Why L-I Curves Kink

Scope

This article explains kinks in the light-current characteristic of semiconductor lasers: what counts as one, the physics that produces them, how to tell the origins apart from the shape of the data, and how a kink-free power specification is measured. It is a reference on the mechanism; the bench procedures for the underlying curves are in Threshold extraction methods and Slope-efficiency extraction, and the one-paragraph version is the LIV kink entry. Background: L-I-V curve, transverse modes, spatial hole burning.

What a kink is

Above threshold an ideal diode laser converts current to light along a straight line whose slope is the slope efficiency. A kink is a localized departure from that line: a step, a change of slope, or a short wobble, confined to a narrow current interval, after which the curve is straight again with a possibly different slope. The confinement is what distinguishes a kink from the smooth downward curvature of thermal rollover, which is a gradual loss of slope as the junction heats, and from the abrupt, permanent collapse of catastrophic optical damage, which is a kink that never recovers.

Kinks are small in absolute terms and easy to miss on a raw plot. A 10% change in slope efficiency at 1 W/A, sustained over a 10 mA window, moves the output by 1 mW. On a 300 mW laser plotted full scale that is 0.3% of the axis, invisible. The first derivative $dL/dI$ plotted against $I$ turns the same event into a 10% step, which is why production test works on the derivative rather than the curve. A companion structure usually appears in $dV/dI$ at the same current, because whatever reorganized the optical field also changed the carrier density and hence the junction voltage.

The specification that comes out of this is kink-free power: the highest power (or current) below which the laser is guaranteed free of kinks by the manufacturer's criterion. The criterion is a window on the local slope: the laser is kink-free up to the current where $dL/dI$ departs from its running value by more than a set fraction, commonly 10% to 20%, evaluated over a sliding window of a few milliamps. The fraction and the window are vendor-specific and belong on the data sheet next to the number. A kink-free power of 300 mW on a laser whose slope is 1 W/A says that no such departure occurs below about 330 mA of drive, and says nothing about what happens above it.

The lateral-mode mechanism

Most kinks in single-mode ridge-waveguide lasers, which is to say most kinks in pump lasers, telecom sources, and high-power single-mode diodes, come from the lateral waveguide. A ridge laser confines light laterally by a small effective-index step $\Delta n$ between the region under the ridge and the region beside it, typically a few times $10^{-3}$. Treat the lateral guide as a symmetric slab: it supports only the fundamental lateral mode when its width is below $\lambda / (2\,\mathrm{NA}_\mathrm{lat})$ with $\mathrm{NA}_\mathrm{lat} = \sqrt{2 n \Delta n}$. At 980 nm with $n = 3.35$, that cutoff width is 3.5 µm for $\Delta n = 3 \times 10^{-3}$, 2.7 µm for $5 \times 10^{-3}$, and 1.9 µm for $10^{-2}$. Ridges are routinely made wider than this, at 3 to 5 µm, because a narrower ridge means higher series resistance, higher facet intensity, and a wider far field. The laser is then single-mode only because the first-order lateral mode has more loss and less gain overlap than the fundamental, not because it cannot exist.

That margin is small, and injection erodes it. Two effects change the lateral index profile with current. Carriers lower the refractive index at about $-1.5 \times 10^{-20}$ cm³ per carrier, so a lateral variation of $10^{18}$ cm$^{-3}$ in carrier density is an index change of $-0.015$, three times the built-in step. Heat raises the index at about $2.5 \times 10^{-4}$ per kelvin, so a 20 K temperature difference between the ridge center and its flanks adds $+5 \times 10^{-3}$, comparable to the step. Below threshold the carrier profile is set by current spreading; above threshold spatial hole burning depletes carriers where the fundamental mode is most intense, at the center of the ridge. Depleting carriers at the center raises the index there, which strengthens the guide, pulls the first-order mode closer to cutoff from the other side, and gives it access to the unburned gain at the edges of the ridge, exactly where the first-order mode has its lobes.

The kink happens when that first-order mode reaches threshold or, more often, when it begins to lase coherently with the fundamental. Two lateral modes with slightly different propagation constants beating together produce a near-field pattern that shifts sideways and a far field that steers off axis by roughly a degree, oscillating or settling to one side depending on the relative phase. Total power changes little; what changes is where it goes. This is the beam-steering kink of the 980 nm pump-laser literature, and it is why a kink that looks negligible on a power meter can be severe in the application: a fiber-coupled module sees a steer of 1° as a coupling loss of about 5% if the lens system's acceptance corresponds to a 1/e² half-angle of 6° at the chip (3% at 8°, 8% at 5°), and a steer that oscillates as a noise term. Laboratory L-I curves taken with an integrating sphere hide this entirely; L-I curves taken through the fiber show it as the kink it is.

The dependence on the built-in step explains the design levers. A deeper ridge etch or a larger index step raises $\mathrm{NA}_\mathrm{lat}$ and pushes the first-order mode further from threshold, at the price of a wider lateral far field and, if the etch reaches the active layer, more surface recombination. A narrower ridge does the same at the price of resistance and facet intensity. Loss added selectively to the first-order mode, by ion implantation or absorbing regions beside the ridge, discriminates against it without changing the fundamental. Whichever lever is used, the kink current moves with temperature, because both the carrier-induced and thermal index terms do, and a kink that shifts by milliamps per kelvin is the modal signature.

Mode hops as small kinks

A different kind of kink comes from the longitudinal spectrum. In a Fabry-Perot laser the gain peak and the cavity mode comb drift with temperature at different rates (the gain peak at about 0.3 nm/K, the modes at about 0.06 to 0.1 nm/K), so as current heats the junction the lasing mode periodically hops to a neighbor. The new mode has a slightly different gain, mirror loss, and coupling to the outside, so the output power steps by a small fraction of a percent to a few percent, and the wavelength steps by one mode spacing at the same current. The signature is the wavelength jump: a mode-hop kink is always accompanied by a discrete spectral change, and it repeats quasi-periodically in current as the comb walks through the gain peak. DFB lasers are built not to do this, and when a DFB shows a hop the cause is usually feedback or a facet-phase problem rather than the intended cavity. The measurement and mode-hop-free tuning ranges that matter for tunable and external-cavity lasers are separate subjects.

Other origins

Vertical-cavity lasers kink where the polarization switches between two nearly degenerate linear states, or where a higher-order transverse mode turns on; the total power is nearly continuous and the polarization-resolved or aperture-resolved power is not, which is the same lesson as beam steering in a different geometry. Broad-area lasers do not so much kink as filament: the wide stripe breaks into self-focused channels whose number and position change with current, and the L-I curve shows small irregular structure rather than a single event. At the aggressive end of any of these, a kink followed by a slope that never recovers, sometimes preceded by a small increase in threshold on the next sweep, is facet damage beginning; stop and examine the facet before deciding it was modal.

Reading the signature

The origins separate cleanly once three things are recorded alongside the L-I curve: the spectrum, the far field or fiber-coupled power, and the behavior on a second sweep at a different heatsink temperature.

The repeat sweep is the cheapest and most decisive test. Modal kinks return at a shifted current when the temperature changes; damage does not return, because the laser is now a different laser; and a kink that sits at exactly the same current regardless of temperature is usually the measurement, not the device: a current-source range change, a thermal transient from a slow sweep, or a reflection inside an integrating sphere, as the LIV kink entry notes.

Measuring kink-free power

The procedure is a fine-stepped L-I with derivative analysis, repeated under conditions that expose modal behavior.

1. Sweep current in steps of 1 mA or finer, with dwell long enough for thermal settling at each point, to at least 20% beyond the intended kink-free rating. Coarse 10 mA steps miss kinks narrower than the step.
2. Compute $dL/dI$ by a smoothed finite difference, and $dV/dI$ from the voltage record. Plot both against current.
3. Apply the criterion: mark the first current at which $dL/dI$ departs from its running value by more than the specified fraction over the specified window. Record the fraction and the window with the result.
4. Repeat at two or three heatsink temperatures spanning the operating range. Report the lowest kink current across temperatures, not the room-temperature one.
5. For fiber-coupled parts, take the L-I through the fiber as well as in the sphere, and record the far field or a lateral beam-pointing readout during the sweep if the application has an aperture.
6. Derate: set the maximum operating current below the lowest kink current by a margin that covers aging, since the lateral index margin narrows as facets and contacts degrade.

The measurement side of all of this, including thermal settling and the difference between pulsed and CW sweeps, is covered in Pulsed versus CW LIV measurement, and what the resulting numbers mean on a data sheet in How to read a laser diode datasheet.

References: M. F. C. Schemmann, C. J. van der Poel, B. A. H. van Bakel, H. P. M. M. Ambrosius, A. Valster, J. A. M. van den Heijkant and G. A. Acket, "Kink power in weakly index guided semiconductor lasers," Appl. Phys. Lett. 66, 920 (1995); J. Guthrie, G. L. Tan, M. Ohkubo, T. Fukushima, Y. Ikegami, T. Ijichi, M. Irikawa, R. S. Mand and J. M. Xu, "Beam instability in 980-nm power lasers: experiment and analysis," IEEE Photon. Technol. Lett. 6, 1409 (1994); W. D. Herzog, B. B. Goldberg and M. S. Ünlü, "Beam steering in narrow-stripe high-power 980-nm laser diodes," IEEE Photon. Technol. Lett. 12, 1604 (2000); L. A. Coldren, S. W. Corzine and M. L. Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), on lateral waveguiding and carrier-induced index change. The lateral cutoff widths, index shifts, and coupling-loss figures above are computed from the stated parameters.