how do we transmit electromagnetic waves throug a cylinderical waveguid?

Answer 1

A waveguide may be either conductive or dielectric. Fiber optic cables are a good example of a dielectric waveguide. Conductive (metallic) waveguides are often used with microwave energy. The walls of the waveguide must be reflective at the wavelength(s) being used or energy will be absorbed. Dielectric waveguides achieve this by using a cladding with a lower refractive index than the core, providing total internal reflection.

Waveguides can be either single-mode or multimode. In a single-mode waveguide, there is only a single solution (or two, if you count polarization) to Maxwell's equations at the wavelength being used. Multimode waveguides support multiple standing wave patterns. Multimode waveguides that support large numbers of modes can be analyzed using ray optics.