Glossary entry

Optical feedback regimes (Tkach–Chraplyvy)

The five ranges of external optical feedback level, in dB relative to the emitted power, that a single-mode semiconductor laser passes through as more light is returned to it: linewidth perturbation, mode hopping, a narrow stable window, coherence collapse, and strong-feedback extended-cavity operation. The scale on which return-loss budgets and isolator specifications are written.

Lasers & gain Fiber & telecomUpdated September 2026

The feedback level $f_{ext}$ is the fraction of a laser's emitted power that is returned to its output facet, quoted in decibels: $f_{ext}\,\mathrm{(dB)} = 10\log_{10}(P_{back}/P_{out})$ . Tkach and Chraplyvy measured the behaviour of 1.5 µm DFB lasers against feedback from a distant reflector and found that it falls into five regimes, ordered by level. The boundaries below are theirs; on a different device, at a different distance, or with a different feedback phase, each boundary moves by several dB, but the sequence does not change.

Regime	Feedback level	Behaviour
I	below about −80 dB	Linewidth narrows or broadens depending on the phase of the returned light
II	−80 to −45 dB	Mode hopping between external-cavity modes; line splitting
III	−45 to −39 dB	A narrow window of stable, re-narrowed single-mode operation
IV	−39 to −8 dB	Coherence collapse: chaotic intensity and phase, linewidth in the GHz range, RIN up by tens of dB
V	above about −8 dB	Strong feedback: with an anti-reflection-coated facet, stable operation on the extended cavity (external cavity laser)

Converting a return loss into a feedback level

The reflector's return loss is not the feedback level; the light crosses everything between laser and reflector twice. With a one-way loss $L$ (dB) between the facet and a reflector of return loss $RL$ (dB),

f_{ext}\,\mathrm{(dB)} \;=\; -\,RL \;-\; 2L

A DFB coupled into fiber with 3 dB loss and facing a mated UPC connector of 50 dB return loss sees $-50 - 6 = -56$ dB, regime II. The same laser facing an open PC connector (14 dB return loss) sees −20 dB, well inside regime IV. An isolator adds its isolation to $L$ once, on the return trip, so a 30 dB isolator moves the UPC case to −86 dB, regime I. Coupling loss is therefore the one loss that helps; the arithmetic is the reason narrow-linewidth transmitters ship with an isolator in the package rather than relying on connector discipline downstream.

Where regime IV begins on a given laser

The onset of coherence collapse is the boundary that matters for links, and Helms and Petermann gave it a closed form:

f_{crit} \;=\; \frac{\tau_{in}^2\,\gamma_R^2}{16\,C_e^2}\;\frac{1+\alpha^2}{\alpha^4}, \qquad C_e = \frac{1-R}{2\sqrt{R}}

where $\tau_{in}$ is the round-trip time inside the laser cavity, $\gamma_R$ the damping rate of the relaxation oscillations (in the K-factor description, $\gamma_R = K f_r^2 + \gamma_0$ ), $R$ the power reflectivity of the output facet, and $\alpha$ the linewidth enhancement factor. For a 300 µm cavity of group index 3.5 ( $\tau_{in} = 7$ ps), a damping rate of $2 \times 10^{10}$ s⁻¹, a cleaved facet ( $R = 0.32$ , $C_e = 0.60$ ), and $\alpha = 3$ , the expression gives $f_{crit} = 4.2 \times 10^{-4}$ , or −34 dB, in the range Tkach and Chraplyvy observed. The dependences are the point of the formula. Taking $\alpha$ from 3 to 5 lowers the threshold to −38.5 dB and taking it to 1.5 raises it to −27 dB; heavily damped lasers (large $\gamma_R$ , the regime of quantum-dot lasers) tolerate proportionally more; and an anti-reflection-coated facet of 2 % reflectivity raises $C_e$ to 3.5, which lowers the threshold by 15 dB relative to the cleaved facet, since the same returned light is now a larger fraction of what the weak mirror reflects.

Measured thresholds land where the formula puts them: quantum-well DFBs collapse at −40 to −30 dB, while quantum-dot lasers on the same test bench show up to 20 dB less sensitivity (Liu 2017). Distance enters through the feedback phase and through whether the reflector is inside the coherence length; short external cavities (centimetres) give phase-coherent feedback and the most structured behaviour, while kilometres of fiber average the phase but do not remove the regime IV instability. The practical rule is to budget levels, not distances.

The regimes are used deliberately as well as avoided. Regime III behaviour is the basis of self-injection locking to a high-Q resonator, regime V of the external cavity laser, and controlled regime IV of chaotic-laser random-number generators. The working reference, with the isolation budget and diagnosis, is Optical feedback in semiconductor lasers: the five regimes and coherence collapse; injection locking covers the related case of light from a second laser.

References: R. W. Tkach and A. R. Chraplyvy, "Regimes of feedback effects in 1.5-µm distributed feedback lasers," Journal of Lightwave Technology 4, 1655 (1986). J. Helms and K. Petermann, "A simple analytic expression for the stable operation range of laser diodes with optical feedback," IEEE Journal of Quantum Electronics 26, 833 (1990). K. Petermann, "External optical feedback phenomena in semiconductor lasers," IEEE Journal of Selected Topics in Quantum Electronics 1, 480 (1995), and Proc. SPIE 2450, 121 (1995). A. Y. Liu, T. Komljenovic, M. L. Davenport, A. C. Gossard, and J. E. Bowers, "Reflection sensitivity of 1.3 µm quantum dot lasers epitaxially grown on silicon," Optics Express 25, 9535 (2017).