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By R. Kingslake

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49) Here p is the density of defects that is taken to be much less than the density of host atoms and effective-field effects have been omitted for simplicity. The 49 3. Analysis of Optical Data refractive index of the host is denoted by no(Og)= e~/2(oj) (the change in index induced by the defect is negligible), and Ak(og) is the absorption induced by the defect. )', d o, (51) m 2 fo' o9' Im[e-1(o')] dog'. 27zZe (52) = nefe(~O)] _, = (50) Here the subscripts e, k, and e- 1 are used to distinguish the partial f sums involving ez(fO), k(o9), and Im[e- 1(o9)], respectively.

1 - Rf) 2 fl+E2(1-2Rf) R=Rf iZRf~ $ T- = (1 - Rf)2E For R f = R~ and 1 2Rf J"~l+Rf 1 - Rf ( 1- 2flsd~ 1 - R 2 E 2 - 1 + Rf - I -- (1 Tf-T~= 2flsds) l+Rf ' l+ R2'] 1 - R2] ' Rf A = 1 - RfE (1 - E o~) -~ 2flsds(1 - 2fl~d~Rf). Approximations hold for E _~ 1-2flsds. ) APPENDIX C REFLECTANCE, R j~ AT j-k INTERFACE lp2 + p 2 _ 2(OC~OCk+ fl~flk) -~ Rjk A A~ -- -~ -- ~ [Pj + Pk + 2%~ + &/~0 (TE, s) = Rjk s r jkr jk ]o I l k $4 + p2p2 _ 2 S 2 ( ~ j ~ k _ fljflk) iks -6X -- ~ -= Rjkp S + PjPR + 2 S 2 ( ~ j ~ k - fljflk) (TM, p).

J. D. Mclntyre and D. E. Aspnes, S u r f . Sci. 24, 417 (1971). Chapter 3 Dispersion Theory, Sum Rules, and Their Application to the Analysis of Optical Data* D. Y. Smith Argonne National Laboratory Argonne, Illinois and M a x - P l a n c k - l n s t i t u t for F e s t k ~ r p e r f o r s c h u n g Stuttgart, Federal Republic of Germany I. Introduction II. Optical Sum Rules and Their Physical Interpretation A. Superconvergence Sum Rules for ~(~) B. Superconvergence Sum Rules for N(~o) C. Superconvergence Sum Rules for Functions of N and D.

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Applied optics and optical engineering. Vol. I: Light. Its generation and modification by R. Kingslake

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