Why does interference does not happen in optical fiber?

Interference in metal wires occurs due to production of magnetic fields by the metal (which produce currents in the metal) due to time varying electrical signals through them. The signal can also be distorted by the presence of electric/magnetic fields close to the wire. read more

When external electromagnetic fields act on a conductive material, they impact the electron transport and so cause interference with the actual signals which are being carried by the medium. Since optical fiber is made up of glass which is non-conductive, the EM interference does not occur. read more

I guess you are referring to optical fiber transmission. In this case light wave is guided by the fiber and no interference occurs with outside signals. However, the main advantages of optical fiber communication over electrical cable transmission is its high bandwidth capability and extremely low loss at two specific wavelengths 1.3 um and 1.55 um. read more

Electromagnetic Interference does occur in coaxial cables, since current does cut across the conductor. Fiber optics are immune to this EMI since signals are transmitted as light instead of current. Thus, they can carry signals through places where EMI would block transmission. read more