If the input pump beam and probe beam of a wideband SOA have same frequency but different power then is it XGM or XPM?
Both XPM and XGM exist in the SOA.
when a signal is injected to the SOA, the refractive index of the active area would be changed, and the variation is related to the power of the injected signal. In this way, when another signal is injected, the signal will experience different phase variation compared to the case when the other signal is injected, as vice-versa. This phenomenon is named as XPM, which is one of the cross-interactions between two signal .
As for XGM, the gain experienced by one signal will be reduced when another signal is injected. When the signal power is high, more carriers are consumed and the gain reduces a lot, and when the signal power is lower, the gain reduces less. So if the probe is a CW laser, as the gain experienced by the CW laser is related the the injected signal, the signal modulated on the signal will be transferred to the CW laser, just in reverse phase.
Hope this will answer your question.
When pump and probe beam has same frequency you are using counter propagating scheme. In co propagating scheme, for XGM the frequencies should be different.
XGM, and XPM are there simultaneously and the effect is dependent on the intensities of the signals. The ultimate effect is gain saturation, which causes also phase change of self(SPM) and another signal(XPM). The phase change is also intensity dependent. For an negligible SPM, the probe intensity should be very small compared to pump intensity and XGM, XPM will be dominating. If the powers of pump and probe are comparable, then XPM, XGM, SPM will be there.
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