '__main__':
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK) TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif not gravity and astigmatism: elif not gravity and astigmatism:
ComputedPotentials.append(IdealTrappingPotential)
# Influence of Astigmatism # Influence of Astigmatism
pass TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = disp_foci, alpha = Polarizability)
TrappingPotential = TrappingPotential + np.zeros((3, len(TrappingPotential))) * TrappingPotential.unit
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
elif gravity and astigmatism:
ComputedPotentials.append(IdealTrappingPotential)
# Influence of Gravity and Astigmatism
m = 164*u.u
gravity_axis = np.array([0, 0, 1])
if tilt_gravity:
R = rotation_matrix(tilt_axis, np.radians(theta))
gravity_axis = np.dot(R, gravity_axis)
gravity_axis_positions = np.vstack((x_Positions, y_Positions, z_Positions)) * gravity_axis[:, np.newaxis]
TrappingPotential = astigmatic_single_gaussian_beam_potential(Positions, np.asarray([w_x.value, w_z.value])*u.um, P = Power, del_y = disp_foci, alpha = Polarizability) + gravitational_potential(gravity_axis_positions, m)
TrappingPotential = (TrappingPotential/ac.k_B).to(u.uK)
else: else:
# Influence of Gravity and Astigmatism TrappingPotential = IdealTrappingPotential
pass
# v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, TrapDepthInKelvin, axis) # v, dv, popt, pcov = extractTrapFrequency(Positions, TrappingPotential, TrapDepthInKelvin, axis)
# plotHarmonicFit(Positions, TrappingPotential, TrapDepthInKelvin, axis, popt, pcov) # plotHarmonicFit(Positions, TrappingPotential, TrapDepthInKelvin, axis, popt, pcov)
ComputedPotentials.append(TrappingPotential) ComputedPotentials.append(TrappingPotential)
# print(np.shape(ComputedPotentials))
ComputedPotentials = np.asarray(ComputedPotentials) ComputedPotentials = np.asarray(ComputedPotentials)
plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels) plotPotential(Positions, Powers, ComputedPotentials, axis, TrapDepthLabels)