OPTICAL DESIGN

using merit-function-sensitivity analysis and performs the refinement with respect to active thicknesses only. This algorithm concept was devised by Ulf Brauneck, an optical coating designer at Schott Schweiz-Schott Suisse SA.

However, manual application of this algorithm is time consuming and requires considerable designer experience, especially when the number of layers is high and not just one, but two or three layers are active. We have developed an automated version of this approach that allows obtaining several nearly quar- ter-wave design solutions using different algorithm settings: number of active layers, possibility of using needle variations, and so on.1

Here, for illustration, we design a blocking filter with target transmittance less than 1% in the spectral ranges from 265 to 332 nm and 445 to 535 nm and more than 99% in the range from 370 to 390 nm [see Fig.

b) QWOT

position processes while retaining the coating’s excellent spectral properties.

Design of blocking and edge filters

Currently, experienced engineers invent their own empirical approaches to avoid complicated design solutions obtained by basic optimization techniques and to acquire designs of a desired structure. In many cases, to design broadband blocking filters (short-pass and

FIGURE 1. Transmittance characteristics for a blocking filter (a) and a near-quarter- wave design solution obtained with a sensitivity-directed refinement (SDR) algorithm.

Layer number

FIGURE 2. Refractive index and extinction coefficients of silver (Ag) films (a), a CIE chromaticity diagram with the color coordinates for the frontand back-reflection colors of the final design (b), the filter’s final design (c), and experimental samples produced at IRB (d).3

1(a); green]. We consider Schott B270 crown glass as a substrate and tantalum pentoxide (Ta2O5) and silicon dioxide (SiO2) as layer materials. As a starting design, we specify a

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combination of two quarter-wave stacks: the layers 1 through 26 have 1.75 quarter-wave optical thicknesses (QWOT) and the layers 27 through 46 have 1.0 QWOT (the reference wavelength is 300 nm).

Transmittance of the starting design is plotted in Figure 1(a), represented by a red curve. In the course of SDR, the thicknesses of only 11 layers were activated; 35 layers stayed frozen. The final design can be seen in Figure 1(b); its transmittance is shown in Figure 1(a) by a black curve. The design, obtained by SDR, is shown to provide excellent spectral performance and at the same time is nearly quarter-wave.

Metal-dielectric composite color coatings

Metal-dielectric composites are attracting interest in coating design because they exhibit surface-plasmon resonance of free electrons, which results in a strong absorption at specific wavelengths that depend on the particle size, shape, spatial distribution, and dielectric environment. Incorporating metal clusters in dielectric coatings can enable even more sophisticated spectral performance for multilayer systems than relying on only traditional absorption or only interference properties.

Metal-dielectric coatings can be easily produced using standard thin-film equipment. Contrary to dielectrics with optical constants n(λ) and k(λ), the effective optical constants of thin metal layers are dependent on layer thickness d as well as on their dielectric environment. Typically, the designers know optical constants n(λ,d) and k(λ,d) of certain combinations—for example, a sandwich: dielectric layer/metal film/dielectric layer. Optical-coating engineers should be aware that when designing such coatings, conventional techniques allowing variations of film thicknesses are not suitable.

OptiLayer suggests specifying a starting design as a sandwich with fixed layer thicknesses and applying a gradual evolution technique with special settings, assuming insertion of new layers either near the substrate or near the ambient medium only. In this case, the sandwich stays frozen. To improve the design performance after this gradual evolution step, a constrained optimization technique can be used.2

For illustration, we designed coatings that have different colors for reflected light from their front and back sides and keep transmittance at a level >50%. The first condition cannot be fulfilled using dielectric layers only since different reflectance from each side requires the use of absorbing layers. For example, if a coating is to have orange and violet colors reflect from its front and back sides, then target color coordinates of reflectance (R) and backside reflectance (BR) in a CIE XYZ color system are x = 0.5, y = 0.4 (orange) and x = 0.2, y = 0.1 (violet).

OptiLayer allows optimizing coatings with respect to spectral target along with color targets, and we specify target integral transmittance in the visible spectral range >50%. We consider a SiO2 (78 nm)/Ag (12 nm)/SiO2 (78 nm) combination as a sandwich structure. The optical constants of this combination are shown in Figure 2(a). Application of a gradual evolution

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technique with subsequent constrained optimization gives the final design structure presented in Figure 2(b). Color coordinates of the final design are shown in the chromaticity color diagram seen in Figure 2(c). Integral transmittance of the final design in the visible spectral range is 56%. A series of similar designs based on gold (Au) with different combinations of reflected

Ultra-fast laser coatings

The use of ultrafast optics is rapidly growing in physics. Dispersive dielectric multilayer mirrors are the key elements controlling group-delay dispersion (GDD) of high-intensity femtosecond laser pulses. They allow generating sub-5-fs pulses directly from the cavity of a titanium:sapphire (Ti:sapphire) laser.

At the current state of the art, typical highly dispersive mirrors contain 70 to 120 layers. Production of such coatings is a challenge for optical coating engineers because dispersive mirrors are extremely sensitive to deposition errors. The usage of

tion rates makes possible accurate time control of layer thicknesses during mirror deposition.

Some errors in layer thicknesses are still inevitable in the course of coating production. We have developed software that can decrease the sensitivity of dispersive mirrors to errors by including design stability into the formulation of the design problem. The robust synthesis method produces stable final designs without using special starting designs.

The key robust design parameters are: (1) a level of absolute (or relative) errors σ and (2) the number of designs in a cloud

OPTICAL DESIGN continued

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.4

REFERENCES:

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: amotchkina@optilayer.com www.optilayer.com. Jennifer J.T. Kruschwitz is principal optical coating engineer at JK Consulting, Rochester, NY.