Antireflection Coatings for the Visible and the Infrared
There are frequent requirements for coatings that span the visible region and also reduce reflectance at an infrared wavelength corresponding to a laser line. These coatings are often required in instruments where visual information and laser light share common optical elements, such as surgical instruments and surveying devices.
General Design Challenges
Designing such coatings is largely a process of trial and error, as manufacturers rarely publish detailed designs. A common final step involves replacing unattainable or difficult indices with symmetrical combinations of better-behaved materials. The design is then refined to account for the dispersion of optical constants in real materials and to compensate for apparent dispersion in symmetrical periods.
This section focuses only on the fundamental design process, neglecting dispersion and typically retaining the ideal values of indices. For simplicity, we assume the substrate is glass with an index of 1.52, and the incident medium is air with an index of 1.0.
Basic Design: A Single Low-Index Layer
The simplest coating for low reflectance in the visible region and at a near-infrared wavelength is a single layer of low-index material with a thickness of three quarter-waves. This coating achieves low reflectance at \( \lambda_0 \) and \( 3\lambda_0 \). However, the lowest achievable index of 1.38 (magnesium fluoride) gives a residual reflectance of 1.25% at the minima. Additionally, the performance in the visible region is narrower compared to a single quarter-wave coating since the layer is three times thicker.
Improved Design: Introducing a High-Index Flattening Layer
A possible improvement is to treat the magnesium fluoride layer as an outer quarter-wave over an inner half-wave. A high-index flattening layer \(( n = 1.8 )\) can be introduced between them:
\[
\text{Design: Air (LHHLL) Glass}
\]
While the flattening layer improves visible performance, it destroys the infrared performance at \( 3\lambda_0 \), where it is only two-thirds of a quarter-wave thick. To solve this issue, the layer must be three half-waves thick in the visible region so that it remains a half-wave (and therefore an absentee) at \( 3\lambda_0 \). This leads to the design:
\[
\text{Design: Air (L6H2L) Glass}
\]
The performance of this design is shown in Figure 4.57, with a reference wavelength of 510 nm. While the performance in the visible region is flattened, the characteristic rises sharply in the blue and red regions.
The minimum in the infrared around 1.53 μm is preserved, albeit slightly skewed due to the half-wave layer. Interestingly, a third deep minimum appears at 840 nm, as shown in the admittance diagram in Figure 4.58. This dip is caused by the high-index layer, which is nearly two half-waves thick at this wavelength.
Reducing the thickness of the high-index layer (e.g., from 1.5 to 1.0 full waves) shifts the dip to a longer wavelength, resulting in the design:
\[
\text{Design: Air (L4H2L) Glass}
\]
This performance is illustrated in Figure 4.59.
Quarter-Half-Quarter Coating with Buffer Layers
A quarter-half-quarter coating provides excellent performance in the visible region but has high reflectance at \( 1.06 \, \mu \text{m} \). Its admittance diagram at \( \lambda_0 \) is shown in Figure 4.33. To address the infrared reflectance, buffer layers can be introduced.
Buffer layers, as devised by Mouchart, have a specific index that aligns with axis crossings of the admittance locus of the coating. They exert no influence at the reference wavelength \( \lambda_0 \) but significantly impact performance at other wavelengths. For the current design, two buffer layers of admittance 1.9 are inserted:
\[
\text{Design: Air (LB’HHB”N) Glass}
\]
Here:
- \( y_L = 1.38 \)
- \( y_H = 2.15 \)
- \( y_N = 1.70 \)
- \( B’ \) and \( B” \) are buffer layers with admittance 1.9.
Trial and error establishes thicknesses of 0.342\( \lambda_0 \) for ( B’ ) and 0.084\( \lambda_0 \) for \( B” \). This reduces reflectance at \( 1.06 \, \mu \text{m} \), as shown in Figure 4.60. However, these buffer layers slightly distort performance in the visible region. Refining the design yields the final configuration:
\[
\text{Design: Air (1.00 1.38 0.2667 1.90 0.3085 2.15 0.5395 1.90 0.1316 1.70 Glass)}
\]
This refined design is also shown in Figure 4.60.
Designs with Two Materials
Many designs currently used for the visible and \( 1.06 \, \mu \text{m} \) involve just two materials of high and low indices. Such designs can be arrived at through symmetrical periods, as discussed earlier. Figure 4.61 shows the performance of a six-layer design derived through computer synthesis:
\[
\text{Design: Air (1.00 1.38 0.3003 2.25 0.1281 1.38 0.0657 2.25 0.6789 1.38 0.0718 2.25 0.0840 Glass)}
\]
Buffer Layers and Half-Wave Absentee Layers
Buffer layers are highly effective in coatings that require low reflectance over a wide spectral region. Unlike half-wave absentee layers, which correct performance rapidly, buffer layers react more slowly, making them ideal for broader reflectance control. However, their refractive index is fixed by the axis crossings of the admittance locus, which limits their application to certain materials.
Refining Buffer Layer Performance
The double Vermeulen structure enables precise adjustments to axis crossings, allowing the index of the high-index layer to align with the coating’s admittance requirements. This technique is illustrated in the first design column of Table 4.6 and Figures 4.62–4.64. By adding a half-wave low-index layer between the coating and the substrate and refining all layers, significant improvements in performance are achieved.
Practical Considerations
The performance of antireflection coatings for low-index substrates is heavily influenced by the lowest refractive index of the design materials. While magnesium fluoride is commonly used, its high tensile stress and need for deposition on a heated substrate make it less ideal. Silicon dioxide, with a higher index of 1.45, is tougher and more stable and is often used as a substitute for inner layers, with magnesium fluoride reserved for the outermost layer.
