Question

Electromagnetic waves propagating between boundaries -wave guides.

Please answer step by step

(b) Assuming in a symmetric step-index planar waveguide, the guide layer has a refractive index ni and the cladding slabs have a refractive index n2, Both ni and n2 are constant (independent of wavelength), and ni >n2. Derive equations, logic steps and draw plots that determine the propagation modes (TE and TM) in the guide

Answer 1

dt dt dt dt ot О"H

ncu) nfini z is diuctn of pn pagation dl 2 Hx, H and E CTE) Hy, Ex and Ez (Tm) Hy wlo ox dx 2 whnu@sJual Pepagatan c、nolant

2. JX

n(x) a2E rn 2 2 Modes β2 < k ng < kẵn Oscillating | Oscillating | Radiating KẾng < β2 < k辧 Oscillating | Exponential | Guided | Gn < kän < β21 Exponential | Exponential O solution kfn β<< kónf Guidance condition ﹀ \ NB Guided and radiating modes form a complete basis on which we can decompose any propagative field

Graphic solution for the existence of TE modes Symmetrical modes (even #) mode mode mode mode f(u) Antisymmetrical modes (odd #) : V 9 V 5 V 1 2 2 0 π/2 π 3π/22m

The guided TM modes TO DO X < 2 2,2 2 Continuity of H,(r) and H, Symmetrical TM Modes Antisymmetrical TM Modes 2