Loss, Dispersion, Sources and Detectors

Tip

Exam Focus

Define attenuation $\alpha=\frac{10}{L}\log_{10}(P_{in}/P_{out})$ [dB/km] and list its causes; classify the five dispersions (modal, material, waveguide, chromatic, PMD); compare LED vs laser diode and PIN vs APD in tables; and quote responsivity $R=I_p/P_{opt}=\eta q\lambda/hc$. The three optical windows (850/1310/1550 nm) recur every year.

Attenuation in Optical Fibre

Attenuation is the reduction of optical power with distance, expressed in dB/km.

Caution

Key Formula — Attenuation coefficient and output power

$$\alpha_{dB}=\frac{10}{L}\log_{10}\!\frac{P_{in}}{P_{out}},\qquad P_{out}(dBm)=P_{in}(dBm)-\alpha_{dB}L-\text{(other losses)}.$$

Cause	Mechanism
Material absorption	Impurity/molecular absorption converts light to heat
Rayleigh scattering	Scattering from microscopic density variations ($\propto\lambda^{-4}$)
Bending loss	Macrobend (tight cable bend) and microbend (pressure/stress)
Connector loss	Misalignment, air gap, dirt, Fresnel reflection
Splice loss	Imperfect fusion/mechanical alignment

Main causes of fibre attenuation.

Silica attenuation spectrum: Rayleigh scattering falls as $\lambda^{-4}$, the OH$^-$ peak sits near 1383 nm, and infrared absorption rises beyond 1600 nm. The three low-loss windows are 850, 1310 and 1550 nm ($\approx0.2\,dB/km$).

Dispersion in Optical Fibre

Dispersion is temporal spreading of a pulse as it travels; excessive spreading overlaps adjacent pulses and causes inter-symbol interference (ISI), limiting the bit-rate$\times$distance product.

Type	Cause	Mainly in
Modal	Different modes travel different path lengths	Multimode
Material	Index varies with wavelength	SMF & MMF
Waveguide	Propagation constant depends on geometry/$\lambda$	SMF
Chromatic	Material $+$ waveguide combined	SMF
PMD	Two polarizations travel at slightly different speeds	High-speed links

Types of dispersion.

Dispersion broadens a narrow input pulse; when broadening approaches the bit period, ISI results.

Graded-index fibre reduces modal dispersion because outer rays travel faster in the lower-index glass. Chromatic dispersion dominates high-speed single-mode links and is managed with narrow-linewidth lasers, dispersion-shifted fibre or dispersion compensation.

Optical Sources: LED and Laser Diode

An optical source converts drive current into light. Photon energy is

$$E=hf=\frac{hc}{\lambda},$$

so the semiconductor bandgap is chosen to match a fibre window.

• LED: forward-biased p–n junction; spontaneous emission gives incoherent, broad-spectrum light; low cost, robust, best for short multimode links.

• Laser diode: above the threshold current, population inversion and the cleaved-facet cavity make stimulated emission dominate, giving coherent, narrow-spectrum, high-power light for long single-mode links.

Feature	LED	Laser diode
Emission	Spontaneous	Stimulated
Light	Incoherent	Coherent, directional
Spectrum	Broad	Narrow
Output power	Low–moderate	High
Modulation speed	Low–moderate	Very high
Threshold	None	Has threshold current
Temperature sensitivity	Low	High
Best suited for	Short MMF links	Long SMF, DWDM

LED versus laser diode.

Photodetectors

A photodetector converts incident optical power into photocurrent, ideally $I_p=R\,P_{opt}$.

Caution

Key Formula — Responsivity

$$R=\frac{I_p}{P_{opt}}=\frac{\eta q}{hf}=\frac{\eta q\lambda}{hc}\quad[A/W],$$

$\eta=$ quantum efficiency, $q=$ electron charge.

PIN Photodiode

A reverse-biased p–i–n diode: photons absorbed in the wide intrinsic layer create electron–hole pairs that the field sweeps out as photocurrent. No internal gain, low noise, fast, simple biasing.

PIN photodiode in which light is absorbed in the wide intrinsic region and the reverse field sweeps carriers to the terminals ($M=1$).

Avalanche Photodiode (APD)

An APD adds a very-high-field multiplication region: primary carriers gain enough energy to create secondary pairs by impact ionization, giving internal gain $M$ so $I_{out}=M R P_{opt}$. Higher sensitivity, but higher bias, more noise and temperature sensitivity.

Avalanche photodiode in which primary carriers from the absorption region undergo impact-ionization gain in a high-field multiplication region ($M>1$).

Feature	PIN	APD
Internal gain	None ($M=1$)	Avalanche gain ($M>1$)
Sensitivity	Moderate	High
Bias voltage	Low	High
Noise	Low	Higher (multiplication noise)
Cost / complexity	Low / simple	High / bias control
Typical use	Short–medium links	Long links, weak signals

PIN versus APD photodiode.

Optical Transmitter and Receiver

The complete link converts coded electrical data to light, transports it through fibre, and reconstructs the electrical output after photodetection.

Complete optical link from line coding and source drive through fibre transmission to photodetection, amplification, filtering, and decision.

Note

Example — Responsivity

A photodiode gives $I_p=8\,\mu\mathrm{A}$ for $P_{opt}=10\,\mu\mathrm{W}$.

$$R=\frac{I_p}{P_{opt}}=\frac{8\times10^{-6}}{10\times10^{-6}}=\boxed{0.8\,A/W}.$$

[!NOTE]

Example — Attenuation coefficient

$P_{in}=2\,mW$, $P_{out}=0.5\,mW$, $L=20\,km$.

$$\alpha=\frac{10}{20}\log_{10}\!\frac{2}{0.5}=0.5\log_{10}4\approx\boxed{0.301\,dB/km}.$$