UNIT 4: Optical Fibre Communication - Exam-Focused Short Notes

Based on RGPV Past Papers (2022-2025). Prioritized by frequency of appearance.

1.0 FIBER OPTICS FUNDAMENTALS & WAVEGUIDE THEORY

1.1 Ray Optics Approach

• Total Internal Reflection (TIR): Condition for guidance: $$\displaystyle n_1 > n_2 $$ and $$\displaystyle \theta_i > \theta_c $$, where $$\displaystyle \theta_c = \sin^{-1}(n_2/n_1) $$.

• Step-Index Fiber:

  • Meridional Rays: Pass through fiber axis. Simple TIR.

  • Skew Rays: Helical path, do not cross axis. More modes, longer path.

• Graded-Index Fiber: Refractive index $n(r)$ decreases parabolically from center: $$\displaystyle n(r) = n_1(1 - 2\Delta (r/a)^g) $$ for $r \leq a$, where $g$ is profile parameter ($$\displaystyle g=2 $$ for parabolic).

  • Rays continuously refract, reducing intermodal dispersion.

• Planar Dielectric Slab Guide:

  • Modes satisfy characteristic equation: For TE modes, $$\displaystyle h d = m\pi + 2\tan^{-1}(\alpha/h) $$, where $$\displaystyle h = \sqrt{k_0^2 n_1^2 - \beta^2} $$, $$\displaystyle \alpha = \sqrt{\beta^2 - k_0^2 n_2^2} $$.

  • Cutoff: Mode exists only if $$\displaystyle \beta > k_0 n_2 $$. Normalized frequency $$\displaystyle V = k_0 a \sqrt{n_1^2 - n_2^2} $$.

  • Number of TE/TM modes $\approx V/\pi$.

1.2 Wave Optics Approach & Modal Analysis

• Normalized Frequency (V-number):

$$\boxed{V = \frac{2\pi a}{\lambda} \sqrt{n_1^2 - n_2^2}}$$

*   Determines number of guided modes.

• Number of Guided Modes:

  • Step-Index: For large $V$, $$\displaystyle M \approx \frac{V^2}{2} $$ (both polarizations). Exact: $$\displaystyle M \approx \frac{V^2}{2} - \frac{V}{2} $$.

  • Graded-Index (power-law): $$\displaystyle M \approx \frac{g}{g+2} \cdot \frac{V^2}{2} $$.

• Mode Field Diameter (MFD): Effective width of fundamental mode field in single-mode fiber. $$\displaystyle w \approx \frac{a}{0.65} + \frac{\lambda}{2\pi n_1 \sqrt{2\Delta}} $$ (approx).

1.3 Key Parameters of Step-Index Fiber

• Relative Index Difference:

$$\boxed{\Delta = \frac{n_1 - n_2}{n_1}}$$

*   Small $\Delta$ ($\approx 0.01$) for low dispersion.

• Numerical Aperture (NA):

$$\boxed{NA = \sqrt{n_1^2 - n_2^2} \approx n_1 \sqrt{2\Delta}} \quad (\text{for small } \Delta)$$

*   Measures light-gathering ability.

• Acceptance Angle ($$\displaystyle \theta_{0,\max} $$):

$$\boxed{NA = n_0 \sin \theta_{0,\max}}$$

*   $$\displaystyle n_0 $$: refractive index of external medium (air $$\displaystyle n_0=1 $$).

*   $$\displaystyle \theta_{0,\max} = \sin^{-1}(NA) $$.

• Critical Angle:

$$\boxed{\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)}$$

[!TIP] Common Exam Trap: When outer medium is not air (e.g., water), $$\displaystyle n_0 \neq 1 $$. Always use $$\displaystyle NA = n_0 \sin \theta_{0,\max} $$.

2.0 SIGNAL DEGRADATION & LOSS MECHANISMS

2.1 Attenuation (Loss)

• Absorption:

  • Intrinsic: UV ($\sim$0.1 μm) and IR ($\sim$1.8 μm) absorption edges due to electronic and vibrational modes of SiO₂.

  • Extrinsic: OH⁻ ions (peak at 1.38 μm, overtone at 0.95 μm), transition metal ions (Fe, Cu). Reduced by high-purity fabrication (MCVD).

• Scattering:

  • Rayleigh Scattering: $$\displaystyle \alpha_{sc} \propto \frac{1}{\lambda^4} $$. Caused by microscopic density/composition fluctuations. Fundamental loss limit (~0.15 dB/km at 1550 nm).

  • Mie Scattering: From large inhomogeneities (>λ), e.g., imperfect waveguide.

• Bending Losses:

  • Macrobending: Radiation loss when bend radius $R$ is small.

  • Critical Radius (approx for step-index):

$$\boxed{R_c \approx \frac{3 n_1 a^3}{\lambda} \cdot \frac{1}{\sqrt{2\Delta}}}$$

*   **Microbending**: Loss from small-scale bends due to lateral stresses, cabling.

*   **Reduction**: Use larger $R$, smaller $\Delta$, protective cabling.

2.2 Dispersion

• Intermodal Dispersion (Modal):

  • Step-Index: $$\displaystyle \Delta \tau = \frac{L \cdot n_1 \Delta}{c} $$ (pulse spread per km).

  • Graded-Index ($$\displaystyle g=2 $$ parabolic): $$\displaystyle \Delta \tau \propto \frac{L \cdot \Delta^2}{c} $$ (much lower).

  • Max Bit Rate-Length Product:

$$\boxed{BL_{\max} \approx \frac{0.44}{\Delta \tau} \quad (\text{for NRZ})}$$

• Intramodal Dispersion (Chromatic):

  • Material Dispersion: $$\displaystyle D_m = -\frac{\lambda}{c} \frac{d^2 n}{d\lambda^2} $$. Zero-dispersion wavelength $$\displaystyle \lambda_0 \approx 1.3 $$ μm for silica.

  • Waveguide Dispersion: $$\displaystyle D_w = -\frac{n_2}{c} \frac{d}{d\lambda}\left(\frac{V}{k_0 a}\right) $$ (depends on core size).

  • Total: $$\displaystyle D_{total} = D_m + D_w $$.

• System Rise Time Budget:

$$\boxed{t_{sys} = \sqrt{t_{tx}^2 + t_{inter}^2 + t_{intra}^2 + t_{rx}^2}}$$

*   $$\displaystyle t_{inter} = \Delta \tau $$ (intermodal), $$\displaystyle t_{intra} = |D_{total}| \cdot L \cdot \Delta \lambda $$ (chromatic).

*   Max bit rate $$\displaystyle B \approx 0.7 / t_{sys} $$.

[!TIP] Key Formula: For step-index multimode, $$\displaystyle \Delta \tau \approx \frac{L n_1 \Delta}{c} $$. Remember units: $L$ in m, $$\displaystyle c=3\times10^8 $$ m/s, $\Delta \tau$ in seconds.

3.0 FIBER FABRICATION TECHNIQUES

• MCVD (Modified Chemical Vapour Deposition):

  1. Deposition: SiCl₄, GeCl₄, O₂ flow in rotating silica tube; soot deposited by oxidation flame.

  2. Sintering: Heat to collapse soot into transparent glass layer.

  3. Repeat: Build core/cladding layers; final collapse to solid preform.

  • Advantage: Precise index profile, high purity.

• OVD (Outside Vapour Deposition): Soot deposited on target rod, then sintered.

• VAD (Vapour Axial Deposition): Soot deposited axially on growing rod; high production rate.

4.0 FIBER CONNECTORS, SPLICES & COUPLERS

4.1 Fiber Connectors

• Types: SC (subscriber connector, push-pull), ST (bayonet), FC (screw), LC (latched, small), MTP/MPO (multi-fiber array).

• Performance:

  • Insertion Loss (IL): $$\displaystyle < 0.3 $$ dB typical.

  • Return Loss (RL): $$\displaystyle > 40 $$ dB (back reflection).

4.2 Fiber Splicing

• Fusion Splicing:

  1. Cleave (perpendicular end-face).

  2. Align cores (microscope/alignment system).

  3. Arc (heat & melt), feed (prevent bulb formation).

  4. Test (OTDR).

  • Loss Mechanisms: Core-cladding misalignment, NA mismatch, end-face contamination, index inhomogeneity.

  • Typical loss: $$\displaystyle < 0.1 $$ dB.

• Mechanical Splicing: Alignment via V-groove or precision sleeve. Faster, cheaper, higher loss (~0.3 dB).

4.3 Optical Couplers & Power Dividers

• FBT (Fused Biconical Taper): Two fibers fused & tapered; power couples via evanescent field.

• PLC (Planar Lightwave Circuit): Lithography on silica waveguide chip; stable, precise splitting ratios.

• Key Parameters:

  • Splitting Ratio: $$\displaystyle P_{out1}/P_{out2} $$ (e.g., 50:50).

  • Excess Loss: $$\displaystyle (P_{in} - P_{total,out})/P_{in} $$ (dB).

  • Insertion Loss: $$\displaystyle P_{in} - P_{specific,out} $$ (dB).

  • Crosstalk/Isolation: $$\displaystyle P_{unwanted}/P_{input} $$ (dB).

  • Directivity: Reflected power to input port.

5.0 OPTICAL SOURCES

5.1 Light Emitting Diode (LED)

• Principle: Spontaneous emission from forward-biased p-n junction.

• Types:

  • Surface-emitting (Burrus): Light perpendicular to junction. Low cost, low bandwidth.

  • Edge-emitting: Light along junction axis. Higher power, better coupling.

• Internal Optical Power:

$$\boxed{P_{in} = \frac{\eta_i I h \nu}{q}}$$

*   $$\displaystyle \eta_i $$: internal quantum efficiency, $I$: current, $h\nu$: photon energy, $q$: electron charge.

• Modulation Bandwidth: Limited by carrier lifetime $$\displaystyle \tau_c $$ and junction capacitance $$\displaystyle C_j $$. $$\displaystyle f_{3dB} \approx \frac{1}{2\pi \tau_c} $$.

• Advantages: Low cost, stable, no temperature control. Disadvantages: Low power, wide spectral width, low bandwidth (~100 MHz).

5.2 Laser Diodes (LD)

• Basic Principle: Stimulated emission in resonant cavity (cleaved facets) under population inversion.

• Resonant Frequency & Mode Spacing (Fabry-Perot cavity of length $L$, effective index $n$):

$$\boxed{\Delta \nu = \frac{c}{2 n L}} \quad \text{or} \quad \boxed{\Delta \lambda = \frac{\lambda^2}{2 n L}}$$

*   Number of longitudinal modes $$\displaystyle \approx \frac{\Delta \lambda_{LED}}{\Delta \lambda} $$.

• Structures: FP-LD (multi-mode), DFB-LD (single-mode, grating), DBR-LD.

• Modulation: Direct modulation (bias current). Limitation: Chirp (frequency shift during pulse) due to carrier index change.

• Example: $$\displaystyle L=250\,\mu m $$, $$\displaystyle n=3.5 $$, $$\displaystyle \lambda=1.55\,\mu m $$ → $\Delta \lambda \approx 0.1,$nm, many modes for FP-LD.

6.0 PHOTODETECTORS

6.1 Photodetection Principles

• Photoconductivity: Light increases conductivity (photocurrent in reverse bias).

• Photovoltaic: Zero bias, generates voltage/current (solar cell mode).

• Quantum Efficiency ($\eta$):

$$\boxed{\eta = \frac{\text{electrons collected}}{\text{photons incident}} = \frac{I_{ph} q}{P_{in} h \nu}}$$

*   **Derivation** (PIN): $$\displaystyle \eta = \frac{\tau_{rec}}{\tau_{rec} + \tau_{tr}} $$, where $$\displaystyle \tau_{rec} $$ = carrier lifetime, $$\displaystyle \tau_{tr} $$ = transit time.

6.2 PIN Photodiode

• Structure: p⁺-i-n⁺. Intrinsic (i) layer wide depletion region.

• Working: Reverse biased. Photons generate EHP in depletion region; carriers drift to electrodes.

• I-V: Dark current $$\displaystyle I_{dark} $$ (small), photocurrent $$\displaystyle I_{ph} = \eta \frac{P_{in} q}{h\nu} $$ (linear).

• Bandwidth: Limited by $RC$ time constant ($R$: load, $C$: junction capacitance) and $$\displaystyle \tau_{tr} $$. $$\displaystyle f_{3dB} \approx \frac{1}{2\pi RC} $$.

6.3 Avalanche Photodiode (APD)

• Principle: Impact ionization in high-field region → avalanche multiplication.

• Multiplication Factor ($M$): $$\displaystyle I = M \cdot I_p $$, where $$\displaystyle I_p $$ = primary photocurrent.

• Excess Noise Factor ($F(M)$): Due to statistical variation in multiplication. $$\displaystyle F(M) > 1 $$.

• Advantage: Internal gain → higher sensitivity than PIN.

• Disadvantage: Higher operating voltage (100-200 V), higher noise (from multiplication), temperature sensitive.

7.0 OPTICAL AMPLIFIERS

7.1 Erbium-Doped Fiber Amplifier (EDFA)

• Principle: Pump at 980 nm or 1480 nm excites Er³⁺ ions to metastable level. Signal at 1550 nm stimulates emission → amplification.

• Gain:

$$\boxed{G = \exp[(\sigma_e N_2 - \sigma_a N_1) L]}$$

*   $$\displaystyle \sigma_e, \sigma_a $$: emission/absorption cross-sections, $$\displaystyle N_1,N_2 $$: population levels, $L$: doped fiber length.

*   **Gain Spectrum**: Peaks at 1530 nm, flattening filters used.

• Conversion Efficiency:

$$\eta_{ce} = \frac{P_{sig,out} - P_{sig,in}}{P_{pump}}$$

• Noise Figure: Limited by Amplified Spontaneous Emission (ASE) from Er³⁺.

• Applications: In-line amplifier, power booster, pre-amplifier.

7.2 Raman Amplifier

• Principle: Stimulated Raman Scattering (SRS). Pump photon at $$\displaystyle \lambda_p $$ loses energy to signal photon at $$\displaystyle \lambda_s $$ ($$\displaystyle \lambda_s > \lambda_p $$).

• Types:

  • Discrete: Separate Raman pump unit.

  • Distributed (DRA): Transmission fiber itself acts as gain medium (pump co-propagates or counter-propagates).

• Advantage: Broad gain bandwidth (flexible wavelength allocation), lower noise than EDFA, uses standard fiber.

8.0 OPTICAL NETWORKING & SYSTEM DESIGN

8.1 Link Power Budget

1. Determine requirements: Bit rate $B$, distance $L$.

2. Calculate total loss:

   • Fiber attenuation: $\alpha \cdot L$ (dB).

   • Connector loss: $$\displaystyle N_c \cdot \alpha_c $$.

   • Splice loss: $$\displaystyle N_s \cdot \alpha_s $$.

   • Safety margin: 3-6 dB.

3. Specify:

   • Transmitter output power $$\displaystyle P_t $$ (dBm).

   • Receiver sensitivity $$\displaystyle P_r $$ (min power for required BER, e.g., $$\displaystyle 10^{-9} $$).

4. Power Budget Equation:

$$\boxed{P_t - P_r \geq \text{Total Loss} + \text{System Margin}}$$

5. Power Penalties: Add for dispersion, modal noise, reflections, etc.

• Example: $$\displaystyle P_t = -3 $$ dBm, $$\displaystyle P_r = -28 $$ dBm → Power budget = 25 dB. If total loss = 20 dB, margin = 5 dB.

8.2 SONET/SDH

• Need: Standard for high-speed digital traffic (voice/data) over fiber.

• Frame Structure (STS-1/OC-1):

  • 9 rows × 90 columns = 810 bytes.

  • Overhead: Section (first 3 columns), Line (next 9 columns), Path (last 78 columns).

  • Payload: 87 columns (STS-1) or 261 columns (STM-1/OC-3).

• Multiplexing: Synchronous byte-interleaved multiplexing (STS-N = N × STS-1).

• Network Elements:

  • ADM (Add-Drop Multiplexer): Key node; adds/drops lower-rate signals.

  • TM (Terminal Multiplexer): Network endpoint.

  • REGEN (Regenerator): Re-timers, re-shapers.

  • DCS (Digital Cross-Connect): Flexible switching.

8.3 Wavelength Division Multiplexing (WDM)

• Principle: Multiple wavelengths (channels) on single fiber.

• Types:

  • CWDM: 18 channels (1270-1610 nm), 20 nm spacing, no amplification.

  • DWDM: 40-160 channels (C-band 1530-1565 nm, L-band), 0.8/0.4 nm spacing, uses EDFA.

• Components:

  • Mux/Demux: Gratings, AWG (Arrayed Waveguide Grating).

  • Optical Amplifiers: EDFA (boosts all channels).

  • Transponders: O-E-O conversion for wavelength conversion.

• MEMS Technology: Micro-mirrors for tunable filters/switches in dynamic WDM.

9.0 OPTICAL FIBER TESTING & MEASUREMENTS

9.1 Optical Time-Domain Reflectometer (OTDR)

• Principle: Launch narrow pulse, measure backscattered (Rayleigh) & reflected (Fresnel) light vs. time.

• Trace Analysis:

  • Slope → Attenuation coefficient (dB/km).

  • Events (splices/connectors) → Insertion loss (step height).

  • Fresnel peak → Connector/break location.

  • Dead zone: Distance after high-reflection event where trace is saturated.

• Measurements: Length, loss per km, event loss, fault location.

• Limitations: Dead zones, requires averaging for noise reduction.

9.2 Other Measurements

• Cut-Back Method: Measure power before/after cutting fiber → attenuation.

• Interferometric Method: Interferometer to measure core diameter, eccentricity.

• Refractometer: Measures refractive index profile (scanning fiber near index-matching liquid).

10.0 PASSIVE OPTICAL NETWORKS (PON) & SYSTEM PERFORMANCE

10.1 Passive Optical Network (PON)

• Architecture: OLT (Central Office) → ODN (Optical Distribution Network, passive splitter) → ONT/ONU (Customer premises).

• Types:

  • APON/BPON: ATM-based, 622 Mbps down, 155 Mbps up.

  • GPON: 2.5 Gbps down, 1.25 Gbps up. T-CONT for QoS.

  • EPON: Ethernet-based, 1 Gbps symmetric. TDMA for upstream (ONUs time-slot assigned).

• Split Ratio: Typically 1:32 or 1:64.

10.2 System Performance Analysis

• Eye Pattern:

  • Open: Good SNR, low jitter.

  • Closure: Due to ISI (dispersion), noise.

  • Jitter: Timing uncertainty.

  • Height: Noise margin.

• Bit Error Rate (BER) for Digital Receiver (Gaussian noise approximation):

$$\boxed{BER = \frac{1}{2} \text{erfc}\left( \frac{Q}{\sqrt{2}} \right) \approx \frac{1}{Q\sqrt{2\pi}} e^{-Q^2/2}}$$

*   $$\displaystyle Q = \frac{I_1 - I_0}{\sigma_1 + \sigma_0} $$, where $$\displaystyle I_1,I_0 $$: mean currents for '1','0', $\sigma$: standard deviations.

• Power Penalties: Additional power required to maintain BER due to:

  • Modal noise, reflection, dispersion, intensity noise (RIN).

[!TIP] Exam Focus: Link Power Budget design (14m) and SONET/SDH architecture (7m) are almost guaranteed questions. Practice numericals for NA, V-number, critical radius, and bit rate from rise time budget.