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I know how a Mach-Zender electro-optical modulator (MZM) works when based on non-linear crystals like LN. On-chip realization of MZMs is often done with $\rm InP$ that is a semiconductor. What is the working principle in this case? How the effective refractive index of one interferometer arm is being changed?

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This is not a complete answer to your question, because I don't know exactly what modulator design you are looking at.

Indium phosphide (and other III-V semiconductors with zincblende crystal structure like gallium arsenide, etc.) does have the necessary properties to exhibit the Pockels effect (source), which is the same effect that produces index of refraction variation in lithium niobate due to an applied electric field. So an MZ modulator can be made with InP by simply applying a strong enough electric field to one arm of the MZ structure.

However it's also possible in a semiconductor to change the index of refraction by injecting mobile electrons or holes into the material (source). This might be more convenient than using the Pockels effect, because it doesn't require high voltages. However it has the drawback of also affecting the attenuation of the path, which will reduce the extinction ratio of the modulator (assuming the reference arm attenuation is kept constant).

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  • $\begingroup$ The realizations I have seen include an integrated SOA that most likely means it is of the second type you have described. $\endgroup$
    – Ang
    Commented Jan 31 at 8:11

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