Frequency chirp is proportional to the rate of change of phase modulation. Within limits, you can achieve an almost arbitrary chirp profile by applying a phase modulation whose amplitude is the integral of the required phase chirp.

Specifically, if you require a sinusoidal frequency chirp, then the effective phase modulation should have a cosine time variation.

If your phase modulation process is cross-phase modulation in a highly non-linear optical fibre, then you need to be aware of the effects of dispersion in the fibre, and its interaction with Kerr effect non-linearity during propagation. Walk-off between pump (modulating signal) and probe (target CW signal) will limit the rate of change of phase. For a sinusoidal modulation, the principal effect of walk-off is to reduce the amplitude of the phase and frequency modulations, and this is readily compensated by increasing the power or modulation depth of the pump. For more complex chirp profiles there is no longer a direct relationship between pump modulation envelope and induced phase shift, so the desired chirp will be more difficult to achieve.

With sufficient dispersion, the envelope of the modulating signal will change over the interaction length, and this may be exacerbated by strong self-phase modulation.

Conversely, if chromatic dispersion is too low, four wave mixing will transfer power from the CW probe signal to new FWM product frequencies. For instance, this may contribute to the large dip in power indicated by the black line in your figure.

Sir A.Robinson

Thanks a lot for your consistent help.

With sufficient dispersion, the envelope of the modulating signal will change over the interaction length, and this may be exacerbated by strong self-phase modulation.

please elaborate this sentence in detail w.r.t my query

regards

A modulated signal can be treated as the sum of multiple optical frequencies within the modulation bandwidth (Fourier analysis). In the presence of chromatic dispersion, the modulation sidebands propagate at different speeds, causing a differential phase shift between sidebands and carrier. This phase shift changes the envelope of the waveform as the signal propagates through the fibre. When this occurs, the induced phase modulation will not be identical to the intensity envelope of the pump at the input to the fibre.

At high optical powers, Kerr-effect non-linearity induces a phase shift proportional to the instantaneous optical intensity (self phase modulation), which modifies the signal spectrum, and how the signal envelope changes during subsequent propagation. Depending on the intensity and dispersion, intensity modulation can be amplified or suppressed compared with the linear propagation regime. In anomalous dispersion fibre, this leads to modulation instability, and is discussed in detail in G. P. Agrawal's "Nonlinear Fiber optics".

Typically, these effects will be less important the walk-off arising from the difference in group velocity between WDM signals. However, without details about your application and operating conditions, this cannot be guaranteed.

More likely, if the product of dispersion and channel separation is too high, then walk-off between channels will low-pass filter the XPM process.

Conversely, if the dispersion and channel separation are too low, and signal powers are high, then FWM will introduce additional phase shifts and transfer energy from the pump and CW target wavelengths to new FWM product wavelengths.