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