We present the design and production approach of an ultra-steep notch filter. The notch filter that does not have thin layers is optimized utilizing the constrained optimization technique, and this is well suitable for accurate monitoring with the electron beam deposition technique. Single layer SiO2 and Ta2O5 films were deposited and carefully characterized in order to determine tooling factors and refractive indices wavelength dependencies accurately. We produced the ultra-steep notch filter with indirect monochromatic monitoring strategy and demonstrated the excellent correspondence to the theoretical spectral performance.
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Notch filters are optical filters that selectively reject a wavelength band and transmit at both shorter and longer wavelengths [1, 2]. Such filters have various scientific and technological applications, including protection from laser radiation, laser-based fluorescence instrumentation, raman spectroscopy, and other applications.
Rugate filters with continuously modulated refractive indices are a promising method to design notch filter . They offer various advantages in optical performances, including extremely broad passbands and perfectly suppressed ripples by apodization [4, 5]. Even though the theoretical aspects of this filter type and the achievable extraordinary spectral characteristics are clarified, the realization and sufficient reproduction of gradient-index filters still pose a challenging problem [6, 7].
Two-material multilayers are the simplest way to design notch filters. Researchers proposed many methods to improve the performance of two-material filters. Utilizing the approach with equivalent layers, high-performance two-material notch filters have been designed and produced [8–10]. However, two-material designs often have very thin layers that are difficult to control precisely, and such notch filters are typically produced by ion beam sputtering which results in a long deposition time and high stress.
The ion-assisted electron-beam deposition technology is the most widely used technology in coating production. It possesses the advantages of high deposition rate and good stress quality. In order to fabricate notch filters with this widely spread deposition technique, layer thickness constraints must be taken into account. An accurate control of index of refraction and thickness of each layer during deposition may be greatly improved if layer thicknesses are not too thin or too thick .
In this paper, we present the design and production approach of an ultra-steep notch filter. The notch filter with layer thicknesses that are close to half-wave of rejection wavelength is optimized utilizing the constrained optimization technique, and therefore are better suitable for accurate monitoring during the deposition. Single layer SiO2 and Ta2O5 films were deposited and characterized for accurate determination of tooling factors and refractive indices wavelength dependencies. We produced the ultra-steep notch filter with indirect monochromatic monitoring strategy by ion-assisted electron-beam deposition and demonstrated an excellent correspondence to the theoretical spectral performance. Moreover, we performed reverse engineering of the deposited filter to show that remaining deviations from the target curve are connected to the low-index layers.
2. Design of the ultra-steep notch filter
We consider the notch filter with the performance that should satisfy the following demands under normal incidence: high transmittance (no back side reflections include) in the wavelength ranges of 400-500 nm and 550-700 nm, and high reflectivity in the spectral region from 500 to 550 nm, as shown by the purple dots in Fig. 1.
In reference , we proposed an approach to design notch filters with layer thicknesses around half-wave of the rejection wavelength. The reason for designing filters without thin layers is as follows. In order to achieve a practical coating design, layer thickness constraints can be an important additional demand that should be taken into account. There may be practically proved lower limits for physical layer thicknesses for conventional deposition processes . Lower thickness limits can be also applied in connection with monitoring strategies used for coating production. For non-quarter wave multilayers, level monitoring is often used . To minimize thickness error, active monochromatic monitoring strategies involving corrections of termination levels require that at least one monitoring signal extremum is registered during a layer deposition [15, 16]. This is possible only if a monitored layer is thick enough.
It may be also desirable to apply upper limits for thicknesses of individual layers. With a large film thickness, essential changes of film structure can take place. Upper constraints for individual layer thicknesses may also help to avoid unreasonably high total optical thickness values.
In this paper we apply the constrained optimization in  for designing of the notch filter. The lower and upper constraints for layer optical thicknesses are 100 and 350nm. The layer thicknesses profile and spectral response of the final design obtained using OptiLayer software  are shown in Fig. 1. The average transmittance is higher than 99%, and the bandwidth of the transmission zone at the −30 dB and −0.5dB attenuation level are 30nm and 52nm respectively, and the steepness is defined by the ratio of two bandwidth values . As compared to the notch filter designs obtained using apodization technique in  some layers near the substrate have been additionally optimized to suppress transmittance ripples in the passbands. However the main structure is still an apodized multilayer stack. Additionally, as we can expect, all layers of the obtained design have optical thicknesses close to half-wave of the central rejection wavelength and therefore are suitable for accurate monitoring during the deposition. Such coating can be produced by ion-assisted electron-beam deposition technology with high deposition rate and good stress quality.
3. Deposition and characterization of single layers
For the coating production we used the Optorun Electron-beam deposition plant. During deposition layers were densified with an RF-type ion source. Thereby, the selected deposition parameters resulted in coatings without any relevant shift after cooling and venting. The deposition temperature was 473K, and the deposition rates were 0.2nm and 0.6nm for Ta2O5 and SiO2 respectively. The indirect monochromatic back-reflection optical monitor is utilized to control thicknesses of deposited layers. A preliminary calibration is done by pre-production depositions of single Ta2O5 and SiO2 layers aimed at accurate determination of tooling factors and refractive indices wavelength dependencies.
We deposited SiO2 film with the thickness of about 440 nm and Ta2O5 film with the thickness of about 300 nm. In each case there are two films: one is on the monitor glass and another one is on the calotte. Both film pairs were monitored at the wavelength of 750 nm (this wavelength was chosen because it is most often present in our monitoring runsheet for the notch filter). Depositions of both film pairs were terminated at a swing level of 50% around the above mentioned thickness values, and the monitoring signals passed two minima and two maxima before termination instants.
After the deposition, spectral responses of the produced samples were measured using Cary5000 spectrophotometer, and the refractive indices and thicknesses were derived using OptiChar characterization software  and verified versus well-known results related to thin films of the same materials . Thicknesses of the films on the test glasses were derived from the swing level, and the ratios of the above thicknesses were used to define tooling factors. Figure 2 shows measured transmittance data for the Ta2O5 films and the transmittance of uncoated substrate. All maxima of the measured transmittance coincide with the transmittance of the uncoated substrate, and this means that the films are fairly homogeneous. The deviations from this curve are in the range of 0.1%-0.2%, which does not exceed an estimated accuracy of transmittance measurement data. Thus the application of homogeneous film models for processing of measurement data is well justified now.
The fitting of measurement data by the model transmittance curve is shown in Fig. 3(a). The obtained wavelength dependencies of the refractive index are depicted in Fig. 3(b). There is an excellent correspondence between Ta2O5 indices on monitor glass and on the calotte substrate, and this allows us to neglect possible small offsets in layer refractive indices and determine only errors in layer thicknesses. Moreover there is also an excellent correspondence between found thicknesses of the Ta2O5 film on monitor glass and the planned value. Found thickness value is 3.55 quarter wave optical thickness (QWOT) at 750nm and the planned value corresponding to the 50% swing is 3.54 QWOT. Thickness of the film on the calotte is 3.64 QWOT. This means that monitor film is thinner with the tooling factor 0.975.
Figure 4(a) presents the fitting of measured reflectance data (gray crosses) by model reflectance (solid curve) at the end of discrepancy function minimization for SiO2 film. And wavelength dependence of the refractive index of the SiO2 film is shown in Fig. 4(b). Here we don not have reflectance data for the SiO2 film on monitor glass, since the deposition area in the monitor glass is too small for the reflectance measurement. Nevertheless, the refractive index of the film on calotte is derived from R data with high enough accuracy. Then we used this fixed index to determine thicknesses of the film on calotte and on monitor glass according the transmittance data shown in the Fig. 5. These thicknesses are 3.88 QWOT and 3.56 QWOT respectively, and this gives tooling factor of 0.917.
4. Fabrication of notch filter
In this experiment we used the indirect monochromatic monitoring with level monitoring method. Specifically the Optorun monochromatic back-reflection monitor was used for the notch filter production. The monitoring strategy is using one monitoring chip to control thicknesses of two subsequent high and low index layers (except for the first layer). The main goal of using several monitoring chips instead of one monitoring chip is to prevent the accumulation of errors in the determination of an instant when a layer deposition should be terminated .
We selected a proper sequence of monitoring wavelengths for all monitoring chips with an attempt to improve an accuracy of registration of termination instants. The idea for choosing the monitoring wavelength is that the monitoring signal of each layer should pass at least one extremum and that the difference between the termination level and last registered signal extremum is in the range of 20%-80% of the difference between previous signal extremums. In this case the reflectance is most sensitive to variations in the thickness of a deposited layer. Note that the ratio of the two above mentioned differences is known as a swing . Swing values are typically expressed in percentage.
We produced the notch filter with the tooling factors and refractive indices derived above. After the deposition, transmittance of the sample was measured at normal incidence in the spectral range from 400 nm to 800 nm using a Cary5000 spectrophotometer. In Fig. 6(a) we compare the measured transmittance data and theoretical transmittance data of the sample. In this figure an excellent agreement between theoretical and experimental data is observed.
Although we produced the notch filter with excellent performance, there are still some deviations between experimental and theoretical transmittance data. These deviations are caused by errors in layer parameters. In this experiment we used stable deposition process that produces high density films. Refractive indices of Ta2O5 and SiO2 thin-film materials deposited are stable and known with a high accuracy. This allows us to neglect possible small offsets in layer refractive indices and to attribute the observed deviations only to errors in layer thicknesses.
According to our monitoring strategy, one chip is used to control two subsequent high-index and low-index layers, and layer depositions are terminated according to theoretically predicted swing levels. It can be theoretically shown that such monitoring strategy provides an accurate control of first high-index layers even in the presence of signal drifts. At the same time it is not possible to make the same statement with respect to low-index layers that are second layers of monitored layer pairs. In Fig. 7, we compare the experimental monitoring curves with the theoretical light values, and it shows good correspondence for high-index materials, but some mismatch for the low-index materials. Thus it is reasonable to assume that the deviations observed in Fig. 6(a) can be related to thickness errors in low index layers.
We performed reverse engineering of the deposited notch filter sample with the help of OptiRE software  using the above assumption. Figure 6(b) shows the fitting of measured notch filter transmittance by the model transmittance when the model with random errors in thicknesses of low index layers was applied. The obtained values of these random errors were all in the range of 3.5% of planned theoretical layer thicknesses. The achieved excellent fitting of measurement data confirms that deviations observed in Fig. 6(a) could be indeed attributed to errors in low index layers.
In summary, we designed ultra-steep notch filters using constrained optimization with lower and upper constraints for layer thicknesses. The filter was produced using indirect monochromatic monitoring strategy with conventional deposition technology. The experimental result shows an excellent correspondence with the theoretical spectral performance. Moreover, reverse engineering was performed to demonstrate that the monitoring procedure provides an accurate control of the high-index layers, and that the remaining deviations from the target curve are due to errors in the low-index layers. In the following study, we are going to work on further improvement of our design-monitoring-production chain by improving an accuracy of monitoring of low-index layers.
This work was partly supported by the National Natural Science Foundation of China (Grant Nos. 61235011, 61008030, 61108014, 61205124), and the National 863 Program.
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