# High Resolution Brillouin Sensing of Micro-Scale Structures
## 1 Introduction  
Micro-scale waveguides--specifically, microfibres, photonic crystal fibres (PCFs), and on-chip waveguides--offer enhanced nonlinearity due to their small core dimensions and also allow for group velocity dispersion tailoring [1]. Due to these unique features, micro-scale waveguides have found applications in supercontinuum generation [2; 3; 4], Raman amplification [5], self-phase [6] and cross-phase modulation [7], four-wave mixing [8], and frequency combs [9]. In these waveguides, not only the optical modes are confined, but also the acoustic modes, which, due to their efficient overlap [1; 10; 11; 12; 13; 14; 15], enable applications ranging from sensing in micro-structures [16; 17; 18; 19] to RF signal processing [20; 21], RF sources [22; 23], narrow-linewidth lasers [24; 25; 26; 27; 28], frequency combs [29], and light storage [30; 31]. The performance of the on-chip waveguides in terms of gain and linewidth is influenced by the geometrical variation along the structure [32; 33; 34]. For example, in micro-fibres, the effect of Brillouin scattering can be suppressed by controlling the core diameter [10]. The diameter of the core also becomes important when coupling in and out of photonic circuits [35]. It was shown that structural irregularities in a PCF lead to a different Brillouin response compared to what is expected from a perfect PCF [36]. Therefore, a detection technique is required to monitor and characterize the opto-acoustic interactions in these structures. The same opto-acoustic interaction, called Brillouin scattering, that enables such functionalities in micro-scale waveguides can be exploited to detect structural irregularities and characterize theiropto-acoustic responses. Stimulated Brillouin scattering (SBS) is an optical nonlinear effect resulting in inelastic scattering of a light wave by an acoustic wave in a medium. SBS involves an optical pump and signal waves and an acoustic wave, which interact with each other under the phase matching and energy conservation condition. The phase matching condition implies that: \(\overrightarrow{k_{p}}-\overrightarrow{k_{s}}=\overrightarrow{q}\), where \(\overrightarrow{k_{p}}\) and \(\overrightarrow{k_{s}}\) are the propagation constants of the pump and signal waves, respectively, and \(\overrightarrow{q}\) is the propagation constant of the acoustic wave. Energy conservation implies that: \(\omega_{p}-\omega_{s}=\Omega\), where \(\omega_{p}\) and \(\omega_{s}\) are the pump and signal frequencies, respectively, and \(\Omega\) is the acoustic angular frequency. The acoustic field takes the form of either transverse, longitudinal, or a superposition of both waves, which can be utilized to measure the geometrical features of the waveguide such as the core diameter [37] and detect waveguide irregularities [38]. However, in order to make a distributed measurement along the waveguide, the SBS response needs to be localized. A conventional SBS measurement involves continuous wave (cw) pump and signal waves which interfere along the entire length of the medium, and therefore, the measured back-scattered signal is an integrated opto-acoustic response. In contrast, a distributed SBS response can be achieved by modifying the intensity or the phase of the pump and signal waves such that the SBS interaction is limited to a certain length in the medium and suppressed elsewhere. The most conventional distributed Brillouin measurement technique, which is called Brillouin optical time domain analysis (BOTDA), is based on a pulsed pump and a cw probe [39; 40; 41], where the pulse duration determines the spatial resolution of the measurement [42]. A more recent technique is the correlation-based Brillouin sensing, which employs low-coherence pump and probe sources, whose correlation length determines the spatial resolution of the measurement [43; 44]. While the spatial resolution in the time domain technique is limited by the pulse duration, the latter overcomes this restriction by three orders of magnitude [45].