//VerilogA for passive,mmi2x2,veriloga //Xuanqi Chen, Zhifei Wang, Yi-Shing Chang, Jiang Xu, Jun Feng, Peng Yang, Zhehui Wang, Luan H. K. Duong, ”Modeling and Analysis of Optical Modulators Based on Free-Carrier Plasma Dispersion Effect,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 39, no. 5, pp. 977-990, May 2020. `include "constants.vams" `include "disciplines.vams" `define MAX_MODES 200 `define MAX_ITER 10000 `define IDX_NUM 50000 `define TOLERANCE 0.0000000001 module mmi2x2(Ipow1,Iphase1,Ilam1,Ipow2,Iphase2,Ilam2,Opow1,Ophase1,Olam1,Opow2,Ophase2,Olam2); parameter real design_lam = 1.55e-6 from (0:inf); parameter real n_ps = 3.45 from (0:inf); parameter real n_sub = 1.45 from (0:inf); parameter real width_MMI = 3e-6 from (0:inf); parameter real width_port = 0.45e-6 from (0:inf); parameter real port_offset = 0.75e-6 from (0:inf); parameter real thickness = 0.22e-6 from (0:inf); parameter real alpha_mmi = 80 from (0:inf); input Ipow1,Iphase1,Ilam1,Ipow2,Iphase2,Ilam2; output Opow1,Ophase1,Olam1,Opow2,Ophase2,Olam2; electrical Ipow1,Iphase1,Ilam1,Ipow2,Iphase2,Ilam2,Opow1,Ophase1,Olam1,Opow2,Ophase2,Olam2; real ulam, ulam0, uwidth_in, uwidth_MMI, uoffset, uthickness, alpha0; real k1_ref, kc_ref; integer mode_num, mode_num_ref; real beta_x_MMI, beta_in, beta_x_in; real neff_MMI[0:`MAX_MODES]; real beta_MMI[0:`MAX_MODES]; real length_MMI; real ky_in, gamma_in; real ky_MMI[0:`MAX_MODES]; real gamma_MMI[0:`MAX_MODES]; real c0; real c0_dis[0:`MAX_MODES]; real icoff[0:`MAX_MODES]; real delta_beta; real ocoff_r[0:`MAX_MODES]; real ocoff_i[0:`MAX_MODES]; real c1r, c1i, c2r, c2i; real in1r, in1i, in2r, in2i, out1r, out1i, out2r, out2i; real sum_outfield1, sum_outfield2, sum_outfield3, sum_outfield4; real sum_singlemode1,sum_singlemode2,sum_singlemode3,sum_singlemode4; real border; integer i, j; real p=1; real h; analog function real findzeropoint_rect_x; input x_lower_input, x_upper_input, Vx; real x_lower_input, x_upper_input, Vx; real iter_count; real x_lower, x_upper; real y_mid; real y_lower, x_mid; begin findzeropoint_rect_x = -1; x_lower = x_lower_input; x_upper = x_upper_input; iter_count = 0; y_mid = 1; while (iter_count<`MAX_ITER && abs(y_mid) > `TOLERANCE) begin x_mid = (x_lower + x_upper) / 2; y_lower = tan(x_lower / 2) - sqrt(pow(Vx,2) - pow(x_lower,2)) / x_lower; y_mid = tan(x_mid / 2) - sqrt(pow(Vx,2) - pow(x_mid,2)) / x_mid; if (abs(y_mid) < `TOLERANCE) begin findzeropoint_rect_x = x_mid; end if (y_mid * y_lower < 0) x_upper = x_mid; else x_lower = x_mid; iter_count = iter_count + 1; end if (findzeropoint_rect_x == -1) $display("No zero point found in the given range. Please try again with different range."); end endfunction analog function real findzeropoint_rect_y; input x_lower_input, x_upper_input, Vy, m; real x_lower_input, x_upper_input, Vy, m; real iter_count; real x_lower, x_upper; real y_mid; real y_lower, x_mid; begin x_lower = x_lower_input; x_upper = x_upper_input; iter_count = 0; y_mid = 1; findzeropoint_rect_y = -1; while (iter_count<`MAX_ITER && abs(y_mid) > `TOLERANCE) begin x_mid = (x_lower + x_upper) / 2; y_lower = tan(x_lower / 2 - m * `M_PI / 2) - sqrt((pow(Vy,2) - pow(x_lower,2))) / x_lower; y_mid = tan(x_mid / 2 - m * `M_PI / 2) - sqrt((pow(Vy,2) - pow(x_mid,2))) / x_mid; if (abs(y_mid) < `TOLERANCE) findzeropoint_rect_y = x_mid; if (y_mid * y_lower < 0) x_upper = x_mid; else x_lower = x_mid; iter_count = iter_count + 1; end if (findzeropoint_rect_y == -1) $display("No zero point found in the given range. Please try again with different range."); end endfunction analog function real eim_rect; input lam, width, thickness, n_ps, n_sub, numflag, mode_index; real lam, width, thickness, n_ps, n_sub; integer numflag, mode_index; real k1, Vx, yx, hx, beta_x, neff_x_MMI, Vy, yy, hxy; real beta_xy[0:`MAX_MODES]; real neff_xy[0:`MAX_MODES]; real beta_xy_out[0:`MAX_MODES]; real neff_xy_out[0:`MAX_MODES]; integer i, m, mode_num; begin k1=2*`M_PI*n_ps/lam; Vx=2*`M_PI/lam*thickness*sqrt((pow(n_ps,2)-pow(n_sub,2))); yx=findzeropoint_rect_x(1e-6,min(`M_PI,Vx),Vx); hx=yx/thickness; beta_x=sqrt(pow(k1,2)-pow(hx,2)); neff_x_MMI=lam*beta_x/(2*`M_PI); Vy=2*`M_PI/lam*width*sqrt((pow(neff_x_MMI,2)-pow(n_sub,2))); i=0; m=0; while (m*`M_PI<Vy) begin yy=findzeropoint_rect_y(m*`M_PI+1e-6,min((m+1)*`M_PI-1e-6,Vy),Vy,m); m=m+1; // if m*`M_PI>=Vy // break hxy=yy/width; beta_xy[i]=sqrt(pow(beta_x,2)-pow(hxy,2)); neff_xy[i]=lam*beta_xy[i]/(2*`M_PI); i=i+1; end mode_num=m-1; if (numflag==1 || numflag==2) begin for (i=0;i<mode_num;i=i+1) begin beta_xy_out[i]=beta_xy[i]; neff_xy_out[i]=neff_xy[i]; end if (numflag==1) eim_rect=neff_xy_out[mode_index]; else eim_rect=beta_xy_out[mode_index]; end else if (numflag==3) begin eim_rect=beta_x; end else if (numflag==4) begin eim_rect=mode_num; end end endfunction analog function real fieldfunc; input y,width,offset,ky,gamma,m,c0; real y,width,offset,ky,gamma,m,c0; real fai; begin fai = m * `M_PI / 2; if (((y - offset) <= (width / 2)) && ((-width / 2) <= (y - offset))) fieldfunc=c0 * cos(ky * (y - offset) - fai); else if ((y - offset) > width / 2) fieldfunc=c0 * cos(ky * width / 2 - fai) * exp(-gamma * ((y - offset) - width / 2)); else fieldfunc=c0 * cos(ky * width / 2 + fai) * exp(gamma * ((y - offset) + width / 2)); end endfunction analog function real normpower_fieldfunc_quad; input width,offset,ky,gamma,m,c0,width_MMI,border; real width,offset,ky,gamma,m,c0,width_MMI,border; real n,h; // real border=width_MMI/2; integer i; real sum; begin n=`IDX_NUM; h=border*2/n; sum=0.5*(pow(abs(fieldfunc(-1*border,width,offset,ky,gamma,m,c0)),2)+pow(abs(fieldfunc(border,width,offset,ky,gamma,m,c0)),2)); for (i=1;i<n;i=i+1) begin sum=sum+pow(abs(fieldfunc(-1*border+i*h,width,offset,ky,gamma,m,c0)),2); end normpower_fieldfunc_quad=1/sqrt(h*sum); end endfunction analog function real infidx_modecoeffcient_quad; input width1,offset1,ky1,gamma1,m1,c01,width2,offset2,ky2,gamma2,m2,c02,border; real width1,offset1,ky1,gamma1,m1,c01,width2,offset2,ky2,gamma2,m2,c02,border; real n,h; // real border=20; integer i; real sum; begin n=`IDX_NUM; h=border*2/n; sum=0.5*(fieldfunc(-1*border,width1,offset1,ky1,gamma1,m1,c01)* fieldfunc(-1*border,width2,offset2,ky2,gamma2,m2,c02)+fieldfunc(border,width1,offset1,ky1,gamma1,m1,c01)* fieldfunc(border,width2,offset2,ky2,gamma2,m2,c02)); for (i=1;i<n;i=i+1) begin sum=sum+fieldfunc(-1*border+i*h,width1,offset1,ky1,gamma1,m1,c01)* fieldfunc(-1*border+i*h,width2,offset2,ky2,gamma2,m2,c02); end infidx_modecoeffcient_quad=h*sum; end endfunction analog initial begin ulam0=design_lam*1e6; uwidth_in=width_port*1e6; uwidth_MMI=width_MMI*1e6; uoffset=port_offset*1e6; uthickness=thickness*1e6; alpha0=alpha_mmi*1e-6; k1_ref = 2 * `M_PI * n_ps / ulam0; kc_ref = 2 * `M_PI * n_sub / ulam0; mode_num_ref = eim_rect(ulam0, uwidth_MMI, uthickness, n_ps, n_sub, 4, 0); for (i=0;i<mode_num_ref;i=i+1) begin beta_MMI[i] = eim_rect(ulam0, uwidth_MMI, uthickness, n_ps, n_sub, 2, i); end length_MMI = p*1.5*`M_PI/(beta_MMI[0]-beta_MMI[1]); //1.5Lpi? // $display("length_MMI=%f",length_MMI); border=20; end analog begin ulam = V(Ilam1) * 1e6; beta_in=eim_rect(ulam, uwidth_in, uthickness, n_ps, n_sub, 2, 0); // $display("beta_in=%f",beta_in); beta_x_in=eim_rect(ulam, uwidth_in, uthickness, n_ps, n_sub, 3, 0); // $display("beta_x_in=%f",beta_x_in); beta_x_MMI=eim_rect(ulam, uwidth_MMI, uthickness, n_ps, n_sub, 3, 0); // $display("beta_x_MMI=%f",beta_x_MMI); mode_num = eim_rect(ulam, uwidth_MMI, uthickness, n_ps, n_sub, 4, 0); // $display("mode_num=%d",mode_num); ky_in = sqrt(pow(beta_x_in,2) - pow(beta_in,2)); // $display("ky_in=%f",ky_in); gamma_in = sqrt(pow(beta_in,2) - pow(kc_ref,2)); for (i=0;i<mode_num;i=i+1) begin neff_MMI[i] = eim_rect(ulam, uwidth_MMI, uthickness, n_ps, n_sub, 1, i); beta_MMI[i] = eim_rect(ulam, uwidth_MMI, uthickness, n_ps, n_sub, 2, i); ky_MMI[i] = sqrt(pow(beta_x_MMI,2) - pow(beta_MMI[i],2)); gamma_MMI[i] = sqrt(pow(beta_MMI[i],2) - pow(kc_ref,2)); // $display("neff_MMI[%d]=%f, beta_MMI[%d]=%f, ky_MMI[%d]=%f, gamma_MMI[%d]=%f",i,neff_MMI[i],i,beta_MMI[i],i,ky_MMI[i],i,gamma_MMI[i]); end c0=normpower_fieldfunc_quad(uwidth_in,0,ky_in,gamma_in,0,1,uwidth_MMI,border); // $display("c0=%f",c0); for (i=0;i<mode_num;i=i+1) begin c0_dis[i]=normpower_fieldfunc_quad(uwidth_MMI,0,ky_MMI[i],gamma_MMI[i],i,1,uwidth_MMI,border); // $display("c0_dis[%d]=%f",i,c0_dis[i]); icoff[i]=infidx_modecoeffcient_quad(uwidth_in,uoffset,ky_in,gamma_in,0,c0,uwidth_MMI,0,ky_MMI[i],gamma_MMI[i],i,c0_dis[i],border); // $display("icoff[%d]=%f",i,icoff[i]); end delta_beta = beta_MMI[0] - beta_MMI[1]; // $display("delta_beta=%f",delta_beta); for (i=2;i<mode_num;i=i+1) begin beta_MMI[i]=beta_MMI[0] - i* (i + 2) * delta_beta / 3; // $display("beta_MMI[%d]=%f",i,beta_MMI[i]); end for (i=0;i<mode_num;i=i+1) begin ocoff_r[i]=icoff[i]*cos(-beta_MMI[i]*length_MMI); ocoff_i[i]=icoff[i]*sin(-beta_MMI[i]*length_MMI)*-1.0; // $display("ocoff_r[%d]=%f, ocoff_i[%d]=%f",i,ocoff_r[i],i,ocoff_i[i]); end h=border*2.0/`IDX_NUM; sum_outfield1=0; sum_outfield2=0; sum_outfield3=0; sum_outfield4=0; for (j=0;j<mode_num;j=j+1) begin sum_singlemode1=0.5*(ocoff_r[j]*fieldfunc(-1*border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border,uwidth_in,uoffset,ky_in,gamma_in,0,c0)+ocoff_r[j]*fieldfunc(border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(border,uwidth_in,uoffset,ky_in,gamma_in,0,c0)); sum_singlemode2=0.5*(ocoff_i[j]*fieldfunc(-1*border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border,uwidth_in,uoffset,ky_in,gamma_in,0,c0)+ocoff_i[j]*fieldfunc(border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(border,uwidth_in,uoffset,ky_in,gamma_in,0,c0)); sum_singlemode3=0.5*(ocoff_r[j]*fieldfunc(-1*border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border,uwidth_in,-uoffset,ky_in,gamma_in,0,c0)+ocoff_r[j]*fieldfunc(border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(border,uwidth_in,-uoffset,ky_in,gamma_in,0,c0)); sum_singlemode4=0.5*(ocoff_i[j]*fieldfunc(-1*border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border,uwidth_in,-uoffset,ky_in,gamma_in,0,c0)+ocoff_i[j]*fieldfunc(border,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(border,uwidth_in,-uoffset,ky_in,gamma_in,0,c0)); for (i=1;i<`IDX_NUM;i=i+1) begin sum_singlemode1=sum_singlemode1+ocoff_r[j]*fieldfunc(-1*border+i*h,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border+i*h,uwidth_in,uoffset,ky_in,gamma_in,0,c0); sum_singlemode2=sum_singlemode2+ocoff_i[j]*fieldfunc(-1*border+i*h,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border+i*h,uwidth_in,uoffset,ky_in,gamma_in,0,c0); sum_singlemode3=sum_singlemode3+ocoff_r[j]*fieldfunc(-1*border+i*h,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border+i*h,uwidth_in,-uoffset,ky_in,gamma_in,0,c0); sum_singlemode4=sum_singlemode4+ocoff_i[j]*fieldfunc(-1*border+i*h,uwidth_MMI,0,ky_MMI[j],gamma_MMI[j],j,c0_dis[j])*fieldfunc(-1*border+i*h,uwidth_in,-uoffset,ky_in,gamma_in,0,c0); end // $display("sum_singlemode1=%f, sum_singlemode2=%f, sum_singlemode3=%f, sum_singlemode4=%f",sum_singlemode1,sum_singlemode2,sum_singlemode3,sum_singlemode4); sum_outfield1=sum_outfield1+h*sum_singlemode1; sum_outfield2=sum_outfield2+h*sum_singlemode2; sum_outfield3=sum_outfield3+h*sum_singlemode3; sum_outfield4=sum_outfield4+h*sum_singlemode4; end c1r=sum_outfield1; c1i=sum_outfield2; c2r=sum_outfield3; c2i=sum_outfield4; // $display("c1r=%f, c1i=%f, c2r=%f, c2i=%f",c1r,c1i,c2r,c2i); in1r=sqrt(V(Ipow1))*cos(V(Iphase1)/360.0*2*`M_PI); in1i=sqrt(V(Ipow1))*sin(V(Iphase1)/360.0*2*`M_PI); in2r=sqrt(V(Ipow2))*cos(V(Iphase2)/360.0*2*`M_PI); in2i=sqrt(V(Ipow2))*sin(V(Iphase2)/360.0*2*`M_PI); out1r=c1r*in1r-c1i*in1i+c2r*in2r-c2i*in2i; out1i=c1r*in1i+c1i*in1r+c2r*in2i+c2i*in2r; out2r=c2r*in1r-c2i*in1i-c1r*in2r+c1i*in2i; out2i=c2r*in1i+c2i*in1r-c1r*in2i-c1i*in2r; V(Opow1) <+ pow(out1r,2)+pow(out1i,2); V(Ophase1) <+ atan2(out1i,out1r)*360.0/(2*`M_PI); V(Olam1) <+ ulam/1e6; V(Opow2) <+ pow(out2r,2)+pow(out2i,2); V(Ophase2) <+ atan2(out2i,out2r)*360.0/(2*`M_PI); V(Olam2) <+ ulam/1e6; end endmodule