Nonlinear four-wave-mixing (FWM) interactions enable a wide variety of photonic functionalities, including wave- length conversion, all-optical switching, signal regeneration, and generation of entangled photons. To achieve efficient FWM interactions the waves either have to be phase-matched, or a quasi-phase-matching (QPM) scheme has to be realized. However, these techniques conventionally require light-guiding media with specific characteristics. We propose a more general QPM scheme for enabling efficient FWM interactions in the presence of a large phase-mismatch. The scheme is based on increasing the distance over which there is FWM gain, while simultaneously decreasing the distance over which there is FWM loss. This is achieved by adiabatically alternating between two phase-mismatch values along the propagation path. We discuss in detail how such phase-mismatch switching (PMS) can be employed to achieve QPM of a FWM process, what the requirements are for optimal FWM efficiency, and how the scheme is impacted by nonlinear dispersion as well as optical losses. Additionally, we describe how QPM by PMS can be implemented with a silicon-on-insulator strip waveguide of which the width is adiabatically varied between two values along the propagation path. By means of numerical simulations, we show that such a waveguide can enhance the wavelength conversion by 20 dB after 1 cm compared to a corresponding constant-width waveguide. For a pump wavelength of 1550 nm, PMS enables efficient conversion (> -21 dB) around a target signal wavelength situated anywhere in the entire near-infrared wavelength domain of 1300-1900 nm.
We present a generic approach to determine the phase mismatch for any optical nonlinear process. When applying
this approach, which is based on the evaluation of local phase changes, to Raman- and Kerr-based four-wave-mixing
in silicon waveguides, we obtain a novel expression for the phase mismatch which is more accurate as
compared to the conventional definition; and which contains additional contributions due to the dispersion of
the four-wave-mixing processes, the so-called four-wave-mixing dispersion. By means of numerical simulations,
we show that this additional dispersion has a significant impact on the evolution of the phase mismatch along
the waveguide, and thus on the conversion efficiency.
We propose an efficient four-wave-mixing-based wavelength conversion scheme in a silicon nanowire ring whereby no
dispersion engineering of the nanowire is required. Instead, we rely on the spatial variation of the Kerr susceptibility
around the ring to quasi-phase-match the wavelength conversion process for TE polarized fields. We show through
numerical modeling that in the absence of dispersion engineering this quasi-phase-matched wavelength conversion
approach can outperform 'conventional' wavelength conversion by as much as 10 dB.
Starting from the propagation equations describing four-wave-mixing-basedwavelength conversion, we investigate
how the conversion efficiency in silicon waveguides is influenced by the frequency difference between the pump
and Stokes input waves. By means of numerical simulations we show that, by detuning this frequency difference
slightly away from Raman resonance, the conversion efficiency does not necessarily decrease, but can even be
more than doubled as compared to Raman-resonant operation. At the same time, other values of the frequency
detuning that still remain well within the Raman linewidth can lead to a more than 10 dB decrease in efficiency.
As such, we show that a high-resolution tuning of the frequency difference is not only necessary to obtain
an optimal conversion efficiency, but also to avoid the detrimental efficiency decrease in case of an inadequate
detuning. Finally, we discuss how the pump-Stokes frequency difference that is optimal for wavelength conversion
varies with the length of the waveguide and with its dispersion characteristics.
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