Relationship between carrier phase and energy of single cycle pulses with different profiles

Dependence of energy of single cycle pulses on the carrier phase has been studied for Gaussina,Lorentzian,hyperbolic secant and sinc pulses.For the above mentioned symmetric profiles,analytical functions termed F's,varying with the ratio of the envelop width Tp to cycle period T0,have been introduced and deduced to quantify the effect of the carrier phase on the pulse energy.Based on the derived analytical expressions of F's,detailed descriptions of the pulse energy variations have been presented.