Fiber Attenuation and Loss Mechanisms

Total internal reflection tells you how to trap light inside a glass thread; it says nothing about how long the light survives once trapped. That second question — how far a signal runs before it fades below the noise — is the province of attenuation, the impairment that turned a laboratory curiosity into a planet-spanning network. The guiding article hands us a bound mode carrying power $P$ ; this article asks where that power goes. Because every loss process acts on the power already present, the losses compound multiplicatively, so power decays exponentially and the natural bookkeeping is logarithmic — the decibel per kilometre that saturates every fiber datasheet. Physically the budget splits in two. Intrinsic losses are fundamental to pure silica: Rayleigh scattering from frozen-in density fluctuations, falling steeply as $\lambda^{-4}$ , and the infrared multiphonon absorption tail of the Si–O bond, climbing exponentially toward long wavelengths. These two curves fall and rise past each other, carving a broad valley near 1.55 μm — the reason a telecom C-band exists at all, and the reason erbium-doped amplifiers, which happen to lase there, became the backbone of long-haul optics. Extrinsic losses — hydroxyl-ion absorption near 1.38 μm, transition-metal impurities, and the radiation loss of a bent guide — can be pushed down but never quite to zero. The triumph of modern fabrication is that commercial single-mode fiber now sits within a whisker of the Rayleigh limit at roughly 0.2 dB/km — a factor of ten thousand better than the glass Charles Kao diagnosed in the 1960s.

Key takeaways

Guided power decays exponentially, $P(z)=P_0e^{-\alpha z}$ ; engineers quote it logarithmically as $\alpha_{\mathrm{dB/km}}=(10/L)\log_{10}(P_0/P_L)$ , tied to the natural coefficient by $\alpha_{\mathrm{dB/km}}\approx4.343\,\alpha$ .
Intrinsic silica loss is a competition between Rayleigh scattering ( $\propto\lambda^{-4}$ , dominant to the blue) and infrared multiphonon absorption (rising exponentially past ~1.6 μm).
The two intrinsic curves cross near 1.55 μm, giving silica its global minimum of ~0.15–0.2 dB/km — the physical origin of the telecom C-band.
Extrinsic terms — OH⁻ water absorption near 1.38 μm, transition-metal ions, macrobending and microbending — add on top and can be engineered down but never eliminated.
Historical windows sit at 850 nm, 1310 nm and 1550 nm; modern low-water-peak fiber opens one continuous band from ~1260 to 1625 nm.
Key idea: fiber loss is a $\lambda^{-4}$ Rayleigh floor plus steeply rising UV and IR absorption tails, plus bending and impurity terms, and their competition hands silica a ~0.2 dB/km minimum near 1.55 μm.

The core insight

Fiber loss is the sum of a $\lambda^{-4}$ Rayleigh scattering floor and steeply rising UV and IR absorption tails, plus bending and impurity terms; their competition yields silica's ~0.2 dB/km minimum near 1.55 μm.

Where this lives today

Every long-haul and submarine link is designed around the loss spectrum drawn above. The 1550 nm C-band (1530–1565 nm) is chosen not only because it is silica's minimum but because it coincides with the gain band of the erbium-doped fiber amplifier — the device that replaced electrical repeaters with all-optical gain, letting a transatlantic cable run on amplifier huts alone. Modern low-water-peak fiber (ITU-T G.652.D) has scrubbed the OH⁻ peak so thoroughly that the whole 1260–1625 nm range is one low-loss band. At the frontier, hollow-core anti-resonant fibers guide light in air rather than glass, sidestepping the Rayleigh floor and pushing measured loss below the 0.14 dB/km solid-silica record. The same physics sets the ceiling on integrated photonics: a silicon or silicon-nitride waveguide loses of order 0.1–1 dB/cm — ten thousand times more per unit length than fiber — capping the quality factor of every microring resonator on chip.

The physical picture

Think of the fiber as a slightly leaky pipe. Each metre removes the same fraction of whatever power is flowing past — not the same absolute amount — so the survivors compound: half of a half of a half. That is the signature of exponential decay, and why loss is measured in decibels, a logarithmic unit that turns the compounding into simple addition. The first figure makes this concrete: launch a milliwatt, lose 0.2 dB every kilometre, and after 100 km only one part in a hundred remains.

Figure

Power decay along a 0.2 dB per km fiber on a decibel axis, where exponential decay becomes a straight line. Launched at 0 dBm, the power falls 20 dB over 100 km — a factor of ×1/100 — approaching the −28 dBm receiver sensitivity.

Why does the loss depend so strongly on colour? Two microscopic mechanisms pull in opposite directions. Rayleigh scattering is the physics that makes the daytime sky blue: the glass froze with sub-wavelength density fluctuations locked in, each a tiny induced dipole that scatters light with a cross-section $\propto\lambda^{-4}$ , so blue and short-infrared light leak out of the core far faster than long-wavelength light — the term falls steeply toward the red. The infrared mechanism is the glass vibrating: a photon whose energy matches an overtone of the Si–O bond stretch is absorbed as heat, and this multiphonon tail climbs exponentially as the wavelength approaches the ~9 μm fundamental. One curve falls, the other rises; where they cross, silica is most transparent. The second figure is what a system engineer reaches for — the measured spectrum, valley near 1.55 μm.

Figure

The attenuation spectrum of single-mode silica fiber. The blue λ⁻⁴ Rayleigh floor falls from 1.70 dB/km at 850 nm, the red infrared tail rises past 1.6 μm, and the ink total dips to ≈0.19 dB/km near 1.55 μm. The green bump is the legacy OH⁻ water peak at 1.38 μm; dashed lines mark the three classic windows.

The core equations

The starting point is a conservation statement per unit length. Over an infinitesimal slice $\mathrm{d}z$ the fiber removes a fixed fraction of the local power, and integrating gives the exponential Beer–Lambert law — the reason every loss quantity here is a coefficient rather than an absolute number.

P(z) = P_0\,e^{-\alpha z} \qquad (1)

where: $P(z)$ — guided power a distance $z$ down the fiber; $P_0$ — launched power at $z=0$ ; $\alpha$ — power attenuation coefficient (units $\mathrm{km^{-1}}$ ); $z$ — propagation distance. Physical reading: because the loss acts on power already present, it compounds, and the decay is multiplicative rather than additive. Fiber literature rarely uses $\alpha$ in $\mathrm{km^{-1}}$ directly; it uses the decibel, defined so that total span loss adds instead of multiplies. The definition takes the ratio of launched to received power over a known length and reports it logarithmically.

\alpha_{\mathrm{dB/km}} = \frac{10}{L}\log_{10}\!\left(\frac{P_0}{P_L}\right) \qquad (2)

where: $\alpha_{\mathrm{dB/km}}$ — attenuation coefficient in decibels per km; $L$ — fiber length (km); $P_0,P_L$ — input and output power. Physical reading: 10 dB is one decade of power lost, 3 dB a factor of two; the per-km form multiplies by length for a span total. The two conventions describe the same decay, so they must be proportional. The linking constant is $10\log_{10}e$ , worth committing to memory.

\alpha_{\mathrm{dB/km}} = 10\log_{10}(e)\,\alpha \approx 4.343\,\alpha \qquad (3)

where: $\alpha$ — power coefficient in $\mathrm{km^{-1}}$ ; $4.343 = 10\log_{10}e$ — the conversion constant. Physical reading: $\alpha=1\ \mathrm{km^{-1}}$ (power down by $1/e$ per km) is 4.343 dB/km — never conflate the two coefficients. The intrinsic floor is Rayleigh scattering. Its inverse-fourth-power law comes straight from dipole radiation theory, and it is the term that makes short wavelengths unusable for long spans.

\alpha_R = \frac{C_R}{\lambda^4} \qquad (4)

where: $\alpha_R$ — Rayleigh contribution; $C_R$ — Rayleigh coefficient, ≈0.7–0.9 $\mathrm{dB\,km^{-1}\,\mu m^4}$ for silica; $\lambda$ — vacuum wavelength. Physical reading: halving the wavelength multiplies the scattering loss by sixteen, so blue light is scattered out an order of magnitude faster than 1.55 μm light. The long-wavelength edge of the window is set by the infrared multiphonon tail — the small absorption surviving below the Si–O fundamental resonance.

\alpha_{\mathrm{IR}} = A\,\exp\!\left(-\frac{a}{\lambda}\right) \qquad (5)

where: $A,\,a$ — empirical constants for silica (a standard fit gives $A\approx7.8\times10^{11}$ dB/km, $a\approx48.5$ μm); $\lambda$ — vacuum wavelength. Physical reading: the tail is negligible at 1.55 μm but climbs by an order of magnitude per 0.1 μm beyond 1.65 μm, killing silica as a medium past ~1.7 μm. The measured loss is the sum of every mechanism at the operating wavelength.

\alpha_{\mathrm{tot}}(\lambda) = \frac{C_R}{\lambda^4} + \alpha_{\mathrm{UV}} + \alpha_{\mathrm{IR}}(\lambda) + \alpha_{\mathrm{OH}}(\lambda) + \alpha_{\mathrm{bend}} \qquad (6)

where: $\alpha_{\mathrm{UV}}$ — ultraviolet electronic (Urbach) tail, tiny in the near-IR; $\alpha_{\mathrm{OH}}$ — hydroxyl-ion overtone peaks, notably ~1.38 μm; $\alpha_{\mathrm{bend}}$ — macro- and microbending radiation loss. Physical reading: the valley near 1.55 μm survives only because every term is simultaneously small there. Bending is the loss a datasheet cannot predict, since it depends on how the cable is installed. Its radiation loss falls exponentially with bend radius.

\alpha_{\mathrm{bend}} = C_1\exp\!\left(-C_2\,R\right) \qquad (7)

where: $R$ — radius of curvature; $C_1,C_2$ — constants set by mode-field radius, index contrast, and wavelength. Physical reading: below a critical radius the mode's outer field would have to outrun $c/n$ to stay attached, so it radiates; longer wavelengths bend-radiate more, so 1625 nm is the worst case. Finally, the quantity a network is designed against: the power budget, which sets how far the signal goes before dropping below the receiver's sensitivity.

P_{\min}\ \text{(dBm)} = P_{\mathrm{tx}} - \alpha_{\mathrm{dB/km}}L - L_{\mathrm{splice}} - M \qquad (8)

where: $P_{\mathrm{tx}}$ — launched power (dBm); $L_{\mathrm{splice}}$ — total splice and connector loss (dB); $M$ — margin reserved for ageing and repair (dB); $P_{\min}$ — received power, which must exceed the detector sensitivity. Physical reading: every term is in decibels, so the budget is a subtraction and the reach follows by solving for $L$ .

Derivation AFrom a leaky slice to the decibel

The goal is to show that a per-length loss produces exponential decay, and to pin down the exact number that converts the physicist's coefficient $\alpha$ (in $\mathrm{km^{-1}}$ ) into the engineer's decibel-per-kilometre. These are the two most confused quantities in the subject, and getting the 4.343 factor from first principles stops anyone treating "3 dB" and "a factor of $1/e$ " as the same. We integrate the slice law, then translate into the logarithmic unit.

Step 1. Over a slice of thickness $\mathrm{d}z$ the fiber removes a fixed fraction of the local power, $\mathrm{d}P = -\alpha\,P\,\mathrm{d}z$ , which rearranges to $\mathrm{d}P/P = -\alpha\,\mathrm{d}z$ . Why: writing the loss as proportional to the power present — not to a fixed amount — is what makes the decay exponential rather than linear.

Step 2. Integrate both sides from $0$ to $z$ : $\ln P - \ln P_0 = -\alpha z$ , and exponentiate to recover $P(z)=P_0 e^{-\alpha z}$ . Why: the logarithm on the left is the fingerprint of compounding loss, and it is exactly why the decibel — itself a logarithm — is the natural unit.

Step 3. Feed this into the decibel definition (2): $\alpha_{\mathrm{dB/km}}=\tfrac{10}{L}\log_{10}(P_0/P_L)=\tfrac{10}{L}\log_{10}(e^{\alpha L})$ , using $P_0/P_L=e^{\alpha L}$ . Why: substituting the physical decay into the measurement definition connects the coefficient you integrate to the number you read off an OTDR.

Step 4. Pull the exponent down with $\log_{10}(e^{x})=x\log_{10}e$ : $\alpha_{\mathrm{dB/km}}=\tfrac{10}{L}\,\alpha L\log_{10}e = 10\log_{10}(e)\,\alpha \approx 4.343\,\alpha$ . Why: the length $L$ cancels, leaving a pure proportionality — the dB/km loss is a fixed 4.343 multiple of the $\mathrm{km^{-1}}$ loss, for all fibers and wavelengths.

Go deeper · Derivation B · 1 minThe inverse-fourth-power Rayleigh law

Derivation BThe inverse-fourth-power Rayleigh law

The goal is to trace silica's fundamental loss floor to its root cause — dipole scattering from frozen-in inhomogeneities — and to see exactly where the $\lambda^{-4}$ comes from, because that single exponent explains the whole short-wavelength side of the spectrum and why telecom migrated toward longer wavelengths. We build the scatterer, invoke the dipole radiation result, and integrate over the fluctuation statistics, keeping only the wavelength scaling.

Step 1. When the glass melt cools through its transition it freezes with microscopic density and composition fluctuations; on scales far below $\lambda$ these act as induced dipoles driven by the passing field, $\mathbf{p}\propto\mathbf{E}$ . Why: identifying the scatterers as sub-wavelength dipoles licenses Rayleigh's dipole formula rather than a full Mie treatment.

Step 2. An oscillating dipole radiates power $P_{\mathrm{scat}}\propto\omega^4|\mathbf{p}|^2$ , so the fraction scattered per unit length carries a factor $\omega^4\propto\lambda^{-4}$ . Why: the fourth power is a property of accelerating charge — radiated power goes as acceleration squared, and a driven oscillator's acceleration scales as $\omega^2$ .

Step 3. Integrating the differential cross-section over the fluctuation statistics gives $\alpha_R = C_R/\lambda^4$ , with all the material content packed into $C_R$ . Why: the statistics fix the size of $C_R$ but cannot touch the $\lambda^{-4}$ — the wavelength scaling is set entirely by the dipole radiation law.

Step 4. Because the fluctuations are frozen at the fictive temperature and never re-equilibrate, $C_R$ depends on glass composition and draw conditions but not on operating temperature or power. Why: this is why Rayleigh loss is a hard floor — you cannot cool or turn it down, only out-run it with a longer wavelength.

Go deeper · Derivation C · 1 minWhere the loss minimum sits

Derivation CWhere the loss minimum sits

The goal is to show that the 1.55 μm window is not a coincidence of engineering but the mathematical minimum of two competing intrinsic terms, and to locate it by balancing their derivatives. Keeping only the falling Rayleigh floor and the rising infrared tail — the UV and OH terms are negligible in a clean fiber between 1.4 and 1.6 μm — the crossover falls out of a one-line minimization and lands where the measured spectrum bottoms out.

Step 1. Retain the two dominant intrinsic contributions, $\alpha(\lambda)=C_R\lambda^{-4}+A\,e^{-a/\lambda}$ , dropping everything small in the near-IR. Why: the minimum is set by the two terms that change fast near 1.55 μm; the slowly varying UV and impurity terms shift the floor, not its location.

Step 2. Differentiate and set to zero: $\dfrac{\mathrm{d}\alpha}{\mathrm{d}\lambda}=-4C_R\lambda^{-5}+A\dfrac{a}{\lambda^{2}}e^{-a/\lambda}=0$ . Why: the first term is negative (Rayleigh keeps falling) and the second positive (IR keeps rising), so a zero of the sum is exactly the wavelength where one hands off to the other.

Step 3. Rearranged, the minimum condition is $4C_R\lambda^{-5}=A\,a\,\lambda^{-2}e^{-a/\lambda}$ : at the optimum the marginal decrease of Rayleigh loss equals the marginal increase of IR loss. Why: balanced marginal rates explain why the valley is broad and flat — near the crossover both slopes are small.

Step 4. Inserting silica's constants ( $C_R\approx0.89$ , $A\approx7.8\times10^{11}$ dB/km, $a\approx48.5$ μm) places the crossover in the 1.5–1.6 μm band with a floor of ≈0.15–0.2 dB/km, matching the measured minimum. Why: the same constants that fit the two tails independently predict the window position without further tuning.

Limiting cases

How the dominant loss term hands off across the spectrum:

Case	Result	Meaning
Short wavelength (visible–850 nm)	$\alpha_R \propto \lambda^{-4}$	Rayleigh scattering dominates; loss is high (~1.7–3 dB/km at 850 nm) but sources and detectors are cheap — the first telecom window.
Minimum-loss window (~1550 nm)	$\alpha \approx 0.15\text{–}0.2\ \mathrm{dB/km}$	Rayleigh floor and IR tail are both small and roughly balanced; silica's global minimum, the telecom C-band.
Long wavelength (greater than 1.7 μm)	$\alpha_{\mathrm{IR}} \sim A\,e^{-a/\lambda}$	Multiphonon Si–O absorption rises steeply and terminates the usable band; fluoride glasses are needed to go further.
Bending	$\alpha_{\mathrm{bend}} \propto e^{-R/R_c}$	Macrobend loss grows exponentially as the bend radius $R$ drops below a critical $R_c$ ; independent of intrinsic material loss.

Common trapDecibels are additive per length, so a small dB/km number still adds up to a large power loss

The decibel's logarithm lulls people into treating 0.2 dB/km as a rounding error. It is not: over 100 km it is 20 dB, and 20 dB is a factor of one hundred in power. Loss adds in dB precisely because it multiplies in linear power — that is the whole reason the unit exists. A second trap hides in the coefficients: $\alpha_{\mathrm{dB/km}}=4.343\,\alpha$ , where $\alpha$ is the power coefficient in $\mathrm{km^{-1}}$ from $P=P_0e^{-\alpha z}$ . They differ by a factor of 4.343, and a formula written in one convention gives nonsense if you feed it the other. When in doubt, check units: anything multiplying a length inside an exponential is a $\mathrm{km^{-1}}$ coefficient, never a dB/km value.

Worked examples

1 · Reading the loss spectrum from Rayleigh scattering (confidence builder)

Using $C_R = 0.89\ \mathrm{dB\,km^{-1}\,\mu m^4}$ , estimate the Rayleigh-limited loss at the three classic windows 850, 1310 and 1550 nm, and find how much better 1550 nm is than 850 nm.

Step 1. Apply $\alpha_R=C_R/\lambda^4$ at each wavelength. At 850 nm, $\lambda=0.85$ μm and $\lambda^4=0.522$ μm⁴, so $\alpha_R=0.89/0.522=\mathbf{1.71\ dB/km}$ . At 1310 nm, $\lambda^4=2.945$ , giving $\alpha_R=0.89/2.945=\mathbf{0.30\ dB/km}$ . At 1550 nm, $\lambda^4=5.77$ , giving $\alpha_R=0.89/5.77=\mathbf{0.154\ dB/km}$ .

Step 2. The infrared tail is negligible at all three (equation 5 gives under 0.02 dB/km at 1.55 μm), so these Rayleigh values sit close to the true intrinsic floor. Adding the IR term at 1.55 μm nudges the total to ≈0.17 dB/km, and residual UV plus imperfections bring a real fiber to the quoted ≈0.19 dB/km — the marked point on the spectrum.

Step 3. The improvement from 850 to 1550 nm is the ratio $(1.55/0.85)^4=(1.824)^4=\mathbf{11.1}$ . Moving one window redward cuts the scattering floor more than tenfold, lengthening the reachable span by the same factor — the single biggest reason telecom abandoned 850 nm for the long haul. Rayleigh loss: 1.71, 0.30, 0.154 dB/km at 850/1310/1550 nm; 1550 nm is ×11 lower than 850 nm.

2 · Unrepeatered reach from a power budget

A link launches $P_{\mathrm{tx}}=0$ dBm into standard C-band fiber ( $\alpha=0.20$ dB/km). The receiver sensitivity is $-28$ dBm, splices and connectors total $L_{\mathrm{splice}}=2$ dB, and the design keeps a margin $M=6$ dB. How far can the signal run before it needs amplification?

Step 1. Set received power to the sensitivity threshold in equation (8) and solve for the span: $L_{\max}=\dfrac{P_{\mathrm{tx}}-P_{\min}-L_{\mathrm{splice}}-M}{\alpha_{\mathrm{dB/km}}}$ .

Step 2. Insert the numbers: the numerator is $0-(-28)-2-6=28-8=20$ dB of budget available for fiber — the power you may spend on glass after paying for connectors and holding back a repair margin.

Step 3. Divide by the fiber loss: $L_{\max}=20/0.20=\mathbf{100\ km}$ — why amplifier huts on long-haul terrestrial routes sit roughly 80–120 km apart. Over that 20 dB the power falls by $10^{20/10}=100$ , matching the first figure. Maximum span ≈ 100 km; the signal arrives a factor of 100 weaker than it left.

3 · Decibels to a surviving power fraction

A 50 km fiber measures 0.22 dB/km with negligible splice loss. What fraction of the launched power reaches the far end?

Step 1. Total loss is additive in decibels: $\alpha_{\mathrm{dB/km}}\times L = 0.22\times50=\mathbf{11\ dB}$ .

Step 2. Convert to a linear power ratio: $P_0/P_L=10^{11/10}=\mathbf{12.6}$ , so the surviving fraction is $1/12.6\approx0.079$ . Checking the natural-log form, $\alpha=11/4.343=2.53\ \mathrm{km^{-1}}$ and $e^{-2.53}=0.0795$ — the conventions agree through 4.343. Output reduced ≈13-fold; ≈7.9 % survives.

Physics of the portrait

The story of fiber loss is the story of one number falling four orders of magnitude in a decade — from the 1000 dB/km of ordinary 1960s glass to the 0.2 dB/km that made intercontinental links possible. One person saw, before anyone had the glass to prove it, that the barrier was dirt, not physics.

Origins · 1 minCharles Kao and how this was discovered

Charles Kao

1933–2018 · the low-loss silica dream that built the optical internet

In 1966, at Standard Telecommunication Laboratories in England, Charles Kao and George Hockham published the paper that founded fiber-optic communications. The prevailing wisdom was that glass fibers, then losing around 1000 dB/km, could never carry signals any useful distance. Kao's insight was that this catastrophic loss was almost entirely extrinsic: it came from transition-metal impurities — chiefly iron, copper and chromium — dissolved in the glass, not from any fundamental limit of silica. He argued that if the glass were purified to parts-per-billion, the residual loss would fall to the intrinsic Rayleigh and infrared floor, which he estimated could be below 20 dB/km — the threshold at which fiber would beat coaxial cable. The claim was audacious because no one had ever made glass that clean. In 1970 the Corning team of Robert Maurer, Donald Keck and Peter Schultz vindicated him with a titania-doped fiber below 20 dB/km, and within a decade the loss reached the 0.2 dB/km Rayleigh limit that still stands. Kao received the 2009 Nobel Prize in Physics "for groundbreaking achievements concerning the transmission of light in fibers for optical communication" — a rare prize for diagnosing what was not fundamental.

History

1854

— Tyndall demonstrates that light follows a curved jet of water by total internal reflection

1966

— Kao and Hockham argue that purified silica could fall below 20 dB/km, blaming impurities not physics

1970

— Maurer, Keck and Schultz at Corning fabricate fiber below 20 dB/km

1979

— Miya and co-workers at NTT reach 0.2 dB/km at 1.55 μm, essentially the Rayleigh limit

2009

— Kao is awarded the Nobel Prize in Physics for the low-loss fiber concept

Going further

Texts. Saleh & Teich, Fundamentals of Photonics, 3rd ed., Ch. 9 (Fiber Optics) · Keiser, Optical Fiber Communications, Ch. 3 (attenuation and the loss spectrum) · Agrawal, Fiber-Optic Communication Systems, Ch. 2 · Hecht, Optics, 5th ed., §5.6 (fiber optics) · Loudon, The Quantum Theory of Light (scattering formalism) · Demtröder, Laser Spectroscopy (Rayleigh scattering and absorption tails).

Provenance. The mechanisms and equations follow Saleh & Teich and Keiser. A verifier should confirm: (1) the decibel conversion $\alpha_{\mathrm{dB/km}}=10\log_{10}(e)\,\alpha\approx4.343\,\alpha$ ; (2) the $\lambda^{-4}$ Rayleigh scaling from dipole radiation (Loudon, Demtröder); (3) the standard silica minimum 0.15–0.2 dB/km near 1.55 μm and the OH⁻ overtone near 1.38 μm; (4) the worked Rayleigh values 1.71 / 0.30 / 0.154 dB/km at 850 / 1310 / 1550 nm with $C_R=0.89$ ; (5) the span-budget arithmetic $20\ \mathrm{dB}/0.20\ \mathrm{dB\,km^{-1}}=100$ km; (6) the 11 dB over 50 km giving a ×12.6 power ratio. The Keiser infrared-tail constants $A\approx7.8\times10^{11}$ dB/km, $a\approx48.5$ μm are standard fitted values; no non-standard numbers are asserted.

Builds on: Total Internal Reflection and Optical Guiding · Step-Index and Graded-Index Optical Fibers · Waveguide Modes and the Wave Equation. Leads to: Chromatic and Modal Dispersion in Fibers · Nonlinear Optical Fibers and Effects · Dispersion Management and Compensation · Microring Resonators and Optical Cavities on Chip.

Ask the tutor: Ask me to walk through a full power budget for a link you have in mind — launch power, fiber loss, splices, margin — and I will solve for the reach step by step.

Why is loss measured in decibels per kilometre instead of just a percentage per kilometre?

Because loss compounds. If a fiber loses 10 % per km, then after two km you have $0.9\times0.9=0.81$ — 19 % gone, not 20 % — and the arithmetic gets ugly over hundreds of km. The decibel is a logarithm, and logarithms turn that multiplication into addition: 0.2 dB/km over 100 km is simply $0.2\times100=20$ dB. You add span losses, splices and margins with a pocket calculator, then convert the total back to a linear ratio once at the end via $10^{\mathrm{dB}/10}$ . The whole power-budget discipline depends on losses being additive, which is exactly what the decibel delivers.

Is Rayleigh scattering the same physics that makes the sky blue?

Yes, essentially. In the atmosphere, air molecules scatter sunlight with a cross-section $\propto\lambda^{-4}$ , so blue is scattered far more than red and the sky glows blue. In a fiber the scatterers are not molecules but frozen-in density and composition fluctuations — sub-wavelength lumps of slightly different index locked in when the melt solidified — but the radiating-dipole physics and the $\lambda^{-4}$ law are identical. The difference is direction: the sky redirects light toward your eye, while in a fiber the scattered light is simply lost from the guided mode. It is the same reason a thick block of the clearest glass still looks faintly bluish along its length.

If the loss minimum is near 1550 nm, why did early systems use 850 nm at all?

History and hardware. In the 1970s the only cheap, reliable sources and detectors were gallium-arsenide devices near 850 nm, so the first commercial systems lived there despite the ~2–3 dB/km loss. As indium-phosphide devices matured, systems moved to the 1310 nm second window (near standard fiber's zero-dispersion wavelength) and finally to 1550 nm, where both the loss minimum and the erbium amplifier sit. The progression tracks not the physics — which always favoured 1550 nm — but the arrival of the lasers, detectors and amplifiers that could exploit it.

What is the difference between macrobending and microbending loss?

Both radiate power out of the guided mode, but at different scales. Macrobending is a smooth curve of the whole fiber — a loop around a spool or a turn around a door frame, radius of millimetres to centimetres; its loss falls exponentially with bend radius, equation (7), and worsens at longer wavelengths where the mode is larger. Microbending is a random series of tiny axial deflections, on the scale of the fiber diameter, caused by pressing the fiber against a rough surface or squeezing it in a tight jacket. It couples the guided mode to radiation and higher-order modes through the ripple, and is controlled by careful cabling and soft coatings, not by the installer's bend radius.

How close is real commercial fiber to the fundamental Rayleigh limit?

Remarkably close. The best standard single-mode fiber reaches about 0.17–0.18 dB/km at 1550 nm, and the record for solid silica is around 0.14 dB/km — essentially all of it Rayleigh scattering with a sliver of infrared tail. Decades of purification have driven the extrinsic terms almost to zero, leaving the intrinsic floor Kao predicted. The only way past it is to change the physics: fluoride glasses push the infrared edge out, and hollow-core fibers guide the light in air, removing the glass Rayleigh floor and dipping below 0.14 dB/km.

Attenuation and dispersion are both called impairments — how do they differ?

They damage a signal in different ways. Attenuation removes energy: the power falls, the signal-to-noise ratio degrades, and once the light drops below the receiver sensitivity it is gone. It is irreversible — you cannot un-scatter a photon — so it must be overcome by more launch power or periodic amplification. Dispersion, by contrast, conserves energy but smears a pulse out in time as different wavelengths or modes travel at different speeds. Because it is a deterministic reshuffling, not a loss, dispersion can in principle be compensated by a component with the opposite dispersion. Attenuation sets how far you can go before amplifying; dispersion sets how fast you can signal before pulses overlap.