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Matlab/Forces_Ashkin_Axial.m

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+%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')