1. 16.711 Lecture 4 Optical fibers Last Lecture Fiber modes Fiber Losses Dispersion in single-mode fibers Dispersion induced limitations Dispersion management The Graded index fibers

2. 16.711 Lecture 4 Mode-coupling Today Mode–coupling 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

3. 16.711 Lecture 4 Mode-coupling Why knowledge of mode coupling is important? Mode–coupling theory 1.DFB Lasers/DBR Lasers 2.VCSEL structure 3.March-Zehnder interferometer 4.Direction coupler 5.Optimized device structures

4. 16.711 Lecture 4 Mode-coupling Recall mode equations Mode–coupling theory TE Mode: Notice: Mode profile E(x, y) doesn’t change with z if no index perturbation. No coupling between different modes if no index perturbation.

5. 16.711 Lecture 4 Mode-coupling index perturbations Mode–coupling theory Generalized propagation equation

6. 16.711 Lecture 4 Mode-coupling Mode–coupling equation perturbation theory, TE mode

7. 16.711 Lecture 4 Mode-coupling discussion of the mode-coupling equation 1.if no index perturbation, A(z) is an constant, goes back to the normal equation. 2.Cn measures how much the index perturbation changes the propagation constant  n. 3.If index perturbation doesn’t vary with z, coupling between the mode depends on the.

8. 16.711 Lecture 4 Mode-coupling directional coupler

9. 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.

10. 16.711 Lecture 4 Mode-coupling directional coupler --- Applications (1) Signal switch (2) WDM coupler

11. 16.711 Lecture 4 Mode-coupling (2) if Application: Y modulator

12. 16.711 Lecture 4 Mode-coupling Phase-mismatched directional coupler General solution E10 =1, E20=0:

13. 16.711 Lecture 4 Mode-coupling Distributed Bragg Reflective (DBR) Structure Mode–coupling equation

14. 16.711 Lecture 4 Mode-coupling Distributed Bragg Reflective (DBR) Structure Small variations Phase matching condition:

15. 16.711 Lecture 4 Mode-coupling General solution Phase matching condition:

16. 16.711 Lecture 4 Mode-coupling Example General Phase matching condition: Grating assistant coupling:

17. 16.711 Lecture 4 Mode-coupling Phase mismatched Bragg Mirror Phase mismatching is related to wavelength,  wavelength sensitive mirror.

18. 16.711 Lecture 4 Mode-coupling Coupling between guided and unguided modes (a) prism coupling (b) grating assisted coupling (c) end-fired coupling

19. 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.

20. 16.711 Lecture 4 Mode-coupling Coupling form waveguide to Free-space Model coupling by scattering:

21. 16.711 Lecture 4 Mode-coupling Coupling to radiating modes at waveguide bends Example: