Facet Coatings and What They Do to a Laser Diode

Scope

This article works through what facet coatings do to a Fabry-Perot laser diode: the mirror loss, the threshold gain, the slope efficiency, and the front-to-back power split, all as functions of the two reflectivities, with the numbers computed for representative devices. It covers why pump lasers wear a 5% front and 95% back, why some telecom chips are left uncoated on one side, and what the choice does to facet intensity, feedback sensitivity, and the monitor photodiode. Background: output coupler, anti-reflection coating, slope efficiency, threshold current; the AR coating calculator designs the thin-film stack that produces a given reflectivity.

Four relations

A cleaved semiconductor facet reflects about 32% at normal incidence (Fresnel reflection between $n \approx 3.5$ and air). Coating it changes that number, and four relations carry the change through to the laser's behavior. With facet power reflectivities $R_1$ (front) and $R_2$ (back), cavity length $L$, internal loss $\alpha_i$, and injection efficiency $\eta_i$:

The mirror loss, the distributed loss equivalent of the light leaving through the facets, is

$$\alpha_m = \frac{1}{2L}\ln\frac{1}{R_1 R_2}.$$

The threshold gain is the sum of internal and mirror loss, $g_\mathrm{th} = \alpha_i + \alpha_m$, and the threshold current rises with it through the gain-current relation of the active region.

The total differential (slope) efficiency counts the fraction of injected carriers above threshold that leave as photons through either facet:

$$\eta_d = \eta_i\,\frac{\alpha_m}{\alpha_i + \alpha_m}.$$

And the share of that output emerging from the front facet is

$$F_1 = \frac{(1 - R_1)\sqrt{R_2}}{(1 - R_1)\sqrt{R_2} + (1 - R_2)\sqrt{R_1}},$$

so the front-facet slope efficiency, the number a data sheet quotes, is $F_1\,\eta_d$.

The numbers

A 1 mm long high-power pump laser with $\alpha_i = 1$ cm$^{-1}$ and $\eta_i = 0.9$:

The uncoated laser wastes half its light out the back. Coating the back facet to 95% alone (last row) sends 96% of the output forward and cuts the mirror loss almost in half, which lowers threshold; the price is a lower total efficiency, because with less mirror loss a larger fraction of the photons die to internal loss before they escape. Adding a front anti-reflection coating raises the mirror loss again, which raises threshold but raises the total efficiency and puts nearly all of it out the front: the 5% / 95% pair delivers 83% of the injected carriers above threshold as front-facet photons against 41% for the uncoated chip, a doubling of the useful slope. Going to 2% on the front buys another two points of efficiency at the cost of a threshold gain 28% higher than the 5% pair; the trade stops paying when the extra threshold current and the extra facet intensity cost more than the slope gains, which for most pump lasers is somewhere between 1% and 5% front reflectivity.

The same arithmetic on a 300 µm telecom chip with $\alpha_i = 10$ cm$^{-1}$ and $\eta_i = 0.8$ gives $\alpha_m = 38$ cm$^{-1}$ uncoated and 51 cm$^{-1}$ at 5% / 95%, front slope efficiencies of 0.32 and 0.66, and a threshold gain of 48 against 61 cm$^{-1}$. Short cavities live on mirror loss: the mirror term dominates the internal term, so coatings move the threshold of a short chip proportionally more than they move a long one, and short high-loss chips are the ones most often left with a partly reflecting front facet to keep threshold down.

What the choice costs

Facet intensity. The light inside the front facet is the forward wave, $P_\mathrm{out}/(1 - R_1)$, plus the part of it the facet reflects. For a 5% facet that is 1.05 plus 0.05, about 1.1 times the output; for a cleaved 32% facet it is 1.47 plus 0.47, about 1.9 times. Since catastrophic optical damage is set by the intensity at the facet and not by the output, the anti-reflection-coated facet reaches an output about 1.7 times higher before it meets the same internal intensity limit, and the coating also passivates the surface, which is the other half of the COD story.

Feedback sensitivity. A laser with a 2% front facet is far more sensitive to light returning from outside than one with a 32% facet, because the external reflection competes with a weaker mirror. The effective feedback strength scales as $(1 - R_1)^2/R_1$ times the external reflectivity: that factor is 1.4 for a cleaved facet and 48 for a 2% facet, so the same connector reflection is 33 times, 15 dB, more effective against the coated laser. The regime boundaries in Optical feedback in semiconductor lasers are quoted for typical facets and shift accordingly. This is also why an anti-reflection-coated chip is the starting point for an external-cavity laser: the coating deliberately hands mirror duty to the external grating.

Monitor photodiode signal. The back facet emits $1/(F_1^{-1} - 1)$ of the front power: 100% for an uncoated pair, 3.7% at 10% / 90%, 1.2% at 5% / 95%. The monitor sits behind the back facet, so the highly reflective coating that maximizes forward output also starves the monitor, and the ratio it measures becomes more sensitive to alignment and far-field changes; this is one contribution to tracking error.

Wavelength and temperature. A dielectric coating's reflectivity varies with wavelength, gently for a quarter-wave stack near its design wavelength and steeply for a single-layer anti-reflection coating away from its minimum. A front facet designed for 2% at 980 nm may be 5% at 960 nm, so a laser tuned by temperature across tens of nanometers has a mirror loss that changes with it, and the wavelength temperature coefficient sets how far the operating point wanders across the coating's curve.

Reading a data sheet with this in mind

A quoted slope efficiency is a front-facet number for a particular coating pair; a chip supplier quoting "total" efficiency, or a bare-chip figure before coating, is quoting something else. A threshold current density in kA/cm² depends on the coatings through $g_\mathrm{th}$ and is only comparable between chips of the same length and coating. And a pump laser's kink-free and COD ratings are set at the facet with the coating in place; the same chip with a different front reflectivity is a different laser on every row of the table. The datasheet article covers the rest of the table.

References: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), ch. 2 and 3, for the mirror-loss, efficiency, and facet-split relations; H. A. Macleod, Thin-Film Optical Filters, 4th ed. (CRC Press, 2010), for the coatings themselves. Every number in the tables above is computed from the four relations with the stated parameters.