/* * WMM-Application: * Unidirectional polarization converter: * double layer magnetooptic raised strip waveguide, * TE/TM mode conversion, coupled mode theory model */ /* * WMM * Wave-matching method for mode analysis of dielectric waveguides * Manfred Lohmeyer * University of Osnabrueck, Department of Physics * Barbarastrasse 7, D-49069 Osnabrueck, Germany * (1999) */ #include #include #include #include"wmminc.h" /* rib waveguide parameters */ #define Wgpnf 2.302 // film refractive index #define Wgpns 1.95 // substrate refractive index #define Wgpnc 1.0 // cover: air #define Wgpl 1.3 // vacuum wavelength [mum] #define WgpFrot 3007.42 // specific Faraday rotation of the two layers (+/-) // [degrees/cm] /* rasied strip waveguide, heigth h, width w */ Waveguide wgdef(double h, double w) { Waveguide g(1, 1); g.hx(0) = 0.0; g.hx(1) = h; g.hy(0) = -w/2.0; g.hy(1) = w/2.0; g.n(0,0) = Wgpns; g.n(0,1) = Wgpns; g.n(0,2) = Wgpns; g.n(1,0) = Wgpnc; g.n(1,1) = Wgpnf; g.n(1,2) = Wgpnc; g.n(2,0) = Wgpnc; g.n(2,1) = Wgpnc; g.n(2,2) = Wgpnc; g.lambda = Wgpl; return g; } /* Mode amplitudes according to coupled mode theory: two coupled modes, Hermitian coupling matrix, b0, b1: propagation constants, kappa: coupling coefficient, c0, c1: initial amplitudes, z: propagation distance j: 0,1; index of the returned amplitude */ Complex cmtcoeff(int j, double b0, double b1, Complex kappa, Complex c0, Complex c1, double z) { double db, rho; Complex m0, m1, a; db = b0-b1; rho = sqrt(db*db/4.0+kappa.sqabs()); switch(j) { case 0: m0 = Complex(cos(rho*z), -db/2.0/rho*sin(rho*z)); m1 = kappa*(-sin(rho*z)/rho); m1 = m1*CCI; break; case 1: m0 = kappa.conj()*(-sin(rho*z)/rho); m0 = m0*CCI; m1 = Complex(cos(rho*z), db/2.0/rho*sin(rho*z)); } a = m0*c0+m1*c1; a = a*expi(-(b0+b1)/2.0*z); return a; } /* analysis parameters */ WMM_Parameters pardef() { WMM_Parameters p; p.vform = HXHY; p.vnorm = NRMMH; p.ccomp = CCALL; p.ini_d_alpha = 0.05; p.ini_N_alpha = 10; p.ini_alpha_max = 2.0; p.ini_steps = 20; p.ref_num = 5; p.ref_exp = 4.0; p.ref_sdf = 0.5; p.fin_d_alpha = 0.01; p.fin_N_alpha = 20; p.fin_alpha_max = 2.0; p.btol = 1.0e-7; p.mshift = 1.0e-10; return p; } /* unidirectional polarization converters: */ int main() { // four different geometries: find the fundamental modes, save them WMM_Parameters par = pardef(); WMM_ModeArray ma; double w, h; int i; // strip height and width double hdata[4] = {0.6341, 0.8260, 1.0118, 1.1975}; double wdata[4] = {0.7976, 0.9951, 1.1914, 1.3865}; for(i=0; i<=3; i+=1) { w = wdata[i]; h = hdata[i]; Waveguide wg = wgdef(h, w); WMM_findfundmode(wg, VEC, SYM, 0.0, 0.0, par, '-', '-', ma); ma(0).write_def('o', 'a'+i); ma.clear(); WMM_findfundmode(wg, VEC, ASY, 0.0, 0.0, par, '-', '-', ma); ma(0).write_def('o', 'a'+i); ma.clear(); } // magnetooptic perturbation: // coupled mode theory for two fundamental modes WMM_Mode tem; WMM_Mode tmm; double pte, ptm; double ktete, ktetm, ktmtm; double kte, ktm, kap; double t, theta, xi; // bottom layer thicknesses double wgptdata[4] = {0.1807, 0.2643, 0.3491, 0.4311}; // magnetization orientation [degrees] double wgpthdata[4] = {62.8, 65.0, 66.2, 67.9}; // for the four geometries for(i=0; i<=3; i+=1) { fprintf(stderr, "\n\n"); // load the unperturbed modes tem.read_def(VEC, SYM, 'o', 'a'+i); tmm.read_def(VEC, ASY, 'o', 'a'+i); // show the actual geometry w = tem.wg.hy(1) - tem.wg.hy(0); h = tem.wg.hx(1) - tem.wg.hx(0); t = wgptdata[i]; theta = wgpthdata[i]; fprintf(stderr, "[%c] h = %g w = %g t = %g theta = %g\n", 'a'+i, h, w, t, theta); // modes are assumed to be normalized pte = 1.0; ptm = 1.0; // two regions with opposite specific Faraday rotation Rect rI(t, -w/2.0, h, w/2.0); // top layer Rect rII(0.0, -w/2.0, t, w/2.0); // bottom layer // compute the entries of the coupling matrix xi = Wgpnf*Wgpl/PI*WgpFrot/180.0*PI/10000.0; ktete = twomrecint(tem, EX, tem, EZ, rI) - twomrecint(tem, EX, tem, EZ, rII); ktete *= xi/val_invomep0(tem.wg.lambda) /2.0/pte; ktmtm = twomrecint(tmm, EX, tmm, EZ, rI) - twomrecint(tmm, EX, tmm, EZ, rII); ktmtm *= xi/val_invomep0(tem.wg.lambda) /2.0/ptm; ktetm = twomrecint(tem, EX, tmm, EY, rI) - twomrecint(tem, EY, tmm, EX, rI) - twomrecint(tem, EX, tmm, EY, rII) + twomrecint(tem, EY, tmm, EX, rII); ktetm *= xi/val_invomep0(tem.wg.lambda) /sqrt(pte)/sqrt(ptm)/4.0; t = theta/180.0*PI; kte = ktete*sin(t); ktm = ktmtm*sin(t); kap = ktetm*cos(t); // phase mismatch and coupling coefficient for forward and // backward propagation, [cm^(-1)], conversion length fprintf(stderr, "F: b_te+k_te-b_tm-k_tm = %g\n", (tem.beta+kte-tmm.beta-ktm)*10000.0); fprintf(stderr, "F: kappa = i %g\n", kap*10000.0); fprintf(stderr, "B: b_te-k_te-b_tm+k_tm = %g\n", (tem.beta-kte-tmm.beta+ktm)*10000.0); fprintf(stderr, "F: -kappa = i %g\n", -kap*10000.0); fprintf(stderr, "L = %g\n", PI/2.0/kap); // plots of the mode power conversion, forward and backward direction, // TE and TM polarization char ftename[20] = "fe_.xyf"; char ftmname[20] = "fm_.xyf"; char btename[20] = "be_.xyf"; char btmname[20] = "bm_.xyf"; FILE *fedat; FILE *fmdat; FILE *bedat; FILE *bmdat; ftename[2] = 'a'+i; ftmname[2] = 'a'+i; btename[2] = 'a'+i; btmname[2] = 'a'+i; fedat = fopen(ftename, "w+"); fmdat = fopen(ftmname, "w+"); bedat = fopen(btename, "w+"); bmdat = fopen(btmname, "w+"); int zi; double z; Complex c; double b0f, b1f, b0b, b1b; b0f = tem.beta+kte; b0b = tem.beta-kte; b1f = tmm.beta+ktm; b1b = tmm.beta-ktm; for(zi = 0; zi<=500; ++zi) { z = zi*(PI/2.0/fabs(kap))/500; c = cmtcoeff(0,b0f,b1f,Complex(0.0,kap),CC1,CC0,z); fprintf(fedat, "%g %g\n", z/1000.0, c.sqabs()); c = cmtcoeff(1,b0f,b1f,Complex(0.0,kap),CC1,CC0,z); fprintf(fmdat, "%g %g\n", z/1000.0, c.sqabs()); c = cmtcoeff(0,b0b,b1b,Complex(0.0,-kap),CC1,CC0,z); fprintf(bedat, "%g %g\n", z/1000.0, c.sqabs()); c = cmtcoeff(1,b0b,b1b,Complex(0.0,-kap),CC1,CC0,z); fprintf(bmdat, "%g %g\n", z/1000.0, c.sqabs()); } fclose(fedat); fclose(fmdat); fclose(bedat); fclose(bmdat); } return 0; }