# High Resolution Brillouin Sensing of Micro-Scale Structures
## 5 Sensing of Micro-Scale Structures
### Non-Distributed Backward Brillouin Measurement  
The dependence of Brillouin backward scattering on the waveguide geometry in micro-structures is evident in the work of [PERSON] et al. [102], where it is shown that the spectrum of the spontaneous Brillouin scattering in a small-core diameter PCF is significantly different from that in a large core diameter PCF, as shown in Figure 5. The large core PCF shows a single peak at frequency 11.2 GHz, corresponding to the dominant longitudinal acoustic mode in the bulk silica, while the small core PCF shows a family of peaks due to the existence of hybrid shear and longitudinal acoustic modes in the sub-wavelength core structure.  
Unlike the conventional silica fibre, where the acoustic modes are in the form of pure longitudinal or shear modes, in the sub-wavelength regime, the acoustic wave could take the form of a surface acoustic wave (SAW) or a hybrid acoustic wave (HAW), consisting both of longitudinal and shear components [34; 102]. SAWs propagate in the direction of the pump, on the surface of the micro-structure with a velocity lower than a pure longitudinal wave and scatter the light wave. Figure 6a shows the SAW spectrum in a microfibre, which was first observed by [PERSON] et al. [11]. [PERSON] et al. reported the first observation of SAWs in a PCF and experimentally demonstrated that the spectrum of SAW is highly dependent on the structure of the PCF, as well as the surface irregularities [12]. The two spectra shown in Figure 6b belong to PCFs with different core diameters. The shift in the Brillouin peak between the two spectra is due to the core diameter difference, while the difference between the amplitudes is linked to the microstructure irregularities [12].  
Figure 5: Comparison of the Brillouin spectrum in a large core diameter photonic crystal fibre (PCF) and a small core diameter PCF [102]. Reprinted with permission from Springer Nature: Nature, Nat. Phys., [102], Copyright 2006. BFS, Brillouin frequency shift.  
The backward Brillouin spectrum was utilized to estimate the core diameter of micro-fibres based on the sensitivity of the opto-acoustic interactions to the geometrical variations in the micro-scale waveguides. [PERSON] et al. [103] demonstrated an in situ measurement of the micro-fibre core diameter with a sensitivity of a few nm based on backward SAW and HAW measurement. After collecting the Brillouin spectrum, it was compared with a numerically-calculated map of the surface, longitudinal, and shear acoustic waves at different core diameters (refer to Figure 7) to estimate the diameter of the core. [PERSON] et al. [10] demonstrated an effect called Brillouin self-cancellation based on the dependence of the backward Brillouin scattering on the core diameter of a microfibre. In this work, it was shown that the opposite effect of moving boundaries and photo-elasticity in the sub-wavelength regime could reduce the back-scattered signal and even cancel it at certain core diameters. This experiment suggests that the spectrum of the backward Brillouin scattering could be less sensitive to the core diameter than forward Brillouin scattering sensing, which will be discussed in the next section.  
Figure 6: Spectrum of surface acoustic wave (SAW) in (**a**) a microfibre [11] (reprinted from [11] and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License) and (**b**) two PCFs with different core diameters [12] (reprinted with permission from [12], OSA).  
Figure 7: Mapping of the experimental surface Brillouin spectrum with the numerically-calculated responses to detect the core diameter of the microfibre under fabrication [103]. Reprinted with permission from [103], OSA.