ИНСТИТУТ ПО ЕЛЕКТРОНИКА НА БАН 

ЛАБОРАТОРИЯ НЕЛИНЕЙНА И ВЛАКНЕСТА ОПТИКА 



НАУЧНОИЗСЛЕДОВАТЕЛСКА ДЕЙНОСТ
1. Diffraction of phasemodulated broadband femtosecond pulsesIn recent years the linear regime of propagation of optical pulses with broadband spectrum in air and transparent media attracts a considerable attention. The attosecond pulses in UV region as well as femtosecond pulses with time duration 515 fs in optical and IR region admit from one to several optical cycles under their envelopes. For such pulses, as it was pointed in [1], the diffraction is not paraxial and on few diffraction lengths their shape takes parabolic form. In the theory developed in [2, 3] it is shown that the nonparaxiality depends on the spectral width Δκ_{z}=Δω/ν_{gr} of the pulse. Thus, one additional possibility appears: Is it possible to use phasemodulated broadband femtosecond pulses with many cycles under their envelope to obtain Fraunhofer type diffraction? In this paper we will numerically investigate Fraunhofer type diffraction of phasemodulated 25 fs laser pulses which admit at least 10 cycles at level e^{1} of the maximum. This study gives us knowledge about the limits and applicability of paraxiality in the frames of femtosecond optics. The linear scalar nonparaxial amplitude equation, governing the evolution of laser pulses in isotropic dispersive media, is written in Local type coordinates [4]:
where A(x,y,τ,z) is the slowly varying amplitude function of the pulse envelope, ν is the group velocity, β=κ_{0}ν^{2}_{gr}κ" is a parameter characterizing the second order of linear dispersion of the medium, z = z and τ=tz/ν.The last two terms in Eq.(1) are called nonparaxial terms, because the rest part gives paraxial spatiotemporal optics. This equation can be solved by using the Fourier method. We studied the evolution of phasemodulated 25 fs laser pulses with a Gaussian spatiotemporal profile in air. The initial condition for numerical investigation of equation (1) is:
where r_{0} is the transverse size (the spot of the pulse), τ_{0} is the temporal size and b=1+ia is a complex number, where a is the linear frequency modulation (chirp of the pulse). Our numerical results have shown that:
In our investigations we have shown that the Fraunhofer type diffraction is not a characteristic only to attosecond or femtosecond pulses with one or few optical cycles under the envelope. There are different methods to obtain broadband laser pulses with many cycles under the envelope. For examples: nonlinear selfphase modulation, optical grating etc. We demonstrated that even in the case of phasemodulated femtosecond pulses with many cycles under the envelope Fraunhofer type diffraction can be observed in the experiments.
2. Optimization of the regime of selfcompression for fs pulses in silica and airOne of the main task of modern laser physics is to obtain ultra short laser pulses. There are different optical schemes for selfcompression based on pair diffraction grating or other optical elements during propagation of pulses in linear regime. The shortening of pulse can be obtained also by using nonlinear mechanisms such as phase selfmodulation (PSM), when a pulse reaches critical power for nonlinear regime in dispersion mediums. The most efficient schemes for compression require carful analyse for collection of possibly optical elements, linear and nonlinear effects to obtain maximal compression. We examine by numerical simulations two different mechanisms for selfcompression of femtosecond pulses in fused silica and air. In the first case we consider selfcompression of a laser pulse during its nonlinear propagation in the anomalous dispersion region of a glass. The numerical experiments are performed for pulses with time duration 100 fs at wavelength 800 nm. In the second case we considered compression of initial chirped 25 fs pulse. Our numerical results show, that after only one pass trough optical diffraction grating the chirped pulse selfcompress in nonlinear regime and obtain X wave deformation. Investigated of propagation of phasemodulated femtosecond pulses with the use of the lens as a phase corrector provides substantially different dynamic depending on the dispersion and coefficient of nonlinearity. It appears that during the evolution of the pulse in a medium with normal linear dispersion, initially shows a strong focusing, and is then diffracted at several diffraction lengths. In case of anomalous dispersion the pulse is compressed significantly. During the evolution of a pulse in a medium with a positive linear dispersion, we initially observe a self  focusing. After the focus of the lens, the paraxiality of the diffraction is preserved and the pulse diffracted in several diffraction lengths without wave front distortion. The propagation in a medium with negative dispersion the initial phase modulation increases the compression of the pulse. Numerical modelling of the optical pulses in a nonlinear regime of propagation with initial phase modulation caused by different optical elements has important application in the modern optical engineering.



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