超快光学 第03章 脉冲(1.ppt

The Negatively Chirped Pulse We have been considering a pulse whose frequency increases linearly with time: a positively chirped pulse. One can also have a negatively chirped (Gaussian) pulse, whose instantaneous frequency decreases with time. We simply allow b to be negative in the expression for the pulse: And the instantaneous frequency will decrease with time: Ultrashort Laser Pulses I Description of pulses Intensity and phase The instantaneous frequency and group delay Zeroth and first-order phase The linearly chirped Gaussian pulse Prof. Rick Trebino Georgia Tech An ultrashort laser pulse has an intensity and phase vs. time. Neglecting the spatial dependence for now, the pulse electric field is given by: Intensity Phase Carrier frequency A sharply peaked function for the intensity yields an ultrashort pulse. The phase tells us the color evolution of the pulse in time. Electric field E (t) Time [fs] The real and complex pulse amplitudes Removing the 1/2, the c.c., and the exponential factor with the carrier frequency yields the complex amplitude, E(t), of the pulse: This removes the rapidly varying part of the pulse electric field and yields a complex quantity, which is actually easier to calculate with. is often called the real amplitude, A(t), of the pulse. Electric field E (t) Time [fs] The Gaussian pulse where tHW1/e is the field half-width-half-maximum, and tFWHM is the intensity full-width-half-maximum. The intensity is: For almost all calculations, a good first approximation for any ultrashort pulse is the Gaussian pulse (with zero phase). Intensity vs. amplitude The intensity of a Gaussian pulse is √2 shorter than its real amplitude. This factor varies from pulse shape to pulse shape. The phase of this pulse is constant, ?(t) = 0, and is not plotted. It’s easy to go back and forth between the electric field and the intensity and phase: The intensity: Calculating the intensity and the phase f(t) = - Im{ln[E(t)]} The phase: Equivale