The propagation properties of the chirped Gaussian pulse through gain-dispersion medium are studied by using the definition of complex wave number and the method of diffraction integral.The analytical expressions for the spectrum distribution and the temporal-spatial distribution of the chirped Gaussian pulse are given for the case of the gain-spectrum of Lorentzian distribution.The propagation properties,such as the spectrum distribution,temporal-spatial distribution,variations of the pulse width and the spectrum width,as well as the spectrum shift,etc,were analyzed in detail.It is shown that the pulse still keeps the Gaussian shape in temporal domain when the chirped Gaussian pulse propagates in the gain-dispersion medium,whereas the pulse will undergo the variation of the pulse width.During the propagation,the decrease of the spectrum width and the spectrum shift can be influenced by the chirped parameter.The larger the chirped parameter is,the more obvious the effects of broadening of pulse width and compression of spectrum width are.Furthermore,the spectrum shift increases with the propagation distance.For the given chirped parameter,the spectrum shift will tend to be a constant along the propagation distance.
The propagation properties of the chirped Gaussian pulse through gain-dispersion medium are studied by using the definition of complex wave number and the method of diffraction integral.The analytical expressions for the spectrum distribution and the temporal-spatial distribution of the chirped Gaussian pulse are given for the case of the gain-spectrum of Lorentzian distribution.The propagation properties,such as the spectrum distribution,temporal-spatial distribution,variations of the pulse width and the spectrum width,as well as the spectrum shift,etc,were analyzed in detail.It is shown that the pulse still keeps the Gaussian shape in temporal domain when the chirped Gaussian pulse propagates in the gain-dispersion medium,whereas the pulse will undergo the variation of the pulse width.During the propagation,the decrease of the spectrum width and the spectrum shift can be influenced by the chirped parameter.The larger the chirped parameter is,the more obvious the effects of broadening of pulse width and compression of spectrum width are.Furthermore,the spectrum shift increases with the propagation distance.For the given chirped parameter,the spectrum shift will tend to be a constant along the propagation distance.
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.
Introduced the main reason of optical pulse spreading in the slow light medium.Assuming a chirped Gaussian input signal pulse,this paper deduced the analytical expression of the output-pulse amplitude envelope,the pulse delay and the broadening factor in the slow light system with a broadband and rectangular Brillouin spectrum under lossless medium and small signal gain approximation.The influence of pump bandwidth and other factors between pulse delay and chirp parameter has been quantitatively analyzed.Simulation results show that adding initial chirp in Gaussian pulse can reduce the pulse broadening.
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.
An asymptotic approach is utilized in order to obtain a unified description of the propagated field dynamics due to an input Gaussian-modulated harmonic wave of arbitrary initial pulse width in a linear, causally dispersive gain medium, described by the single resonance Lorentz model. The asymptotic method of analysis is applied on the unified, exact integral representation of the propagated field, which is characterized by a unified complex phase function that depends upon the input field and gain medium parameters as well as upon the propagation distance in the medium. In order to apply the asymptotic method, an analysis of the evolution of the saddle point locations, which depend upon the dispersive properties of the gain medium, the temporal width, and the carrier frequency of the input Gaussian pulse as well as upon the propagation distance and of the topography of the real part of the unified phase function in the complex ω plane, must be performed. Upon the subsequent numerical application of the asymptotic method, the predictions of the unified asymptotic approach are found to be in exceptional agreement with the respective results of a purely numerical experiment for all considered initial pulse widths and lead to a unified model of Gaussian pulse propagation in a gain Lorentzian medium. According to this model, the propagated field is composed of pulse components, each being due to the asymptotic contribution of a respective relevant saddle point of the unified phase function. The instantaneous angular frequency of oscillation and the stationary point(s) of the envelope of each such pulse component are then obtained from the real and imaginary parts, respectively, of the corresponding relevant saddle point as it evolves in the complex ω plane. This theoretical approach may then yield particularly useful physical insights into attosecond pulse propagation.
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|.