# 16.711 Lecture 4 Optical fibers Last Lecture Fiber modes Fiber Losses Dispersion in single-mode fibers Dispersion induced limitations Dispersion management

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• 16.711 Lecture 4 Optical fibersLast Lecture Fiber modes Fiber Losses Dispersion in single-mode fibers Dispersion induced limitations Dispersion management The Graded index fibers

• 16.711 Lecture 4 Mode-couplingToday Modecoupling theory Directional coupler Coupling between guided and un-guided modes Coupling from waveguide to free space Mode coupling by scattering Coupling to radiating modes at waveguide bands

• 16.711 Lecture 4 Mode-coupling Why knowledge of mode coupling is important?Modecoupling theoryDFB Lasers/DBR LasersVCSEL structureMarch-Zehnder interferometerDirection couplerOptimized device structures

• 16.711 Lecture 4 Mode-coupling Recall mode equationsModecoupling theory TE Mode: Notice: Mode profile E(x, y) doesnt change with z if no index perturbation. No coupling between different modes if no index perturbation.

• 16.711 Lecture 4 Mode-coupling index perturbationsModecoupling theory Generalized propagation equation

• 16.711 Lecture 4 Mode-couplingModecoupling equation perturbation theory, TE mode

• 16.711 Lecture 4 Mode-coupling discussion of the mode-coupling equationif no index perturbation, A(z) is an constant, goes back to the normal equation.Cn measures how much the index perturbation changes the propagation constant n.If index perturbation doesnt vary with z, coupling between the mode depends on the .

• 16.711 Lecture 4 Mode-coupling directional coupler

• 16.711 Lecture 4 Mode-coupling directional coupler --- solution of the differential equation set(1) E2(z=0) =0: Output field power is half of the exciting waves. the field of the unexcited waveguide is delayed by /2 with respect to the exciting wave.

• 16.711 Lecture 4 Mode-coupling directional coupler --- Applications(1) Signal switch (2) WDM coupler

• 16.711 Lecture 4 Mode-coupling(2) if Application: Y modulator

• 16.711 Lecture 4 Mode-coupling Phase-mismatched directional coupler General solution E10 =1, E20=0:

• 16.711 Lecture 4 Mode-coupling Distributed Bragg Reflective (DBR) Structure Modecoupling equation

• 16.711 Lecture 4 Mode-coupling Distributed Bragg Reflective (DBR) Structure Small variationsPhase matching condition:

• 16.711 Lecture 4 Mode-coupling General solutionPhase matching condition:

• 16.711 Lecture 4 Mode-coupling ExampleGeneral Phase matching condition:Grating assistant coupling:

• 16.711 Lecture 4 Mode-coupling Phase mismatched Bragg MirrorPhase mismatching is related to wavelength, wavelength sensitive mirror.

• 16.711 Lecture 4 Mode-coupling Coupling between guided and unguided modes (a) prism coupling (b) grating assisted coupling (c) end-fired coupling

• 16.711 Lecture 4 Mode-coupling end-fired coupling Coupling efficiency: fm(x) is the outgoing guided mode profile, and fg(x) is the incoming waveguide excited mode profile.

• 16.711 Lecture 4 Mode-coupling Coupling form waveguide to Free-space Model coupling by scattering:

• 16.711 Lecture 4 Mode-coupling Coupling to radiating modes at waveguide bends Example:

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