UPM, DIAC. Open Course. March TIME DISPERSION 3.1 Introduction 3.2 Modal Dispersion 3.3 Chromatic Dispersion 3.4 PMD 3.5 Total Dispersion 3.6 Dispersion Compensation

INTRODUCTION (I) Time Dispersion Fundamentals – Light is spread out (in time) as it travels through the fiber – Parameter: Pulse Widening (measured at 50%), Δt = T RX -T TX – Dispersion causes INTERSYMBOL INTERFERENCE

INTRODUCTION (II) Types of Dispersion – Modal Dispersion, Δt mod Intermodal: between different modes – Chromatic Dispersion, Δt cro Intramodal: inside each mode Mechanisms – Material – Waveguide – PMD, Δt pmd Polarization Mode Dispersion Between orthogonal polarizations

INTRODUCTION (III) Bandwidth per Unit Length (I) – Relation between parameters Dispersion, Δt, increases with fiber length (in metallic lines is approx. constant) Dispersion causes ISI → limits bandwidth and Rb – BANDWIDTH DEPENDS ON FIBER LENGTH Bandwidth = BW(L) Parameter: Bandwidth per Unit Length (per = multiplication!) E.g: the fiber has 10 GHz·km

INTRODUCTION (IV) Bandwidth per Unit Length (II) – Single-Mode Fiber Dispersion, Δt, is linear with fiber length, L BW is linear with L Parameter Bandwidth per Unit Lenght: an ordinary multiplication Example: 10 GHz·km  5 GHz · 2 km  2 GHz · 5 km

MODAL DISPERSION (I) Fundamentals – Cause: light is spread out in modes – Working: each mode takes a different path → different arrival t – Dispersion increases with fiber length. Not linear – Dispersion only exists in multimode propagation All rays travel at the same velocity (n 1 constant), but they go through different paths. Therefore, they arrive at different times

MODAL DISPERSION (II) Modal Disp. —Step-Index Versus Graded Index – GI fiber compensates: longer paths are faster – SI fiber does not compensate – Δt mod(SI) ≈ 1000·Δt mod(GI)

MODAL DISPERSION (III) Bandwidth per Unit Legth —Multimode Fiber – BW in a L(km) fiber L(km): total fiber length B 0 (MHz·km): BW per unit length, “Intermodal BW”  : Mode Coupling Coefficient – Modes interchange energy —dispersion is compensated – 0.5    1 (   coupling  ) – Typical values: SI fiber; GI fiber – BW is not linear with L!

MODAL DISPERSION (IV) Modal Disp. Calculation – Modal disp. in a L(km) fiber B[L](GHz): BW in L(km) of fiber B 0 (MHz·km): intermodal BW γ: mode coupling coefficient – Δt mod is not linear with L!

CHROMATIC DISPERSION (I) Fundamentals (I) – Colors arrive at different times – Types Due to material, Δt mat Due to waveguide effect, Δt wg – Total chromatic dispersion, Δt cro : both contributions are added – Chrom. disp. increases linearly with fiber length IN t OUT t

CHROMATIC DISPERSION (II) Fundamentals (II) – Operation principles Material Dispersion – Optical sources have a spectral BW,  – Fiber refractive index varies (slightly) with the wavelength – Colors go through different paths with different speeds Waveguide Dispersion – Arises from the distribution of light between core and cladding

CHROMATIC DISPERSION (III) Example of Chromatic Dispersion: Rainbow (I)

CHROMATIC DISPERSION (IV) Example of Chromatic Dispersion: Rainbow (II) MATLAB SIMULATION Refractive index of water: n(red) = 1.3 n(blue) = 1.4 REAL VALUES Refractive index of water: n(red) = n(blue) = 1.343

CHROMATIC DISPERSION (V) Chromatic Disp. Calculation – Equation Compensation: Δt wg is usually opposite to Δt mat L(km): fiber length Δλ(nm): optical source spectral BW M(λ)[ns/(km·nm)]: “(Whole) Chromatic Dispersion Coefficient” Dispersion minimum at 1310 nm

PMD (I) Fundamentals – PMD = Polarization Mode Dispersion – Light travels in not one but two orthogonal polarizations – Each polarization travels at different speed – Cause: flaws in circularity Manufacture faults Mechanical strengths

PMD (II) PMD Calculation – Equation L(km): fiber length P[B][ns/(√km)]: PMD coefficient. It depends on BW (or R b ) and Δλ – Dispersion is not linear with L (it is linear with the square root of L) – Dispersion depends on BW

TOTAL DISPERSION Total Dispersion Calculation – Sum of squares of all dispersions – In multimode fiber, Δt mod dominates – In single-mode fiber  Δt mod – PMD is only important with Rb > 10 Gb/s – Equation —total dispersion in an L(km) fiber

DISPERSION COMPENSATION (I) Why Is Compensation Needed? – Dispersion limits data rate and distance

DISPERSION COMPENSATION (II) Operation Principles of Compensation – Modal dispersion An optimal refractive profile (optimal g) minimizes disp. – Chromatic dispersion Using narrow spectral width optical sources Compensating material and waveguide effects (at certain λ) Inserting devices to compensate (DCUs: Dispersion Compensating Units; DCFs: Dispersion Compensating Fiber; Gratings) – PMD Difficult, since dispersion varies with t It requires feedback Special ad hoc device

DISPERSION COMPENSATION (III) Example: DCF – Basics Inserting DCF’s with opposite sign dispersion E.g. every 100 km DCF’s Normal fiber TX Distance from TX (km) Without compensation With compensation Accumulated Dispersion (ps/nm)

DISPERSION COMPENSATION (IV) Example: DCU (I)

DISPERSION COMPENSATION (V) Example: DCU (II)

DISPERSION COMPENSATION (VI) Example: DCU (III)

DISPERSION COMPENSATION (VII) Example: PMDC – PDMC: PMD Compensator – With feedback and signal regeneration