Internal loss (α_i)

The internal loss $\alpha_i$ of a laser is the rate, per unit length of travel, at which photons in the lasing mode are absorbed or scattered inside the cavity. It is the modal loss of the waveguide with the active region held at transparency, and it is counted separately from the mirror loss $\alpha_m$, which is light leaving through the facets as useful output. In semiconductor lasers $\alpha_i$ is typically 2–20 cm⁻¹: around 10 cm⁻¹ is common for InP-based multi-quantum-well lasers at 1.3–1.55 µm, and GaAs-based high-power pump lasers built with thick, lightly doped waveguides report values near 1 cm⁻¹ or below. Because 1 cm⁻¹ is 4.34 dB/cm, a 10 cm⁻¹ cavity loses 43 dB/cm, against about 2 dB/cm for a silicon photonic wire, which is acceptable because the path inside a laser chip is a fraction of a millimeter.

Sources of internal loss

The dominant contribution in long-wavelength lasers is free-carrier absorption, and in particular intervalence-band absorption by holes in the p-doped cladding and in the active region itself. It grows with doping and with the injected carrier density, and so with temperature and current. Scattering from rough ridge sidewalls, interface roughness between layers and absorption in metal contacts or doped contact layers that the mode tail reaches add the rest. Design against internal loss consists of keeping the mode away from heavily doped p-layers, grading the doping, and widening the waveguide so that a smaller fraction of the mode sits in lossy material.

Mirror loss and the threshold condition

The mirror loss spreads the facet transmission over the cavity length $L$:

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

For a 500 µm cleaved InP laser with $R_1 = R_2 = 0.32$, $\alpha_m = 22.8$ cm⁻¹. The laser threshold requires the modal gain to cover both, $\Gamma g_\text{th} = \alpha_i + \alpha_m$, so with $\alpha_i = 10$ cm⁻¹ the active region must supply a modal gain of 32.8 cm⁻¹, of which 30 % offsets internal loss. Over one pass of this cavity, the internal loss alone transmits $e^{-\alpha_i L} = 0.61$ of the light.

Effect on efficiency

The photons generated above threshold divide between the two loss channels in proportion to their rates, so the differential quantum efficiency is

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

with $\eta_i$ the internal quantum efficiency. For the 500 µm laser above and $\eta_i = 0.8$:

Lowering the internal loss is the main route to long, high-power cavities: a long cavity spreads heat and lowers the facet power density, but its small $\alpha_m$ makes the efficiency depend strongly on $\alpha_i$. The internal loss also sets the photon lifetime together with the mirror loss, $1/\tau_p = v_g(\alpha_i + \alpha_m)$.

Measuring internal loss

A single laser cannot separate $\alpha_i$ from $\eta_i$. The standard method cleaves lasers of several lengths from one wafer, measures the slope efficiency of each and converts it to $\eta_d$, then fits

$$\frac{1}{\eta_d} = \frac{1}{\eta_i} + \frac{\alpha_i}{\eta_i \ln(1/R)}\,L .$$

The intercept gives $\eta_i$ and the slope gives $\alpha_i$: for $\eta_i = 0.8$, $\alpha_i = 10$ cm⁻¹ and $R = 0.32$, the line has intercept 1.25 and slope 1.10 per millimeter of cavity. The procedure and its pitfalls are worked through in slope efficiency and differential quantum efficiency from LIV measurements. A spectral alternative uses the Hakki–Paoli method on the amplified spontaneous emission below threshold: at photon energies below the band edge the active region neither absorbs nor amplifies, so the measured net modal gain there levels off at $-\alpha_i$.

Pitfalls

The length fit assumes $\eta_i$ and $\alpha_i$ do not vary with length, which fails when short devices run at much higher carrier density and temperature at threshold; data should be taken in pulsed mode, with lengths spread over at least a factor of three. Cleaved facet reflectance is not exactly the plane-wave Fresnel value, and an error in $R$ moves the extracted $\alpha_i$ in proportion to $\ln(1/R)$. Slope efficiencies must count both facets, or be corrected for the split between them when the facets are coated.

Common questions

What is a typical internal loss for a semiconductor laser?

About 2–20 cm⁻¹. InP-based telecom lasers commonly sit near 10 cm⁻¹; GaAs-based high-power lasers designed for low loss reach about 1 cm⁻¹ or less.

What is the difference between internal loss and mirror loss?

Internal loss is light absorbed or scattered inside the cavity and lost as heat or stray light. Mirror loss is light transmitted through the facets, which is the laser's output. Both must be supplied by gain at threshold, but only the mirror share appears as output power.

How does internal loss change with temperature?

It usually rises, because free-carrier absorption grows with the higher carrier density needed for threshold at elevated temperature. This is one of the contributions to the fall of slope efficiency with temperature.

References: L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012); G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, 1993); B. W. Hakki and T. L. Paoli, "Gain spectra in GaAs double-heterostructure injection lasers," J. Appl. Phys. 46, 1299 (1975).