Abstract
Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.
Highlights
Slow light propagation in photonic crystal (PhC) waveguides has attracted significant attention for its potential to increase the efficiency of nonlinear optical phenomena over short path lengths [1,2]
Slow light propagation in PhC waveguides has been shown to produce efficient thirdharmonic generation (THG) [13] (another χ(3) based nonlinear process), which manifests as the out-of-plane emission of visible light from the conversion of a near-infrared optical pump coupled into the waveguide
The fact that the third harmonic (TH) power is almost constant in this spectral window emphasizes the slow light dependence of THG, and the apparent negligible role of phase matching in this case, in agreement with the results reported in Ref [13]
Summary
Slow light propagation in photonic crystal (PhC) waveguides has attracted significant attention for its potential to increase the efficiency of nonlinear optical phenomena over short path lengths [1,2]. Following theoretical work that predicted such enhancement [2,3,4,5], several experimental demonstrations have confirmed this effect in the context of self-phase modulation [6,7,8,9], interaction with free carriers [6,8], two- [6,7,8,9] and three- [10] photon absorption in both III-V semiconductors [8,9,10] and silicon [6,7] These results demonstrate that slow light modes in PhC waveguides can induce nonlinear effects at lower input powers and in shorter waveguides [11] than fast light modes [12]. Slow light propagation in PhC waveguides has been shown to produce efficient thirdharmonic generation (THG) [13] (another χ(3) based nonlinear process), which manifests as the out-of-plane emission of (green) visible light from the conversion of a near-infrared optical pump coupled into the waveguide (see Fig. 1). We interpret these results as the coupling of the TH light to the continuum of radiation modes above the light line, which provides a relatively efficient pathway for THG in a system where the quasi-guided modes are (i) poorly matched with the fundamental mode, and (ii) have a finite lifetime, lowered by the absorption of silicon in the visible
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