Characteristics of coating designs

Antireflection coatings are used to reduced the surface reflectance of optical components, to reduce the reflectance of an interface between two massive optical media with different refractive indices, to match a coating design optimized for one massive optical medium into another, or to match two coating designs optimized for different massive media into each other when they are combined into a compound filter. It is relatively easy to eliminate the reflectance around one or two wavelength positions. Yet the reduction of the reflectance over an extended wavelength region is rather difficult, especially when the ratio of the wavelengths at the edges of the low-reflectance region exceeds two [72-73].

There are two types of antireflection coatings. One type consists of a single layer which must have a lower refractive index than the substrate. The second type consists of a multilayer stack of high index and low index materials similar to the HR system [74]. For the single layer system the relationship between reflection and coating index is given by the following expression:

(

)

It then follows that a substrate can have zero reflection when coated with a material whose refractive index is equal to the square root of the index of that substrate. The zero reflection is achieved at the wavelength,λ , for which the films optical thickness is λ . These coatings are therefore generally called quarter-wave 4 antireflection coatings.

Typical optical substrates have refractive indices in the range 1.45-1.55 and therefore require coatings with indices in the range 1.20-1.24 for zero reflection. No

dense coatings can be prepared with an index this low because of a lack of suitable materials. Antireflection coatings of moderate performance can be prepared from MgF2 (index 1.38) and Na3AlF6 (index 1.36) by conventional evaporative means.

E-beam-deposited antireflection coatings generally consist of two or four layers of alternating high index and low index materials. The two-layer coatings show a rapid increase in reflection as the wavelength or incident angle is changed from the design angle. The four-layer coating has a larger bandwidth and also a larger production tolerance for layer thickness [75-76].

Figures 3.8 (a) to (d) show the simulation spectrum characteristics with different commonest conditions [77]. A quarter-wave layer is a quarter-wave strictly at only one wavelength. Figure 3.8 (a) we show the quarter-wave for three different reference wavelengths, it can be find obviously, the reflectance minimum are always at the major wavelength (reference wavelength).

λ

(a)

λ

(b)

(c)

λ λ

Figure 3.8. (a) The characteristic curves of a λ optical thickness with different 4 reference wavelengths, (b) the characteristics of the reflectance of a practical quarter-wave single layer (n = 1.38) coated on substrates with different refractive index, (c) the reflectance of 1 4−14 two layer coating design on different refraction index substrates. The transmittance performance will be degrading as the index is higher than a constant about 1.8, (d) the reflectance of 1 4−12−14 three layer coating design on different refraction index substrates.

High reflectors are coatings which maximize the reflectance of an optical surface in a specified wavelength region. The high-reflectance zone of dielectric stacks can be widened by combining stacks with different center wavelengths [78].

The coatings consist of stacks of near-quarter-wave optical thickness layers of alternating low index and high index materials. For most visible and near-IR

(d)

λ λ

λ

applications, dielectric oxides are the materials of choice. The low index material is predominantly SiO2 although Al2O3 and some metal fluorides are occasionally used.

The initial choice of coating materials is based largely on the index of refraction and transmission range of the material. Low absorption is obviously needed so that materials do not absorb light at the wavelength of interest.

The other factor we should notice is the damage threshold problem [79-83]. The energy density at which laser-induced damage occurs is defined as the damage threshold. The design and cost of high-power laser systems are often controlled by the laser damage thresholds of optical films because the coatings typically have lower damage thresholds than do other optical components (glass, crystals) in the system.

The cost of optical components scales roughly with the area of the optic. For a constant total energy to be transported, the area of the optic, and therefore the cost, must increase as the damage threshold influence decreases. The damage, observable by a wide range of techniques including optical microscopy, can appear as pinpoints of scattered light or have features reminiscent of meteorite impacts. In the example of intracavity frequency doubling, the energy of the fundamental wavelength is very high inside the cavity, and in general, the damage threshold of the dielectric thin film is much lower than the optics such as laser mirrors, crystal materials. Intense photo irradiation of solid surfaces can result in irreversible damage to optical materials.

Such damage has been particularly important in the development of laser systems.

The spatially non-uniform beam profile propagating from the originally damaged optic can also lead to damage of additional components down line. The transmission ranges for materials used for damaged-resistant coatings are given in Fig. 3.9. The transmission range is limited at short wavelengths by the band gap of the material and at long wavelengths (low energy) by molecular vibrational absorption.

Figure 3.9. Transmissions range of dielectric materials that have been used for high-damage-threshold coatings work [84].

Even assuming that cost is not an issue, a high-power laser system would be limited by the mechanical stability of large optics. Coating performance is strongly tied to the ratio of the index of refraction of the materials making up the stack. High ratios provide wider bandwidths and require fewer layers to obtain a specific optical performance (i.e., reflectivity, polarizer rejection ratio). The indices of refraction of common damage-resistant coating materials are given in Fig. 3.10 [62, 84].

Figure 3.10. Refractive indices of dielectric materials that have been used for high-damage-threshold coatings work [84].

Figure 3.11 (a) shows the high reflectance characteristics. The design of the solid line is a stack includes 10 quarter-wave layers where the low index material is SiO2, the high index material is TiO2, and the layer next by the air is the low index material. The sketch is shown as Fig. 3.12.

In a simple quarter-wave design the maximums (and minimums) in the standing-wave electric-field (SWEF) pattern occur at layer interface, the SWEF of Fig.

3.12 was shown in Fig. 3.13.

Figure 3.11 (a) Reflectance of periodic quarter-wave multilayer design. L: SiO2, H1: TiO2, H2: Ta2O5.

Figure 3.11 (b) Peak reflectance (Rp) of the periodic quarter-wave multilayer.

Rp = 99.77 % Rp = 92.84 % Rp = 99.30 % Rp = 96.78 % Rp = 98.54 %

Figure 3.12. Reflectance of the design 1/(LH1)^p/1.52 with n(L) = 1.45 and n(H1) = 2.25, p = 5.

Figure 3.13. Standing-wave electric field distribution in a multilayer dielectric reflector. Standard all-quarter-wave reflector, reflectance of the design is shown in Fig.

3.12.

λ

sub.

SiO2 SiO2 SiO₂ SiO₂ SiO₂ TiO₂ TiOTiO₂ TiO_{2 2} TiO₂

air

0.25λ λ λ

The curve with cross marks in Fig. 3.11 (a) is the design, where the out layer is the high index material and the reflectance is higher than the design as the out layer is low index material as the solid line. The sketch is shown as Fig. 3.14. The SWEF is also shown in Fig. 3.15.

Figure 3.14. Reflectance of the design 1/(H1L)^p/1.52 with n(L) = 1.45 and n(H1) = 2.25, p = 5.

Figure 3.15. Standing-wave electric field distribution in a multilayer dielectric reflector. Standard all-quarter-wave reflector, reflectance of the design is shown in Fig.

3.14.

λ

SiO2 SiO2 SiO2 SiO2 SiO2

TiO₂ TiOTiO₂ TiO_{2 2} TiO₂

air sub.

0.25λ λ λ

The long dash curve in Fig. 3.11 (b), we show the design, where the first and the last layer are all high index material. The reflectance is much higher than the previous two designs we mentioned. Increasing the layers the reflectance could be improved. For example, the curve with triangle dot, which 16 layers included in the quarter-wave stack as shown in Fig. 3.11 (a), the reflectance, is improved by a factor of 1.03 compared to the curve with cross marks which 10 layers in the quarter-wave stack. As we replaced the TiO2 by Ta2O5 where the index is 2.1 around the reference wavelength of 1064 nm, the bandwidth is apparently narrower as the short dash curve in Fig. 3.11. This means that for a quarter-wave stack, the larger the index difference between the high index and low index material, the wider the FWHM. The high reflection zone can be also seen to be limited in extent. On either side of a plateau, the reflectance falls abruptly to a low, oscillatory value. The addition of extra layers does not affect the width of the zone of high reflectance, but increase the reflectance within it and the number of oscillations outside.

It was mentioned that a high reflectance can be obtained from a stack of quarter-wave dielectric layers of alternating high and low indices. This is because the beams reflected from all the interfaces in the assembly are of equal phase when they reach the front surface, where they combine constructively. For a high reflectance optical coating, it is easy to reach the target by increasing the quarter-wave layers. For process reliability, cost reduction, and thermal stress of thin films, the layer numbers and layer thickness should be controlled as small as we could. Figure 3.16 shows the quarter-wave layer numbers verses the bandwidths with larger than 99.8% reflectance, the substrate is glass, the high index materials are TiO2 and Ta2O5 individually, the low index material is SiO2. It is found that the range which larger than 99.8% forms by TiO2/SiO2 stack is larger than by Ta2O5/SiO2 stack. In the same layer numbers, the

wavelength tolerance range of TiO2/SiO2 is also larger than Ta2O5/SiO2, because the index difference is much large for the TiO2/SiO2, from the equation

(

)

λ λ₀

[85].

Figure 3.16. Computed the bandwidths which reflectance >99.8% of a multi-layer quarter-wave stack of SiO2/Ta2O5 and SiO2/TiO2 on a substrate of index 1.52. The reference wavelength is 1064 nm.

Figure 3.17 is the peak reflectance comparison of the Ta2O5/SiO2 and TiO2/SiO2 quarter-wave stacks, from the equation, the reflectance in air or free space

Layer #

(

)

It is fined that the greater the number of layers p the greater the reflectance.

Figure 3.17. Computed the peak reflectance of a multi-layer quarter-wave stack of SiO2/Ta2O5 and SiO2/TiO2 on a substrate of index 1.52. The reference wavelength is 1064 nm.

At oblique incidence, the performance of reflectance is also different as shown in Fig. 3.18.

Figure 3.18. Comparison of the reflectance of different incident angles by a layer MgF2 coating centered on 550 nm using glass as the substrate. The larger the incident angles, the smaller the peak transmittance.

This is because the phase thicknesses become smaller when the tilt increases, the minimum reflectance move to shorter wavelength as the tilt increases. This effect is true for small tilts as proved below. For oblique incident, the phase thickness in equation (3.1.16) should be corrected.

Figure 3.19. Geometric explanation of why the effective optical thickness decreases with increasing angle of the incident light*.

α0

α

As shown in Fig. 3.19:

Phase difference at DC AD

For large tilts, the changes in the admittances become important and also the detuning of the layer thicknesses because high index layers are affected less than low index ones, and so there is a splitting of the performance for each plane of polarization and also a progressive degradation of the characteristic as shown in Fig.

3.20 [86-87].

Figure 3.20. Effective indices at an angular for some typical refractive indices (incident medium is air).

Incident angle (deg)

The contrast between the admittances for s-polarized light becomes greater compared to that at normal incidence while the contrast for p-polarization characteristics becomes weaker. This implies that s-polarization reflectance become more pronounced, while p-polarization reflectance become weaker as shown in Fig.

3.21.

Figure 3.21. s-polarization and p-polarization reflectance of the high reflectance design with incidence angles from 0^o to 10^o.