Ultra-Weak FBG Array Physics — High-Density Distributed Fiber Optic Sensing

From FBG to Ultra-Weak FBG: The Physics of Multiplexing Capacity

Using ultraviolet phase-mask inscription and related techniques, a periodic refractive index modulation can be introduced into the core of an optical fiber, forming a Fiber Bragg Grating (FBG). This structure reflects a narrow spectral band centered at the Bragg wavelength (λ_B), enabling wavelength-based sensing of physical parameters.

In conventional FBGs, the grating region typically extends over a length of approximately 8–10 mm and consists of a large number of periodic index variations acting as weak reflective interfaces. The overall reflectivity of a single grating is generally in the range of 10% to above 90%. Such relatively high reflectivity leads to pronounced shadowing effects along the fiber, which limit the number of gratings that can be effectively multiplexed in a single sensing line.

Ultra-weak Fiber Bragg Gratings (UW-FBGs) are characterized by significantly reduced reflectivity, typically below 0.1%, and shorter grating lengths, often less than 5 mm (Refer to Figure 1.). The lower reflectivity reduces both shadowing and multiple reflection effects, allowing a much larger number of gratings to be distributed along a single fiber. As a result, it becomes feasible to construct sensing arrays with hundreds to thousands of measurement points within one fiber.

How Shadowing and Multiple Reflection Limit — and Define — Array Capacity

Large-scale FBG arrays are fundamentally constrained by two physical mechanisms: shadowing effect and multiple reflection.

The shadowing effect arises from the cumulative attenuation of optical power along the fiber. As light propagates through a sequence of gratings, each grating extracts a portion of the incident power. In high-reflectivity configurations, this leads to a rapid decrease in available optical power for downstream sensors, resulting in non-uniform signal strength and reduced measurement reliability.

This behavior is illustrated in Figure 2, where higher reflectivity levels (e.g., −27 dB to −30 dB) show a pronounced decay in return power as the number of sensors increases. In contrast, lower reflectivity configurations maintain a more stable power distribution along the array.

The multiple reflection effect introduces an additional limitation. Reflected signals from individual gratings can undergo secondary reflections between neighboring gratings, generating unwanted interference components. As the number of sensors increases, these parasitic reflections accumulate, leading to crosstalk and distortion of the measured signal.

As shown in Figure 3, the level of reflected crosstalk power increases nonlinearly with the number of gratings, especially at higher reflectivity levels. This effect becomes a dominant factor limiting the maximum achievable sensor count.

By reducing the grating reflectivity into the ultra-weak regime (typically below 0.1%), both shadowing and multiple reflection effects are significantly mitigated. This enables a more uniform optical power distribution along the entire fiber — critical for oil and gas energy asset monitoring where downhole and subsea deployments demand consistent signal quality across kilometer-scale arrays — and suppresses crosstalk accumulation, allowing a substantially larger number of sensing points to be integrated along a single fiber.