In fiber optic connection technology, achieving low loss demands high precision during connection. This precision requirement is commonly referred to as “tolerance.” Simply put, “tolerance” is the maximum allowable deviation when aligning two fibers. Examples include misalignment (lateral offset) and tilt (angular deviation).

The magnitude of these tolerances directly determines whether light can be efficiently transmitted from the core of one fiber to the core of another.

For multimode fiber systems: Due to the large core area and multimode transmission characteristics, tolerance limits are relatively relaxed. Efficient power transfer occurs when the receiving fiber’s core diameter and numerical aperture are not smaller than those of the transmitting fiber. However, reverse transmission may suffer significant losses due to brightness degradation.

Notably: When the receiving fiber’s core diameter is slightly larger than the transmitting fiber’s, it might seem beneficial for coupling but can actually induce complex mode field distortion. This manifests as guided modes from the input fiber failing to fully convert into guided modes of the receiving fiber, leading to partial energy leakage into the cladding.

For single-mode fiber systems: Achieving efficient coupling requires highly consistent fundamental mode field distributions (especially the effective mode field area) between the two fibers. They are also extremely sensitive to both lateral displacement and angular deviation.

Lateral Misalignment Loss: Loss caused by core misalignment (lateral offset) is termed misalignment loss or lateral displacement loss. It is the primary source of insertion loss in fiber connections, particularly significant for single-mode fibers.

The diagram below illustrates lateral displacement (misalignment) during coupling of two single-mode fibers：

Neglecting other factors, the connection loss due to lateral misalignment can be approximated as:

The chart below quantitatively shows misalignment loss caused by parallel core offset (lateral misalignment) at a single-mode fiber mechanical splice:

Angular Misalignment Loss: Angular deviation occurs when the end faces of two fibers are not perfectly parallel (i.e., their axes do not coincide, forming an angle). This prevents part of the light from being effectively transferred from one fiber to the other, resulting in signal power loss.

Schematic diagram of angular misalignment:

Loss caused by angular deviation Δθ follows an exponential decay relationship:

Where `n` is the refractive index of the external material and `w` is the mode field diameter (MFD). This formula indicates that fibers with larger MFDs are more sensitive to angular tolerance. For the same angular deviation, the loss increases geometrically as the MFD (`w`) or operating wavelength (`λ`) increases.

The chart below shows loss at a mechanical splice for single-mode fibers with different MFDs (or w/λ ratios) under varying angular misalignments:

Mode Field Diameter (MFD) Mismatch Loss: Another significant source of coupling loss is MFD mismatch. The Mode Field Diameter is defined as the distance between the points where the optical intensity distribution drops to 1/e² of its maximum value on the axis (center). MFD is closely related to the operating wavelength and typically increases with wavelength.

Example:* Typical MFD values for single-mode fiber are 9.2±0.5 µm at 1310 nm and 10.5±1.0 µm at 1550 nm.

**Important:** MFD is *not* the physical core diameter. It characterizes the actual distribution range of optical energy within the fiber, which is particularly critical for single-mode fibers. When the MFDs of the two coupled fibers are perfectly equal (MFD₁ = MFD₂), the optical field mode output from the transmitting fiber can couple ideally (or efficiently) into the mode field region of the receiving fiber.

When the transmitting fiber’s MFD is larger than the receiving fiber’s MFD (MFD₁ > MFD₂), the larger optical field output attempts to enter the receiving fiber’s smaller effective acceptance region, leading to coupling loss.

The magnitude of coupling loss depends on the degree of mismatch between the two MFDs. Greater differences result in larger losses. A fundamental formula to calculate this loss (in dB) is:

Loss ≈ -10 * log₁₀[ (4 * (MFD₁/MFD₂ + MFD₂/MFD₁)⁻²) ]

The chart below shows insertion loss at a single-mode fiber mechanical splice due to Mode Field Diameter (MFD) mismatch:

Therefore, in engineering practice, fiber alignment techniques are typically employed to achieve efficient coupling. Typical direct alignment methods include the V-groove method and the three-rod method.

Schematic diagram of a multi-fiber V-groove structure:

Thank you for reading. Suggestions for improvement are welcome if any inaccuracies are noted.

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