117 lines
2.6 KiB
Matlab
117 lines
2.6 KiB
Matlab
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if 0
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pmd = 0.2 * ( 1e-12 / sqrt(1e3) ) ; % 0.1 ps/sqrt(km) -> 1e-9 -> s/sqrt(m)
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L = 1000; % m
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corr_len = 100;
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num_wave_plates = 100;
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wp_len = L / num_wave_plates; %waveplate length
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dgd = pmd * sqrt(L);
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fdac = 120e9; % GHz
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fsim = fdac * 512 ; %oversampled simulation frequency
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dt = 1/fsim; % sample time
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nt = 4; % sampled signal length
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omega = 2*pi*[(0:nt/2-1),(-nt/2:-1)]/(dt*nt) ; %angular frequency vector for optical signal of length nt
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omega = 2*pi*fsim ; %angular frequency vector for optical signal of length nt
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for rlz = 1:20000
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db0 = [];
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db1 = [];
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delta_beta = [];
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db0 = (rand(num_wave_plates,1)*2*pi - pi); % normal distr. between -pi <-> +pi
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db1 = sqrt(3*pi/8)*(dgd/fsim)/ num_wave_plates .* omega; % linear increasing delta beta 1
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%loop over waveplates
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for n_wp = 1:length(db0)
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delta_beta(n_wp,:) = (db1+db0(n_wp))./corr_len;
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end
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dphi = delta_beta*wp_len; %phase shift due to propagation constant = beta * L
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if rlz == 1
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figure()
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plot(cumsum( delta_beta ));
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end
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dphi_end(rlz) = sum( dphi );
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end
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figure;
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histogram((dphi_end),100);
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deltaT = mean(abs(dphi_end));
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%H = exp(-1j*dphi); % Filter to apply phase shift in freq. domain
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end
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PMD = 0.1 * ( 1e-12 / sqrt(1e3) ); %PMD s/sqrt(m)
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L = 10e3; %m
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sigma_dgd = PMD * sqrt(L); % in sec.
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disp(['variance of DGD in pico seconds: ',num2str(sigma_dgd*1e12)]);
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disp(['variance of DGD in pico seconds: ',num2str(sigma_dgd*1e12)]);
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dgd = [];
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for i = 1:4
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dgd(i,:) = DGD(sigma_dgd,10000);
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end
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rms = PMD * sqrt(40e3) * 1e12 ; % in sec.
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t = [0:0.01:100];
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z2 = sqrt(2/pi).*(t.^2)/(rms.^3).*exp(-t.^2/(2*rms^2)) ;
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figure;
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histogram(dgd*1e12,1000,"Normalization","pdf");
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hold on
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plot(t(1:200),z2(1:200),'r');
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hold off
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function z = DGD(sigma_dgd,N)
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%PMD = sqrt( (PMD*1e12)^2/3 );
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% PMD = PMD * 1/( 1e-12 / sqrt(1e3) );
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sigma_dgd = sigma_dgd*1e12;
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x = [0:N];
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almaga = randn(3,N)*sigma_dgd;
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y = almaga.^2;
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z0 = sqrt(sum(y,1));
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disp(mean(z0));
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disp(std(z0));
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% disp(var(z0));
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z1 = [];
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for l = 0:0.1:N
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z1 = [z1 sum(z0(1,:)>l & z0(1,:)<l+0.1) / N ];
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end
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z = z0 *1e-12;
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rms = sigma_dgd;
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t = [0:0.01:N];
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z2 = sqrt(2/pi).*(t.^2)/(rms.^3).*exp(-t.^2/(2*rms^2)) ;
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figure;
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histogram(z0,1000,"Normalization","pdf");
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hold on
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plot(t(1:200),z2(1:200),'r');
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return
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end
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