{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "normref.mws " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "reflection and tra nsmission at normal incidence, one and two boundaries." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 59 "transmission coeff f or frustrated total internal reflection" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "f stands for exp(i k1x x) and g stan ds for exp(i k2x x)" }}{PARA 0 "" 0 "" {TEXT -1 49 "k1 is the propagat ion vector in the middle region" }}{PARA 0 "" 0 "" {TEXT -1 46 "k2 is \+ the propagation vector in the far region" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 65 "transmission coefficient is (ExH)t / (E xH)i = (Et/Ei)^2 (nt/ni)," }}{PARA 0 "" 0 "" {TEXT -1 67 "where nt and ni are indices of refraction, transmitted and incident" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 " Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warni ng, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "assume(r>0,a>0,z>0,b>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "m:=matrix(2,2,[[1/2*(a+b)*f/g,1/2*(a-b)/f/g],[1/2*(a-b)*f*g,1/ 2*(a+b)*g/f]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG-%'MATRIXG6#7 $7$,$*(,&%#a|irG\"\"\"%#b|irGF.F.%\"fGF.%\"gG!\"\"#F.\"\"#,$*(,&F-F.F/ F2F.F0F2F1F2F37$,$*(F7F.F0F.F1F.F3,$*(F,F.F1F.F0F2F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "n0:=subs(f=1,g=1,a=1,b=n[1]/n[2],evalm(m) ); #1st surf@x=0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#n0G-%'MATRIXG6# 7$7$,&#\"\"\"\"\"#F,*&&%\"nG6#F,F,&F06#F-!\"\"F+,&F+F,F.#F4F-7$F5F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "n1:=(subs(a=1,b=I*q/r,eval m(m))); # 2nd surf @x=d" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#n1G-%'MA TRIXG6#7$7$,$*(,&\"\"\"F-*(%\"IGF-%\"qGF-%#r|irG!\"\"F-F-%\"fGF-%\"gGF 2#F-\"\"#,$*(,&F-F-F.F2F-F3F2F4F2F57$,$*(F9F-F3F-F4F-F5,$*(F,F-F4F-F3F 2F5" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "n2:=evalm(n0);#n2:=evalm(n1 &* n0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#n2G-%'MATRIXG6#7$7$,&#\"\"\"\"\"#F,*&&%\"nG6 #F,F,&F06#F-!\"\"F+,&F+F,F.#F4F-7$F5F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "A3_A1:=n2[1,1]-n2[1,2]*n2[2,1]/n2[2,2];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%&A3_A1G,(#\"\"\"\"\"#F'*&&%\"nG6#F'F'&F+6#F(! \"\"F&*&,&F&F'F)#F/F(F(,&F&F'F)F&F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "This is the general way to proceed, finding real and imag inary parts, then squaring" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "realpart:=evalc(Re(A3_A1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%) realpartG,(#\"\"\"\"\"#F'*&&%\"nG6#F'F'&F+6#F(!\"\"F&*&,&F&F'F)#F/F(F( ,&F&F'F)F&F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "imagpart: =evalc(Im(A3_A1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)imagpartG\"\" !" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "stotal:=simplify(n[2]/ n[1]*(realpart^2+imagpart^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'s totalG,$*(&%\"nG6#\"\"#\"\"\"&F(6#F+F+,&F'F+F,F+!\"#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "This expression is simpler in this case b ecause the amplitude ratio is real." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "s:=simplify(n[2]/n[1]*A3_A1^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,$*(&%\"nG6#\"\"#\"\"\"&F(6#F+F+,&F'F+F,F+!\"#\" \"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "trcoeff:=evalf(subs( n[2]=1.5,n[1]=1,s));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(trcoeffG$\" +++++'*!#5" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }