129 lines
3.2 KiB
Python
129 lines
3.2 KiB
Python
import numpy as np
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from scipy import special
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from scipy import integrate
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from scipy import constants
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n1 = 1.3337 # index of refraction of the immersion medium
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n2 = 1.4607 # index of refraction of the fused silica at wavelength 523 nm
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NA = 1.25 # numerical aperture
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f = 2.0e-3 # objective lens focus or WD
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Rsp = 1.03e-6 # sphere radius
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P = 4.4e-3 # power of the laser
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ratio = 1.0 # the ratio of the beam radius to the aperture radius
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th_max = np.arcsin(NA / n1) # maximum angle of incidence
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# radius of a Gaussian beam (1:1 with input aperture condition)
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r_max = f * np.tan(th_max)
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n = n2 / n1 # n2/n1
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w0 = ratio * r_max # beam radius
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F0 = n1 * P / constants.speed_of_light; # resulting force
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# Angle of refraction
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def theta_r(th):
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return np.arcsin(n1 / n2 * np.sin(th))
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# Fresnel reflectivity
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def reflectivity(th, psi):
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theta = theta_r(th)
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return (np.tan(th - theta) ** 2 / np.tan(th + theta) ** 2) * np.cos(psi) ** 2 + \
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(np.sin(th - theta) ** 2 / np.sin(th + theta) ** 2) * np.sin(psi) ** 2
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# Fresnel transparency
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def transparency(th, psi):
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return 1 - reflectivity(th, psi)
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# force factors
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def q_s(th, psi):
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R = reflectivity(th, psi)
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T = transparency(th, psi)
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theta = theta_r(th)
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return 1 + R * np.cos(2 * th) - T ** 2 * \
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(np.cos(2 * th - 2 * theta) + R * np.cos(2*th)) / \
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(1 + R ** 2 + 2 * R * np.cos(2*theta))
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def q_g(th, psi):
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R = reflectivity(th, psi)
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T = transparency(th, psi)
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theta = theta_r(th)
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return R * np.sin(2 * th) - T ** 2 * \
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(np.sin(2 * th - 2 * theta) + R * np.sin(2 * th)) / \
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(1 + R ** 2 + 2 * R * np.cos(2 * theta))
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def q_mag(th, psi):
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return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
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# Average factors (circular polarization)
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def q_s_avg(th):
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return 0.5 * (q_s(th, 0) + q_s(th, np.pi/2))
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def q_g_avg(th):
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return 0.5 * (q_g(th, 0) + q_g(th, np.pi/2))
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def q_mag_avg(th):
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return np.sqrt(q_s_avg(th) ** 2 + q_g_avg(th) ** 2)
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# Angles
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def phi_i(r):
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return np.arctan(r / f)
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def gamma(beta, r):
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return np.arccos(np.cos(np.pi / 2 - phi_i(r)) * np.cos(beta), dtype=np.cfloat)
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def th_i_z(r, z):
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return np.arcsin(z / Rsp * np.sin(phi_i(r)), dtype=np.cfloat)
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def th_i_y(beta, r, y):
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return np.arcsin(y / Rsp * np.sin(gamma(beta, r)), dtype=np.cfloat)
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def q_g_z(r, z):
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return -q_g_avg(th_i_z(r, z)) * np.sin(phi_i(r))
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def q_s_z(r, z):
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return q_s_avg(th_i_z(r, z)) * np.cos(phi_i(r))
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def q_g_y(beta, r, y):
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return q_g_avg(th_i_y(beta, r, y)) * np.cos(phi_i(r), dtype=np.cfloat)
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def q_s_y(beta, r, y):
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return q_s_avg(th_i_y(beta, r, y)) * np.sin(gamma(beta, r), dtype=np.cfloat)
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# Intensity distributions
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def gauss_peak():
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A = (1 - np.exp(-2*r_max ** 2 / w0 ** 2))
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return 2*A / (np.pi * w0 ** 2)
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def gauss(r):
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return np.exp(-2 * r ** 2 / w0 ** 2)
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def bessel(r):
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return special.jv(0, 2.405 / w0 * r) ** 2
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def bessel_peak():
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return 4.81 / (w0 * r_max * np.exp(0.5)) * 2 * np.pi * integrate.quad(lambda r: r * special.jv(0, 2.405 / w0 * r) ** 2,
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0, r_max, epsabs=1e-12, epsrel=1e-6)[0]
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def uniform(r):
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return P / (np.pi * r_max ** 2) * np.ones(r.shape)
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