It is shown that, variation of the sign and size of the chirp coefficient (C) of the pulse has considerable effect on spectral properties of the pulse and the effect is closely relative to size of the pulse area. When the pulse with smaller area, 2π pulse, propagates in the medium, pulse splitting doesn't occur and the pulse evolves gradually to an approximate normal Gaussian pulse (C=0); new high frequency component doesn't basically appear; with increasing value of C, oscillation amplitude of blue shift and red shift components increases and blue shift component oscillates more severely; moreover, the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component increases obviously. When the 4π pulse propagates in the medium, the pulse will split into sub-pulses with different numbers and shapes, new high frequency component can be produced, but the strength of the high frequency component is smaller; similar to the case of 2π pulse, blue shift component oscillates more severely; in addition, the strength of the spectral component with higher frequency decreases evidently with increasing value of C. When the pulse with larger area, 8π pulse, propagates in the medium, the pulse splitting is similar to that in the 4π pulse case, but supercontinuum spectrum with larger strength, higher frequency and wider frequency range than that in the 4π pulse case can be obtained; varying the sign and size of C can not produce new high frequency component, but can change strength of different frequency components in the spectrum, thus can get high frequency components with higher strength
It is shown that, variation of the sign and size of the chirp coefficient (C) of the pulse has considerable effect on spectral properties of the pulse and the effect is closely relative to size of the pulse area. When the pulse with smaller area, 2π pulse, propagates in the medium, pulse splitting doesn't occur and the pulse evolves gradually to an approximate normal Gaussian pulse (C=0); new high frequency component doesn't basically appear; with increasing value of C, oscillation amplitude of blue shift and red shift components increases and blue shift component oscillates more severely; moreover, the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component increases obviously. When the 4π pulse propagates in the medium, the pulse will split into sub-pulses with different numbers and shapes, new high frequency component can be produced, but the strength of the high frequency component is smaller; similar to the case of 2π pulse, blue shift component oscillates more severely; in addition, the strength of the spectral component with higher frequency decreases evidently with increasing value of C. When the pulse with larger area, 8π pulse, propagates in the medium, the pulse splitting is similar to that in the 4π pulse case, but supercontinuum spectrum with larger strength, higher frequency and wider frequency range than that in the 4π pulse case can be obtained; varying the sign and size of C can not produce new high frequency component, but can change strength of different frequency components in the spectrum, thus can get high frequency components with higher strength
We investigate propagation of femtosecond chirped Gaussian laser pulse in a dense three-level Λ-type atomic medium by using the numerical solution of the full Maxwell-Bloch equations without the slowly varying envelope and the rotating-wave approximations, and the solution is obtained by PC-FDTD method. It is shown that, variation of the sign and size of the chirp coefficient has considerable effect on pulse propagation property, and the effect is closely relative to size of the pulse area. When the area of chirped pulse is smaller than 4π, splitting doesn’t occur and the chirped pulse evolves gradually to an approximate normal Gaussian pulse (C=0), and this characteristic doesn’t vary with the chirp coefficient varying. However, variation of the chirp coefficient will changed the amplitude and group velocity of the pulse. For the positive chirp(C>0), amplitude and group velocity of the pulse decrease with chirp coefficient increasing, for the negative chirp(CC increasing. Both the chirped pulses with area equal to larger than 4π will split into sub-pulses of different numbers and shapes, the time and number of the pulse splitting will be determined by the sign and size of the chirp coefficient. But in the two cases, the pulse splitting patterns are much different, and the effects of the coefficient are also different. When the pulse area equals 4π, larger chirp coefficient will lead to increased sub-pulse number, but when the pulse area is larger than 4π, larger chirp coefficient will lead to decreased sub-pulse number. In addition, regardless of pulse area being larger or smaller, changing sign and size of the chirp coefficient always produces obvious effect on the atomic population.
The interference resonant propagation and spectral properties of a superposition of two femtosecond chirped Gaussian pulses with equal pulse area and same size but opposite sign of the chirp coefficient (C) in a three-level Λ-type atomic medium is investigated by using the numerical solution, which is obtained by the finite-difference time-domain (FDTD) method and the iterative predictor–corrector (PC) method for the full Maxwell–Bloch equations. It is found that, for the double pulses with smaller area, (2π, 2π) double pulses, the pulse splitting occurs when the value of the |C| is smaller, and only the variation of pulse shape is present but the pulse splitting no longer occur when the value of the |C| increases to a certain value; New high frequency component doesn’t basically appear and the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component is not varied obviously with the value of |C| increasing. For the double pulses with larger areas, the case of pulse splitting is similar to that of (2π, 2π) pulses, but the strength of the spectral component with higher frequency increase evidently comparing with the case of (2π, 2π) double pulses. Moreover, the value of the |C| also has an obvious effect on population, different population evolutions can be achieved by adjusting the value of |C|.
We theoretically investigate the effect of the atomic densities N on propagation and spectral property of femtosecond chirped Gaussian pulse in a three-level Λ-type atomic medium by using the numerical solution of the full Maxwell- Bloch equations. It is shown that, when the positive chirped pulse with area 3π, propagate in the medium with smaller N, pulse splitting doesn’t occur and many small oscillations at the trailing edge of the pulse appear, in addition, the level |2< population ρ22 of the pulse exhibits an oscillation feature with time evolution, moreover, the spectral component near the central frequency of the pulse shows an oscillation characteristic too, and the propagation and spectral property of the negative chirped 3π pulse is very similar to that of the positive chirped 3π pulse. For the positive chirped 3π pulse pulses, propagate in the medium with larger N, pulse splitting also doesn’t occur but many small oscillations both at leading edge and the trailing edge of the pulse appear, and the population ρ22 of the pulse only exhibits an scarcely oscillation feature with time evolution, at the same time many oscillations both in blue shift and red shift components of the pulse appear but the spectral component near the central frequency of the pulse oscillate more severely, and the propagation and spectral property of the negative chirped 3π pulse is very similar to that of the positive chirped 3π pulse, but comparing with the case of the negative chirped 3π pulse, the propagation of the positive chirped 3π pulse is delayed at the same distance and the delayed time becomes longer with the distance increasing.
We investigate effect of atomic densities (N) on propagation and spectral property of large area femtosecond Gaussian pulse (the pulse area is larger than 2π) in a three-level Λ-type atomic medium by using the numerical solution of the full Maxwell-Bloch equations without the slowly varying envelope and the rotating-wave approximations, and the solution is obtained by PC-FDTD method. It is shown that, variation of value of the atomic density has considerable effect on propagation and spectral property and the effect is closely relative to size of the pulse area. For the pulse with area 4π, propagate in the dilute medium with smaller atomic density, clear pulse splitting doesn’t occur, slight pulse spectrum broadening appears, the strength of the spectral component with higher frequency increases with the distance increasing; when the pulse propagates in the dilute medium with larger atomic density and in the dense medium, the main pulse splits into two sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much larger than that in the dense medium. For the pulse with larger area 8π, the case of the pulse propagates in the dilute medium with smaller atomic density is similar to that of the 4π pulse; but when the pulse propagates in the dilute medium with larger atomic density and in the dense medium, the case is considerably different from that for 4π pulse, the main pulse splits into three sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much smaller than that in the dense medium.
We investigate effect of atomic densities( N) on propagation and spectral property of femtosecond Gaussian pulses in a three-level Λ- type atomic medium by using numerical solution of full Maxwell-Bloch equations. It is shown that,for pulses with smaller area 2π,propagate in mediums with different N,pulse splitting does not occur and strength of spectral component near central frequency decreases considerably as N increases. For pulses with area 4π,pulse splitting could occur when pulses propagate in dilute medium with greater atomic density and in dense medium,and pulse spectral bandwidth and strength of spectral component with higher frequency increase with increasing of N in dilute medium. Spectrum broadening in dense medium is much smaller than that in dilute medium with greater atomic density. For pulses with larger area 8π,pulse splitting is similar to that of 4π pulses. Pulse spectral bandwidth and strength of spectral component with higher frequency increase monotonously with increasing of N. And spectrum broadening in dense medium is much larger than that in dilute medium with smaller atomic density.
By the numerical analyzing and simulation, we investigate effect of carrier envelope phase on propagation of femtosecond chirped Gaussian laser pulse in a dense three-level Λ-type atomic medium. It is shown that, when the small area 2π negative chirped pulses (or the 2π positive chirped pulses) with different value of initial carrier envelope phase φ0 propagate in the medium, splitting don’t occur and the chirped pulses evolve gradually to approximate normal Gaussian pulses with equal amplitude and group velocity, and the phase differences between them remain the same as the case of initial input pulses. When the 4π negative chirped pulses with different φ0 propagate in the medium, the pulses will split into at least two sub-pulses and the amplitude of the first sub-pulse is far more than the second sub-pulse; These first sub-pulses have equal amplitudes and propagating with equal group velocity in the medium, and the phase differences between these first sub-pulses remain the same as the case of initial input pulses; The amplitudes of these second sub-pulses are not equal and don’t change monotonously with linearly increasing of φ0 but take on a invert S-shaped pattern, and the phase differences between these second sub-pulses are different. The case of 4π positive chirped pulses is similar to the case of 4π negative chirped pulses, but the amplitudes of these second sub-pulses split off from the 4π positive chirped pulses have no obvious changes compared with the case of 4π negative chirped pulses.