Split up files

Matlab/Forces_Ashkin_Axial.m

@@ -1,112 +0,0 @@
-%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')

Matlab/angles.m

@@ -0,0 +1,21 @@
+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.m

@@ -0,0 +1,65 @@
+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
+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))
+grid
+xlabel('$\theta$, $^{\circ}$', 'Interpreter', 'latex')
+ylabel('Q')
+
+% Intensity profile plots
+rho = linspace(-r_max, r_max, 500);
+figure
+plot(rho, I(rho)/max(I(rho)),'k')
+grid
+xlabel('r, м')
+ylabel('I(r)')
+
+% Integration
+G0 = 2/(A*pi^2*r_max^2*w0^2);
+Qres_g = @(z) G0 * integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qgz(r,z)),0,2*pi,0,r_max,...
+    'Method','iterated','AbsTol',1e-6,'RelTol',1e-6);
+
+Qres_s = @(z) G0 * integral2(@(beta,r) r.*I(r).*...
+    iscomplex(Qsz(r,z)),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/coefficients.m

@@ -0,0 +1,9 @@
+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

@@ -0,0 +1,37 @@
+% 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/intensity.m

@@ -0,0 +1,7 @@
+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/iscomplex.m

@@ -1,11 +1,3 @@
 function S = iscomplex(A)
-[n,m] = size(A);
+    S = A .* double(imag(A) == 0);
-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

Matlab/load_constants.m

@@ -0,0 +1,13 @@
+Rsp = 1.0e-6; % sphere radius [m]
+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; % 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]
+P = 20.0e-3; % power of the laser [W]
+F0 = n1*P/c0; % resulting force [N]
+th_max = asin(NA/n1); % maximum incidence angle
+r_max = f * tan(th_max); % radius of a Gaussian beam (1:1 with input aperture condition)
+aperture = 1.0;
+w0 = aperture * r_max; % Gaussian beam waist radius [m]