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August 25, 2026 September 9, 2026

Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides - Notes

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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

Published 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.

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.

From S. Manna et al., Journal of Optics 18(7), 075801 (2016), DOI 10.1088/2040-8978/18/7/075801. © 2016 IOP Publishing Ltd.

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.

From S. Manna et al., Journal of Optics 18(7), 075801 (2016), DOI 10.1088/2040-8978/18/7/075801. © 2016 IOP Publishing Ltd.

How to cite

Article access and reuse

This article was published on a subscription basis by IOP Publishing. IOP permits authors to share the accepted manuscript under its author-rights policy and to reuse their original figures with appropriate acknowledgement. The local file reviewed here is the typeset Version of Record, so the PDF is not hosted. The two selected figures are reproduced with full citation and copyright notice.

Related publications

Connections within F. Ramiro-Manzano's publication record, selected from shared research topics and evidence reviewed in the source papers.

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What this paper adds to the related work

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What the related paper adds

This later paper extends the research direction developed in Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides. This theoretical paper interprets small optical fluctuations on a nonlinear guided beam as Bogoliubov excitations of a one-dimensional photon fluid. It predicts how Kerr nonlinearity and losses reshape their dispersion and proposes a stimulated four-wave-mixing and interferometric experiment to measure that dispersion directly.

What this paper adds to the related work

This paper provides an earlier basis for the later development reported in Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide. This study demonstrates stimulated degenerate four-wave mixing in silicon-nanocrystal waveguides at telecom wavelengths. It measures a large nonlinear refractive index and a broad conversion bandwidth, while also identifying two-photon absorption as the main limitation and the mid infrared as the more favourable operating region.

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What the related paper adds

This earlier paper establishes a scientific basis for Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides. This review connects the unusual quantum-confined properties of silicon nanocrystals to two application tracks. It brings bistable cavities, nonlinear mode imaging and four-wave mixing into one photonic framework, then links nanocrystal luminescence to entropy generation for secure communications.

What this paper adds to the related work

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Featured image for Multi-Mode Interference Revealed by Two-Photon Absorption in Silicon-Rich SiO₂ Waveguides
Journal article
Applied Physics Letters 106, 071109 (2015)
Multi-Mode Interference Revealed by Two-Photon Absorption in Silicon-Rich SiO₂ Waveguides
S. Manna, F. Ramiro-Manzano, M. Ghulinyan, M. Mancinelli, F. Turri, G. Pucker and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides. This work turns two-photon-excited luminescence into a direct image of otherwise invisible infrared modes in silicon-nanocrystal waveguides. The measured spatial beat patterns expose multimode interference, agree with finite-element simulations and simultaneously quantify the unusually large two-photon absorption of the nanocrystal material.

What this paper adds to the related work

Building on the earlier contribution Multi-Mode Interference Revealed by Two-Photon Absorption in Silicon-Rich SiO₂ Waveguides, this paper advances the research line. This study demonstrates stimulated degenerate four-wave mixing in silicon-nanocrystal waveguides at telecom wavelengths. It measures a large nonlinear refractive index and a broad conversion bandwidth, while also identifying two-photon absorption as the main limitation and the mid infrared as the more favourable operating region.

Complete multipanel composition showing pump and probe time traces, simulated temperature map, optical energy density and intrinsic quality-factor contributions
Journal article
Optics Letters 38(18), 3562-3565 (2013)
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F. Ramiro-Manzano, N. Prtljaga, L. Pavesi, G. Pucker and M. Ghulinyan

What the related paper adds

This earlier paper establishes a scientific basis for Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides. This paper demonstrates thermo-optical bistability in a fully integrated silicon-nanocrystal microresonator. Time-resolved measurements and modelling separate refractive-index modulation from heat dissipation, show that the silica host carries away the heat, and preserve the cavity quality factor even at comparatively high pump powers.

What this paper adds to the related work

Building on the earlier contribution Thermo-Optical Bistability with Si Nanocrystals in a Whispering-Gallery-Mode Resonator, this paper advances the research line. This study demonstrates stimulated degenerate four-wave mixing in silicon-nanocrystal waveguides at telecom wavelengths. It measures a large nonlinear refractive index and a broad conversion bandwidth, while also identifying two-photon absorption as the main limitation and the mid infrared as the more favourable operating region.

Il Nuovo Saggiatore journal identification graphic on a cyan background
Journal article
Il Nuovo Saggiatore 28(1-2), 5-15 (2012)
La nanofotonica in silicio e la fotonica con il nanosilicio: una piattaforma per ampliare il successo della fotonica in silicio
A. Anopchenko, F. J. Aparicio Rebollo, P. Bettotti, F. Bianco, P. Bellutti, M. Cazzanelli, K. Fedus, E. Froner, D. Gandolfi, M. Ghulinyan, N. Kumar, Y. Jestin, P. Ingenhoven, S. Larcheri, L. Lunelli, M. Mancinelli, A. Marconi, E. Moser, L. Pasquardini, C. Pederzolli, C. Potrich, N. Prtljaga, G. Pucker, F. Ramiro-Manzano, E. Rigo, M. Scarpa, F. Sgrignuoli, A. Tengattini and L. Pavesi

What the related paper adds

This earlier paper establishes a scientific basis for Stimulated Degenerate Four-Wave Mixing in Si Nanocrystal Waveguides. This broad review positions silicon and silicon-nanocrystal photonics as a shared platform for resonators, nonlinear optics, light emission and integrated devices. It connects material properties to circuit functions and provides the wider technological setting in which the more focused experiments in this publication record sit.

What this paper adds to the related work

Building on the earlier contribution La nanofotonica in silicio e la fotonica con il nanosilicio: una piattaforma per ampliare il successo della fotonica in silicio, this paper advances the research line. This study demonstrates stimulated degenerate four-wave mixing in silicon-nanocrystal waveguides at telecom wavelengths. It measures a large nonlinear refractive index and a broad conversion bandwidth, while also identifying two-photon absorption as the main limitation and the mid infrared as the more favourable operating region.

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

InterferenceThe 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.MaterialsThe 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. 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 conclusion is a wavelength-specific design strategy, not a generic claim of lossless conversion.
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