Signal-to-Noise Ratio of Dispersive Photonic Signal Processors Employing Thermal Carriers With Smooth Spectrum and Direct Detection

An exact theory describing the intensity PSD of photonic signal processors based on modulated thermal sources with smooth spectrum, first-order dispersion and intensity-noise-limited direct detection is presented. The theory is applied to the evaluation of the signal-to-noise ratio (SNR) of Microwave Photonic Filters (MPF) and of systems based on Incoherent Frequency-to-Time Mapping (IFTM) and Time-Spectrum Convolution (TSC) driven by thermal carriers whose optical spectra (continuous or sliced) is smooth at microwave scales. It is shown that the noise PSD of MPF based on low-index amplitude modulation coincides with the white-noise PSD of unmodulated, continuous wave (cw) polarized thermal light. In turn, both IFTM and TSC show modulation-dependent noise PSDs resulting in an SNR not better than cw, which decreases with pulse spreading. For IFTM the SNR is poor, with typical values of a few dB, whereas the SNR of TSC interpolates between the cw SNR and that of IFTM, thus showing a range of parameters where the SNR of IFTM is outperformed.