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