Coupled Polarization Tensors

This notebook calculates coupled tensor elements (Subscript[ϵ, Q]^K)(j,j')needed in the density matrix equations written in irreducible tensor notation

Download Clebsch-GordanGordan subroutine from where you store it or use Mathematica version    ClebschGordan[{(Subscript[j, 1]),(Subscript[m, 1])},{(Subscript[j, 2]),(Subscript[m, 2])},{j,m}]

Program

<<c:\pberman\mathematica\5.2\clebsh.m

kron[G_,G1_]:=If[G==G1,1,0]

ϵ[K_,Q_,j_,jp_]:=Sum[(-1)^qp ϵ[q,j]Conjugate[ϵ[-qp,jp]]CG[{1,q},{1,qp},{K,Q}],{q,-1,1},{qp,-1,1}]

***must read in values for individual field polarization**

linearly - polarized fields

*** field 1 is x-polarized**

ϵ[q_,1]:=(kron[q,-1]-kron[q,1])/Sqrt[2]

**field 2 is y-polarized**

ϵ[q_,2]:=-I(kron[q,-1]+kron[q,1])/Sqrt[2]

Table[ϵ[k,q,1,1],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,2,2],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,1,2],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,2,1],{k,0,2},{q,k,-k,-1}]

sigma plus - sigma minus polarization

*** field 1 is sigma plus-polarized**

ϵ[q_,1]:=kron[q,-1]

**field 2 is sigma minus-polarized**

ϵ[q_,2]:=kron[q,1]

Table[ϵ[k,q,1,1],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,2,2],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,1,2],{k,0,2},{q,k,-k,-1}]

Table[ϵ[k,q,2,1],{k,0,2},{q,k,-k,-1}]