Optical fiber
Optical fiber is a thin, flexible strand of highly transparent glass, typically silica, with a diameter comparable to a human hair, designed to transmit light signals over long distances with minimal attenuation through total internal reflection between a central core and surrounding cladding.[1][2] The core, made of high-purity glass, carries modulated light pulses encoding data, while the cladding, with a lower refractive index, confines the light via repeated internal reflections, preventing escape and enabling propagation with losses as low as 0.2 dB per kilometer at optimal wavelengths.[1][3] This technology's practical realization stemmed from the 1966 theoretical work of Charles K. Kao and George A. Hockham at Standard Telecommunication Laboratories, who calculated that silica glass impurities could be reduced sufficiently to achieve attenuation below 20 dB/km, making long-haul communication viable—a threshold met commercially in 1970 by Corning Incorporated using chemical vapor deposition.[3][4] Kao's insight, recognizing scattering and absorption as dominant loss mechanisms addressable by purification rather than inherent material limits, earned him the 2009 Nobel Prize in Physics.[3][5] Optical fibers surpass copper cables in bandwidth capacity—supporting terabits per second via wavelength-division multiplexing—signal fidelity over thousands of kilometers without amplification, and resistance to electromagnetic interference, forming the physical substrate for global internet backbones, submarine cables, and high-speed metropolitan networks.[6][7] Beyond telecommunications, applications extend to distributed sensing for structural health monitoring, endoscopy in medicine, and illumination in harsh environments, leveraging fibers' dielectric nature, flexibility, and ability to operate in extreme temperatures.[8]Physical Principles
Refractive Index and Total Internal Reflection
The refractive index n of an optical material is defined as the ratio of the speed of light in vacuum to its speed in the medium, quantifying how much the material slows electromagnetic waves.[9] In optical fibers, this property determines light propagation, with the core exhibiting a higher refractive index n_1 than the surrounding cladding n_2, typically achieved through doping pure silica (pure fused silica has n \approx 1.458 at 633 nm).[10] For standard silica-based single-mode fibers, n_1 is approximately 1.468 and n_2 about 1.462 at 1550 nm, yielding a relative index difference \Delta = (n_1 - n_2)/n_1 \approx 0.003 (0.3%), while multimode fibers may have \Delta up to 0.02 (2%) for larger core diameters.[11] This index contrast, often on the order of 0.1% to 2%, ensures light confinement without significant leakage.[12] Total internal reflection (TIR) occurs at the core-cladding interface when a light ray propagating in the higher-index core strikes the boundary at an incidence angle \theta_i greater than the critical angle \theta_c = \sin^{-1}(n_2 / n_1), causing 100% reflection back into the core with no transmission into the cladding, assuming ideal interfaces.[13] This phenomenon, derived from Snell's law (n_1 \sin \theta_i = n_2 \sin \theta_r), sets \theta_r = 90^\circ at the critical condition, beyond which no real refracted ray exists and evanescent waves decay rapidly in the cladding.[14] For typical silica fibers with n_1 \approx 1.47 and n_2 \approx 1.46, \theta_c is around 80° to 85° relative to the interface normal, meaning rays launched near the fiber axis (within a small acceptance cone) undergo repeated TIR, enabling low-loss guidance over kilometers.[13] [15] In step-index fibers, TIR forms the basis of meridional and skew ray propagation, where discrete reflections at the boundary trap light modes, with the numerical aperture \mathrm{NA} = \sqrt{n_1^2 - n_2^2} defining the maximum launch angle for guided rays (e.g., NA ≈ 0.1–0.2 for telecom fibers).[9] Graded-index fibers, however, primarily rely on continuous refraction due to a parabolic index profile decreasing from core center to cladding, curving ray paths to minimize dispersion without invoking frequent TIR events at the boundary; confinement still depends on the overall index step to the cladding.[16] Imperfect surfaces or index mismatches can lead to partial leakage, but TIR efficiency exceeds 99.9% in high-quality fibers under design conditions.[17] This principle, first demonstrated with water jets by Daniel Colladon in 1841 and later formalized for fibers, underpins the waveguide behavior essential for signal transmission.[13]Waveguiding in Optical Fibers
Optical fibers function as dielectric waveguides by confining electromagnetic waves through total internal reflection at the core-cladding interface, where the core exhibits a higher refractive index than the surrounding cladding.[13] This confinement occurs when light rays incident on the interface at angles greater than the critical angle undergo complete reflection back into the core, as dictated by Snell's law: n_1 \sin \theta_1 = n_2 \sin \theta_2, with total internal reflection ensuing for \theta_1 > \theta_c = \arcsin(n_2 / n_1).[13] For typical silica-based fibers with n_{\text{core}} \approx 1.46 and n_{\text{cladding}} \approx 1.45, the critical angle is approximately 83.2°, limiting guided rays to those within a narrow acceptance cone of about 14° half-angle.[13] The numerical aperture (NA), defined as \text{NA} = \sqrt{n_{\text{core}}^2 - n_{\text{cladding}}^2}, quantifies the light-gathering capacity and determines the maximum entrance angle for guided propagation via \sin \theta_a \approx \text{NA}.[18] In the ray-optic approximation, valid for multimode fibers with large cores, light follows discrete zigzag paths reflecting off the core boundaries.[18] However, precise waveguiding is described by solutions to Maxwell's equations in cylindrical coordinates, yielding guided modes—self-consistent transverse field distributions that propagate with a constant profile and axial phase factor e^{i \beta z}, where \beta is the propagation constant.[19] The number of guided modes depends on the normalized frequency parameter V = \frac{2\pi a}{\lambda} \text{NA}, with a as core radius and \lambda as wavelength.[18] For step-index fibers, single-mode operation occurs when V < 2.405, supporting only the fundamental LP_{01} mode per polarization, beyond which higher-order modes like LP_{11} emerge, leading to multimode propagation.[20][18] Single-mode fibers exhibit mode cutoff wavelengths above which guidance fails for higher modes, restricting multimode behavior to shorter wavelengths.[18] In multimode fibers, the approximate number of modes scales as V^2 / 2, enabling higher capacity but introducing intermodal dispersion.[19] The weakly guiding approximation, valid for small index contrasts typical in telecommunications fibers (\Delta n / n \ll 1), simplifies mode analysis to linearly polarized (LP) modes.[19]Modal Propagation and Fiber Types
In optical fibers, light propagates via discrete electromagnetic modes that satisfy the boundary conditions of the cylindrical core-cladding waveguide structure, derived from solving Maxwell's equations. These modes include linearly polarized (LP) modes, with the fundamental LP01 (HE11) mode possessing no cutoff frequency and a non-zero field at the axis. The number of guided modes is governed by the V-parameter, defined as V = (2πa/λ)√(n12 - n22), where a is the core radius, λ the wavelength, and n1, n2 the core and cladding refractive indices, respectively; for V < 2.405 at operating wavelengths like 1310 nm or 1550 nm, only the fundamental mode propagates.[12][21] Single-mode fibers (SMF) are designed with a small core diameter of approximately 8–10 μm to ensure V < 2.405, supporting propagation of only the fundamental mode and thereby eliminating modal (intermodal) dispersion, which enables high-bandwidth transmission over distances exceeding 100 km without repeaters.[22] These fibers typically operate at wavelengths of 1310 nm or 1550 nm, where attenuation is minimized, and are standard for telecommunications backbones per ITU-T G.652 specifications.[23] Multimode fibers (MMF), with larger core diameters of 50 μm or 62.5 μm (cladding 125 μm), support numerous modes (hundreds to thousands depending on V), leading to modal dispersion as different modes follow paths of varying optical lengths, limiting bandwidth-length product to around 500 MHz·km for step-index types but up to 5000 MHz·km for advanced graded-index variants like OM5.[24][23] Multimode fibers are classified into step-index and graded-index subtypes based on refractive index profile. Step-index MMF features a uniform core index with an abrupt step to the cladding, resulting in ray paths that are meridional or skew, with higher-order modes experiencing longer effective paths and thus greater delay, exacerbating pulse broadening.[24] Graded-index MMF employs a parabolic refractive index profile decreasing from the core center, compensating for path length differences by slowing axial rays and speeding peripheral ones, which reduces differential mode delay and increases bandwidth by factors of 10–100 over step-index equivalents.[24][25]| Fiber Type | Core Diameter (μm) | Typical Bandwidth-Length Product (MHz·km) | Application Range |
|---|---|---|---|
| Step-Index MMF | 50 or 62.5 | ~200–500 | Short links (<100 m) |
| Graded-Index MMF (e.g., OM3/OM4) | 50 | 2000–4700 | Data centers (up to 550 m at 10 Gbps) |
| Single-Mode | 8–10 | >100,000 (limited by chromatic dispersion) | Long-haul (tens to hundreds of km) |