power is completely transferred into the other waveguide. But it is back after a distance of even multiple of the coupling lengths (2Lc, 4Lc, 6Lc, etc). If the …, waveguiding mode traverses a distance of odd multiple of the half coupling length (Lc/2, 3Lc/2, 5Lc/2, etc), the optical power is equally distributed in the two guides. …, 8-2 Matrix Solutions of Linear Systems Eg. Solve . (Sol.) -1diagonalizable det, λ=2, , λ1=2, , λ2=-1, Eg. Solve . (Sol.) 2 det, λ=2, of (λ-2)2not diagonalizable dim(V)-Rank(A-2I)=12=Multiplicity λ=2, Eg. Solve . (Sol.) -1, -1. f(λ)=-λ3+3λ+2=0, λ=2, For of (λ+1)2diagonalizable dim(V)-Rank(A+I)=2=Multiplicity λ=-1, or λ=-1, λ=2, Eg. . (Sol.) , λ=-1+i, , λ=-1-i, , Eg. Solve +. (Sol.) -3, det=λ2+4λ+3=0, λ=-1, and λ1=-1 λ2=-3, . Particular solution: = Xp TYp, Xp’=AXp+g(t)TYp’=ATYp+g(t)Yp’=T-1ATYp+ T(t) Choose such that , , T =
power is completely transferred into the other waveguide. But it is back after a distance of even multiple of the coupling lengths (2Lc, 4Lc, 6Lc, …, etc). If the waveguiding mode traverses a distance of odd multiple of the half coupling length (Lc/2, 3Lc/2, 5Lc/2, …, etc), the optical power is equally distributed in the two guides. 8-2 Matrix Solutions of Linear Systems Eg. Solve . (Sol.) det, λ=2, -1diagonalizable λ1=2, , λ2=-1, , Eg. Solve . (Sol.) det, λ=2, 2 dim(V)-Rank(A-2I)=12=Multiplicity of (λ-2)2not diagonalizable λ=2, Eg. Solve . (Sol.) f(λ)=-λ3+3λ+2=0, λ=2, -1, -1. For λ=-1, dim(V)-Rank(A+I)=2=Multiplicity of (λ+1)2diagonalizable λ=-1, or λ=2, Eg. . (Sol.) , λ=-1+i, , λ=-1-i, , Eg. Solve +. (Sol.) det=λ2+4λ+3=0, λ=-1, -3, λ1=-1 and λ2=-3, . Particular solution: Xp = TYp, Xp’=AXp+g(t)TYp’=ATYp+g(t)Yp’=T-1ATYp+ T(t) Choose T such that , , =
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