## 3 Results and Discussion
### Numerical Simulation Results  
Using the simulation method described above, the feedback contribution in different particle positions were assayed by calculating the irradiance distribution and the feedback light power re-entering-cavity coupling efficiency \(r_{ext}\) profile (sensing volume). Different parameters configurations were considered in this model to analyze the OFI sensor performance in different system schemes, and to emphasize the model availability in the practical applications. Firstly, the OFI flowmetry sensor working in a macroscale reactor was investigated to understand the impact of channel dimension on the spectrum. The 2D incident profile and the feedback-power ratio \(r_{ext}\) distribution through the macroscale PDMS channel (Figure 2b) are illustrated in Figure 3. In Figure 3a, one can observe that after the focalization with the lens pair, the entire laser focusing spot was only located in a small area (around 200 \(\upmu\)m \(\times\) 6 \(\upmu\)m) close to the center of the channel. This laser illumination spatial limitation gave rise to an impressed coupling efficiency \(r_{ext}\) distribution volume in a same dimension order (Figure 3b). Only the particles passing through a central area around 200 \(\upmu\)m can contribute efficiently to the feedback signal into the laser. The numerical simulations were repeated in the cases of the two microscale DF channels (Figure 4). In comparison to the case in macroscale channel, the feedback behavior in the microscale channel is more complicated. In Figure 4a, the illumination profile here presents the same magnitude (\(10^{6}\)). Contrary to the macroscale PDMS channel, due to the tiny channel dimension, only part of the laser spot can be coupled inside the microchannel in spite of the same tight focalization. Considering that the confocal parameter (twice the Rayleigh range) of the laser is approximatively 80 \(\upmu\)m, comparable with the channel dimension (96 \(\upmu\)m), the laser beam 1/e\({}^{2}\) radius inside the channel can be approximated to be constant at roughly 3 \(\upmu\)m, which is represented as a parallel profile in Figure 4a. Figure 3: Two-dimensional simulation profile inside a 1 mm \(\times\) 1 mm PDMS channel. (**a**) Illumination power density profile; (**b**) feedback–power ratio profile. Then, the feedback light power re-entering-cavity coupling efficiency \(r_{ext}\) in the channel where no high reflectivity gold coating was deposited on the rear interface is computed and its distribution is plotted in Figure 4b, where it exhibited a strong enhancement close to the rear interface. The probable explanation of this phenomenon can be the result of the forward scattered light that was focused by the particle and then reflected on the rear interface [22]. In order to evaluate the particle size effect on this phenomenon, we have changed the simulation parameter to a particle diameter of 552 nm. The distribution of \(r_{ext}\) in this condition is presented in Figure 4c. As compared with the distribution computed with 4.89 um PS particles, we did not observe any enhancement of \(r_{ext}\) near the rear wall of the channel and the volume within which the particle scattering light can re-enter the cavity is comparable with the illumination profile. The maximum of \(r_{ext}\) locates in the channel center, at the laser focal point. Because the scattered light power directly depends on the particle cross-section, the \(r_{ext}\) value with the 552 nm PS particles were around 100 times lower than the one of 4.89 um. On the other hand, such a small particle does not focus the forward scattered light efficiently onto the rear interface, which explains the absence of \(r_{ext}\) enhancement. At last, we model the case of the same size channel with a 50 nm thick additional high reflectivity gold film on the rear interface to increase the effect of the reflection of the forward scattering light. The coupling efficiency profile is plotted in Figure 4d for 4.89 um particles.