Anti-reflective (AR) coatings are optical coatings that reduce light reflection at surfaces, enhancing light transmission for various optical applications like lenses and mirrors. The coatings work based on the principles of light interference and refractive indices, where specific thicknesses can lead to destructive interference and minimal reflection. Limitations include variations in indices of refraction at different angles of incidence and across a spectrum of wavelengths.

1. A Primer on Anti-Reflective or AR Coatings
Introduction to Anti-Reflective Coatings
An AR coating is an optical coating applied to a surface to reduce the amount of light reflected off the
surface. It is typically used for optical applications where the coating is applied to the front of an
interface between air and a lens, glass barrier, or mirror. AR coatings are designed to maximize the
amount of light that transmits or enters the surface while minimizing the light lost to reflection. The
coatings improve the efficiency of optical instruments, enhance contrast in imaging devices, and reduces
scattered light that can interfere with the optical performance of telescopes, cameras, and binoculars,
and decreases glare on eyeglasses.
The physics of how light travels through a medium and behaves at interfaces between two different
mediums dictates how an AR coating works and behaves. AR coatings take advantage of the
electromagnetic-wave properties of light to enhance transmittance. We’ll review the basics physics
behind how AR coatings work, introduce several common types of AR coatings and their applications
and discuss the characteristics of AR coatings.
How Anti-Reflective Coatings Work
When a light wave traveling through air encounters a new medium, some of the incident light transmits
through the medium, while some of it reflects off the interface between the air and the medium. The
amount of light that is transmitted and reflected is calculated using Fresnel’s Equations which are
dependent on the indices of refraction for the air and the medium. Each medium has an index of
refraction that is calculated as follows:
n_x = c/v
Where c is the speed of light in a vacuum, and v is the speed of light in the medium.
Fresnel’s Equation defines the fraction of light that is reflected as follows:
R_{air-medium} = [(n_{air} - n_{medium}) /
(n_{air} + n_{medium})]^2
If a thin-film coating is applied to the front of the interface, there are two reflections – one at the
interface between the air and the coating and another at the interface between the coating and the
medium. Each of these reflections has a corresponding fraction of reflected light or Rair-coating and
Rcoating-medium respectively.

2. If the thickness of the thin film is a quarter of a wavelength of the lightwave (λ/4), then the light
reflected at the coating-medium interface travels half a wavelength further than the light reflected at
the air-coating interface. The result is destructive interference of the reflected light or the elimination of
reflection (see Figure 1). This is an ideal AR coating.
Take, for example, light traveling in air that encounters crown glass which is commonly used for lenses
and optical components. Air has an index of refraction of 1.0003. Using the speed of light in crown glass
which is ~1.97 x 108 meters/second, the index of refraction for crown glass is calculated as 1.52.
Using Fresnel’s Equations for reflection, approximately 4% of the incident light is reflected at the air-
glass interface.
Fresnel’s equations can be used to find the index of refraction for the ideal AR coating as the geometric
mean of the product of refraction indices for air and crown glass. So, an ideal AR coating has an index of
refraction equal to 1.23. This ideal material would eliminate all reflection off of the crown glass.
Limitations of Anti-Reflective Coatings
The index of refraction depends on the Angle of Incidence (or AoI) while Fresnel’s equation is valid only
for a normal angle of incidence. Suffice to say, a larger AoI will result in a higher index of refraction.
Many optical applications operate across a spectrum wavelength ranges, including infrared (700nm to
1mm), visible (400nm to 700nm), and ultraviolet (100nm to 400nm). The exception is lasers which are
tuned to a narrow band of wavelength ranges.

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