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Quantum Optics for Engineers by F.J. Duarte

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Appendix D: Multiple-Prism Dispersion Series

D.1  Multiple-Prism Dispersion Series

In Chapter 5, the generalized multiple-prism dispersion equation, applicable to multiple-prism arrays of any geometry, configuration, or materials, is given as (Duarte, 2009)

λϕ2,m=±2,mλnm±(k1,mk2,m)1(1,mλnm(±)λϕ2,(m1))

(D.1)

For positive refraction only, this equation becomes (Duarte and Piper, 1982, 1983)

λϕ2,m=2,mλnm+(k1,mk2,m)1(1,mλnm±λϕ2,(m1))

(D.2)

where the ± sign refers to either a positive (+) or compensating configuration (−).

In Chapter 5, Equation D.2 is expressed in a series format directly applicable to the geometry at hand. Duarte and Piper (1982) also provide further examples of simple special cases leading to explicit ...

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