Antireflection coatings, essential for both single-wavelength and broadband applications, are among the most widely used coatings globally. Their performance capabilities and limitations are governed by several fundamental optical design principles.

Antireflection (AR) coatings, the most widely used optical coatings worldwide, are designed to suit a range of applications, from single-wavelength use (for narrowband lasers) to broad spectral bands such as 380–1550 nm or 3 to 12 μm.

Whether constructed with a single layer or multiple layers, the essential properties of ideal AR coatings—and their real-world approximations—are characterized by reflectance and transmittance across different wavelengths. Reflectance relative to thickness and refractive index versus thickness are just some of the ways to visualize the potential and constraints of today’s AR coating technology.

Antireflection Basics

An uncoated surface of crown glass, such as Schott’s NBK7 with a refractive index of approximately 1.52 at 550 nm, reflects about 4.26% of incident light across the visible spectrum. In camera and microscope lenses, this reflection leads to ghost images and loss of transmittance of the desired image flux. To address these reflections, the concept of a single-layer antireflection (AR) coating was patented in the 1930s by Smakula, and John Strong reported a single-layer AR (SLAR) coating in 1936.

The core principle of AR coatings is that light reflected from the outer surface of a single coating layer can interfere with light reflected at the interface between the coating layer and the substrate. Reflection can be minimized or eliminated if the refractive index of the coating (n₂) equals the square root of the product of the substrate’s refractive index (n₃) and that of the surrounding medium (n₁, usually air or vacuum), expressed as n₂ = √(n₁ × n₃).

This principle results in zero reflectance at the wavelength where the path delay between the front and back reflections in the coating equals 180° (or multiples thereof), creating a quarter-wave optical thickness (QWOT) at that wavelength. For example, at 510 nm, this condition is met on a substrate with a refractive index of 1.52 by a coating with a refractive index of 1.233, which is the square root of 1.52 (see Fig. 1).

Single-Layer AR Coatings

With a refractive index around 1.38, magnesium fluoride (MgF₂) reduces reflection on an NBK7 substrate to about 1.26%, rather than eliminating it completely. However, for substrates with a refractive index of 1.9 and an MgF₂ coating (index 1.38), reflection can be reduced to 0% at the design wavelength (QWOT). For example, an uncoated glass substrate with an index of 1.9 would reflect 9.63% of incident light, but a single-layer AR (SLAR) coating of MgF₂ brings this reflection down to 0% at 550 nm.

This MgF₂ SLAR coating can serve as an effective AR coating for lasers operating at 550 nm, and the layer’s thickness can be adjusted to achieve a QWOT at other laser wavelengths as required.

Two- and Three-Layer AR Coatings

To overcome the refractive index limitations for a single-wavelength laser AR coating (within a narrow bandwidth), a two-layer approach with high and low index materials is often effective. First, a thin layer (non-QWOT) of high-index material (e.g., index 2.3) is deposited onto the substrate. This combination behaves more like a 1.9 index glass substrate, making a subsequent layer with a 1.38 index closer to the ideal AR index for this configuration at the target wavelength.

This high- and low-index combination is commonly known as a “V-Coat,” as its narrow bandwidth reflectance curve forms a “V” shape near 0% reflectance. For more broadband antireflection, a three-layer broadband AR (BBAR) coating can be applied on an NBK7 substrate.

This BBAR coating consists of one QWOT of medium-index material (1.65), two QWOTs of high-index material (2.1), and one QWOT of low-index material (1.38), often referred to as a QHQ or MHL design.

AR coating designs are further illustrated through a reflectance vs. layer thickness plot for single-layer, two-layer, and three-layer configurations on NBK7 glass (see Fig. 2).

The single-layer AR (SLAR) coating reduces reflection smoothly from the substrate’s 4.26%. In the two-layer design, reflectance initially rises with the thickness of the high-index layer, then falls to 0% at the design wavelength as the low-index layer is added.

The three-layer design sees reflectance rising through the first and part of the second layer before dropping to 0% through the final layer. This three-layer configuration forms the basis for most BBAR coatings used globally.

An Ideal BBAR

To create a coating that functions effectively across a wide wavelength range, certain design principles are essential. For instance, with a substrate index of 4.0, such as germanium in the infrared spectrum, the square root equation suggests that an optimal QWOT AR coating layer should have an index of 2.0.

When two layers are used, their indices and thicknesses can be optimized further to achieve a broader AR band (see Fig. 3). This approach can be expanded to three, four, or even five layers by following a refractive index profile that gradually steps down in index relative to thickness.

For these refractive-index step-down profiles, the scale is displayed as the reciprocal of wavelength (1/cm) or frequency for optimal visualization (see Fig. 4). Notice that the AR bandwidth increases with the number of steps (layers) in the design. Each design begins to function effectively as an AR coating at a minimum frequency of about 300 cm⁻¹ (corresponding to a maximum wavelength of 33.3 μm). The maximum frequency, or shortest wavelength of the AR band, is determined by the number of layers.

In the theoretical extreme of an infinite number of layers, the refractive index profile would form a Gaussian shape. The total thickness of this ideal AR coating would be just over two QWOTs at the longest wavelength, or the lowest frequency in the pass band (300 cm⁻¹). Remarkably, the AR band of this ideal coating would then extend continuously from this longest wavelength to all shorter wavelengths, providing unparalleled broadband antireflection.

Lithographically Textured Surfaces

With advances in lithographic techniques and etchable materials, it’s now possible to create surfaces with microscopic textures that approximate the index-vs.-thickness profiles needed for highly effective broadband AR (BBAR) coatings. For these etched surfaces, individual features must be smaller in height and width than the shortest wavelength in the desired AR band.

The optimal etched AR coating features a series of pyramids with smoothly curved slopes (see Fig. 5). This design ensures that the average area ratio between air (or vacuum) and the substrate material at each vertical level mirrors the step profile on the left side of Fig. 4. In some cases, a pyramidal profile with straight edges can sufficiently approximate this ideal etched profile for certain AR coating applications.

For an ultra-broadband AR coating, the ideal index-of-refraction profile, from the substrate to the surrounding medium (typically air or vacuum), follows a Gaussian-like curve. This profile transitions from the substrate’s index to that of the medium over a distance of approximately one half-wave optical thickness at the longest wavelength within the AR band. Simpler homogeneous coatings can approximate this profile for narrower AR bands, while lithographically etched substrates can achieve similar results in certain materials.

In cases where the AR requirement is limited to a single wavelength (as with lasers), single- or double-layer AR coatings can provide effective performance.