brknvddll/optical-trap-forces
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Added old files

Browse Source
This commit is contained in:
BrokenVoodooDoll
2023-03-14 22:05:56 +04:00
parent ab9b93500c
commit 55c80094b8
8 changed files with 737 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

112
Matlab/Forces_Ashkin_Axial.m Normal file
View File

@@ -0,0 +1,112 @@
%all distances in m
clear
close all
clc
format compact
% 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
n1 = 1.33; % index of refraction of the immersion medium
n2 = 1.6; % index of refraction of the fused silica at wavelength 523 nm
n = n2/n1; % n2/n1
c0 = 3e8; % speed of light
NA = 1.25; % numerical aperture
th_max = asin(NA/n1); % maximum angle of incidence
f = 100.0e-3; % objective lens focus or WD
r_max = f*tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
Rsp = 1.0e-6; % sphere radius
P = 20.0e-3; % power of the laser
thr = @(th) asin(n1/n2*sin(th)); % refraction angle
%reflectivity
R = @(th,psi) (tan(th-thr(th)).^2./tan(th+thr(th)).^2).*cos(psi).^2+...
(sin(th-thr(th)).^2./sin(th+thr(th)).^2).*sin(psi).^2;
%transparency
T = @(th,psi) 1-R(th,psi);
% Factors
Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
2*thr(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*thr(th)));
Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
2*thr(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*thr(th)));
Qmag = @(th, psi) sqrt(Qs(th, psi).^2 + Qg(th, psi).^2);
% Average factors (circular polarization
Qs_avg = @(th) 0.5*(Qs(th, 0) + Qs(th, pi/2));
Qg_avg = @(th) 0.5*(Qg(th, 0) + Qg(th, pi/2));
Qmag_avg = @(th) sqrt(Qs_avg(th).^2 + Qg_avg(th).^2);
% Angles
phi = @(r) atan(r/f);
thi = @(r,z) asin(z/Rsp.*sin(phi(r)));
Qgz = @(r,z) -Qg_avg(thi(r,z)).*sin(phi(r));
Qsz = @(r,z) Qs_avg(thi(r,z)).*cos(phi(r));
% Intensity profile
a = 1.0;
w0 = a*r_max;
%I = @(r) P/(pi*r_max^2); % uniform distribution
A = (1-exp(-2*r_max.^2/w0^2));
I0 = P*2/(pi*w0^2)/A;
I = @(r) I0*exp(-2*r.^2/w0^2); % Gaussian TEM00 beam
%A = 2*pi*integral(@(r) r.*besselj(0,2.405/w0*r).^2,0,r_max)/P0;
%w0_bb = 0.5*r_max;
%I0 = P*2/(pi*w0^2);
%I = @(r) I0*besselj(0,2.405/w0_bb*r).^2.*exp(-2*r.^2/w0^2); % Bessel beam
% Intensity profile graphics
rho = linspace(-r_max, r_max, 500);
figure
plot(rho, I(rho)/max(I(rho)),'k')
grid
xlabel('r, ì')
ylabel('I(r)')
sdf('my')
% Integration
Qres_g = @(z) 1/(pi*r_max^2)*2/(A*pi*w0^2)*integral2(@(beta,r) r.*I(r).*...
iscomplex(Qgz(r,z)),0,2*pi,0,r_max,...
'Method','iterated','AbsTol',1e-12,'RelTol',1e-6);
Qres_s = @(z) 1/(pi*r_max^2)*2/(A*pi*w0^2)*integral2(@(beta,r) r.*I(r).*...
iscomplex(Qsz(r,z)),0,2*pi,0,r_max,...
'Method','iterated','AbsTol',1e-12,'RelTol',1e-6);
% Calulation
N = 200;
z = linspace(-2*Rsp,2*Rsp,N);
Axial_g = zeros(1,N);
Axial_s = zeros(1,N);
for ii = 1:N
Axial_g(ii) = Qres_g(z(ii));
Axial_s(ii) = Qres_s(z(ii));
end
F0 = n1*P/c0; % net force
Axial_g = fliplr(Axial_g);
Axial_s = fliplr(Axial_s);
Axial = Axial_g + Axial_s;
z = -fliplr(z);
%Graphics
figure
plot(z,F0*Axial_g,'b-.',z,F0*Axial_s,'r--',z,F0*Axial,'k')
legend('F_{g}','F_{s}','F_{t}')
xlabel('r, ì')
ylabel('F, Í')
grid
sdf('my')

48
Matlab/Forces_Ashkin_Ray_Efficiencies.m Normal file
View File

@@ -0,0 +1,48 @@
close all
clear
format compact
clc
% 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
a = 1.0e-6; % radius of the bead
n1 = 1.0; % index of rafraction of the medium
n = 1.4607; % n2/n1
n2 = n*n1; % index of refraction of the fused silica
c0 = 3e8; % speed of light
%reflectivity
R = @(th,psi) (tan(th-asin(n1/n2*sin(th))).^2./...
tan(th+asin(n1/n2*sin(th))).^2).*cos(psi).^2+...
(sin(th-asin(n1/n2*sin(th))).^2./...
sin(th+asin(n1/n2*sin(th))).^2).*sin(psi).^2;
%transparency
T = @(th,psi) 1-R(th,psi);
r = @(th) asin(n1/n2*sin(th));
% Factors
Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
2*r(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*r(th)));
Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
2*r(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*r(th)));
Qmag = @(th, psi) sqrt(Qs(th, psi).^2 + Qg(th, psi).^2);
t = linspace(0, pi/2, 1000);
t_deg = t*180/pi;
pol = pi/4;
figure
plot(t_deg, Qs(t, pol),'r--', t_deg, -Qg(t, pol),'b-.', t_deg, Qmag(t, pol),'k');
grid
xlabel('\theta, deg')
ylabel('Q')
legend('Q_s','Q_g','Q_t','location','northwest')
sdf('my')

106
Matlab/Forces_Ashkin_Transverse.m Normal file
View File

@@ -0,0 +1,106 @@
%all distances in m
close all
clear
clc
format compact
% 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
n1 = 1.33; % index of refraction of the immersion medium
n2 = 1.6; % index of refraction of the fused silica at wavelength 523 nm
n = n2/n1; % n2/n1
c0 = 3e8; % speed of light
NA = 1.25; % numerical aperture
th_max = asin(NA/n1); % maximum angle of incidence
f = 100.0e-3; % objective lens focus or WD
r_max = f*tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
Rsp = 1.0e-6; % sphere radius
P = 20.0e-3; % power of the laser
thr = @(th) asin(n1/n2*sin(th)); % refraction angle
%reflectivity
R = @(th,psi) (tan(th-thr(th)).^2./tan(th+thr(th)).^2).*cos(psi).^2+...
(sin(th-thr(th)).^2./sin(th+thr(th)).^2).*sin(psi).^2;
%transparency
T = @(th,psi) 1-R(th,psi);
% Factors
Qs = @(th, psi) 1 + R(th, psi) .* cos(2*th) - T(th,psi).^2 .* (cos(2*th -...
2*thr(th)) + R(th, psi) .* cos(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*thr(th)));
Qg = @(th, psi) R(th, psi) .* sin(2*th) - T(th,psi).^2 .* (sin(2*th -...
2*thr(th)) + R(th, psi) .* sin(2*th)) ./ (1 + R(th,psi).^2 +...
2*R(th,psi) .* cos(2*thr(th)));
% Average factors (circular polarization
Qs_avg = @(th) 0.5*(Qs(th, 0) + Qs(th, pi/2));
Qg_avg = @(th) 0.5*(Qg(th, 0) + Qg(th, pi/2));
% Angles
phi = @(r) atan(r/f);
gamma = @(beta,r) acos(cos(pi/2-phi(r)).*cos(beta));
thi = @(beta,r,y) asin(y/Rsp.*sin(gamma(beta,r)));
Qgy = @(beta,r,y) Qg_avg(thi(beta,r,y)).*cos(phi(r));
Qsy = @(beta,r,y) Qs_avg(thi(beta,r,y)).*sin(gamma(beta,r));
% Intensity profile
a = 1.0;
w0 = a*r_max;
%I = @(r) P/(pi*r_max^2); % uniform distribution
A = (1-exp(-2*r_max.^2/w0^2));
I0 = 2*P/(pi*w0^2)*A;
I = @(r) I0*exp(-2*r.^2/w0^2); % Gaussian TEM00 beam
%P0 = exp(0.5)*w0*0.0025/4.81;
%A = 2*pi*integral(@(r) r.*besselj(0,2.405/w0*r).^2,0,r_max)/P0;
%I = @(r) 1/(A*P0)*besselj(0,2.405/w0*r).^2; % Bessel beam
% Intensity profile graphics
rho = linspace(-r_max, r_max, 500);
figure
plot(rho, I(rho)/max(I(rho)),'k')
grid
xlabel('r, m')
ylabel('I(r)')
sdf('my')
% Integration
Qres_g = @(y) 1/(pi*r_max^2)*integral2(@(beta,r) r.*I(r).*...
iscomplex(Qgy(beta,r,y)),0,2*pi,0,r_max,...
'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
Qres_s = @(y) 1/(pi*r_max^2)*integral2(@(beta,r) r.*I(r).*...
iscomplex(Qsy(beta,r,y)),0,2*pi,0,r_max,...
'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
% Calulation
N = 150;
y = linspace(-2*Rsp,2*Rsp,N);
Transverse_g = zeros(1,N);
Transverse_s = zeros(1,N);
for ii = 1:N
Transverse_g(ii) = abs(Qres_g(y(ii)));
Transverse_s(ii) = Qres_s(y(ii));
end
Transverse = abs(Transverse_g) + Transverse_s;
F0 = n1*P/c0; % net force;
%Graphics
figure
plot(y,F0*Transverse_g,'r--',y,F0*Transverse_s,'b-.',y,F0*Transverse,'k')
legend('F_{g}','F_{s}','F_{t}')
xlabel('r, ì')
ylabel('F, Í')
grid
sdf('my')

11
Matlab/iscomplex.m Normal file
View File

@@ -0,0 +1,11 @@
function S = iscomplex(A)
[n,m] = size(A);
S = zeros(n,m);
for ii = 1:n
for jj = 1:m
S(ii,jj) = A(ii,jj)*double(isreal(A(ii,jj)));
end
end
end

85
Matlab/sdf.m Normal file
View File

@@ -0,0 +1,85 @@
function sdf(varargin)
% SDF Set the line width and fonts of a figure
%
% sdf(fig)
%
% where fig is the figure number. If the figure number is omitted, the
% currently active figure is updated. Edit the file to set you own style
% settings.
%
% sdf(fig, 'stylename')
% applies a pre-configured style from the File-->Export Setup menu of the
% figure's window. The stylename should be one of the 'Export Styles'
% section of the dialog.
%
% The function allows applying the same settings as through the
% File-->Export Setup-->Apply menu of the figure, but much faster and
% without the annoying clicking.
%
% Example
% figure(1); t=0:0.1:10; plot(t, sin(t));
% sdf(1)
% pause
% sdf(1,'PowerPoint')
% Andrey Popov, Hamburg, 2009
%% Parse the input data
default = true;
if nargin == 0 % no input - take current fig and apply default style
fig = gcf();
else % at least 1 input
if ischar(varargin{1}) % style name
default = false;
style_name = varargin{1};
fig = gcf();
else
fig = varargin{1};
figure(fig); % just in case it does not exist
if nargin == 2
default = false;
style_name = varargin{2};
end
end
end
%% Apply a style
if default % Apply a default style
style = struct();
style.Version = '1';
style.Format = 'eps';
style.Preview = 'none';
style.Width = 'auto';
style.Height = 'auto';
style.Units = 'centimeters';
style.Color = 'rgb';
style.Background = 'w'; % '' = no change; 'w' = white background
style.FixedFontSize = '10';
style.ScaledFontSize = 'auto';
style.FontMode = 'fixed';
style.FontSizeMin = '8';
style.FixedLineWidth = '2';
style.ScaledLineWidth = 'auto';
style.LineMode = 'fixed';
style.LineWidthMin = '0.5';
style.FontName = 'auto';
style.FontWeight = 'auto';
style.FontAngle = 'auto';
style.FontEncoding = 'latin1';
style.PSLevel = '2';
style.Renderer = 'auto';
style.Resolution = 'auto';
style.LineStyleMap = 'none';
style.ApplyStyle = '0';
style.Bounds = 'loose';
style.LockAxes = 'on';
style.ShowUI = 'on';
style.SeparateText = 'off';
hgexport(fig,'temp_dummy',style,'applystyle', true);
else % Apply an existing style, defined as in the Export dialog
% The files are in folder fullfile(prefdir(0),'ExportSetup');
style = hgexport('readstyle',style_name);
hgexport(fig,'temp_dummy',style,'applystyle', true);
end

152
Python/trap_forces_axial.py Normal file
View File

@@ -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()

65
Python/trap_forces_efficiencies.py Normal file
View File

@@ -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()

158
Python/trap_forces_transverse.py Normal file
View File

@@ -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()