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Applied Optics

Applied Optics


  • Vol. 21, Iss. 11 — Jun. 1, 1982
  • pp: 2055–2068

Equivalent layers in oblique incidence: the problem of unsplit admittances and depolarization of partial reflectors

Zdeněk Knittl and Helena Houserková  »View Author Affiliations

Applied Optics, Vol. 21, Issue 11, pp. 2055-2068 (1982)

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Ohmer's algorithm for the complete exact synthesis of three-layer equivalent periods has been generalized for oblique incidence, and a theory was developed for periods with unsplit equivalent admittances, observing simultaneously the corresponding equivalent phase thicknesses. In a parallel development general conditions were deduced for the depolarization of outer media by quarterwave extensions of the central system. In combination, these building blocks enable the design of depolarized partial reflectors. A number of concrete designs are presented on various reflection levels.

© 1982 Optical Society of America

Original Manuscript: July 17, 1981
Published: June 1, 1982

Zdeněk Knittl and Helena Houserková, "Equivalent layers in oblique incidence: the problem of unsplit admittances and depolarization of partial reflectors," Appl. Opt. 21, 2055-2068 (1982)

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  12. In a less effective but more general way a depolarized semireflector could be constructed even if we do not succeed in keeping the ϕe at 90°, but the deviation from the λ/4 condition should only be moderate. Anyway, in this detuned case the phase jumps get out of control and it is only the amplitudes that can be depolarized.
  13. V. R. Costich, Appl. Opt. 9, 866 (1970). [CrossRef] [PubMed]
  14. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), p. 361.
  15. Denoting tanϕ1 = y, tanϕ2 = x, the condition for the intersectional point in a three layer is Px2 + Qx + F = 0, where P = Ay2 + B/y2 + C, Q = Dy + E/y, and A, B, C, D, E, and F are algebraic functions of the nν and Yνp, Yνs, ν = 1,2. Choosing a set of y, one obtains the corresponding set of x (if real). The intersectional levels Ye and ϕe are determined afterward.
  16. No analytical proof has been attempted to prove that M and N are true straight lines, even when they appear so graphically.
  17. It being known that approximately ϕe = ∑ϕν, it may appear surprising that, with ϕ2 in the range (180°, 360°), the equivalent thicknesses ϕe may have the small values indicated in Fig. 3. The explanation is in the accompanying values ϕ1, not shown for brevity. Thus, e.g., in the case of ϕe = 90°, for ϕ2 > 90° they turn out to be negative and the expected sum total is maintained: ϕ2 = 180° implies ϕ1 = −45°, etc. For realistic purposes the negative ϕ1 may be converted positive by adding 180° to each (compare other examples of conversion in the main text), thus increasing the total phase thickness by 360°. Thus the ϕe -labeling in Fig. 3 may also be understood modulo 360°. Alternatively it could also go by the values sinϕe which would be more universal. Figure 3 is only meant as an additional illustration of the limited appearance of the intersections not as a design nomogram.

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