Waveguide Modes in Optical Fiber

Fiber Parameters

Core radius a (μm)4.0 n_core1.460 n_clad1.450 Wavelength λ (nm)1310 Mode (LP_lm)

Fiber Properties

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V-number

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Guided modes

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LP mode

Science

A step-index fiber guides light by total internal reflection. The LP (linearly polarized) modes satisfy the characteristic equation with Bessel functions:

J_{l-1}(ua)/J_l(ua) = −(w/u)K_{l-1}(wa)/K_l(wa)

where u²+w²=(2πa/λ)²(n₁²−n₂²) = V². Single-mode condition: V < 2.405 (first zero of J₀). The V-number determines how many modes the fiber supports:

V = (2πa/λ)·√(n₁²−n₂²) = (2πa/λ)·NA

Real optical fiber communication uses single-mode fiber (V ~ 2) to prevent modal dispersion.