################################################## # L=1 T-matrix elements for homogeneous sphere # Eps, Mu = relative permittivity, permeability # a0 = k0*R # note \overline{f(x)} == f(x) + x*df/dx ################################################## I={0.0,1.0} # spherical bessel function j_1(x) and \overline{j_1}(x) j1(x) = ( abs(x) < 1.0e-2 ? x*(1.0-x*x/10.0)/3.0 : (sin(x)-x*cos(x))/(x*x) ) j1Bar(x) = ( abs(x) < 1.0e-2 ? (2.0/3.0)*x*(1.0-x*x/5.0) : sin(x)-j1(x) ) # spherical Hankel function h_1(x) h1(x) = ( abs(x) < 1.0e-2 ? (-I/(x*x) - I/2.0) : exp(I*x)*(-I-x)/(x*x) ) h1Bar(x) = ( abs(x) < 1.0e-2 ? (I-0.5*I*x*x+2*x*x*x/3.0)/(x*x) : exp(I*x)*(I+x-I*x*x)/(x*x) ) T1M(Eps,Mu,a0,a1) = -1.0*( Mu*j1(a1)*j1Bar(a0) - j1(a0)*j1Bar(a1) ) \ / ( Mu*j1(a1)*h1Bar(a0) - h1(a0)*j1Bar(a1) ); T1N(Eps,Mu,a0,a1) = -1.0*( Eps*j1(a1)*j1Bar(a0) - j1(a0)*j1Bar(a1) ) \ / ( Eps*j1(a1)*h1Bar(a0) - h1(a0)*j1Bar(a1) ); TM(Eps,Mu,a0) = T1M( Eps, Mu, a0, sqrt(Eps*Mu)*a0 ); TN(Eps,Mu,a0) = T1N( Eps, Mu, a0, sqrt(Eps*Mu)*a0 ); ################################################## ################################################## ################################################## E10COARSE='Run1/E10Sphere_327.TMatrix' E10FINE='Run1/E10Sphere_1362.TMatrix' E10M5COARSE='Run1/E10M5Sphere_327.TMatrix' E10M5FINE='Run1/E10M5Sphere_1362.TMatrix' Alpha1=0 # I will plot the diagonal T-matrix element for the Alpha2=1 # spherical waves with indices (L,M,P)=(1,-1,0) # and (L,M,P)=(1,-1,1) set logscale xy set terminal x11 1 set yrange [:2.0] set xlabel '$\omega R/c$' set ylabel '$|T|$' ################################################## ################################################## ################################################## set key at 4,0.001 spacing 6 set title '$T_1^M$ for $\epsilon_r=10$ sphere' plot E10COARSE u (ifeq($2,Alpha1,ifeq($6,Alpha1,$1))):(D2($10,$11)) \ t '$T_1^M$ {\sc scuff}, $N$=327' \ w p pt 7 ps 1.5 \ ,E10FINE u (ifeq($2,Alpha1,ifeq($6,Alpha1,$1))):(D2($10,$11)) \ t '$T_1^M$ {\sc scuff}, $N$=1362' \ w p pt 6 ps 1.5 \ ,abs(TM(10,1,x)) t '$T_1^M$ (theory)' w l lw 2 #call 'latex' 'E10_T1M' set terminal x11 2 set title '$T_1^N$ for $\epsilon_r=10$ sphere' set key at 4,0.01 spacing 6 plot E10COARSE u (ifeq($2,Alpha2,ifeq($6,Alpha2,$1))):(D2($10,$11)) \ t '$T_1^N$ {\sc scuff}, $N$=327' \ w p pt 7 ps 1.5 \ ,E10FINE u (ifeq($2,Alpha2,ifeq($6,Alpha2,$1))):(D2($10,$11)) \ t '$T_1^N$ {\sc scuff}, $N$=1362' \ w p pt 6 ps 2 \ ,abs(TN(10,1,x)) t '$T_1^N$ (theory)' w l lw 2 #call 'latex' 'E10_T1N' ################################################## ################################################## ################################################## set key at 4,0.01 spacing 6 set title '$T_1^M$ for $\{\epsilon_r,\mu_r\}=\{10,5\}$ sphere' plot E10M5COARSE u (ifeq($2,Alpha1,ifeq($6,Alpha1,$1))):(D2($10,$11)) \ t '$T_1^M$ {\sc scuff}, $N$=327' \ w p pt 7 ps 1.5 \ ,E10M5FINE u (ifeq($2,Alpha1,ifeq($6,Alpha1,$1))):(D2($10,$11)) \ t '$T_1^M$ {\sc scuff}, $N$=1362' \ w p pt 6 ps 1.5 \ ,abs(TM(10,5,x)) t '$T_1^M$ (theory)' w l lw 2 call 'latex' 'E10M5_T1M' set terminal x11 2 set title '$T_1^N$ for $\{\epsilon_r,\mu_r\}=\{10,5\}$ sphere' set key at 4,0.01 spacing 6 plot E10M5COARSE u (ifeq($2,Alpha2,ifeq($6,Alpha2,$1))):(D2($10,$11)) \ t '$T_1^N$ {\sc scuff}, $N$=327' \ w p pt 7 ps 1.5 \ ,E10M5FINE u (ifeq($2,Alpha2,ifeq($6,Alpha2,$1))):(D2($10,$11)) \ t '$T_1^N$ {\sc scuff}, $N$=1362' \ w p pt 6 ps 2 \ ,abs(TN(10,5,x)) t '$T_1^N$ (theory)' w l lw 2 call 'latex' 'E10M5_T1N'