Refactoring

Matlab/Forces_Ashkin_Transverse.m

@@ -1,106 +0,0 @@
-%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')

Matlab/angles.m

@@ -1,21 +0,0 @@
-load_constants
-
-function angle = th_r(theta)
-    angle = asin(n1 / n2 * sin(theta));
-end
-
-function angle = ph_i(r)
-    angle = atan(r / f);
-end
-
-function angle = th_i(r, z)
-    angle = asin(z / Rsp .* sin(ph_i(r)));
-end
-
-function angle = gamma(beta, r)
-    angle = acos(cos(pi/2 - ph_i(r)) .* cos(beta));
-end
-
-function angle = theta(beta, r, y)
-    angle = asin(y / Rsp .* sin(gamma(beta, r)));
-end

Matlab/axial.asv

@@ -0,0 +1,70 @@
+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
+
+load_constants
+
+% Factors plots
+
+theta = linspace(0, pi/2, 500);
+figure
+plot(theta, qs_factor(theta, pi/4, n1, n2), ...
+    theta, -qg_factor(theta, pi/4, n1, n2), ...
+    theta, qmag_factor(theta, pi/4, n1, n2))
+grid
+xlabel('$\theta$, $^{\circ}$', 'Interpreter', 'latex')
+ylabel('Q')
+
+% Intensity profile plots
+rho = linspace(-r_max, r_max, 500);
+figure
+I = gauss(rho, r_max, w0, P);
+I0 = max(I);
+plot(rho, I/I0, 'k')
+grid
+xlabel('r, м')
+ylabel('I(r)')
+
+% Integration
+G0 = gauss_peak(r_max, w0, P);
+Qres_g = @(z) 2 * pi * G0 * integral2(@(beta, r) r .* gauss(r, r_max, w0, P) .* ...
+    iscomplex(qg_z_factor(r, z, n1, n2, Rsp, f)), 0, 2*pi, 0, r_max, ...
+    'Method', 'iterated', 'AbsTol', 1e-6, 'RelTol', 1e-6);
+
+Qres_s = @(z) 1 / (pi * r_max^2) * integral2(@(beta, r) r .* gauss(r, r_max, w0, P) .* ...
+    iscomplex(qs_z_factor(r, z, n1, n2, Rsp, f)), 0, 2*pi, 0, r_max, ...
+    'Method', 'iterated', 'AbsTol', 1e-6, 'RelTol', 1e-6);
+
+% Calulation
+N = 200;
+z = linspace(-2*Rsp, 2*Rsp, N);
+Axial_g = zeros(1, N);
+Axial_s = zeros(1, N);
+
+wb = waitbar(0, 'Calculating...');
+for ii = 1:N
+    Axial_g(ii) = Qres_g(z(ii));
+    Axial_s(ii) = Qres_s(z(ii));
+    waitbar(ii / N, wb, 'Calculating...');
+end
+close(wb);
+
+Axial_g = fliplr(Axial_g);
+Axial_s = fliplr(Axial_s);
+Axial = Axial_g + Axial_s;
+z = -fliplr(z);
+
+% Plots
+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, м')
+ylabel('F, Н')
+grid

Matlab/axial.m

@@ -8,13 +8,14 @@ format compact
 % There are axial forces only
 
 load_constants
-import factors.*
 
 % Factors plots
 
 theta = linspace(0, pi/2, 500);
 figure
-plot(theta, Qs(theta, pi/4), theta, -Qg(theta, pi/4), theta, Qmag(theta, pi/4))
+plot(theta, qs_factor(theta, pi/4, n1, n2), ...
+    theta, -qg_factor(theta, pi/4, n1, n2), ...
+    theta, qmag_factor(theta, pi/4, n1, n2))
 grid
 xlabel('$\theta$, $^{\circ}$', 'Interpreter', 'latex')
 ylabel('Q')
@@ -22,26 +23,28 @@ ylabel('Q')
 % Intensity profile plots
 rho = linspace(-r_max, r_max, 500);
 figure
-plot(rho, I(rho)/max(I(rho)),'k')
+I = gauss(rho, r_max, w0);
+I0 = max(I);
+plot(rho, I/I0, 'k')
 grid
 xlabel('r, м')
 ylabel('I(r)')
 
 % Integration
-G0 = 2/(A*pi^2*r_max^2*w0^2);
+G0 = gauss_peak(r_max, w0);
-Qres_g = @(z) G0 * integral2(@(beta,r) r.*I(r).*...
+Qres_g = @(z) 2 * pi * G0 * integral2(@(beta, r) r .* gauss(r, r_max, w0) .* ...
-    iscomplex(Qgz(r,z)),0,2*pi,0,r_max,...
+    iscomplex(qg_z_factor(r, z, n1, n2, Rsp, f)), 0, 2*pi, 0, r_max, ...
-    'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
+    'Method', 'iterated', 'AbsTol', 1e-12, 'RelTol', 1e-6);
 
-Qres_s = @(z) G0 * integral2(@(beta,r) r.*I(r).*...
+Qres_s = @(z) 2 * pi * G0 * integral2(@(beta, r) r .* gauss(r, r_max, w0) .* ...
-    iscomplex(Qsz(r,z)),0,2*pi,0,r_max,...
+    iscomplex(qs_z_factor(r, z, n1, n2, Rsp, f)), 0, 2*pi, 0, r_max, ...
-    'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
+    'Method', 'iterated', 'AbsTol', 1e-12, 'RelTol', 1e-6);
 
 % Calulation
 N = 200;
-z = linspace(-2*Rsp,2*Rsp,N);
+z = linspace(-2*Rsp, 2*Rsp, N);
-Axial_g = zeros(1,N);
+Axial_g = zeros(1, N);
-Axial_s = zeros(1,N);
+Axial_s = zeros(1, N);
 
 wb = waitbar(0, 'Calculating...');
 for ii = 1:N
@@ -58,7 +61,9 @@ z = -fliplr(z);
 
 % Plots
 figure
-plot(z,F0*Axial_g,'b-.',z,F0*Axial_s,'r--',z,F0*Axial,'k')
+plot(z, F0 * Axial_g, 'b-.', ...
+    z, F0 * Axial_s, 'r--', ...
+    z, F0 * Axial, 'k')
 legend('F_{g}','F_{s}','F_{t}')
 xlabel('r, м')
 ylabel('F, Н')

Matlab/bessel.m

@@ -0,0 +1,4 @@
+% Bessel beam
+function b = bessel(r, r_max, w0, P)
+    b = bessel_peak(r_max, w0, P) * besselj(0, 2.405/w0 * r).^2;
+end

Matlab/bessel_peak.m

@@ -0,0 +1,3 @@
+function peak = bessel_peak(r_max, w0, P)
+    peak = P * 4.81 / (w0 * r_max * exp(0.5)) * 2 * pi * integral(@(r) r.*besselj(0, 2.405/w0 * r).^2, 0, r_max) / P0;
+end

Matlab/coefficients.m

@@ -1,9 +0,0 @@
-function reflectivity = R(th, psi)
-    reflectivity = (tan(th - th_r(th)).^2 ./ tan(th + th_r(th)).^2) .* ...
-        cos(psi).^2 + ...
-        (sin(th - th_r(th)).^2 ./ sin(th + th_r(th)).^2) .* sin(psi).^2;
-end
-   
-function transparency = T(th, psi)
-    transparency = 1 - R(th, psi);
-end

Matlab/factors.m

@@ -1,37 +0,0 @@
-% Factors
-function factor = Qs(th, psi)
-    factor = 1 + R(th, psi) .* cos(2*th) - T(th, psi).^2.*...
-    (cos(2*th - 2*th_r(th)) + R(th, psi) .* cos(2*th)) ./ ...
-    (1 + R(th, psi).^2 + 2*R(th, psi) .* cos(2*th_r(th)));
-end
-
-function factor = Qg(th, psi)
-    factor = R(th, psi) .* sin(2*th) - T(th, psi).^2 .* ...
-        (sin(2*th - 2*th_r(th)) + R(th, psi) .* sin(2*th)) ./ ...
-        (1 + R(th, psi).^2 + 2*R(th, psi) .* cos(2*th_r(th)));
-end
-
-function factor = Qmag(th, psi)
-    factor = sqrt(Qs(th, psi).^2 + Qg(th, psi).^2);
-end
-
-% Average factors
-function factor = Qs_avg(th)
-    factor = 0.5*(Qs(th, 0) + Qs(th, pi/2));
-end
-
-function factor = Qg_avg(th)
-    factor = 0.5*(Qg(th, 0) + Qg(th, pi/2));
-end
-
-function factor = Qmag_avg(th)
-    factor = sqrt(Qs_avg(th).^2 + Qg_avg(th).^2);
-end
-
-function factor = Qgz(r, z)
-    factor = -Qg_avg(th_i(r, z)) .* sin(ph_i(r));
-end
-
-function factor = Qsz(r, z)
-    factor = Qs_avg(th_i(r, z)) .* cos(ph_i(r));
-end

Matlab/gamma_angle.m

@@ -0,0 +1,3 @@
+function angle = gamma_angle(beta, r, focus)
+    angle = acos(cos(pi/2 - phi_i(r, focus)) .* cos(beta));
+end

Matlab/gauss.m

@@ -0,0 +1,4 @@
+% Gaussian TEM00 beam
+function g = gauss(r, r_max, w0)
+    g = exp(-2 * r.^2 / w0^2);
+end

Matlab/gauss_peak.m

@@ -0,0 +1,4 @@
+function peak = gauss_peak(r_max, w0)
+    A = (1 - exp(-2*r_max.^2 / w0^2));
+    peak = 2*A / (pi * w0^2);
+end

Matlab/intensity.m

@@ -1,7 +0,0 @@
-load_constants
-
-function g = gauss(r)
-    A = (1-exp(-2*r_max.^2 / w0^2));
-    I0 = 2*P / (pi * w0^2 * A);
-    g = I0 * exp(-2 * r.^2 / w0^2); % Gaussian TEM00 beam
-end

Matlab/load_constants.m

@@ -1,13 +1,14 @@
-Rsp = 1.0e-6; % sphere radius [m]
+Rsp = 1.03e-6; % sphere radius [m]
-n1 = 1.33; % index of refraction of the immersion medium
+n1 = 1.3337; % index of refraction of the immersion medium
-n2 = 1.6; % index of refraction of the fused silica at wavelength 523 nm
+n2 = 1.4607; % index of refraction of the fused silica at wavelength 523 nm
 n = n2/n1; % relative refraction index
 c0 = 3e8; % speed of light [m/s]
 NA = 1.25; % numerical apertur  e
-f = 100.0e-3; % objective lens focus or WD [m]
+f = 2.0e-3; % objective lens focus or WD [m]
-P = 20.0e-3; % power of the laser [W]
+P = 51.7e-3; % power of the laser [W]
 F0 = n1*P/c0; % resulting force [N]
 th_max = asin(NA/n1); % maximum incidence angle
+
+ratio = 1.0; % the ratio of the beam radius to the aperture radius
 r_max = f * tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
-aperture = 1.0;
+w0 = ratio * r_max; % Gaussian beam waist radius [m]
-w0 = aperture * r_max; % Gaussian beam waist radius [m]

Matlab/phi_i.m

@@ -0,0 +1,3 @@
+function angle = phi_i(r, focus)
+    angle = atan(r / focus);
+end

Matlab/qg_avg_factor.m

@@ -0,0 +1,3 @@
+function factor = qg_avg_factor(th, n1, n2)
+    factor = 0.5*(qg_factor(th, 0, n1, n2) + qg_factor(th, pi/2, n1, n2));
+end

Matlab/qg_factor.m

@@ -0,0 +1,8 @@
+function factor = qg_factor(th, psi, n1, n2)
+    R = reflectivity(th, psi, n1, n2);
+    T = transmittance(th, psi, n1, n2);
+    theta_refl = th_r(th, n1, n2);
+    factor = R .* sin(2*th) - T.^2 .* ...
+        (sin(2*th - 2*theta_refl) + R .* sin(2*th)) ./ ...
+        (1 + R.^2 + 2*R .* cos(2*theta_refl));
+end

Matlab/qg_y_factor.m

@@ -0,0 +1,3 @@
+function factor = qg_y_factor(beta, r, y, n1, n2, Rsp, focus)
+    factor = qg_avg_factor(th_i_y(beta, r, y, Rsp, focus), n1, n2).*sin(gamma_angle(beta, r, focus));
+end

Matlab/qg_z_factor.m

@@ -0,0 +1,3 @@
+function factor = qg_z_factor(r, z, n1, n2, Rsp, focus)
+    factor = -qg_avg_factor(th_i_z(r, z, Rsp, focus), n1, n2) .* sin(phi_i(r, focus));
+end

Matlab/qmag_avg_factor.m

@@ -0,0 +1,3 @@
+function factor = qmag_avg_factor(th, n1, n2)
+    factor = sqrt(qs_avg_factor(th, n1, n2).^2 + qg_avg_factor(th, n1, n2).^2);
+end

Matlab/qmag_factor.m

@@ -0,0 +1,3 @@
+function factor = qmag_factor(th, psi, n1, n2)
+    factor = sqrt(qs_factor(th, psi, n1, n2).^2 + qg_factor(th, psi, n1, n2).^2);
+end

Matlab/qs_avg_factor.m

@@ -0,0 +1,3 @@
+function factor = qs_avg_factor(th, n1, n2)
+    factor = 0.5*(qs_factor(th, 0, n1, n2) + qs_factor(th, pi/2, n1, n2));
+end

Matlab/qs_factor.m

@@ -0,0 +1,9 @@
+function factor = qs_factor(th, psi, n1, n2)
+    R = reflectivity(th, psi, n1, n2);
+    T = transmittance(th, psi, n1, n2);
+    theta_refl = th_r(th, n1, n2);
+
+    factor = 1 + R .* cos(2*th) - T.^2.*...
+    (cos(2*th - 2*theta_refl) + R .* cos(2*th)) ./ ...
+    (1 + R.^2 + 2*R .* cos(2*theta_refl));
+end

Matlab/qs_y_factor.m

@@ -0,0 +1,3 @@
+function factor = qs_y_factor(beta, r, y, n1, n2, Rsp, focus)
+   factor = qs_avg_factor(th_i_y(beta, r, y, Rsp, focus), n1, n2).*cos(phi_i(r, focus));
+end

Matlab/qs_z_factor.m

@@ -0,0 +1,3 @@
+function factor = qs_z_factor(r, z, n1, n2, Rsp, focus)
+    factor = qs_avg_factor(th_i_z(r, z, Rsp, focus), n1, n2) .* cos(phi_i(r, focus));
+end

Matlab/reflectivity.m

@@ -0,0 +1,6 @@
+function R = reflectivity(th, psi, n1, n2)
+    theta_refl = th_r(th, n1, n2);
+    R = (tan(th - theta_refl).^2 ./ tan(th + theta_refl).^2) .* ...
+        cos(psi).^2 + ...
+        (sin(th - theta_refl).^2 ./ sin(th + theta_refl).^2) .* sin(psi).^2;
+end

Matlab/th_i_y.m

@@ -0,0 +1,3 @@
+function angle = th_i_y(beta, r, y, Rsp, focus)
+    angle = asin(y / Rsp .* sin(gamma_angle(beta, r, focus)));
+end

Matlab/th_i_z.m

@@ -0,0 +1,3 @@
+function angle = th_i_z(r, z, Rsp, focus)
+    angle = asin(z / Rsp .* sin(phi_i(r, focus)));
+end

Matlab/th_r.m

@@ -0,0 +1,3 @@
+function angle = th_r(theta, n1, n2)
+    angle = asin(n1 / n2 * sin(theta));
+end

Matlab/theta_angle.m

@@ -0,0 +1,3 @@
+function angle = theta_angle(beta, r, y, Rsp, focus)
+    angle = asin(y / Rsp .* sin(gamma(beta, r, focus)));
+end

Matlab/transmittance.m

@@ -0,0 +1,3 @@
+function T = transmittance(th, psi, n1, n2)
+    T = 1 - reflectivity(th, psi, n1, n2);
+end

Matlab/transverse.m

@@ -0,0 +1,56 @@
+%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
+
+load_constants
+
+% Intensity profile graphics
+rho = linspace(-r_max, r_max, 500);
+I = gauss(rho, r_max, w0);
+I0 = max(I);
+figure
+plot(rho, I/I0, 'k')
+grid
+xlabel('r, m')
+ylabel('I(r)')
+
+% Integration
+Qres_g = @(y) integral2(@(beta, r) r .* gauss(r, r_max, w0) .* ...
+    iscomplex(qg_y_factor(beta, r, y, n1, n2, Rsp, f)), 0, 2*pi, 0, r_max, ...
+    'Method', 'iterated', 'AbsTol', 1e-6, 'RelTol', 1e-6);
+
+Qres_s = @(y) integral2(@(beta, r) r .* gauss(r, r_max, w0) .* ...
+    iscomplex(qs_y_factor(beta, r, y, n1, n2, Rsp, f)), 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);
+
+wb = waitbar(0, 'Calculating...');
+for ii = 1:N
+    Transverse_g(ii) = abs(Qres_g(y(ii)));
+    Transverse_s(ii) = Qres_s(y(ii));
+    waitbar(ii / N, wb, 'Calculating...');
+end
+close(wb);
+
+Transverse = abs(Transverse_g) + Transverse_s;
+
+%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

Matlab/uniform.m

@@ -0,0 +1,4 @@
+% Beam with uniform distribution
+function u = uniform(r, w0, r_max, P)
+    u = P / (pi*r_max^2);
+end