# Recent Advances in Brillouin Optical Correlation-Domain Reflectometry
## 2 Basic Principle of BOCDR  
When a light beam is injected into an FUT, it interacts with acoustic phonons, generating backscattered light called Stokes light. This phenomenon is called spontaneous Brillouin scattering. Caused by the exponential decay of the acoustic phonons, the backscattered Brillouin light spectrum, known as BGS, takes the shape of a Lorentzian function with the bandwidth of several tens of megahertz. If the power of the pump light is higher than the Brillouin threshold power \(P_{\mathrm{th}}\), the Stokes light caused by spontaneous Brillouin scattering acts as a seed of stimulated scattering, and there occurs a transition from spontaneous Brillouin scattering to SBS; as a result, the Stokes light power is drastically enhanced. This transition can be promoted using a so-called pump-probe technique, in which a probe light beam (frequency-downshifted by the BFS) is additionally injected into the other end of the FUT. This is the reason why SBS-based distributed sensor configurations, such as BOTDA, BOFDA, and BOCDA, require light injection into both ends of the FUT. In Brillouin scattering, whether it is spontaneous or stimulated, the frequency at which the peak power is obtained in the BGS is downshifted by several gigahertz from the incident light frequency, and the amount of this frequency shift is called BFS. In optical fibers, the BFS \(\
u_{\mathrm{B}}\) is given by [1]:  
\[\
u_{\mathrm{B}}=\frac{2 nv_{\mathrm{A}}}{\lambda_{\mathrm{p}}}, \tag{1}\]  
where \(n\) is the refractive index, \(\
u_{\mathrm{A}}\) is the acoustic velocity in the fiber, and \(\lambda_{\mathrm{p}}\) is the wavelength of the incident pump light. If tensile strain is applied or temperature is changed in a standard silica single-mode fiber (SMF), the BFS shifts to higher frequency in proportion to the applied strain (+480 MHz/%) [3] and the temperature change (+1.18 MHz/K) [4] at 1.55 \(\upmu\)m. In some specialty fibers, such as tellurite glass fibers and polymer optical fibers (POFs), it is known that the BFS moves to lower frequency with increasing applied strain (\(-230\) MHz/% [38] and \(-122\) MHz/% [39; 40], respectively) and temperature (\(-1.14\) MHz/K [41] and \(-4.09\) MHz/K [39; 40], respectively). In both cases, we can derive the strain amplitude and temperature change by measuring the BFS in the fiber. One of the most essential features of Brillouin-based sensors is their distributed sensing capability. In BOCDR, distributed sensing is achieved using a technique called the synthesis of an optical coherence function (SOCF). The conceptual setup of BOCDR is schematically shown in Figure 1. The optical output from a laser diode is divided into pump and reference light beams. The pump light is injected into the FUT, and the Stokes light is directed into a photodiode (PD). The reference light is used as an optical local oscillator. The electrical beat signal of the two light beams is monitored using an electrical spectrum analyzer (ESA). Since there is a frequency difference of approximately 11 GHz between the Stokes light and the reference light, this configuration is called a self-heterodyne scheme. In order to resolve the position in the FUT, the optical frequency of the laser output is modulated in a sinusoidal waveform by directly modulating the injection current of the laser. From the viewpoint of temporal averaging, the coherence function is synthesized into a series of periodical peaks [25], of which the period is inversely proportional to the frequency of the sinusoidal modulation \(f_{\mathrm{m}}\). We control\(f_{\mathrm{m}}\) to generate only one correlation peak within the range of the FUT, so that only the Brillouin scattering generated at the position correspondent to the peak has high correlation with the reference light, and then gives high heterodyne output. The peak frequency observed using the ESA gives the BFS caused at the position. By sweeping\(f_{\mathrm{m}}\), the position of the correlation peak is scanned along the FUT, and thus the distribution of the BGS or the BFS is obtained.