Question 1 - (a) A planar waveguide has refractive indices n₁ = 3.60, n₂ = 3.30, and thickness d = 7.50 μm. If light of free-space wavelength 1.50 μm is coupled into the waveguide, how many TE modes can propagate?

(b) What will be θ, n_eff and β for m = 3.

(c) Sketch E(x) for m = 3.

(d) Calculate v_p (phase velocity) and v_g for m = 3.

(e) If d is made variable, then in what range of d will modes with m = 3 exist?

Question 2 - (a) A step index fiber has core index n₁ = 1.49 and Δ = 0.02, and is single-mode only for free-space wavelengths λ > 1.25 μm. Determine the radius of the fiber core.

(b) The same fiber is used with a signal wavelength of 1.7 μm. Determine n_eff and β for the fiber mode.

(c) For the same fiber and wavelength

I- Determine the mode field diameter and

II- Determine the radial distance from the fiber axis at which the light intensity is reduced to 5% of the peak (on-axis) value.