Generation and propagation of high-order harmonics in high-pressure gases

Generation and propagation of high-order harmonics in high-pressure (0.5--4 atm) gases by intense, ultrashort laser pulses is numerically investigated. The calculations are performed utilizing a self-consistent solution of the time-dependent Schr\"odinger and one-dimensional wave equations. The results obtained from the second-order and from the reduced first-order wave equations are compared. It is shown that at high pressure and for the high-order harmonics the use of the reduced first-order wave equation is not adequate. At very high pressure ({~}4 atm) a new regime of phase matching was observed. The applicability of the reduced first-order wave equation is also discussed.