Impact of two-photon absorption on self-phase modulation in silicon waveguides

Abstract

We study the effects of two-photon absorption on the self-phase modulation (SPM) process in silicon waveguides while including both free-carrier absorption and free-carrier dispersion. An analytical solution is provided in the case in which the density of generated carriers is relatively low; it is useful for estimating spectral bandwidth of pulses at low repetition rates. The free-carrier effects are studied numerically with emphasis on their role on the nonlinear phase shift and spectral broadening. We also consider how the repetition rate of a pulse train affects the SPM process.

Monolithic nonlinear pulse compressor on a silicon chip

“…The semiconductor nature of silicon implies a small optical band gap, leading to possible nonlinear losses in the form of two-photon absorption (TPA) and free-carrier absorption (FCA). Because of TPA-and FCA-related losses, an input pulse with high peak power experiences a rapid reduction in its amplitude as it propagates into the silicon nanowire waveguide 23,27,28 . As the extent of spectral broadening from self-phase modulation scales with the peak power of the pulse, the reduction in pulse amplitude inside the nanowire waveguide limits the final pulse bandwidth and hence the compression factor.…”

“…Consequently, free-carrier accumulation, which drastically reduces the input peak power, is precluded. At higher data rates, self-phase modulation is compromized 28 and compression cannot occur. To circumvent this problem, methods such as ion implantation 31 or reverse biased P-I-N junctions 32 may be used to greatly reduce free-carrier lifetimes to below 20 ps and in so forth, eliminate free-carrier accumulation at higher data rates.…”

“…Yin and Agrawal 28 reported that the relation, ν.τ c ≤ 0.2, (where ν is the laser repetition rate and τ c is the free-carrier lifetime) should be satisfied for self-phase modulation-induced spectral broadening to take place without detriment 28 . Therefore, by adopting the aforementioned methods to reduce free-carrier lifetimes, our nonlinear pulse compressor may efficiently operate at the commonly used rate of 10 Gbit s − 1 before multiplexing in 1.28 Tb s − 1 OTDM systems 8,9 .…”

“…functions of both input peak power and dispersive grating length are studied by numerically solving the nonlinear Schrödinger equation 20 , taking into account two photon and free-carrier effects 23,27,28 . The waveguide dispersion and effective waveguide modal area were obtained using a fully vectorial beam propagation method.…”

Saturation of the Raman amplification by self-phase modulation in silicon nanowaveguides

“…The instantaneous Kerr effect symmetrically broadens the spectrum, while the timedependent buildup of the carrier density creates a nonlinear phase contribution, which produces a blue shift in the spectrum. 11 The spectral broadening induced by the Kerr and the FCR 3 is expected to be on the order of 1-2 nm for input intensities on the order of a few GW/cm 2 , typically used in Raman amplification 4 experiments. This is consistent with our observations.…”