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Acoustic build-up in on-chip stimulated Brillouin scattering.

Wolff C, Steel MJ, Eggleton BJ, Poulton CG - Sci Rep (2015)

Bottom Line: In addition, the corresponding resonance line is broadened with the development of side bands.In contrast, we argue that intra-mode forward SBS is not expected to show these effects.Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides.

View Article: PubMed Central - PubMed

Affiliation: Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS).

ABSTRACT
We investigate the role of the spatial evolution of the acoustic field in stimulated Brillouin scattering processes in short high-gain structures. When the gain is strong enough that the gain length becomes comparable to the acoustic wave decay length of order 100 microns, standard approximations treating the acoustic field as a local response no longer apply. Treating the acoustic evolution more accurately, we find that the backward SBS gain of sub-millimetre long waveguides is significantly reduced from the value obtained by the conventional treatment because the acoustic mode requires several decay lengths to build up to its nominal value. In addition, the corresponding resonance line is broadened with the development of side bands. In contrast, we argue that intra-mode forward SBS is not expected to show these effects. Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides.

No MeSH data available.


Related in: MedlinePlus

Qualitative illustration of the acoustic build-up effect in a suspended silicon waveguide.The arrows indicate power flux in the optical pump wave (green), the Stokes wave (red) and the acoustic wave (blue) in a short suspended backward SBS setup assuming weak pump depletion. The line graph to the left illustrates the evolution of the respective amplitudes (arbitrary units) throughout the waveguide. Note that the acoustic wave requires some length to build up, thereby reducing the overall SBS effect.
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f1: Qualitative illustration of the acoustic build-up effect in a suspended silicon waveguide.The arrows indicate power flux in the optical pump wave (green), the Stokes wave (red) and the acoustic wave (blue) in a short suspended backward SBS setup assuming weak pump depletion. The line graph to the left illustrates the evolution of the respective amplitudes (arbitrary units) throughout the waveguide. Note that the acoustic wave requires some length to build up, thereby reducing the overall SBS effect.

Mentions: Silicon nanowires motivate our work because they are the first structures in the literature where the detailed acoustic evolution might play a role, but our work applies to any short waveguide. We start with general coupled-mode theory and make no assumptions about material properties. In backward SBS and a special type of forward SBS (more specifically: inter-mode forward SBS), the acoustic group velocity is large and the sound wave needs of the order of 100μm to build up as illustrated in Fig. 1. This is an important fact, because this length scale of 100μm is also the maximal length over which a nanowire can be suspended in a standard SOI process without having too much to worry about sagging and it touching the silicon substrate. The acoustic build-up effectively shortens the waveguide for SBS-purposes and results in a reduction of the total SBS response over the waveguide. We show how the acoustic decay length can be estimated from the acoustic wave vector and the mechanical quality factor. Further symptoms of this effect are a broadening of the SBS-resonance and the appearance of side bands. In conventional (intra-mode) forward SBS, the acoustic group velocity vanishes and no such effect is expected. This difference of the acoustic build-up in very short waveguides may contribute to the explanation of why to date no backward SBS has been observed in suspended silicon systems that exhibit significant forward SBS12. We note that other factors such as nonlinear losses would also be expected to play a role in the effectiveness of SBS processes. We have recently investigated this point17 and found that nonlinear losses are indeed important in certain regimes. A key conclusion however is that forward and backward SBS are impacted in identical fashions for moderate Stokes power, and so cannot account for the particular challenge of observing backward SBS in silicon waveguides. For this reason, we neglect these effects in the current work allowing us to obtain analytic solutions which highlight the particular physics role of acoustic build-up. A complete numerical model would ultimately be required to account for all these effects.


Acoustic build-up in on-chip stimulated Brillouin scattering.

Wolff C, Steel MJ, Eggleton BJ, Poulton CG - Sci Rep (2015)

Qualitative illustration of the acoustic build-up effect in a suspended silicon waveguide.The arrows indicate power flux in the optical pump wave (green), the Stokes wave (red) and the acoustic wave (blue) in a short suspended backward SBS setup assuming weak pump depletion. The line graph to the left illustrates the evolution of the respective amplitudes (arbitrary units) throughout the waveguide. Note that the acoustic wave requires some length to build up, thereby reducing the overall SBS effect.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4559895&req=5

f1: Qualitative illustration of the acoustic build-up effect in a suspended silicon waveguide.The arrows indicate power flux in the optical pump wave (green), the Stokes wave (red) and the acoustic wave (blue) in a short suspended backward SBS setup assuming weak pump depletion. The line graph to the left illustrates the evolution of the respective amplitudes (arbitrary units) throughout the waveguide. Note that the acoustic wave requires some length to build up, thereby reducing the overall SBS effect.
Mentions: Silicon nanowires motivate our work because they are the first structures in the literature where the detailed acoustic evolution might play a role, but our work applies to any short waveguide. We start with general coupled-mode theory and make no assumptions about material properties. In backward SBS and a special type of forward SBS (more specifically: inter-mode forward SBS), the acoustic group velocity is large and the sound wave needs of the order of 100μm to build up as illustrated in Fig. 1. This is an important fact, because this length scale of 100μm is also the maximal length over which a nanowire can be suspended in a standard SOI process without having too much to worry about sagging and it touching the silicon substrate. The acoustic build-up effectively shortens the waveguide for SBS-purposes and results in a reduction of the total SBS response over the waveguide. We show how the acoustic decay length can be estimated from the acoustic wave vector and the mechanical quality factor. Further symptoms of this effect are a broadening of the SBS-resonance and the appearance of side bands. In conventional (intra-mode) forward SBS, the acoustic group velocity vanishes and no such effect is expected. This difference of the acoustic build-up in very short waveguides may contribute to the explanation of why to date no backward SBS has been observed in suspended silicon systems that exhibit significant forward SBS12. We note that other factors such as nonlinear losses would also be expected to play a role in the effectiveness of SBS processes. We have recently investigated this point17 and found that nonlinear losses are indeed important in certain regimes. A key conclusion however is that forward and backward SBS are impacted in identical fashions for moderate Stokes power, and so cannot account for the particular challenge of observing backward SBS in silicon waveguides. For this reason, we neglect these effects in the current work allowing us to obtain analytic solutions which highlight the particular physics role of acoustic build-up. A complete numerical model would ultimately be required to account for all these effects.

Bottom Line: In addition, the corresponding resonance line is broadened with the development of side bands.In contrast, we argue that intra-mode forward SBS is not expected to show these effects.Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides.

View Article: PubMed Central - PubMed

Affiliation: Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS).

ABSTRACT
We investigate the role of the spatial evolution of the acoustic field in stimulated Brillouin scattering processes in short high-gain structures. When the gain is strong enough that the gain length becomes comparable to the acoustic wave decay length of order 100 microns, standard approximations treating the acoustic field as a local response no longer apply. Treating the acoustic evolution more accurately, we find that the backward SBS gain of sub-millimetre long waveguides is significantly reduced from the value obtained by the conventional treatment because the acoustic mode requires several decay lengths to build up to its nominal value. In addition, the corresponding resonance line is broadened with the development of side bands. In contrast, we argue that intra-mode forward SBS is not expected to show these effects. Our results have implications for several recent proposals and experiments on high-gain stimulated Brillouin scattering in short semiconductor waveguides.

No MeSH data available.


Related in: MedlinePlus