158 lines
4.3 KiB
Python
158 lines
4.3 KiB
Python
# These calculations are based on Ashkin's article "Forces of a single-beam
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# gradient laser trap on a dielectric sphere in the ray optics regime".
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# There are transverse forces only
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import integrate
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from scipy import special
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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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n = n2 / n1 # n2/n1
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NA = 1.25 # numerical aperture
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th_max = np.arcsin(NA / n1) # maximum angle of incidence
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f = 2.0e-3 # objective lens focus or WD
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r_max = f * np.tan(th_max) # radius of a Gaussian beam (1:1 with input aperture condition)
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Rsp = 1.03e-6 # sphere radius
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P = 14e-3 # power of the laser
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# Angles
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def r(th):
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return np.arcsin(n1 / n2 * np.sin(th, dtype=np.cfloat))
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def phi(dr):
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return np.arctan(dr / f, dtype=np.cfloat)
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def gamma(db, dr):
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return np.arccos(np.cos(np.pi / 2 - phi(dr)) * np.cos(db), dtype=np.cfloat)
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def thi(db, dr, dy):
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return np.arcsin(dy / Rsp * np.sin(gamma(db, dr)), dtype=np.cfloat)
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# Fresnel reflectivity
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def r_f(th, psi):
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return (np.tan(th - r(th)) ** 2 / np.tan(th + r(th)) ** 2) * np.cos(psi) ** 2 + \
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(np.sin(th - r(th)) ** 2 / np.sin(th + r(th)) ** 2) * np.sin(psi) ** 2
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# Fresnel transparency
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def t_f(th, psi):
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return 1 - r_f(th, psi)
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# force factors
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def q_s(th, psi):
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return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
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(np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
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(1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
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def q_g(th, psi):
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return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
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(np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
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(1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
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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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def q_g_z(db, dr, dy):
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return q_g_avg(thi(db, dr, dy)) * np.cos(phi(dr), dtype=np.cfloat)
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def q_s_z(db, dr, dy):
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return q_s_avg(thi(db, dr, dy)) * np.sin(gamma(db, dr), dtype=np.cfloat)
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# Intensity profile
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a = 1.0
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w0 = a * r_max
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def intensity_uniform(dr):
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return 1 / (np.pi * r_max ** 2)
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def intensity_gaussian_tem00(dr):
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amp = (1 - np.exp(-2 * r_max ** 2 / w0 ** 2))
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p_0 = np.pi * w0 ** 2 / 2
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return 1 / (amp * p_0) * np.exp(-2 * dr ** 2 / w0 ** 2)
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def intensity_bessel(dr):
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p_0 = np.exp(0.5) * w0 * 0.0025 / 4.81
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def temp_f(w):
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return w * special.jv(0, 2.405 / w0 * w) ** 2
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amp = integrate.quad(temp_f, 0, r_max)
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return 1 / (2 * np.pi * amp[0]) * special.jv(0, 2.405 / w0 * dr) ** 2
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# Intensity profile graphics
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rho = np.linspace(-r_max, r_max, 500)
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fig1 = plt.figure(1, figsize=(10, 6))
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plt.plot(rho, intensity_gaussian_tem00(rho), 'k')
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plt.grid()
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plt.xlabel('r, m', fontsize=18)
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plt.ylabel('I(r)', fontsize=18)
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plt.show()
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# Integration
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def q_res_g(dy, func):
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ans = integrate.dblquad(lambda dr, db, dy: dr * func(dr) * q_g_z(db, dr, dy) * (~np.iscomplex(q_g_z(db, dr, P))).astype(float),
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0, 2 * np.pi, 0, r_max, args=(dy, ),
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epsabs=1e-4, epsrel=1e-6)
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return ans[0]
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def q_res_s(dy, func):
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ans = integrate.dblquad(lambda dr, db: dr * func(dr) * q_s_z(db, dr, dy) * (~np.iscomplex(q_g_z(db, dr, P))).astype(float),
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0, 2 * np.pi, 0, r_max,
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epsabs=1e-4, epsrel=1e-6)
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return ans[0]
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# Calculation
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n = 150
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y = np.linspace(-2 * Rsp, 2 * Rsp, n)
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transverse_g = np.abs(np.array([q_res_g(x, intensity_gaussian_tem00) for x in y]))
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transverse_s = np.array([q_res_s(x, intensity_gaussian_tem00) for x in y])
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f_0 = n1 * P / constants.c # net force
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transverse = transverse_g + transverse_s
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# Graphics
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fig2 = plt.figure(2, figsize=(10, 6))
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plt.plot(y, transverse_g, 'b-.', lw=1, label='$F_{g}$')
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plt.plot(y, transverse_s, 'r--', lw=1, label='$F_{s}$')
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plt.plot(y, transverse, 'k', lw=1, label='$F_{t}$')
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plt.xlabel('r, m', fontsize=18)
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plt.ylabel('F, m', fontsize=18)
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plt.legend()
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plt.grid()
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plt.show() |