Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides

S. Manna; M. Bernard; S. Biasi; F. Ramiro Manzano; M. Mancinelli; M. Ghulinyan; G. Pucker; L. Pavesi

Research · Publication & note

Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides

Journal of Optics · Journal article · 14 June 2016

S. Manna, M. Bernard, S. Biasi, F. Ramiro-Manzano, M. Mancinelli, M. Ghulinyan, G. Pucker and L. Pavesi

Journal of Optics

Volume 18 · Issue 7

Article 075801

2016

Abstract

Parametric frequency conversion via four-wave mixing (FWM) in silicon nanocrystal (Si NC) waveguides is observed at 1550 nm. To investigate the role of Si NC, different types of waveguides containing Si NC in a SiO₂ matrix were fabricated. Owing to the increase of the dipole oscillator strength mediated by the quantum confinement effect, the non-linear refractive index (n₂) of Si NCs is found to be more than one order of magnitude larger than the one of bulk Si. Coupled differential equations for the degenerate FWM process taking into account the role of Si NC were numerically solved to model the experimental data. The modeling yields an effective n₂ for Si NCs in SiO₂ waveguides which is similar to the one of Si waveguides. We also measured a large signal to idler conversion bandwidth of ∼22 nm. The large non-linear refractive index is joined with a large two photon absorption coefficient which makes the use of Si NC in non-linear optical devices mostly suitable for mid-infrared applications.

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Figures

Cross sections and simulated TE mode profiles of silicon-nanocrystal channel and stripe waveguides — **Figure 1.** Cross sections of the silicon-nanocrystal channel and stripe waveguides with their fundamental TE mode profiles. The silicon-rich silicon-oxide region is the layer in which the nanocrystals form.

Measured four-wave-mixing spectra for silicon-nanocrystal channel and stripe waveguides at several pump and signal powers — **Figure 4.** Representative four-wave-mixing spectra for the channel waveguide at two pump and signal power combinations and for the stripe waveguide at a third combination.

Research fields

Top-down

Silicon-nanocrystal-rich silica is patterned into channel and stripe waveguides with different core dimensions and nanocrystal concentrations. These integrated structures provide controlled interaction lengths for telecom-band four-wave mixing.

Simulations & fits

Coupled propagation equations include linear loss, two-photon absorption, free carriers and the nanocrystal contribution to the Kerr response. Numerical fitting of signal and idler conversion isolates an effective nonlinear index and explains the measured conversion bandwidth.

Characterization

Degenerate pump–probe spectra around 1550 nm quantify generated idler power, propagation loss and two-photon absorption for the different waveguides. The comparison shows a strong nanocrystal-enhanced nonlinearity accompanied by absorption that favours operation farther into the mid-infrared.

RESEARCH TOPICS

InterferenceDegenerate four-wave mixing produces an idler only when pump, signal and idler satisfy energy conservation and sufficient phase matching. The stripe waveguide yields stronger conversion than the channel device because its propagation constants and modal overlaps reduce the mismatch. Comparing the two geometries makes the interference requirement experimentally visible: identical nonlinear material does not guarantee equal wavelength conversion if the generated field accumulates the wrong phase along the guide.

MaterialsSilicon nanocrystals are formed by annealing silicon-rich oxide for 1.5 hours at 1150 °C in nitrogen. After separating the nanocrystal contribution from the silica matrix, the extracted nonlinear index is more than three orders of magnitude above silica, two above silicon nitride and one above bulk silicon. The effective device nonlinearity is lower because only part of the mode overlaps the nanocrystals. The paper therefore reports both an intrinsic material advantage and the dilution imposed by the composite waveguide.

MultimodeStripe and channel cross-sections support different transverse field distributions, changing how pump, signal and idler overlap with one another and with the nanocrystal-rich region. That modal difference appears directly in the channel's lower idler-conversion efficiency. Geometry also controls dispersion and hence phase matching over wavelength. The comparison shows that nonlinear-waveguide design must optimise mode shape and propagation constant together; increasing confinement alone does not ensure more useful mixing.

NonlinearThe conversion model includes stimulated four-wave mixing together with two-photon absorption, excited-carrier absorption and carrier lifetime. The measured signal-to-idler bandwidth is about 22 nm, but nonlinear loss limits the achievable efficiency near telecom wavelengths. The authors propose moving beyond roughly 2 μm, where two-photon absorption in silicon is reduced, as a route to retain the strong χ⁽³⁾ response with less carrier penalty. The conclusion is a wavelength-specific design strategy, not a generic claim of lossless conversion.