Abstract
We demonstrate continuous wave four-wave mixing in silicon photonic crystal waveguides of 396 μm length with a group index of ng=30. The highest observed conversion efficiency is -24 dB for 90 mW coupled input pump power. The key question we address is whether the predicted fourth power dependence of the conversion efficiency on the slowdown factor (η≈S4) can indeed be observed in this system, and how the conversion efficiency depends on device length in the presence of propagation losses. We find that the expected dependencies hold as long as both realistic losses and the variation of mode shape with slowdown factor are taken into account. Having achieved a good agreement between a simple analytical model and the experiment, we also predict structures that can achieve the same conversion efficiency as already observed in nanowires for the same input power, yet for a device length that is 50 times shorter.
Highlights
Using slow light to enhance nonlinear effects in planar waveguide structures has recently developed into a very promising concept in Photonics
By controlling the effective speed of propagation of optical waveguide modes, one can increase the energy density in the waveguide and enhance the light-matter interaction [1,2,3]. Such slow light enhancement has already been demonstrated in photonic crystal (PhC) waveguides for many third-order susceptibility (χ(3)) nonlinear processes such as self-phase modulation [4,5,6,7], third-harmonic generation [7,8], and four-wave mixing (FWM) [9,10,11,12,13,14]
Several researchers have already observed the enhancement of the FWM process in the slow light regime [11,12,13,14], but the predicted S4 dependence has not yet been observed, which may be due to effects such as group velocity dispersion (GVD), propagation losses and mode shape variation
Summary
By controlling the effective speed of propagation of optical waveguide modes, one can increase the energy density in the waveguide and enhance the light-matter interaction [1,2,3] Such slow light enhancement has already been demonstrated in photonic crystal (PhC) waveguides for many third-order susceptibility (χ(3)) nonlinear processes such as self-phase modulation [4,5,6,7], third-harmonic generation [7,8], and four-wave mixing (FWM) [9,10,11,12,13,14]. As already pointed out by Melloni et al [10], the conversion process is rather sensitive to losses, limiting practical devices to relatively short lengths It has recently been recognized [17,18] that the mode size increases as a function of group index, reducing the effective nonlinear parameter. By taking all of these effects into account, we develop a modified S4 enhancement formula and demonstrate good agreement with experimental values
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