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“Slow Light” in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index: Reply

V. I. Kovalev, N. E. Kotova, and R. G. Harrison

Open Access Open Access

Abstract

We show that the claims in the Comment are misleading and in instances contradictory.

©2010 Optical Society of America

The authors of [1] acknowledge that our solution of the basic SBS equations in [2] is “substantially correct” but challenge our interpretation of the solution. They base this on a number of claims, which we numerate below as: [P(X), L(X), KW], where P(X) is the paragraph number, L(X) is the line number in the paragraph and KW is the key words in their Comment. Our Reply follows these claims. We first address the primary claims.

  • 1. [P(Abstract), L(4,5), “pump spectral broadening was not effective in increasing the interaction bandwidth”] and [P(2), L(1,2), “pump spectral broadening has close to no impact on the spectral width of the interaction”].
These claims misrepresent our work. Firstly the only interaction considered in [2], is the SBS interaction; neither “slow light” (SL) nor group index are interactions by definition. Our analytic solutions (Eqs. (9)–(12) in [2] and Eq. (1) in [1]) describe unambiguously and quantitatively the effect (or impact) of spectral broadening of both pump and input Stokes signals on the spectral characteristics of both the output Stokes signal and of the generated acoustic wave in the SBS interaction.
  • 2. [P(4), L(12), “the gain spectrum maps the spectrum of the pump.”].
Use of the term “gain” is the reason for widespread misunderstandings of the basic physics of SBS and its applications. We have explicitly shown in [2] and [3] that an external Stokes signal (the first term on the RHS of Eq. (1) of [1]) propagates through a “SBS-medium” without gain. Any observed increase of the output Stokes signal is a consequence of increased reflectivity of the pump radiation by the induced acoustic wave (second term on the RHS of Eq. (1) of [1]). The input Stokes pulse triggers the processes of inducing the acoustic wave, which subsequently reflects the pump radiation. As such the spectrum of the generated Stokes signal, that is the reflected pump signal, “maps” the spectrum of the pump when it is broadband, as described by our solutions, and not that of the input Stokes signal (see [2–4]).
  • 3. [P(7), L(3-6), “(we) deny ... that delaying through SBS is a “slow light” effect.”].
We confirm that in both our publications, [2] and [3], we deny that the widely observed experimental pump-induced delay between the input and output Stokes pulses in SBS can be attributed to the group-delay (otherwise “slow light”) effect. According to the basics of group index induced delay or advancement, it appears when a medium’s refractive index increases or decreases through the spectrum of a pulse. The “slow/fast light” occurs when such dispersion is substantially enhanced (and constant) through the spectrum of a pulse. The main reason for an enhanced dispersion of the refractive index in the SBS interaction is modulation of medium’s density in the induced acoustic wave, the spectrum of which determines the spectrum of the enhanced dispersion. Since the resonant frequency of that spectrum is very far away from the Stokes signal carrier frequency, its contribution to dispersion around the Stokes frequency is negligibly small. Consequently, as discussed in [2] and [3], the delay of a Stokes pulse in SBS cannot arise from group index effects as claimed in the Comment and Refs 1 and 2 in [1].

We now address other claims of the Comment.

  • 1. [P(1), L(1,2) “SBS has been demonstrated … control the group velocity of light”] and [P(2), L(2,3), “(our results) contradict(ing) … (to) these experimental works”].
We know of no direct experimental evidence that a pump induced delay between the input and output Stokes pulses in SBS results from the group velocity effect. According to our work [3], experimentally observed delays are well accounted for by the inertia of acoustic wave excitation in SBS.
  • 2. [P(2), L(4,5), “(our work) contradicts the basic principle of SBS suppression”].
Our work [2] concerns the spectral characteristics of SBS only. The energy conversion efficiency, which concerns SBS suppression, may be obtained through integration of Eqs. (9)–(12) and taking the square-modulus of this. We do not see why this may result in contradicting “the basic principle of SBS suppression”. Actually we showed in [3] that the conversion efficiency reduces when the spectral width of the Stokes signal increases.
  • 3. [P(2), L(7), “an erroneous assumption that misled”].
Unfortunately the authors do not specify which assumption in our work is “erroneous”.
  • 4. [P(4), two sentences L(6-11)].
These two sentences are actually a truncated and strangely modified form of the detailed discussion of the issues in paragraph 2 on page 17322 of [2].
  • 5. [P(5), “the acoustic wave spectrum does not … map the optical wave spectrum”].
We are fully aware that the spectrum of the acoustic wave cannot be notably modified through the SBS resonant condition (Eq. (2) in [1]). We do not understand why the authors have raised, indeed laboured, this point as it is not relevant. It is also not clear where “243 GHz” (see [L(14)]) comes from. For SBS in silica optical fibres (n ≅ 1.45, VA ≅ 6 km/s, ΓB ≅ 2π × 16 ≅ 100 MHz [the natural SBS linewidth at λ ≅ 1.55 μm]) Eq. (2) gives Δω p ≅ 1700 GHz!! Furthermore, this is a low estimate since ΓB in real fibres can be much broader [5–7].
  • 6. [P(6), L(5,6), “end-to-end nonlinear phase shift”].
We do not understand the physical mechanism of this, and how it is linked to “the Brillouin interaction”. Our solutions explicitly show that the phase of an input Stokes signal (first term on the RHS of Eq. (1) in [1]) is not affected by the SBS interaction when it (the input signal) propagates through the medium.
  • 7. [P(7), L(1), “the group velocity of an arbitrary medium”].
We are not dealing with a medium moving with a group velocity. If the authors of [1] mean the group velocity of an optical pulse in a medium, then we agree that this cannot be derived directly from “the microscopic polarization response”. It is determined by the dispersion of the macroscopic polarization response, which is the nontrivial sum of the microscopic polarizations, and is also dependant on the pulse’s spectrum.
  • 8 [P(7), L(6-8), “Brillouin slow light … comes from the nonlinear phase induced in the signal by the reflected wave”].
That is something really new to SBS. So far, the published theoretical studies on SBS and SL in SBS claim that the nonlinear phase is induced by the pump radiation [5,8,9].
  • 9. [P(7), L(8-13), “exclude ... the list of possible “slow light” systems”].
We are reasonably sure that many material systems exist in nature or can be engineered artificially in which the “slow light” effect can be realized. But this does not mean that this applies to systems based on the SBS interaction.

References and Links

1. M. Gonzalez-Herraez and L. Thevenaz, “”Slow Light” in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index: comment,” to be published in Opt. Express (2010). [CrossRef]   [PubMed]  

2. V. I. Kovalev, N. E. Kotova, and R. G. Harrison, ““Slow Light” in stimulated Brillouin scattering: on the influence of the spectral width of pump radiation on the group index,” Opt. Express 17(20), 17317–17323 (2009). [CrossRef]   [PubMed]  

3. V. I. Kovalev, N. E. Kotova, and R. G. Harrison, “Effect of acoustic wave inertia and its implication to slow light via stimulated Brillouin scattering in an extended medium,” Opt. Express 17(4), 2826–2833 (2009). [CrossRef]   [PubMed]  

4. V. I. Kovalev, N. E. Kotova, and R. G. Harrison, ““Slow Light” in Stimulated Brillouin Scattering: on the influence of the spectral width of pump radiation on the group index: reply,” Opt. Express 18(2), 1791–1793 (2010). [CrossRef]   [PubMed]  

5. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Acadamic Press, San Diego, CA, 2006).

6. V. I. Kovalev and R. G. Harrison, “Observation of inhomogeneous spectral broadening of stimulated Brillouin scattering in an optical fiber,” Phys. Rev. Lett. 85(9), 1879–1882 (2000). [CrossRef]   [PubMed]  

7. V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27(22), 2022–2024 (2002). [CrossRef]  

8. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94(15), 153902 (2005). [CrossRef]   [PubMed]  

9. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22(11), 2378–2384 (2005). [CrossRef]  

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