1. 1. Thermo-optic switch based on total internal reflection
The refractive index n1 of the waveguide is The material has the temperature effect:
If we want effective switch at T = 30K what’s the  angle between the two waveguides?

2. 2. Array waveguide grating (AWG)L0
L0 +(m-1)L D d
The refractive index of the waveguide is Nc=1.459, and the refractive index of the slab is ns= D = 250µm, and d = 50µm. The wavelength  =1.5µm. What’s the length increment L if we want the AWG has the resolution of 1nm. f = 1cm

3. 3. Splitter
 = 100µm-1 1 3
For A1(0) = A1, A2(0) =0
A1(z)
A2(z)
Un-connected port 4
What’s the coupling length needed to have 20% splitting ratio?

4. 4. Waveguide gratings
A1(z)|z=0 = A1(0)
A1(z)
 = 100µm-1
A2(z) )|z=L = 0
A2(z)
What’s the length of the grating needed to achieve 98% reflections?