In their Comment [1], the authors challenge our procedure of solving the SBS equations by separating the Stokes field generated by SBS reflection of the pump from the Stokes and pump fields inducing the acoustic wave [2]. This appears to be the principle concern expressed in the Comment. They consider it to be incorrect at least in “standard fibres” in which they assert that such a distinction is “purely formal, as the roles played by the fields cannot be separated”. Actually their assertion contradicts the physical nature of the SBS phenomenon [3], which is reflection of a pump wave incident on a medium by a sound wave induced in the medium through electrostriction, by the interference pattern of a pump and a Stokes wave generated from spontaneous Brillouin scattering or introduced externally. The traditional theoretical description of SBS is based on a set of three wave equations, two nonlinear optical wave equations and a driven acoustic wave equation [4], which are usually reduced to a set of three first order equations for the slowly varying amplitudes of the fields. It is this set of coupled SBS equations that the authors use in their Ref [5], namely Eqs. (1) in [5]. The fact that the generation of the acoustic wave is described explicitly by a relaxation-type equation, Eq. (1)(c)) in [5], demonstrates that the pump field, which is involved in acoustic wave generation, cannot be that generating the new Stokes field in Eq. (1)(b)) of [5]. Similarly a Stokes wave involved in the acoustic wave generation cannot be the new Stokes wave generated by reflection of the pump wave. The reason for this is that the acoustic wave amplitude is determined, according to Eq. (1)(c)) in [5], by the pump and Stokes fields not only at a given moment, but also at preceding times. Consequently the two pump fields and two Stokes fields are generically different. We note that this feature is explicitly presented in the Comment (Eq. (1) in [1]) which was obtained by the authors in their earlier work, (Eq. (5) in [5]).

The question then arises: are there any conditions in SBS theory for which the two pump fields and also the two Stokes fields can be considered without distinguishing between them? The answer is yes. This is when the SBS interaction described by Eqs. (1) in [5] is considered to be under steady state (SS) conditions. Technically this means that the time derivatives are dropped in these equations (see at p.420 in [6]). Physically this condition means that the pump, Stokes and acoustic fields are all purely monochromatic. Equations (2)&(3) in [1] are of this form which can only follow under this SS approximation. The essential difference between these equations is that in the first equation the two pump fields and two Stokes fields are both considered indistinguishable while in the second the Stokes fields are distinguished. The second case is closer to physical reality, but still results from using the SS approximation. As such by their nature neither equation can describe SBS in which pulses are involved as in “slow light” and Brillouin fibre sensing. In other words any attempt to describe a pulsed SBS interaction using Eqs. (2)&(3) in [1] is an attempt to use them beyond the range of their validity.

Actually in their earlier work [5], the authors of the Comment tried to treat Eqs. (1) in [5] without imposing the SS approximation. They obtained Eq. (12) in [5] for the acoustic wave amplitude Q, which is ‘’formally identical” (see the 10th line of the Comment) to our Eq. (9) in [2]. This is not surprising because ‘’formally” the same equation was transformed by the same Fourier transformation (FT) method. The difference between their work and ours emerges at the stage of transforming the equation for the Stokes field, Eq. (1)(b)) in [5]. In their work [5], the authors dropped the time derivative term in Eq. (15) in [5] in its re-expression (see RHS of this equation), which automatically means that the SS approximation is used. As such, Eq. (5) in [5] and Eq. (1) in [1] cannot, for the reasons discussed above, adequately account for a non-monochromatic (pulsed) Stokes and/or pump field as the authors suppose.

A further claim in the Comment is that “positive feedback” is responsible for creating the “slow light response in the medium”. This is not scientifically supported and we fail to see how it can be justified. According to the basic principles of the “slow light” phenomenon [7], which by its nature is an enhanced group delay phenomenon, two essential ingredients must co-exist, namely a pulse to be delayed and an enhanced and constant value dispersion of the refractive index of the medium over the spectral content of the pulse. Neither concerns “positive feedback”.

It is also claimed that “the fiber acts as a linear medium, whose transfer function is a Lorentzian gain line, according to which the input pulse will be delayed …”, and “the SBS-induced bandwidth (SIB) can be larger than the Stokes pulse spectrum …” (see after Eq. (2) in [1]). The claims are built on earlier works [8,9], in which the SS approximation (monochromatic optical and acoustic waves) was used and the bandwidth of the “transfer function” (the “Lorentzian gain line”) considered to arise from the decay of the acoustic wave. However both are wrong; the SS approximation is inappropriate for the reasons given above and the bandwidth assignment is based on speculation.

In our work [2] we showed that the SIB referred to above, which may have relevance to the “slow light” phenomenon, is actually the bandwidth of the medium’s response. Since that response behaves like a driven damped oscillator its spectrum is dependant on the spectrum of the driving force. In SBS that spectrum may be either the spectrum of the pump, the Stokes or the convolution of both (see Eq. (12) in [5] and Eq. (9) in [2]). So, the SIB, which is then the bandwidth of the damped oscillator, cannot be greater than that of the driving force. The SIB can however certainly be smaller. This happens when the bandwidth of the driving force is greater than the natural bandwidth (reversed decay time) of the oscillator. The SIB is then of order of the natural bandwidth of the oscillator. Since the induced group index is the frequency-derivative of the refractive index spectral profile its spectral width can never be broader than the spectral width of the index [10], which is governed by the SIB. Finally the resonant frequency of the medium’s response (Brillouin frequency) is at the hypersonic frequency range. Since this frequency range is far from optical radiation frequencies, it cannot modify the propagation constant of a Stokes signal regardless of its strength.