Laser mirror

A laser mirror is a reflector designed for a laser's wavelength, angle of incidence and power. The common type is a dielectric high reflector (HR): a stack of alternating high- and low-index oxide layers, each a quarter wavelength thick in the material, on a polished glass or fused silica substrate. Standard catalog parts reflect more than 99.5% at their design wavelength, many exceed 99.9%, and mirrors made for precision cavities reach total losses of a few parts per million. Metal mirrors (protected aluminum, silver or gold) reflect less, roughly 90% for aluminum in the visible and 95–99% for silver and gold at longer wavelengths, but work over a much broader range and at almost any angle.

The quarter-wave stack

Each boundary between layers reflects a little light, and with quarter-wave thicknesses all these reflections return in phase. The structure is the same distributed Bragg reflector used in VCSELs and fiber gratings. For $N$ high/low pairs plus a final high-index layer on a substrate of index $n_s$, in air,

$$R = \left(\frac{1-Y}{1+Y}\right)^2,$$ $$Y = \left(\frac{n_H}{n_L}\right)^{2N}\frac{n_H^2}{n_s}.$$

With Ta₂O₅ ($n_H \approx 2.10$) and SiO₂ ($n_L \approx 1.45$) at 1064 nm on fused silica, the layers are 127 nm and 183 nm thick. Ten pairs give $R = 99.920\%$ and fifteen pairs $R = 99.998\%$, a transmission of 20 ppm. Real mirrors fall short of these values by their absorption and scatter, which are set by the coating process and the substrate polish; ion-beam sputtered coatings on superpolished substrates have the lowest losses.

The high-reflectance band has a fractional full width

$$\frac{\Delta\lambda}{\lambda_0} = \frac{4}{\pi}\arcsin\frac{n_H-n_L}{n_H+n_L},$$

which is 0.234 for Ta₂O₅/SiO₂, about 250 nm around 1064 nm. Outside it the reflectance drops and oscillates, which is how the dichroic mirror and many edge filters work. Broadband designs chirp the layer thicknesses to cover a wider range; chirped mirrors for femtosecond lasers also shape the group-delay dispersion.

Specifications

A laser-mirror specification usually lists:

• reflectance at the design wavelength and angle, often separately for s and p polarization at 45°, where $R_s$ exceeds $R_p$ and the p band is narrower;
• laser-induced damage threshold (LIDT), in J/cm² for a stated pulse duration and wavelength, or as a power density for continuous beams;
• surface flatness (for example λ/10 at 633 nm) and surface quality (scratch-dig);
• substrate material and back-surface finish.

Damage thresholds depend strongly on pulse duration, wavelength, beam size and test method. A frequently used rule of thumb scales nanosecond thresholds with the square root of pulse duration, which is only a rough guide between similar coatings. The operating fluence should stay well below the rated value, with margin for hot spots in the beam.

Measuring high reflectance

For $R$ above about 99.9%, comparing reflected and incident power with a power meter is limited by the meter's accuracy of a few percent. Cavity ring-down is used instead: two identical mirrors form an optical cavity of length $L$, light is switched off, and the stored power decays with time constant

$$\tau = \frac{L}{c\,(1-R)}.$$

For $L = 0.5$ m and $R = 99.99\%$, $\tau = 16.7$ µs, easily measured with a photodiode. The same loss sets the cavity's finesse, $\pi\sqrt{R}/(1-R)$, about 31 000 in this example and about 3 100 for $R = 99.9\%$.

Where it matters

Inside a laser, the end mirror is an HR and the other mirror is a partially transmitting output coupler; every 0.1% of unwanted loss raises the threshold of a low-gain laser. In ultrastable optical cavities and gravitational-wave detectors, mirror loss and coating thermal noise are limiting factors. In beam steering the effect accumulates: ten reflections from 99% mirrors deliver 90.4% of the light, while ten from 90% aluminum mirrors deliver 34.9%.

Pitfalls

A dielectric mirror designed for 0° shifts its band to shorter wavelengths at 45° and becomes polarization dependent, so the design angle must match the use. Outside its band a dielectric HR transmits substantially, which can send stray beams behind the mirror mount. Metal mirrors change the polarization state on oblique reflection and absorb several percent, which heats them under high power. Fingerprints and dust raise scatter and absorption, and contaminated spots are where damage starts; mirrors are cleaned only when necessary, with solvent and lens tissue, following the coating maker's guidance.

Common questions

What is the difference between a laser mirror and an ordinary mirror?

Household mirrors are silver or aluminum on the back of glass, so light crosses the glass twice and a weak ghost reflects from the front. Laser mirrors are front-surface, usually dielectric, with specified reflectance, flatness and damage threshold at the laser wavelength.

Why does a laser mirror look transparent or colored?

A dielectric HR reflects only within its stopband. A mirror for 1064 nm reflects little visible light and looks nearly clear, sometimes tinted by the side lobes of its reflectance curve.

Can one mirror be used for several lasers?

Only if all the wavelengths fall within its high-reflectance band at the operating angle. Broadband dielectric or metal mirrors cover several lasers with some loss of reflectance.

References: H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010); A. E. Siegman, Lasers (University Science Books, 1986); E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 9; B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019), Ch. 7.