Zur Theorie der Wechselschichten aus schwachabsorbierenden Substanzen und ihre Verwendung als Interferometerspiegel

Abstract

Nit 3 Abbildungen Inhaltsubersich tEs wird mit Hilfe der Matrizenmethode die Absorption von 1.14und ?J2-Wechselschichten aus schwachabsorbierenden, dielektrischen Substa.nzen berechnet. Ferner wird der EinfluB der Absorption bei Verwendung dieser Schichten als Interferometerspiegel untersucht.

Properties of Weakly Absorbing Multilayer Systems in Terms of the Concept of Potential Transmittance

“…This expression is the same as that derived by different means by Giacomo [3] and Koppelmann [4], and it shows that the absorptance of a reflector is independent of the number of layers provided it exceeds about four . Moreover, it has been shown [3,4] that this absorptance occurs in highly reflecting dielectric mirrors at the expense of their reflectance .…”

“…It illustrates that since the reflectance at the design wavelength is usually very small, the absorptance in filters occurs at the expense of the transmittance . Furthermore, the values of 1 -TMAX calculated from the simple analytical expression of equation (24) agree closely with the exact values when the basic approximation of equation (4) The range of validity of equation (4) can be established by considering the extreme case of the spacing layer of the filter . Thus, according to the previously stated condition for the validity of equation (4),…”

“…S" is also very small provided that S' is not unusually large . Accordingly, equation (2) may be written 0 =1-A0 (4) where 00 = 2F [fS' +g sins' cos(p + S')], 1 + jrJ 2 2lrl f 1-rl2 and g= 1 -I r l2 .…”

“…p1=O or ir, (7 .2) depending, respectively, on whether l is an odd or even integer, and (1+Ca) 2 ' If the expressions of equations (7 .1)-(7 .3) are substituted into equation (4) for the potential transmittance, Ot , of the individual layers it follows that A01 = rrkj r1 fi , ( 8 ) where f, = (C l + C -1 )12, and l = n L n L = L, or fl , =n "R /n'. = 1711 , depending, respectively, on whether 1 is even or odd .…”

“…Moreover, it has been shown [3,4] that this absorptance occurs in highly reflecting dielectric mirrors at the expense of their reflectance . Consequently, as the number of layers in the reflector is increased, its reflectance tends to 1-A m and not to unity as it would in the absence of absorption .…”