Modeling the Phase Response of an Optical Filter with Application to Cascaded Filtering in an Optical Link

Abstract

To accurately characterize the effects of optical filters, it is crucial to model the filter's frequency response as precisely as possible. Given that the amplitude response of an optical filter can be obtained through theoretical models and/or experiments, the main objective of this thesis is to investigate techniques for determining the optical filter's phase response from its amplitude response.

To achieve this, the Hilbert transform technique and the direct numerical integration technique based on Kramers-Kronig relations are utilized. The most accurate method is to calculate the filter's group delay response and then integrate it to obtain the phase response through the direct numerical integration technique. The integration is approximated using the trapezoidal rule. Additionally, maximum out-of-band attenuation and smoothing in a specific interval around the intersection of the filter slope and the maximum out-of-band attenuation are applied to the amplitude response to align it with practical devices.

The second objective of this thesis is to determine the phase response of the WSS filter based on its amplitude response using the most effective technique. The amplitude response of the WSS filter is modeled analytically and also measured using a Finisar WaveShaper 1000S and a broadband noise source as input.

The simulation results show that, after applying maximum out-of-band attenuation of 54 dB and smoothing in a 6 GHz interval around the intersection, the group delay response of a 38 GHz wide WSS filter changed non-linearly between -20 to 80 ps and, correspondingly, the phase response changed between -2 to 16 rad in the [0, 150] GHz frequency range.

Finally, an application of obtaining the optical filter's phase response is demonstrated in this study. For this purpose, the impact of incorporating the phase response in the cascaded filtering effect in an optical link is studied. The simulated optical link comprised 10 spans, and a 28 Gbaud DP 64-QAM signal is subjected to a distributed ASE noise configuration. Generalized Mutual Information (GMI) is calculated as a system performance metric. The results indicate that the phase response can have a significant impact on signal performance in an optical system. Moreover, the impact of the location of cascaded WSS filters in the system, including the phase response of the cascaded WSS filters, is investigated.