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Download Handbook of Laser Technology: Applications by Colin E. Webb, Julian D. C. Jones PDF

By Colin E. Webb, Julian D. C. Jones

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36) is the dispersion relation for extraordinary waves. (1) (2) (1) For f = 0 it follows that Dβ = 0 and Dα = 0, and further that Dα = Dα (2) and Dβ = −Dβ . 37) where k1 (β, α) = k1 ek (β, α), k2 (β, α) = k2 (β)ek (β, α), and for notation simplification, the dependence of the spherical unit vectors eα and eβ on the spherical angles β and α is omitted. 39) respectively. For isotropic media, the only nonzero λ functions are λββ and λαα , and we have λββ = λαα = λ. , k1 = k2 = k, and the dispersion relation is k 2 = k02 εµ .

6. The particle coordinate system Oxyz and the beam coordinate system Oxb yb zb have the same spatial orientation 20 1 Basic Theory of Electromagnetic Scattering where (ρ0 , ϕ0 , z0 ) are the cylindrical coordinates of r 0 , Ψ0 = jQ exp −jQ ρ20 + ρ2n w02 , Q= 1 , j − 2z0 /l ρn = 1 ks n+ 1 2 , and u = 2Q ρ0 ρn . w02 The normalization constant Kmn is given by Kmn = 2jn n(n + 1) 2n + 1 for m = 0, and by jn+|m| Kmn = (−1)|m| n+ 1 |m|−1 2 2n + 1 (n + |m|)! · n(n + 1) (n − |m|)! for m = 0. If both coordinate systems coincide (ρ0 = 0), all expansion coefficients are zero unless m = ±1 and √ ρ2 a1n = −a−1n = jn−1 2n + 1 exp − n2 w0 √ ρ2 b1n = b−1n = jn−1 2n + 1 exp − n2 w0 , .

3 Internal Field ∞ −Dβ (β, α) = −ε n 1 4πjn+1 n=1 m=−n 1 2n(n + 1) 27 mπn|m| (β)cmn + τn|m| (β)dmn ejmα and ∞ Dα (β, α) = −ε n 1 n+1 4πj n=1 m=−n 1 2n(n + 1) jτn|m| (β)cmn + jmπn|m| (β)dmn ejmα , respectively. 45) 0 + j ελββ (β)mπn|m| (β)ejk2 (β,α)·r eα ejmα sin β dβ dα , and Y hmn (r) = − 1 4πjn+1 +j 2π 1 2n(n + 1) 0 π mπn|m| (β)ejk1 (β,α)·r eβ 0 ελββ (β)τn|m| (β)ejk2 (β,α)·r eα ejmα sin β dβ dα . 42), the electromagnetic fields are expressed in terms of the unknown expansion coefficients cmn and dmn .

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