Research On An Adaptive Algorithm For The Propagation Of Highly Chirped High-power Laser Pulses

The chirp is indispensable in ultrashort laser pulse technology. The generatedpulses often carry a big frequency chirp in practical application, in which the chipparameter reaches103104or bigger. Being one of important parameters thatmanipulate the pulse, chirp not only regulates the magnitude of pulse broadening butalso affects the shape of the self-phase modulation broadened spectrum duringpropagation. Chirped pulses have been applied extensively to many fields such asoptical fiber communication systems, population inversion or transfer, pulsecompression technique and chirped pulse amplification. A commonly used researchapproach is the time-domain beam propagation method (TD-BPM) to simulate theultrashort pulse propagation in fibers. According to the sampling theorem, the numberof sampling points for the TD-BPM varies linearly with the chirp parameter becauseof the chirp phase of chirped pulse. Therefore, too many sampling points are essentialto obtain correct numerical results for highly chirped pulse propagation. The memoryresources and run time to compute the pulse propagation increase correspondinglywith the rise of sampling points so as to reduce the computational efficiency. In thispaper, we propose an adaptive algorithm which is devoted to efficiently compute thelinear and nonlinear propagation of highly chirped high power pulses. The maincontent is summarized as follows:1. An adaptive algorithm to solve the linear propagation of highly chirped highpower laser pulses is proposed. Comparing with the TD-BPM, the new algorithm candecrease the number of sampling points by orders of magnitude to achieve the sameaccuracy. The basis of the method is to separate the chirped phase from chirped pulseso that the linear propagation of chirped pulse is transformed into the linearpropagation of the envelope without the initial chirp. The validity of the adaptivealgorithm is demonstrated both theoretically and numerically. Numerical simulationsshow that the number of samples in time necessary to simulate the chirped pulsepropagation by the TD-BPM varies linearly with the initial chirp, but that of the newalgorithm is the same one would need to simulate the propagation of the envelopewithout the initial chirp. In other words, no matter how much large is the chirpparameter, the number of sampling points for the new algorithm always maintains asmall value. 2. An adaptive algorithm to compute the nonlinear propagation of highly chirpedhigh power laser pulses is developed. Comparing with the TD-BPM, the newalgorithm not only greatly improves the computational accuracy of pulse in thevicinity of the temporal focus but also saves a lot of the computational resources. Thevalidity of the nonliear adaptive algorithm is demonstrated according to the differentshapes of the input pulse propagation. Numerical results show that the number ofsampling points required by the TD-BPM increases with increasing chirp parameterfor a given distance, while the new algorithm always keeps a small value. For a givenchirp parameter, the number of sampling points required by the TD-BPM varies withdistance, while the new algorithm always keeps a small value. Moreover, samplingpoints of the new algorithm are|f z|/ftimes those of the TD-BPM to achieve thesame accuracy, where f is the temporal focal length and z is the distance. As aresult, the closer the propagation distance is to the temporal focal length, the moreefficient the new algorithm is.