Consider a symmetric slab waveguide. The waveguide condition for propagating modes will have integer multiples of...

 

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Consider a symmetric slab waveguide. The waveguide condition for propagating modes will have integer multiples of phase with the constraints set as follows kondcos(m) 0(0m) = 2, dcos(0m) - 0(0m) = m Where, d is the core thickness, Ao is the free-space wavelength, 0(6m) is the phase change on TIR for mode m, and m = 0, 1, 2, 3 ... is an integer. The core-cladding angle of incidence is Since (m) depends on the core-cladding incident angle via the Fresnel equations, it is not possible to solve this equation directly. A) Use a graphical approach to find the core-cladding angle of incidence for the m =14 mode for TE light when d=30 m, 20 =1300 nm, n=1.58, n2=1.31. Hint: Plot (14) + 14 and 2dn cos(014) /20 on the same graph versus 0m, and the intersection of the two plots will give you the solution. sin20m- 0(0m) = 2tan-1 cos (0m) B) What are the number of modes that can travel through the waveguide? Use a graphical Approach. Assume only TE mode. Consider a symmetric slab waveguide. The waveguide condition for propagating modes will have integer multiples of phase with the constraints set as follows kondcos(m) 0(0m) = 2, dcos(0m) - 0(0m) = m Where, d is the core thickness, Ao is the free-space wavelength, 0(6m) is the phase change on TIR for mode m, and m = 0, 1, 2, 3 ... is an integer. The core-cladding angle of incidence is Since (m) depends on the core-cladding incident angle via the Fresnel equations, it is not possible to solve this equation directly. A) Use a graphical approach to find the core-cladding angle of incidence for the m =14 mode for TE light when d=30 m, 20 =1300 nm, n=1.58, n2=1.31. Hint: Plot (14) + 14 and 2dn cos(014) /20 on the same graph versus 0m, and the intersection of the two plots will give you the solution. sin20m- 0(0m) = 2tan-1 cos (0m) B) What are the number of modes that can travel through the waveguide? Use a graphical Approach. Assume only TE mode.