M. The parameter σ is related to the accuracy of the deposition
process and can be estimated experimentally. To provide more
stable designs, the cloud size M should not be too small; at the
same time, large M values slow down calculations significantly.
A balanced value for M is 100 to 200. If the layer thicknesses of
an N-layer pivotal design are di, then the layer thicknesses of a
design in the cloud are di + δi, where δi are normally distributed
random values with zero mean and root-mean-squared (rms) σ.
For demonstration, we consider the design problem of a highly dispersive mirror. The mirror has to compensate GDD of
-200 fs2 in the spectral range from 700 to 900 nm. We consider B260 glass as a substrate and niobium pentoxide (Nb2O5)
and SiO2 as layer materials.
First, using a gradual evolution technique, we obtain a conventional design with GDD and reflectance shown in Figure
3(a); the stability condition is not taken into account. The
number of layers in this design is 88, and the total physical
thickness is 9. 3 µm.
Next, we use the robust design algorithm for the same problem.
Based on deposition experience, we estimate absolute errors in
layer thicknesses are at the σ = 0.5 nm level. We obtain a 66-lay-
er robust design with spectral characteristics shown in Figure
3(b). Both designs (conventional and robust) have comparable
spectral performances in the 700 to 900 nm wavelength range.
To estimate the sensitivity of the resulting designs to thickness errors, we performed a standard statistical analysis with
a specified level of absolute errors of 0.5 nm. The gray area
confined by green curves represents a corridor of errors in
GDD. We observe significant reduction of the sensitivity of
GDD to layer-thickness errors for the robust design as compared to the conventional one.
Vladimir Pervak of the Max-Planck-Institute of Quantum
Optics (Munich, Germany), an experienced optical-coating engineer and a winner of several Optical Interference Coatings
(OIC) design contests, uses OptiLayer for the design of dispersive mirrors. Deposition experiments performed by Pervak
demonstrate that spectral characteristics of the robust designs
exhibit much better reproducibility of target spectral characteristics than those of conventional designs.
1. U. Brauneck et al., “Automated sensitivity-directed algorithm for designing
of broadband blocking filters,” submitted to Appl. Opt.
2. T. Amotchkina et al., Proc. SPIE 8186, 816809 (2011).
3.V. Janicki et al., Opt. Express 19, 25521 (2011).
4.V. Pervak et al., Opt. Express 19, 2371 (2011).
Tatiana Amotchkina, Michael Trubetskov, and Alexander
Tikhonravov work at OptiLayer, Munich, Germany; email: amotch-
firstname.lastname@example.org www.optilayer.com. Jennifer J. T. Kruschwitz is
principal optical coating engineer at JK Consulting, Rochester, NY.