Need some assistance in solving the following problem set. Please also provide schematic if possible. Thank you in advance!

Please explain how one can design a cavity with single mode waveguide for such a laser. No

calculations are needed. You can provide a schematic of the laser cavity $(3$ pts $)$ and explain

your method to obtain the single waveguide structure $(3$ pts $).$

Given the band diagram for the laser in operation as shown below, please explain how to

realize gain for lasing. $(6$ pts$)$

After the laser is made, your advisor would like you to modify the structure to realize a light

emitting diode around $1\mathrm{.}5\backslash$mu m$1\mathrm{.}5\backslash$mu m$.$ Hint: for

simplicity, you can use the waveguide mode index to calculate the reflection at the

interfaces between different materials