adding bayer-helms coupling coeffiecent routines into simtools

src/new/coupling_coefficients/FT_bayer_helms_Sg.m

+function [ Sg ] = FT_bayer_helms_Sg( n1,n2,X,X_bar,F,F_bar)
+%FT_BAYER_HELMS_SG Summary of this function goes here
+%   Detailed explanation goes here
+
+    if mod(n1,2) == 0
+        mu1_max = n1/2;
+    else
+        mu1_max = (n1-1)/2;
+    end
+
+    if mod(n2,2) == 0
+        mu2_max = n2/2;
+    else
+        mu2_max = (n2-1)/2;
+    end
+
+    Sg = 0;
+
+    for mu1 = 0:mu1_max
+        for mu2 = 0:mu2_max
+
+            sig_max = min(mu1,mu2);
+
+            tmp = 0;
+
+            for sig = 0:sig_max
+                tmp = tmp + (-1)^sig * F_bar^(mu1-sig) * F^(mu2-sig) / (factorial(2*sig) * factorial(mu1-sig) * factorial(mu2 - sig));
+            end
+
+            Sg = Sg + tmp * (-1)^mu1 * X_bar^(n1-2*mu1) * X^(n2-2*mu2) / (factorial(n1-2*mu1) * factorial(n2 - 2*mu2));
+        end
+    end
+end
+

src/new/coupling_coefficients/FT_bayer_helms_Su.m

+function [ Sg ] = FT_bayer_helms_Su( n1,n2,X,X_bar,F,F_bar)
+%FT_BAYER_HELMS_SG Summary of this function goes here
+%   Detailed explanation goes here
+    Sg = 0;
+
+    if n1 > 0 && n2 > 0
+        if mod(n1-1,2) == 0
+            mu1_max = n1/2;
+        else
+            mu1_max = (n1-1)/2;
+        end
+
+        if mod(n2-1,2) == 0
+            mu2_max = n2/2;
+        else
+            mu2_max = (n2-1)/2;
+        end
+
+        Sg = 0;
+
+        for mu1 = 0:mu1_max
+            for mu2 = 0:mu2_max
+
+                sig_max = min(mu1,mu2);
+
+                tmp = 0;
+
+                for sig = 0:sig_max
+                    tmp = tmp + (-1)^sig * F_bar^(mu1-sig) * F^(mu2-sig) / (factorial(2*sig+1) * factorial(mu1-sig) * factorial(mu2 - sig));
+                end
+
+                Sg = Sg + tmp * (-1)^mu1 * X_bar^(n1-2*mu1-1) * X^(n2-2*mu2-1) / (factorial(n1-2*mu1-1) * factorial(n2 - 2*mu2-1));
+            end
+        end
+    end
+end
+

src/new/coupling_coefficients/FT_bayer_helms_kn.m

+function [ kn ] = FT_bayer_helms_kn( gp1, gp2, gp_idx, n1, n2, gamma)
+%FT_BAYER_HELMS_KN Summary of this function goes here
+%   Detailed explanation goes here
+    
+    K = 0.5i .* conj(gp1.q(gp_idx) - gp2.q(gp_idx)) ./ imag(gp1.q(gp_idx));
+    K0 = (gp1.zr(gp_idx) - gp2.zr(gp_idx))./gp2.zr(gp_idx);
+    
+    n1_fac = factorial(n1);
+    n2_fac = factorial(n2);
+    
+    X_bar = 0;
+    X = 0;
+    
+    if gamma ~= 0.0
+        theta = gp2.w0(gp_idx)./gp2.zr(gp_idx);
+        gg0 = gamma./theta;
+        X_bar = 1./ (sqrt(1+conj(K))) * (-1*(gp2.z(gp_idx)/gp2.zr(gp_idx)-1i)*gg0);
+        X     = 1./ (sqrt(1+conj(K))) * (-1*(gp2.z(gp_idx)/gp2.zr(gp_idx)+1i*(1+2*conj(K)))*gg0);
+    end
+    
+    F = K./(2.*(1+K0));
+    F_bar = conj(K)./2;
+    Ex = exp( -(X.*X_bar * 0.5));
+    
+    kn = (-1)^n2_fac * Ex * sqrt(n1_fac*n2_fac) * ...
+        (1+K0)^(n1/2+0.25) * (1-conj(K))^(-(n1+n2+2)/2) ...
+        * (FT_bayer_helms_Sg(n1,n2,X,X_bar,F,F_bar) - FT_bayer_helms_Su(n1,n2,X,X_bar,F,F_bar));
+end
+

src/new/coupling_coefficients/FT_bayer_helms_knm.m

+function [ knm ] = FT_bayer_helms_knm( gp_in, gp_out, n1, m1, n2, m2, gamma_x, gamma_y )
+%FT_BAYER_HELMS_KNM Summary of this function goes here
+%   Detailed explanation goes here
+    knm = FT_bayer_helms_kn(gp_in,gp_out,1,n1,n2,gamma_x) * FT_bayer_helms_kn(gp_in,gp_out,2,m1,m2,gamma_y);
+end
+

src/new/coupling_coefficients/examples/FTE_bayer_helms_tilt.m

+% Plots x axis tilt coupling into higher order modes using bayer-helms
+% equations
+
+clear all;
+
+z = 0;
+w0 = 1e-3;
+lambda = 1064e-9;
+zr = pi*w0^2/lambda;
+q = z + 1i*zr;
+gp = FT_init_gauss_param(lambda, 1, 'q',q);
+gamma = logspace(-8, -2, 100);
+
+for i=1:length(gamma)
+    k00_00(i) = FT_bayer_helms_knm(gp, gp, 0,0,0,0, gamma(i), 0);
+    k00_10(i) = FT_bayer_helms_knm(gp, gp, 0,0,1,0, gamma(i), 0);
+    k00_20(i) = FT_bayer_helms_knm(gp, gp, 0,0,2,0, gamma(i), 0);
+    k00_30(i) = FT_bayer_helms_knm(gp, gp, 0,0,3,0, gamma(i), 0);
+    k00_40(i) = FT_bayer_helms_knm(gp, gp, 0,0,4,0, gamma(i), 0);
+end
+
+figure();
+semilogx(gamma, abs(k00_00), gamma, abs(k00_10), gamma, abs(k00_20), gamma, abs(k00_30), gamma, abs(k00_40));
+xlabel('\gamma_x (misalignment) [rad]');
+ylabel('|k_{nmn''m''}|');
+title(sprintf('Coupling from x tilt into higher order modes, w_0=%Gm, z=%Gm', w0, z));
+legend('k_{0000}','k_{0010}','k_{0020}','k_{0030}','k_{0040}','Location','Best');
\ No newline at end of file