1. Discrete Versus Multi-Index Designs
Standard optical thin film systems are normally realized using discrete designs of two different refractive indices [Fig. 1(a)
]. For these systems, the complete technology chain from design up to reverse engineering has been highly developed. Practically all layer systems for normal incidence can be realized in this way. But for oblique incidence, polarization effects occur—especially in cemented systems. From our experience, conventional designs for cemented systems often become very complex, and include a high number of thin layers. Also, polarization control for oblique systems may be very difficult or even impossible to achieve.
Fig. 1. Schematic diagram of (a) discrete versus (b) gradient designs.
Gradient or multi-index designs offer additional degrees of freedom for designing complex systems [Fig. 1(b)
]. Unfortunately the technology chain for these systems is still in an initial phase. Design methods are not available, and the technology for continuous refractive index profiles has not been introduced into routine production yet.
shows an example of how designs can be simplified by using mixed layers with adapted refractive index for a simple beam splitter that is color neutral in the visible spectral range with an extra feature in the near infrared. Design (a) uses two standard coating materials. It consists of 107 layers, many of them very thin (
), with a total thickness of 6.3 μm. Design (b) has practically the same optical performance, but uses a mixed layer with a well-adapted refractive index. With this design, complexity is significantly reduced—only 25 layers with thickness
, and a total thickness of only 3.1 μm.
Fig. 2. Example for improved polarization control. Two cemented 45° beam splitter designs: (a) standard coating materials and (b) mixed layer.
Fig. 3. Realization of mixed layers using Zeiss magnetron sputter tool.
Mixed layers with refractive indices well adapted to the design problem can not only simplify designs, but also enable designs that are impossible using a conventional two-layer solution. Here we show two examples. Both have two 45° prisms cemented together. The first example is a nonpolarizing edge filter shown in Fig. 4
. By using five different indices, the spectral offset between
-edges is only a few nanometers.
Fig. 4. Multi-index example 1: nonpolarizing edge filter.
The second example is a nonpolarizing beam splitter, shown in Fig. 5
. Using three different refractive indices, the design polarization ratio
is practically zero.
Fig. 5. Multi-index example 2: nonpolarizing beam splitter.
The interesting question behind the examples shown is, “how do we find these simplifying or enabling refractive indices?”
2. Zeiss Design Software for Rugate and Gradient Designs
One technology that can be used to produce gradient coatings is the codeposition of two materials with a variable composition ratio
. The refractive index of the resulting mixed material is a function of the volume ratio, which can be determined experimentally, or derived theoretically [1
1. S. W. Anzengruber, E. Klann, R. Ramlau, and D. Tonova, “Numerical methods for the design of gradient-index optical coatings,” Appl. Opt. 51, 8277–8295 (2012). [CrossRef]
]. Thus, the dependence of the gradient coating refractive index on the depth (
) can be represented by the function
, which complies with the condition
. From the coating technology point of view, the design problem of gradient coatings can be formulated as follows: “find a coating design with a volume ratio function
and a thickness
, that fulfills the required optical tolerances and can be produced with the available coating technology” (Fig. 6
Fig. 6. Schematic diagram of the rugate design problem.
In our recent publication [1
1. S. W. Anzengruber, E. Klann, R. Ramlau, and D. Tonova, “Numerical methods for the design of gradient-index optical coatings,” Appl. Opt. 51, 8277–8295 (2012). [CrossRef]
], this design problem is formulated as a nonlinear optimization problem for composition (
) and thickness (
is a least-square function defined as
or including a penalty term
Fulfilling the constraint guarantees that the coating design can be realized with physically available materials.
In formulas (2
) and (3
is the target optical performance, defined as a number of wavelengths
and angles of incidence
. It can be an arbitrary function of the reflection and transmission. In formula (3
), a penalized least-square functional is considered. The penalty functional
can be chosen in different ways, to realize certain properties of the solution, e.g., the constraint on
, or the differentiability of the solution. The parameter
is a nonnegative number. The optimization problem (1
) can be solved with different nonlinear inverse methods with box constraints.
shows three calculated rugate composition profile examples as a function of layer thickness together with the spectral optical performance. For absorption free layers, the composition profile can be easily transferred to the refractive index profile. For practical purposes, the rugate design is often too difficult to realize. Therefore the design software has a second module that allows us to transfer the rugate design to a quasi-gradient design. This is illustrated in Fig. 8
Fig. 7. Gradient-design examples. (a) Notch filter, (b) edge filter, and (c) band pass filter. Composition profile (left) and spectral performance (right).
Fig. 8. Transformation to quasi-gradient designs.
Transformation to quasi-gradient designs can be done in two different ways.
The first way is to let the software choose the best possible approximation of the index profile—using either constant or variable layer thickness. This way is especially interesting when we want to take advantage of the supposed improved properties of rugate systems, such as layer stress or laser durability.
The second way is to specify the refractive indices to be used, and transfer it to a multi-index design. This way is very helpful to find the simplifying or enabling refractive indices we are looking for.
3. Selected Example Design: Omnidirectional Antireflection Coating
An omnidirectional antireflection (AR) coating (Fig. 9
) from the field of laser optics was selected as the example design.
Fig. 9. Schematic sketch of an omnidirectional AR coating.
In a first step we designed a number of wide angle of incidence (AOI) AR coatings with different bandwidths and reflection lower than 1% for all AOIs and wavelengths. It is known that the maximal AOI, for which such coatings could be designed, depends on the desired spectral bandwidth. In order to find out this dependency, we designed a number of AR coatings centered at
, with spectral bandwidths of 1, 40, 80, 160, and 240 nm with nearly the same physical thickness (
). The obtained maximum AOI as a function of the relative bandwidth
is shown in Fig. 10
Fig. 10. Calculated maximum AOI for as a function of the relative spectral bandwidth. Example design has .
The design with a spectral bandwidth of 40 nm was selected for realization. The rugate design is shown in Fig. 11
, and its spectral reflection versus AOI in Fig. 12
. Reflection stays well below 1% up to the maximum incidence angle of 60°.
Fig. 11. Rugate AR design volume fraction profile.
Fig. 12. Rugate AR design spectral performance.
In a second step, we transferred the selected rugate AR design to three different thin film systems as shown in Fig. 13
Fig. 13. Rugate AR design transferred to (a) 35-layer binary, (b) 44-layer multi-index, and (c) 159-layer best approximation.
The first system is a 35-layer binary, as shown in Fig. 13(a)
. It was designed using OptiLayer. It is thinner than the other two systems, and therefore is the least complex. On the other hand, this design has higher reflection values. Reflection is just slightly below the optimization target value of 1%.
The second system is a 44-layer multi-index representation, shown in Fig. 13(b)
, and the third system is a 159-layer best approximation of the rugate index profile, shown in Fig. 13(c)
. The total layer thickness is nearly identical. The resulting refractive index profile is very near to the original one shown in Fig. 11
All three AR design examples were coated and characterized at Laser Zentrum Hannover.
4. Experimental Results
A. IBS Coater
An adapted ion beam sputtering (IBS) was used, which offers several advantages employed for the deposition of the complex quasi-gradient index coatings (Fig. 14
). Besides the ability to realize layers of mixed materials with superior layer properties, the selected IBS concept offers high process stability. The corresponding IBS machine is equipped with a three-grid rf ion source operated at 2.5 MHz for sputtering. In addition to using noble (argon) gas for ion source operation, oxygen can be supplied using a separate gas inlet to enable a reactive IBS process. Thus, the oxide layer materials
are deposited by sputtering silicon and titanium targets, respectively.
Fig. 14. IBS process with zone target for cosputtering.
In the present study, the two pure materials and define the lowest and the highest refractive indices. Within these limits, the layer refractive indices can be tuned by depositing mixtures of these oxides with a high precision in mixing ratio.
A co-sputtering process is used to mix
. In the chosen configuration, the ion beam is directed to a rectangular zone target consisting of a silicon and a titanium zone bonded side by side. The target is mounted on a linear motion stage to tune the material mixing ratio by positioning the zone boundary relative to the fixed ion beam. The mixing ratio is determined by the fraction of the different target material areas interacting with the ion beam [2
2. D. Ristau, “Ion beam sputtering—state of the art and industrial application,” in Proceedings of the 8th International Conference on Coatings on Glass and Plastics, 2010, pp. 203–208.
]. As in the standard IBS configuration, the substrate holder is rotated for thickness and mixing ratio homogenization purposes. The optical constants of the deposited layers are determined by the mixing ratio. Due to high process stability and reproducibility, the refractive indices can be calibrated reliably with respect to the absolute position of the target assembly (Fig. 15
Fig. 15. Zone target: refractive index is a function of target position.
The process is controlled by an optical broadband monitoring (BBM) system [3
3. M. Lappschies, B. Görtz, and D. Ristau, “Optical monitoring of rugate filters,” Proc. SPIE 5963, 59631Z (2005). [CrossRef]
], which directly measures calibrated transmittance spectra on the moving substrates. These in situ
measurements cover a wavelength range from 400 to 1000 nm at an exposure time of a few milliseconds. Fully automated processes are enabled using the BBM software, which imports the multilayer design, including the material data as refractive indices or extinction coefficients. Based on this input, the current thickness of the growing layers can be very precisely calculated from the measurements, and evaluated for layer termination. If required, the BBM software can be complemented by software modules, e.g., for computational manufacturing experiments or automated online design reoptimization.
B. Deposition Procedure for Rugate Layer Structures
For the proposed rugate structures of 44 and 159 layers, respectively, different refractive index values have to be realized. Moreover, the process state for each index value will be different—the structures show no periodicity. During the process, the in situ transmittance spectra of the witness sample were measured after each layer precisely. These data were used to evaluate the refractive index value and thickness of each layer. It was observed that an index variation of up to 0.1 to the target values occurred. Such a deviation is not tolerable for the given optical specification. Therefore, an automatic thickness reoptimization of the remaining layers was allowed. The decision was made to limit reoptimization to 55° AOI, to stay on the safe side and avoid a possible over-optimization.
C. Optical Measurement
Ex situ transmittance and reflectance spectra were measured using a Perkin Elmer instrument. All coatings are absorption free in the design spectral region around 800 nm. For determination of the angle-dependent reflectance, transmittance at the desired wavelength was measured for and polarization employing an integrating sphere as a detector element. The samples were coated only on one face; thus the signal is influenced by the reflectance of the coated side and the reflectance of the fused silica/air interface. To determine the reflectance of the single coated side, the single side angle-dependent transmittance of a fused silica/air interface was subtracted from the measured data.
Finally, the - and -pol data were averaged giving the nonpolarized reflectance. An error budget of approximately 0.2% is being assumed for the data evaluation.
D. Determination of Laser-Induced Damage Threshold Values
Laser-induced damage threshold (LIDT) values were measured at LZH [4
4. C. J. Stolz and D. Ristau, “Thin film femtosecond laser damage competition,” Proc. SPIE 7504, 75040S (2009). [CrossRef]
] using an 800 nm laser with a pulse length of 180 fs and a repetition rate 1 kHz. The measurements were performed according to ISO21254-2. Up to 100,000 pulses were applied on the sites in the measurement matrix. All LIDT measurements were performed under 0° incidence angle.
E. Experimental Results: 35-Layer Binary
The 35-layer high low stack design was deposited straightforwardly, employing the optical broad monitoring system for deposition control. A reoptimization procedure was not used. All measured spectra are in excellent agreement with the re-engineered design curve (Fig. 16
). Also, a superior conformity with the target design curve could be achieved. Angle-dependent reflectance data present reflectivity values below 1.2% in maximum up to 60°. Similar to the spectral data, the angle-dependent data are in good agreement with the calculations (Fig. 17
Fig. 16. Measured and calculated transmittance spectra of the deposited design. Measured spectral performance is in good agreement with the design.
Fig. 17. Measured reflectance at 800 nm versus AOI is in good agreement with the calculated one.
The multilayer structure uses only the pure materials
. Based on the design, the energy distribution in the stack can be calculated. For the wavelength 800 nm, the E-field distribution is presented in Fig. 18
. In comparison to the E-field distribution of the two other structures, the maximum field strength is larger. An LIDT value of about
is determined for the wide angle binary AR coating (Table 1
Table 1. Femtosecond LIDT Values Determined at 800 nm
Fig. 18. Calculated E-field distribution of the 35-layer binary at 800 nm.
F. Experimental Results: 44-Layer Multi-Index
As expected, the ex situ
transmittance measurements of the coated substrates show excellent agreement with the reoptimized design (Fig. 19
). Similar to the high-low stack design, the measured reflectance data in dependence of the incident angle indicate only small deviations from the calculated values. Low reflectivity values up to an angle of 55° were measured (Fig. 20
). The E-field distribution is smoother compared to the high-low design, due to the reduced refractive index change (Fig. 21
). The measured LIDT value of
significantly increased, compared to the binary stack (Table 1
Fig. 19. Measured and calculated transmittance spectra of the 44-layer design. The spectral performance is in good agreement with the design.
Fig. 20. Measured reflectance versus AOI is in good agreement with the calculated characteristic.
Fig. 21. Calculated E-field distribution of the 44-layer multi-index design.
G. Experimental Results: 159-Layer Best Approximation
The 159-layer design presents again a rugate approach, here with an increased number of layers. Ex situ
transmittance data fit excellently to the reoptimized data (Fig. 22
), and also the conformity of the reflectance data in dependence of the incident angle with the calculated values is satisfactory. Furthermore, this approach showed the lowest reflectivity values up to an angle of 55° (Fig. 23
). The E-field distributions are similar to the 44-layer design (Fig. 24
). In spite of the even smoother change of index and field strengths, the measured LIDT value of
is higher than for the discrete stack, but the value does not reach the LIDT level of the 44-layer system.
Fig. 22. Measured and calculated transmittance spectra of the 159-layer design. The spectral performance is in good agreement with the design.
Fig. 23. Measured reflectance versus AOI is in good agreement with the calculated characteristic.
Fig. 24. Calculated E-field distribution of the 159-layer best approximation.
H. Production Errors
Production errors were estimated by comparing standard OptiLayer error analysis to the measured spectral performance. The results for the binary system are shown in Fig. 25
, and for the rugate in Fig. 26
, respectively. All production errors, layer thickness and refractive index, are well below 1%.
Fig. 25. Error simulation: 100 tests, 95% probability corridor. Binary thickness error: 1% rms.
Fig. 26. Error simulation: 100 tests, 95% probability corridor. Rugate thickness error, 0.5% rms; refractive index error, 1% rms.
This study of standard high-low stack and rugate designs showed that optical coatings can be realized with both approaches. Moreover, the design development of rugate systems using the Carl Zeiss software package can be implemented. The given solutions could be transferred into more practical deposition designs, still using mixed material layers, allowing a straightforward coating deposition.
In this investigation, an IBS process with a zone target arrangement was utilized to deposit mixtures of the materials and . The adjustment of refractive index values was achieved with the aid of a calibrated index-position correlation. However, for the presented gradient index problems, the index variation to the target level was too large to achieve the optical specification in a standard process. Therefore, an automatic reoptimization scheme, adjusting the remaining layers in thickness with respect to the optical specifications, was employed. It should be mentioned that the structure of the starting design is still maintained. The optical in situ data, gathered during deposition, allow the correct adjustment of the coating systems. Thus, the design is precisely known, which was proven by the excellent agreement of measured transmittance and reflectance data and the angle-dependent investigations with the calculated data based on the coating design.
Omnidirectional AR coating covering the range from 0° to 55° providing reflectivity values less than 1% could be achieved with the rugate systems. Considering the total thickness of the three approaches, it can be concluded that for the omnidirectional AR coating, the thinnest solution was realized by the standard stack with a total thickness of approximately 3.4 μm. In the case of the mixed materials designs, the index contrast is comparably lower, resulting in an increased total thickness of approximately 4.4 μm.
Femtosecond LIDT values were measured under an AOI of 0°. The LIDT value of the design solutions with mixed materials, which means less content, showed the highest LIDT value of approximately . Assuming that the damage threshold in the femtosecond regime is mainly determined by the band gap, this finding is in agreement with the expectations. Also, an increased total thickness for the mixed layer system does not lead to a decrease of the LIDT value; the converse is the case.
Gradient index coatings or rugate systems provide stimulating properties for the design of functional coatings. In comparison to standard two materials designs, an additional dimension provided by the refractive index variation is available. This can be utilized to tailor the coating behavior with respect to optical functionality, LIDT value, and stress levels.