Advanced physics

7. A round trip phase requirement means that, after a round trip inside a resonator, the beam has to have the same phase as in the beginning. In essence, for a laser beam inside a resonator of length L, this may be written as: ( 32) - 0(21) = 97. where q is any integer, z and z are the positions of the two mirrors. (a) Considering only the on axis portion of the laser beam (no loss of generality), show that this condition leads to the following relation for the longitudinal wave-numbers: kat1 - kq =