Optical window

An optical window is a plate of transparent material with two flat, polished faces, used to pass light through a boundary while changing the beam as little as possible. Windows seal vacuum chambers, gas cells and cryostats, protect lenses and sensors from dust and debris, and form the output ports of laser housings. The design choices are the material, chosen for transmittance at the working wavelength and for mechanical and thermal properties; the surface flatness, typically specified between $\lambda/4$ and $\lambda/20$ at 633 nm; the parallelism or deliberate wedge between the faces; and the coating. An uncoated N-BK7 window transmits about 92% of visible light, the loss coming almost entirely from reflection at its two surfaces.

Reflection loss

At normal incidence each uncoated surface reflects a fraction given by the Fresnel equations,

$$R = \left(\frac{n-1}{n+1}\right)^2 ,$$

and a non-absorbing plate with incoherent multiple reflections transmits

$$T = \frac{1-R}{1+R} .$$

High-index infrared materials lose half their light or more without coatings, which is why germanium and zinc selenide windows are nearly always used with anti-reflection coatings. A good broadband coating on glass brings the loss to below about 0.5% per surface, and a single-wavelength V-coating lower still.

Materials

Approximate useful transmission ranges, which depend on grade and thickness, are about 0.2–2 µm for UV-grade fused silica, 0.35–2 µm for N-BK7, 0.2–5 µm for sapphire, 0.15–9 µm for calcium fluoride, 0.6–16 µm for zinc selenide and 2–14 µm for germanium. Sapphire is chosen for hardness, scratch resistance and pressure rating; fused silica for low absorption, low thermal expansion and resistance to laser damage; calcium fluoride for ultraviolet and mid-infrared work across the infrared bands. Germanium's absorption rises as it heats, which limits its use with high-power CO₂ lasers. For pressure windows the required thickness scales as the aperture diameter times the square root of the pressure-to-strength ratio, with a safety factor applied to the material's rupture modulus.

Effects on the beam

A window is not optically neutral in every beam geometry.

Focus shift. In a converging or diverging beam, a plate of thickness $t$ moves the focus away from the lens by

$$\Delta z = t\left(1 - \frac{1}{n}\right),$$

1.02 mm for a 3 mm N-BK7 plate. In fast beams it also adds spherical aberration, which is why objectives and high-NA lenses are designed for a specific cover glass or window thickness.

Lateral displacement. A plate tilted by $\theta$ shifts a beam sideways by

$$d = t\sin\theta\left(1 - \frac{\cos\theta}{\sqrt{n^2 - \sin^2\theta}}\right),$$

0.18 mm for the 3 mm N-BK7 plate at 10°. The beam direction is unchanged if the faces are parallel.

Wedge. Faces that are not parallel deviate the beam by about $(n-1)\alpha$ for a small wedge angle $\alpha$: a 30 arcmin wedge in N-BK7 deviates it by 15.5 arcmin, about 4.5 mrad.

Etalon fringes. With a coherent laser, the two reflections from a parallel-faced window interfere, and the plate acts as a weak etalon. For uncoated N-BK7 the transmission then varies between 100% and 84.5% as the wavelength, temperature or tilt changes, a swing of about 15 percentage points that appears as intensity noise and as fringes across the beam. Wedged windows, AR coatings, or a tilt that separates the reflections suppress it.

Where windows are used, and their pitfalls

Laser output ports, vacuum viewports, detector and camera covers, and gas and liquid cells all use windows. In gas lasers and some cells, windows are set at the Brewster angle, 55.5° for fused silica at 633 nm, where p-polarized light passes with no reflection loss and without a coating.

Tilting a window by a few degrees keeps back reflections out of a laser cavity, but in a converging beam the tilt adds astigmatism. Uneven mounting stress distorts the transmitted wavefront and induces birefringence. In high-power beams, surface contamination is a common cause of damage.

Common questions

How much light does an optical window lose?

For an uncoated glass window, about 8% in total, almost entirely by reflection at the two surfaces; with anti-reflection coatings on both faces, typically below 1%.

Why are some windows wedged?

A wedge of a fraction of a degree sends the reflections from the two faces in different directions, which prevents etalon fringes in coherent light and keeps a single ghost reflection from coinciding with the main beam.

What is the difference between a window and a lens?

A window has flat faces and, in a collimated beam at normal incidence, changes neither the direction nor the convergence of the beam. A lens has curved faces and changes the convergence. In a focused beam a window still shifts the focus by $t(1 - 1/n)$ through refraction.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 4 and 9; M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 1 and 7; W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008).