Optimum and suboptimum memoryless nonlinearities for the detection of ultrashort light pulses in Gaussian noise

Detection of ultrashort light pulses with conventional bandlimited photodetectors can lead to substantial performance degradation in digital lightwave communication systems. All-optical nonlinear processing of the received field prior to the optical to electrical conversion can greatly overcome this problem. In this letter, through a decision-theoretic framework and using a basic invariance property of the photodetector, we obtain the optimal zero-memory nonlinear element and evaluate its performance. Possible suboptimum nonlinearities are also investigated and their performance is examined. The results in this letter strongly justify the intuitive use of power-law devices, such as those implemented via two photon absorption (TPA) or second harmonic generation (SHG), in the detection of ultrashort light pulses and show how by using them almost optimal performance can be achieved.