Lecture 10. Dielectric Waveguides and Optical Fibers

Lecture 10 Dielectric Waveguides and Optical Fibers Slab Waveguide, Modes, V-Number Modal, Material, and Waveguide Dispersions Step-Index Fiber, Multimode and Single Mode Fibers Numerical Aperture, Coupling Loss Bit-Rate, dispersion and optical bandwidth Graded-index fibers Absorption and Scattering

Dispersion! Intermode (Intermodal) Dispersion: Multimode fibers only! Materials Dispersion Group velocity depends on N g and hence on λ! Waveguide Dispersion Group velocity depends on waveguide structure! Chromatic Dispersion Material dispersion + Waveguide Dispersion! Profile Dispersion! Polarization Dispersion Intramodal Dispersion

Intermode Dispersion (MMF)

Material Dispersion (SMF) Group Velocity

Material Dispersion (SMF)

Waveguide Dispersion (SMF) Wavelength Dependent!!

Waveguide Dispersion (SMF)

Intramodal Dispersions (SMF)

Chromatic Dispersion (SMF)

Intramode Dispersion (SMF) The electric field of TE 0 mode extends more into the cladding as the wavelength increases. As more of the field is carried by the cladding, the group velocity increases.

a V n n n n n i = = 1/ 1 1/ 1 cladding ) ( 1 sin λ π θ λ π α V V a w o ) 1 ( + Mode Field Width w o Mode Field Width w 0

Gaussian Beam Profile

Mode Field Diameter

Profile Dispersion

! Materials Dispersion Intramode Dispersion! Waveguide Dispersion! Profile Dispersion

Polarization Dispersion

Dispersion Modified Fibers & Compensation

Nonzero Dispersion Shifted Fiber

Chromatic Dispersion

Dispersion Flattened Fiber Fiber with flattened dispersion slope (schematic) (Corning)

Commercial Fibers

Dispersion Compensation

Dispersion and Maximum Bit Rate BIT RATE CAPACITY (bits per second) B 0.5 Δτ 1/ ( bits/sec) FWHM or FWHP FWHM: Full Width at Half Maximum FWHP: Full Width at Half Power

NRZ and RTZ T Information 1 0 1 1 0 1 0 0 1 NRZ RZ Return-to-zero (RTZ) bit rate or data rate. Nonreturn to zero (NRZ) bit rate = RTZ bitrate

Maximum Bit Rate B Δτ 1 σ is Root Mean Square (RMS) deviation σ = 0.45 τ 1 Full Width Root Mean Square (rms) spread is Δt rms = σ. (The RTZ case)

Bit Rate & Bit Rate Product Maximum Bit Rate Dispersion B 0.5 σ = 0.59 Δτ 1/ Δτ 1/ L = D ch Δλ 1/ BL 0.5L σ = 0.5 D ch σ λ = 0.59 D ch Δλ 1/ ( Gb s 1 km) Bit Rate Distance BL is: inversely proportional to dispersion inversely proportional to line width of laser (so, we need narrow frequency lasers!)

Intramodal & Intermodal Dispersion B 0.5 σ = 0.59 Δτ 1/ Maximum Bit Rate σ = + σ intermodal σ intramodal ) ( ) ( ) 1 / 1/ intermodal 1/ intramodal ( Δτ = Δτ + Δτ

Optical & Electrical Bandwidth An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, f op. f op 0.75B 0.19 σ f el 0.71 f op

Pulse Shape and Maximum Bit Rate

Intermode Dispersion (MMF)

Graded Index (GRIN) Fiber

Graded Index (GRIN) Fiber B' n c c B θ B' c/n b θ B' Ray A B'' n b b O 1 θ B c/n a θ A M Ray 1 n a a O' Which ray reaches O faster??

Graded Index (GRIN) Fiber! A ray in thinly stratifed medium becomes refracted as it passes from one layer to the next upper layer with lower n and eventually its angle satisfies TIR.! In a medium where n decreases continuously the path of the ray bends continuously.

Graded Index (GRIN) Fiber n(r) = n 1 1 Δ r γ a for ρ < a n(r) = n 1 1 Δ = n for ρ > a for γ = a " parabolic profile" Minimum Intermodal Dispersion γ o (4 + δ )(3 + δ ) + δ Δ 5 + δ Profile Dispersion Parameter δ = n λ 1 dδ N g1δ dλ Minimum Intermodal Dispersion σ intermode L σ = σ intermodal Step Index Fiber n 1 0 3c Δ +σ intramodal

GRIN FIBERS Commercial Fibers SMF FIBERS

Graded Index (GRIN) Fiber & Rod Lenses NA = NA( r) = [ n( r) n ] 1/ Number of modes in a graded index fiber Effective numerical aperture for GRIN fibers NA 1/ 1/ GRIN (1/ )( n1 n ) γ V M γ + GRIN Rod Lenses Point O is on the rod face center and the lens focuses the rays onto O' on to the center of the opposite face. The rays from O on the rod face center are collimated out. O is slightly away from the rod face and the rays are collimated out.