Example: \(n_1=2.35, n_2=1.45, n_a=1.52, n_a=1\), width of high reflection zone \(\Delta\lambda_0=16\) nm, reflectance in the vicinity of the central wavelength 532 nm is R(λ0)=99.99%.
Using NOTCH CALCULATOR (Columns F,G or I,J) we find that in the case of structure S1 \(p=0.06\) is suitable and in the case of structure S2 \(p=0.12\) is suitable.
Specifying \(p=0.12\) (Cell B6), we find from Columns A and D that starting from \(n=56\), R(λ0)>99.99%.
Specifying a starting design with \(n=64\) (128 layers) and p=0.12, i.e.
\(n_s |\left(3.88 A \;\;0.12 B\right)^n| n_a\)
and applying need optimization technique, we obtain a 140-layer design shown in the right pane.
Design process is illustrated in our video example at YouTube .
Layer thicknesses of the starting design are 220 nm and 11 nm.
Thicknesses of almost all layers in the final design are 217 and 12 nm, that is very close to the layer thicknesses of the starting design.
Width of the high reflection zone is 16 nm and reflectance in the high reflection zone takes the values > 99.99%.
See the details in the publication:
T.V. Amotchkina, "Analytical estimations for the reference wavelength reflectance and width of high reflection zone of two-material periodic multilayers," Appl. Opt. 52, 4590-4595 (2013).