# High Resolution Brillouin Sensing of Micro-Scale Structures
## 5 Sensing of Micro-Scale Structures
### Non-Distributed Forward Brillouin Measurement  
Forward Brillouin scattering has been exploited to measure the core diameter of a micro-fibre by monitoring the forward BFS [37], which is inversely related to the diameter of the micro-fibre, as expressed in Equation (2). In addition, the effect of geometry on the transverse opto-acoustic responses in micro-scale waveguides has been studied in different platforms. [PERSON] et al. [104] showed that the existence of the air hole areas in a PCF enhances some transverse acoustic modes while suppressing the others by introducing additional boundary conditions over which phonons are spatially distributed, a behaviour that is different from a conventional dispersion-compensation fibre (DCF). [PERSON] et al. in [1] showed that unlike the conventional silica fibre, which has a weak forward Brillouin interaction, a sub-wavelength PCF provides a strong interaction between the laser light and the transverse acoustic modes by tightly trapping them together within the small core of the PCF. The effect of boundary forces, namely radiation pressure on opto-acoustic responses of an on-chip silicon nano-structure, has been experimentally demonstrated by [PERSON] et al. [14], where a pillar-shaped silicon waveguide exhibited significant Brillouin gain due to the trapping of the acoustic mode in the under-etched silicon waveguide and its strong overlap with the transverse optical mode as a result of the radiation pressure. In a different study, [PERSON] et al. [15] demonstrated an enhancement on the Brillouin amplification in on-chip silicon waveguides by designing a suspended silicon membrane, which guides optical and acoustic modes separately and ensures strong opto-acoustic coupling between them.  
In order to characterize fully the opto-acoustic interactions in the micro-scale waveguides, information regarding the longitudinal fluctuations along the waveguide is required. This is evident from the work of [PERSON] et al. [36], where it is experimentally demonstrated that the spectral width of the integrated Brillouin spectrum in a PCF is affected by structural imperfections. The existence of degenerate acoustic peaks in the elasto-optic coefficient plot shown in Figure 8a, which is calculated for the actual PCF sample compared to that of a perfect PCF (Figure 8b), is attributed to the transverse structural irregularities such as defect holes, angles, and pitches, which cannot be detected by a non-distributed SBS measurement. In addition, [PERSON] et al. [105] theoretically showed that the opto-acoustic strength and the spectral linewidth of the Brillouin response in the nano-scale Brillouin waveguides are sensitive to fabrication imperfections.  
The mentioned works so far showed how to detect geometry-dependent opto-acoustic responses and estimate the core diameter of the entire micro-structure with high sensitivity. However, in order to detect longitudinal variations along the waveguide, a distributed SBS measurement is required, which is discussed in the following section.  
Characterization of the opto-acoustic responses in terms of the longitudinal fluctuations in micro-scale waveguides requires a distributed measurement of the backward Brillouin spectrum with high spatial resolution. Several studies were conducted using the distributed Brillouin sensing techniques mentioned previously to characterize the opto-acoustic responses of micro-scale waveguides, which are discussed in this section.  
Figure 8: Finite element model (FEM)-based numerical simulation of (**a**) the elasto-optic coefficient of the PCF under test (reprinted with permission from [36], OSA) and (**b**) the elasto-optic coefficient of the perfect PCF [36] (reprinted with permission from [36], OSA).