The Mode Field Diameter (MFD) in an optical fiber is often calculated using approximate mathematical models, as the exact calculation involves solving Maxwell’s equations for the fiber geometry. For single-mode fibers, the MFD can be expressed as:
Gaussian Approximation Formula
The most commonly used formula is derived from the Gaussian intensity profile approximation:
MFD ≈ 2 × ω₀
Where:
ω₀ is the mode field radius, which is the radius at which the field intensity drops to 1/𝑒² (approximately 13.5%) of its maximum value.
Empirical Formula for Step-Index Fiber
For a step-index single-mode fiber, the MFD can be approximately given by:
MFD ≈ 2 × a × [0.65 + 1.619 / V⁸ + 2.879 / V¹⁶]
Where:
a is the core radius of the fiber.
V is the normalized frequency (V-number), defined as:
V = (2πa / λ) × √(n₁² – n₂²)
λ is the operating wavelength in vacuum.
n₁ is the refractive index of the core.
n₂ is the refractive index of the cladding.
This formula is an approximation valid for single-mode fibers with step-index profiles.
Normalized Mode Field Diameter
To simplify calculations, normalized MFD values can sometimes be provided for specific wavelengths and fiber types.
The MFD increases with higher wavelengths (longer λ), as the mode spreads more into the cladding.
The V-number determines the number of supported modes; single-mode operation occurs when V < 2.405.
Accurate computation of MFD may require numerical simulations, particularly for fibers with complex refractive index profiles, such as graded-index fibers.
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