Optics and Photonics Journal, 2011, 1, 124-129
doi:10.4236/opj.2011.13021 Published Online September 2011 (http://www.SciRP.org/journal/opj)
Copyright © 2011 SciRes. OPJ
Synthesis of Chained Achromatic Layer Systems Forming
Controlled Low Transmittance Bands
Mohamed Medhat, Samy S. Farag
Physics Department, Faculty of Science, Ain Shams University, Cairo, Egypt
E-mail: mmedhat61@hotmail.com
Received June 2, 2011; revised July 4, 2011; accepted July 16, 2011
Abstract
The approach utilized in the design of achromatic periods formed of two layers a high-index and a low-index
is developed by combining the first two periods together. These two periods are therefore reduced to three
layers a central one, an upper layer and a lower layer. Both the upper and lower layers are matched to the
central at two different wavelengths. This forms the so called a combined achromatic period or the basic unit.
Multilayers showing low transmittance bands are then synthesized of this basic unit. Parameters used in the
synthesis of such multilayers are pointed out and their control role is investigated.
Keywords: Thin Films, Design, Light Propagation
1. Introduction
Recalling the procedure followed in forming two layer
combination [1-3] which are matched according to the
relation
HHH LLL
oN oN
hnG hnG
(1)
where nH and nL are the refractive indices for the high-
and low-layers, respectively, and the h are the physical
thicknesses. Multilayers systems of N such achromatic
periods were formed so that each period matched at spe-
cified wavelength λoN, where N stands for period number.
The different wavelengths, at which the different periods
are formed, are specified according to the quantity ξ de-
fined as
dd dd
oN HHoNLLoN
HH LL
hn hn
nh nh
(2)
In the present work equation (1) is modified to [4]
HHH LLL
oN oN
hnG hnG
MN
(3)
where and N are real numbers [5]. M
Another modification is introduced here in the multi-
layer synthesis process. In a previous work [2,3] multi-
layers of achromatic periods (Equ ation (1)) were built up
by calculating the first achromatic period then subse-
quent periods were automatically built up by the way of
(1) and (2). In the present work the first achromatic pe-
riod is calculated by choo sing an initial cen tral layer then
an upper layer is calculated by matching to this central at
the design starting wavelength, by way of (3), then a
lower layer is matched to the central at another wave-
length. The convention of lower and upper is considered
according to positions of substrate and surrounding me-
dium with respect to the first central. Once the above
three layers are calculated they are considered as the ba-
sic unit. The process of building this basic unit is the
same as combining the two middle layers in the first two
achromatic periods. Subsequent layers are calculated by
considering the lower layer in the basic unit a central for
the following layer, in a chained manner, and so on. By
this means each layer, except the first and the last layers
in whole system, serves as a central layer.
2. Design
Six quantities are first specified, namely the film materi-
als, starting wavelength, number of layers, design num-
ber
, and N. Table 1 shows design details for a
multilayer formed of Zinc Sulphide and Cryolite. These
materials are chosen here only for illustration without
having any particular significance in the theory i.e. any
two materials (high and low) will work. The first central
layer is chosen as a high index layer which is calculated
as a quarter of the starting wavelength 1060 nm. is
M
M