Diffraction efficiency as a function of lambda and theta for  a volume transmission grating

From Optical Imaging and Spectroscopy (Wiley - OSA 2009)
By David J. Brady
www.opticalimaging.org
Figures 9.18, 9.20, 9.43, 9.44

theta=Pi/12;
dEps=5 10^(-2);
K=4 Pi Sin[theta];
krz[dT_,dL_]:=2 Pi Cos[theta+dT]/(1+dL);
krx[dT_,dL_]:=2 Pi Sin[theta+dT]/(1+dL);
ksx[dT_,dL_]:=krx[dT,dL]-K;
ksz[dT_,dL_]:=Sqrt[(4 Pi^2)/(1+dL)^2-ksx[dT,dL]^2];
gamma[dT_,dL_]:=Sqrt[(krz[dT,dL]-ksz[dT,dL])^2+dEps^2 (2 Pi)^4/(krz[dT,dL] ksz[dT,dL])]/2;
L=Pi /(2 gamma[0,0]);
R[dT_,dL_]:=Cos[gamma[dT,dL] L]-(I (krz[dT,dL]-ksz[dT,dL])/(2 gamma[dT,dL])) Sin[gamma[dT,dL] L];
S[dT_,dL_]:=(4 Pi^2/(2 gamma[dT,dL] ksz[dT,dL]))dEps* Sin[gamma[dT,dL] L];
Eta[dT_,dL_]:=Abs[S[dT,dL]]^2;

dog=Plot3D[Eta[Pi dt/180,dl],{dt,-15,15},{dl,-.1,.1},PlotPoints->50,Mesh->False,Lighting->{{"Directional",GrayLevel[.8,.5],{{5,5,4},{5,5,0}}}},AxesLabel->{Δθ,Δλ}]

Plot[Eta[dt*Pi/180,0],{dt,-15,15},PlotRange->All,PlotPoints->50,Axes->False,Frame->True,FrameLabel->{Δθ}]

dkLam[theta_]:=Abs[D[(1/lam)(1-Sqrt[Sin[theta]^2(1-2 lam)^2+Cos[theta]^2]),lam]/.lam->1]/2;
dkTheta[theta_]:=Abs[D[(1-Sqrt[(Sin[thetap]-2 Sin[theta] )^2+Cos[thetap]^2]),thetap]/.thetap->theta];

ap=Plot[dkLam[Pi theta/180],{theta,0,180},Axes->False,Frame->True,FrameLabel->{θ,Δk},PlotStyle->{Black},PlotLabel->"(a)"]

ab=Plot[dkTheta[Pi theta/180],{theta,0,180},Axes->False,Frame->True,FrameLabel->{θ,Δk},PlotStyle->{Black},PlotLabel->"(b)"]

Show[GraphicsArray[{{ap},{ab}}]]

theta=Pi/12;
dEps=5 10^(-2);
K=4 Pi Sin[theta];
krz[dT_,dL_]:=2 Pi Cos[theta+dT]/(1+dL);
krx[dT_,dL_]:=2 Pi Sin[theta+dT]/(1+dL);
ksx[dT_,dL_]:=krx[dT,dL]-K;
ksz[dT_,dL_]:=Sqrt[(4 Pi^2)/(1+dL)^2-ksx[dT,dL]^2];
gamma[dT_,dL_]:=Sqrt[(krz[dT,dL]-ksz[dT,dL])^2+dEps^2 (2 Pi)^4/(krz[dT,dL] ksz[dT,dL])]/2;
L=Pi /(2 gamma[0,0]);
R[dT_,dL_]:=Cos[gamma[dT,dL] L]-(I (krz[dT,dL]-ksz[dT,dL])/(2 gamma[dT,dL])) Sin[gamma[dT,dL] L];
S[dT_,dL_]:=(4 Pi^2/(2 gamma[dT,dL] ksz[dT,dL]))dEps* Sin[gamma[dT,dL] L];
Eta[dT_,dL_]:=Abs[S[dT,dL]]^2;

dog=DensityPlot[Eta[Pi dt/180,dl],{dt,-15,15},{dl,-.1,.1},PlotPoints->50,Mesh->False,FrameLabel->{Δθ,Δλ},PlotRange->All,ColorFunction->Function[{dt,tl,z},GrayLevel[1-z]],PlotLabel->"(a)"]

theta=Pi/12;
dEps=5 10^(-3);
K=4 Pi Sin[theta];
krz[dT_,dL_]:=2 Pi Cos[theta+dT]/(1+dL);
krx[dT_,dL_]:=2 Pi Sin[theta+dT]/(1+dL);
ksx[dT_,dL_]:=krx[dT,dL]-K;
ksz[dT_,dL_]:=Sqrt[(4 Pi^2)/(1+dL)^2-ksx[dT,dL]^2];
gamma[dT_,dL_]:=Sqrt[(krz[dT,dL]-ksz[dT,dL])^2+dEps^2 (2 Pi)^4/(krz[dT,dL] ksz[dT,dL])]/2;
L=Pi /(2 gamma[0,0]);
R[dT_,dL_]:=Cos[gamma[dT,dL] L]-(I (krz[dT,dL]-ksz[dT,dL])/(2 gamma[dT,dL])) Sin[gamma[dT,dL] L];
S[dT_,dL_]:=(4 Pi^2/(2 gamma[dT,dL] ksz[dT,dL]))dEps* Sin[gamma[dT,dL] L];
Eta[dT_,dL_]:=Abs[S[dT,dL]]^2;

dogb=DensityPlot[Eta[Pi dt/180,dl],{dt,-15,15},{dl,-.1,.1},PlotPoints->50,Mesh->False,FrameLabel->{Δθ,Δλ},PlotRange->All,ColorFunction->Function[{dt,tl,z},GrayLevel[1-z]],PlotLabel->"(b)"]

Show[GraphicsArray[{dog,dogb}]]

dogc=DensityPlot[Eta[Pi dt/180,dl]+Eta[Pi (dt-2)/180,dl]+Eta[Pi (dt+2)/180,dl],{dt,-15,15},{dl,-.1,.1},PlotPoints->50,Mesh->False,FrameLabel->{Δθ,Δλ},PlotRange->All,ColorFunction->Function[{dt,tl,z},GrayLevel[1-z]]]