Added old files

2023-03-14 22:05:56 +04:00
parent ab9b93500c
commit 55c80094b8
8 changed files with 737 additions and 0 deletions
--- a/Python/trap_forces_axial.py
+++ b/Python/trap_forces_axial.py
@@ -0,0 +1,152 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime".
+# There are axial forces only
+
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+from scipy import integrate
+from scipy import special
+from scipy import constants
+
+n1 = 1.3337  # index of refraction of the immersion medium
+n2 = 1.4607 # index of refraction of the fused silica at wavelength 523 nm
+n = n2 / n1 # n2/n1
+NA = 1.25  # numerical aperture
+th_max = np.arcsin(NA / n1)  # maximum angle of incidence
+f = 2.0e-3  # objective lens focus or WD
+r_max = f * np.tan(th_max)  # radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.03e-6  # sphere radius
+P = 4.4e-3  # power of the laser
+
+
+# angle of refraction
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th))
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - r(th)) ** 2 / np.tan(th + r(th)) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - r(th)) ** 2 / np.sin(th + r(th)) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+# Average factors (circular polarization
+def q_s_avg(th):
+    return 0.5 * (q_s(th, 0) + q_s(th, np.pi/2))
+
+
+def q_g_avg(th):
+    return 0.5 * (q_g(th, 0) + q_g(th, np.pi/2))
+
+
+def q_mag_avg(th):
+    return np.sqrt(q_s_avg(th) ** 2 + q_g_avg(th) ** 2)
+
+
+# Angles
+def phi(dr):
+    return np.arctan(dr / f)
+
+
+def thi(dr, dz):
+    return np.arcsin(dz / Rsp * np.sin(phi(dr)), dtype=np.cfloat)
+
+
+def q_g_z(dr, dz):
+    return -q_g_avg(thi(dr, dz)) * np.sin(phi(dr))
+
+
+def q_s_z(dr, dz):
+    return q_s_avg(thi(dr, dz)) * np.cos(phi(dr))
+
+
+# Intensity profile
+a = 1.0
+w0 = a * r_max
+
+
+def intensity_uniform():
+    return P / (np.pi * r_max ** 2)
+
+
+def intensity_gaussian_tem00(dr):
+    i_0 = P * 2 / (np.pi*w0 ** 2)
+    return i_0 * np.exp(-2 * dr ** 2 / w0 ** 2)
+
+
+def intensity_bessel(dr):
+    w0_bb = 0.5 * r_max
+    i_0 = P * 2 / (np.pi * w0 ** 2)
+    return i_0 * special.jv(0, 2.405 / w0_bb * dr) ** 2 * np.exp(- 2 * dr ** 2 / w0 ** 2)
+
+
+# Intensity profile graphics
+sns.set()
+sns.set_style("darkgrid")
+
+rho = np.linspace(-r_max, r_max, 500)
+fig1 = plt.figure(1, figsize=(10, 6))
+plt.plot(rho, intensity_gaussian_tem00(rho), 'k')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('I(r)', fontsize=18)
+
+
+# Integration
+def q_res_g(dz, func):
+    ans = integrate.quad(lambda x: x * func(x) * q_g_z(x, dz) * (~np.iscomplex(q_g_z(x, dz))).astype(float),
+                               0, r_max, epsabs=1e-12, epsrel=1e-6)
+    return 2 * np.pi * ans[0]
+
+
+def q_res_s(dz, func):
+    ans = integrate.quad(lambda x: x * func(x) * q_s_z(x, dz) * (~np.iscomplex(q_s_z(x, dz))).astype(float),
+                               0, r_max, epsabs=1e-12, epsrel=1e-6)
+    return 2 * np.pi * ans[0]
+
+
+# Calculation
+n = 200
+z = np.linspace(-2 * Rsp, 2 * Rsp, n)
+
+axial_g = [q_res_g(x, intensity_gaussian_tem00) for x in z]
+axial_s = [q_res_s(x, intensity_gaussian_tem00) for x in z]
+
+f_0 = n1 * P / constants.c  # net force
+
+axial_g = np.array(axial_g[::-1])
+axial_s = np.array(axial_s[::-1])
+axial = axial_g + axial_s
+z = -z[::-1]
+
+# Graphics
+fig2 = plt.figure(2, figsize=(10, 6))
+plt.plot(z, f_0*axial_g, 'b-.', lw=1, label='$F_{g}$')
+plt.plot(z, f_0*axial_s, 'r--', lw=1, label='$F_{s}$')
+plt.plot(z, f_0*axial, 'k', lw=1, label='$F_{t}$')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('F, N', fontsize=18)
+plt.legend(fontsize=18)
+plt.show()
--- a/Python/trap_forces_efficiencies.py
+++ b/Python/trap_forces_efficiencies.py
@@ -0,0 +1,65 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime
+
+# all distances in mm
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+a = 1.0 * 1e-6  # radius of the bead
+n1 = 1.33  # index of refraction of the medium
+n = 1.8  # n2/n1
+n2 = n * n1  # index of refraction of the fused silica
+c0 = 3 * 1e8  # speed of light
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - np.arcsin(n1 / n2 * np.sin(th))) ** 2 /
+            np.tan(th + np.arcsin(n1 / n2 * np.sin(th))) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - np.arcsin(n1 / n2 * np.sin(th))) ** 2 /
+            np.sin(th + np.arcsin(n1 / n2 * np.sin(th))) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# angle of refraction
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th))
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+t = np.linspace(0, np.pi / 2, 1000)
+t_deg = t * 180 / np.pi
+pol = np.pi / 4
+
+plt.figure(figsize=(13, 8))
+plt.plot(t_deg, q_s(t, pol), 'r--', label='Q_s')
+plt.plot(t_deg, -q_g(t, pol), 'b-.', label='Q_g')
+plt.plot(t_deg, q_mag(t, pol), 'k', label='Q_t')
+plt.grid()
+plt.xlabel(r'$\theta$, deg', fontsize=18)
+plt.ylabel('Q', fontsize=18)
+plt.legend(fontsize=18)
+plt.title('Beam efficiencies', fontsize=20)
+plt.show()
--- a/Python/trap_forces_transverse.py
+++ b/Python/trap_forces_transverse.py
@@ -0,0 +1,158 @@
+# These calculations are based on Ashkin's article "Forces of a single-beam
+# gradient laser trap on a dielectric sphere in the ray optics regime".
+# There are transverse forces only
+
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy import integrate
+from scipy import special
+from scipy import constants
+
+n1 = 1.3337  # index of refraction of the immersion medium
+n2 = 1.4607 # index of refraction of the fused silica at wavelength 523 nm
+n = n2 / n1 # n2/n1
+NA = 1.25  # numerical aperture
+th_max = np.arcsin(NA / n1)  # maximum angle of incidence
+f = 2.0e-3  # objective lens focus or WD
+r_max = f * np.tan(th_max)  # radius of a Gaussian beam (1:1 with input aperture condition)
+Rsp = 1.03e-6  # sphere radius
+P = 14e-3  # power of the laser
+
+
+# Angles
+def r(th):
+    return np.arcsin(n1 / n2 * np.sin(th, dtype=np.cfloat))
+
+
+def phi(dr):
+    return np.arctan(dr / f, dtype=np.cfloat)
+
+
+def gamma(db, dr):
+    return np.arccos(np.cos(np.pi / 2 - phi(dr)) * np.cos(db), dtype=np.cfloat)
+
+
+def thi(db, dr, dy):
+    return np.arcsin(dy / Rsp * np.sin(gamma(db, dr)), dtype=np.cfloat)
+
+
+# Fresnel reflectivity
+def r_f(th, psi):
+    return (np.tan(th - r(th)) ** 2 / np.tan(th + r(th)) ** 2) * np.cos(psi) ** 2 + \
+           (np.sin(th - r(th)) ** 2 / np.sin(th + r(th)) ** 2) * np.sin(psi) ** 2
+
+
+# Fresnel transparency
+def t_f(th, psi):
+    return 1 - r_f(th, psi)
+
+
+# force factors
+def q_s(th, psi):
+    return 1 + r_f(th, psi) * np.cos(2 * th) - t_f(th, psi) ** 2 * \
+           (np.cos(2 * th - 2 * r(th)) + r_f(th, psi) * np.cos(2*th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2*r(th)))
+
+
+def q_g(th, psi):
+    return r_f(th, psi) * np.sin(2 * th) - t_f(th, psi) ** 2 * \
+           (np.sin(2 * th - 2 * r(th)) + r_f(th, psi) * np.sin(2 * th)) / \
+           (1 + r_f(th, psi) ** 2 + 2 * r_f(th, psi) * np.cos(2 * r(th)))
+
+
+def q_mag(th, psi):
+    return np.sqrt(q_s(th, psi) ** 2 + q_g(th, psi) ** 2)
+
+
+# Average factors (circular polarization)
+def q_s_avg(th):
+    return 0.5 * (q_s(th, 0) + q_s(th, np.pi/2))
+
+
+def q_g_avg(th):
+    return 0.5 * (q_g(th, 0) + q_g(th, np.pi/2))
+
+
+def q_mag_avg(th):
+    return np.sqrt(q_s_avg(th) ** 2 + q_g_avg(th) ** 2)
+
+
+def q_g_z(db, dr, dy):
+    return q_g_avg(thi(db, dr, dy)) * np.cos(phi(dr), dtype=np.cfloat)
+
+
+def q_s_z(db, dr, dy):
+    return q_s_avg(thi(db, dr, dy)) * np.sin(gamma(db, dr), dtype=np.cfloat)
+
+
+# Intensity profile
+a = 1.0
+w0 = a * r_max
+
+
+def intensity_uniform(dr):
+    return 1 / (np.pi * r_max ** 2)
+
+
+def intensity_gaussian_tem00(dr):
+    amp = (1 - np.exp(-2 * r_max ** 2 / w0 ** 2))
+    p_0 = np.pi * w0 ** 2 / 2
+    return 1 / (amp * p_0) * np.exp(-2 * dr ** 2 / w0 ** 2)
+
+
+def intensity_bessel(dr):
+    p_0 = np.exp(0.5) * w0 * 0.0025 / 4.81
+
+    def temp_f(w):
+        return w * special.jv(0, 2.405 / w0 * w) ** 2
+    amp = integrate.quad(temp_f, 0, r_max)
+    return 1 / (2 * np.pi * amp[0]) * special.jv(0, 2.405 / w0 * dr) ** 2
+
+
+# Intensity profile graphics
+rho = np.linspace(-r_max, r_max, 500)
+fig1 = plt.figure(1, figsize=(10, 6))
+plt.plot(rho, intensity_gaussian_tem00(rho), 'k')
+plt.grid()
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('I(r)', fontsize=18)
+plt.show()
+
+
+# Integration
+def q_res_g(dy, func):
+    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),
+                            0, 2 * np.pi, 0, r_max, args=(dy, ),
+                            epsabs=1e-4, epsrel=1e-6)
+    return ans[0]
+
+
+def q_res_s(dy, func):
+    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),
+                            0, 2 * np.pi, 0, r_max,
+                            epsabs=1e-4, epsrel=1e-6)
+    return ans[0]
+
+
+# Calculation
+n = 150
+y = np.linspace(-2 * Rsp, 2 * Rsp, n)
+
+transverse_g = np.abs(np.array([q_res_g(x, intensity_gaussian_tem00) for x in y]))
+transverse_s = np.array([q_res_s(x, intensity_gaussian_tem00) for x in y])
+
+f_0 = n1 * P / constants.c  # net force
+
+transverse = transverse_g + transverse_s
+
+
+# Graphics
+fig2 = plt.figure(2, figsize=(10, 6))
+plt.plot(y, transverse_g, 'b-.', lw=1, label='$F_{g}$')
+plt.plot(y, transverse_s, 'r--', lw=1, label='$F_{s}$')
+plt.plot(y, transverse, 'k', lw=1, label='$F_{t}$')
+plt.xlabel('r, m', fontsize=18)
+plt.ylabel('F, m', fontsize=18)
+plt.legend()
+plt.grid()
+plt.show()