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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

Behavior of the acoustic power level Lb = 10 log10 (/2b/2//B0/2) normalized to the naively expected power level at z = 0 (panel a), the Stokes power level  (panel b) and the gain degradation (panel c) of a finite waveguide on resonance (λ = α/2) as a function of waveguide length Z in units of acoustic decay lengths α−1 in comparison with the naive expectation based on Eq. (10).Each set of lines with the same color represents the finite (solid lines) and idealized (dotted lines) behavior for one value of the parameter Λ (forward and backward SBS for Λ > λ and Λ < λ, respectively). The three panels show how the acoustic field approaches its nominal value only after several decay lengths whereas the SBS gain is systematically reduced to the value of an ideal waveguide that is shorter by roughly α−1. Note the dramatic and nearly linear gain reduction for Zα < 2, which is furthermore fairly independent of Λ.
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f2: Behavior of the acoustic power level Lb = 10 log10 (/2b/2//B0/2) normalized to the naively expected power level at z = 0 (panel a), the Stokes power level (panel b) and the gain degradation (panel c) of a finite waveguide on resonance (λ = α/2) as a function of waveguide length Z in units of acoustic decay lengths α−1 in comparison with the naive expectation based on Eq. (10).Each set of lines with the same color represents the finite (solid lines) and idealized (dotted lines) behavior for one value of the parameter Λ (forward and backward SBS for Λ > λ and Λ < λ, respectively). The three panels show how the acoustic field approaches its nominal value only after several decay lengths whereas the SBS gain is systematically reduced to the value of an ideal waveguide that is shorter by roughly α−1. Note the dramatic and nearly linear gain reduction for Zα < 2, which is furthermore fairly independent of Λ.

Mentions: Figure 2a shows the absolute value of Eq. (13) on resonance (κ = 0) for various values of μ (solid lines) together with corresponding values derived from Eq. (10) (dotted lines). Observe that at large , the phonon intensity evolves in accord with Eq. (10), growing exponentially in the positive direction for forward SBS (Λ > λ), and in the negative direction for backward SBS (Λ < λ). Note that the exponential growth exponent is slightly reduced for devices with extremely high gain, i.e. in the range λ2/10 < /μ/ < λ2. This is a minor effect and will usually be negligible in comparison to the findings that we present in the following. For , the phonon intensity is much reduced, indicating that several decay lengths are required for the phonon field to accumulate.


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

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

Behavior of the acoustic power level Lb = 10 log10 (/2b/2//B0/2) normalized to the naively expected power level at z = 0 (panel a), the Stokes power level  (panel b) and the gain degradation (panel c) of a finite waveguide on resonance (λ = α/2) as a function of waveguide length Z in units of acoustic decay lengths α−1 in comparison with the naive expectation based on Eq. (10).Each set of lines with the same color represents the finite (solid lines) and idealized (dotted lines) behavior for one value of the parameter Λ (forward and backward SBS for Λ > λ and Λ < λ, respectively). The three panels show how the acoustic field approaches its nominal value only after several decay lengths whereas the SBS gain is systematically reduced to the value of an ideal waveguide that is shorter by roughly α−1. Note the dramatic and nearly linear gain reduction for Zα < 2, which is furthermore fairly independent of Λ.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Behavior of the acoustic power level Lb = 10 log10 (/2b/2//B0/2) normalized to the naively expected power level at z = 0 (panel a), the Stokes power level (panel b) and the gain degradation (panel c) of a finite waveguide on resonance (λ = α/2) as a function of waveguide length Z in units of acoustic decay lengths α−1 in comparison with the naive expectation based on Eq. (10).Each set of lines with the same color represents the finite (solid lines) and idealized (dotted lines) behavior for one value of the parameter Λ (forward and backward SBS for Λ > λ and Λ < λ, respectively). The three panels show how the acoustic field approaches its nominal value only after several decay lengths whereas the SBS gain is systematically reduced to the value of an ideal waveguide that is shorter by roughly α−1. Note the dramatic and nearly linear gain reduction for Zα < 2, which is furthermore fairly independent of Λ.
Mentions: Figure 2a shows the absolute value of Eq. (13) on resonance (κ = 0) for various values of μ (solid lines) together with corresponding values derived from Eq. (10) (dotted lines). Observe that at large , the phonon intensity evolves in accord with Eq. (10), growing exponentially in the positive direction for forward SBS (Λ > λ), and in the negative direction for backward SBS (Λ < λ). Note that the exponential growth exponent is slightly reduced for devices with extremely high gain, i.e. in the range λ2/10 < /μ/ < λ2. This is a minor effect and will usually be negligible in comparison to the findings that we present in the following. For , the phonon intensity is much reduced, indicating that several decay lengths are required for the phonon field to accumulate.

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