Slots in patch antenna

1. What is the purpose of include slot in patch antenna?
2. What is the difference between the u,e,s,w and l slots in patch antenna?
3. Any formulas to calculate the length and width of slots

making slots in the patch can have many many purpose.
slots can be used be for getting Notch band, slots can be used for getting High gain and slots can be used for getting High Bandwidth also.
Different alphabetical shapes of slots can give you different enhancement in parameters.
I dont think there is any such formula to calculate the length and width.