Three Level Systems

[Music] good morning so welcome back to introduction to photonics so we've been talking about analyzing light generation and amplification so we got to the point of looking at an example case of where we need an optical amplifier we took the example case with an optical fiber communication system and we defined this specific gain medium that is erbium

which is doped in silica as a possible gain medium to achieve amplification at 1550 nanometers why are we picking 1550 nanometers so the losses for the fiber will be very low so so that's why we are looking at that wavelength and then we are going around searching for an amplifier that can possibly or

compensate for the losses in the optical fiber during propagation and so we took the example of an erbium silica fiber amplifier odium doped fiber amplifier in short it's called EDFA and then we jumped on to understanding this amplification process itself so we looked at an elemental gain medium just involving transition between two levels

and for that sort of a medium we defined we found the gain the expression of the gain is given by exponential of gamma multiplied by the length of the amplifier where gamma itself is expressed as n into sigma where n corresponds to the in version that you can achieve so that is essentially the number of excited

ions versus the number of ions at the ground state that's n 2 minus N 1 and multiplied by Sigma where Sigma we define as the transition cross-section and we assumed that the transition cross-section is is actually equal for both the you know emission as well as the absorption right so that's how we

came up with this common term we will of course go back and question this because if you look at the absorption cross section absorption emission cross section of erbium you find that when you look at the cross section as a function of wavelength you find that the absorption cross section which is given