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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

Resonance shape according to Eq. (16) for a wide range of waveguide lengths Z normalized to the peak gain of a long-waveguide approximation (0 dB-point).As the length is reduced to one acoustic decay length, the resonance broadens in a non-Lorentzian fashion, which becomes most prominent for Zα < 1. The graph values for various Z at the point  correspond to the values plotted in Fig. 2c for Λ ≈ 1.
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f3: Resonance shape according to Eq. (16) for a wide range of waveguide lengths Z normalized to the peak gain of a long-waveguide approximation (0 dB-point).As the length is reduced to one acoustic decay length, the resonance broadens in a non-Lorentzian fashion, which becomes most prominent for Zα < 1. The graph values for various Z at the point correspond to the values plotted in Fig. 2c for Λ ≈ 1.

Mentions: Finally, one would expect that the SBS resonance broadens as the effective gain is clamped by the effect described above. We can see this from Eq. (14) by taking the logarithm of the Stokes amplitude at the waveguide’s end (z = Z) and dividing it by the factor μZ, i.e. the part of the exponent in Eq. (10) that does not depend on the Lorentzian R. This new quantity describes the SBS-gain distribution as a function of the detuning parameter κ and the waveguide length and is constructed to be directly compared to the ideal long waveguide resonance R in Eq. (8). We can see in Fig. 2c that the gain reduction is rather robust with respect to the coupling strength μ, so we may expect this to be true for the resonance shape as well. This justifies that we assume the term μ/λ2 to be small and approximate to leading order:where we have used ln(1 + x) ≈ x in the second step. The leading term 1/(2λ*) = 1/(α − iκ) is exactly the Lorentzian resonance R that we expect for an infinitely long waveguide18. For a moderately long waveguide, the exponential remains negligible and the effective waveguide length is basically just reduced by one acoustic decay length α−1. For shorter waveguides, both the term 1/(2Zλ*) and the exponential term broaden the resonance and distort it into a non-Lorentzian shape as depicted in Fig. 3. As a consequence of the linear asymptotic behavior of the curves in Fig. 2c for small , the gain of a short waveguide is not increased by reducing acoustic losses. Instead, the resonance line is deformed into a non-Lorentzian shape with a number of slowly decaying side bands and the total gain saturates at a maximum value. The result Eq. (16) was developed in a weak-gain approximation and is independent of the acousto-optic coupling. Small deviations can be expected in cases with strong interaction.


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

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

Resonance shape according to Eq. (16) for a wide range of waveguide lengths Z normalized to the peak gain of a long-waveguide approximation (0 dB-point).As the length is reduced to one acoustic decay length, the resonance broadens in a non-Lorentzian fashion, which becomes most prominent for Zα < 1. The graph values for various Z at the point  correspond to the values plotted in Fig. 2c for Λ ≈ 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Resonance shape according to Eq. (16) for a wide range of waveguide lengths Z normalized to the peak gain of a long-waveguide approximation (0 dB-point).As the length is reduced to one acoustic decay length, the resonance broadens in a non-Lorentzian fashion, which becomes most prominent for Zα < 1. The graph values for various Z at the point correspond to the values plotted in Fig. 2c for Λ ≈ 1.
Mentions: Finally, one would expect that the SBS resonance broadens as the effective gain is clamped by the effect described above. We can see this from Eq. (14) by taking the logarithm of the Stokes amplitude at the waveguide’s end (z = Z) and dividing it by the factor μZ, i.e. the part of the exponent in Eq. (10) that does not depend on the Lorentzian R. This new quantity describes the SBS-gain distribution as a function of the detuning parameter κ and the waveguide length and is constructed to be directly compared to the ideal long waveguide resonance R in Eq. (8). We can see in Fig. 2c that the gain reduction is rather robust with respect to the coupling strength μ, so we may expect this to be true for the resonance shape as well. This justifies that we assume the term μ/λ2 to be small and approximate to leading order:where we have used ln(1 + x) ≈ x in the second step. The leading term 1/(2λ*) = 1/(α − iκ) is exactly the Lorentzian resonance R that we expect for an infinitely long waveguide18. For a moderately long waveguide, the exponential remains negligible and the effective waveguide length is basically just reduced by one acoustic decay length α−1. For shorter waveguides, both the term 1/(2Zλ*) and the exponential term broaden the resonance and distort it into a non-Lorentzian shape as depicted in Fig. 3. As a consequence of the linear asymptotic behavior of the curves in Fig. 2c for small , the gain of a short waveguide is not increased by reducing acoustic losses. Instead, the resonance line is deformed into a non-Lorentzian shape with a number of slowly decaying side bands and the total gain saturates at a maximum value. The result Eq. (16) was developed in a weak-gain approximation and is independent of the acousto-optic coupling. Small deviations can be expected in cases with strong interaction.

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