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Matlab/Forces_Ashkin_Ray_Efficiencies.m

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+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')