Abstract
For our recently designed continuous-wave and single-frequency ring laser with intra-cavity isolator, we have formulated a rate-equation theory which accounts for two sources of mutual back-scattering between the clockwise and counterclockwise modes, i.e. induced by side-wall irregularities and due to inversion-grating-induced spatial hole burning. With this theory we first confirm that for a ring laser without intra-cavity isolation, from sufficiently large pumping strength on, the inversion-grating-induced bistable operation (i.e. either clockwise or counterclockwise) will overrule the back-reflection-induced coupled-mode operation (i.e. both clockwise and counterclockwise). We then analyze the robustness of unidirectional operation in case of intra-cavity isolation against the intra-cavity back-reflection mechanism and grating-induced mode coupling and derive for this case an explicit expression for the directionality in the presence of external optical feedback, valid for sufficiently strong isolation. The predictions posed in the second reference remain unaltered in the presence of the mode coupling mechanisms here considered.
Highlights
In state-of-the-art photonic integrated circuits (PICs) it is desirable to integrate one or more lasers on a single chip together with components such as modulators, splitters and filters
A fundamental problem is the sensitivity of a semiconductor laser to external optical feedback (EOF), which can lead to unstable dynamics
In order to protect the laser from EOF inside the PIC, it is not possible to use the conventional solution in fiber- or free-space optics, based on magnetic materials, since a suitable integrated optical isolator is not available [1]
Summary
In state-of-the-art photonic integrated circuits (PICs) it is desirable to integrate one or more lasers on a single chip together with components such as modulators, splitters and filters Such a device needs only electrical inputs and one or more optical outputs that allow direct coupling to optical fibers. The actual mode of operation is not predetermined and external optical perturbations could induce switching to the other mode, even for EOF as small as ~-40dB [4] This kind of sensitivity can be reduced considerably by applying a one-sided strong reflector [5], but EOF exceeding 30 dB can still lead to unstable behavior. The on-chip isolation is modeled by a roundtrip-loss difference between CW and CCW modes, derived from the corresponding transmission roundtrip differences
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