Education of the republic of uzbekistan tashkent state technical university named after islam karimov

UDK 535:530.182 
 
NUMERICAL EXPERIMENT OVER THE OPTICAL PARAMETRIC 
AMPLIFICATION OF SHORT LASER PULSES IN CRYSTALS WITH REGULAR 
DOMAIN STRUCTURES UNDER SELF-ACTION CONDITIONS 
 
U.K. Sapaev 
1
*, O.I. Sabirov
1
, N.A. Akbarova
1
, N.Sh. Matyakubov
2 
1
Tashkent State Technical University named after I. Karimov, 100095, Tashkent, Uzbekistan 
2
Department of Chemical and Biological Engineering, Jeju National University, 
Jeju 63243, Republic of Korea 
 
Abstract. 
Despite the many types of frequency conversion processes, parametric amplification 
of light plays an important role in nonlinear optics and laser technology. This nonlinear optical 

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Electrical and Computer Engineering
175 
process is below studied numerically. The process of optical parametric amplification of short 
laser pulses in nonlinear photonic crystals under conditions of non-stationarity and self-action 
is numerically analyzed. The process was analyzed considering the dispersion of the medium 
up to the third order and nonlinear susceptibilities of the third order. On the basis of the 
obtained results, the optimal conditions under which the maximum efficiency of this nonlinear 
optical process can be achieved are analyzed. Numerical experiment was carried out for the 
pump, signal and idler wave wavelengths
1
3, 4
m



, 
3
1,064
m



and 
2
1,5486
m



, 
correspondingly. While pulse durations of the pump and signal waves were chosen for three 
different cases:
100
fs


,
50
fs


 and
20
fs


. It was shown that signal wave efficiency is 
increased despite of the influences of the Kerr nonlinearities and dispersions of the nonlinear 
lattice. Maximum efficiency conversion of the signal wave was calculated 25 %, 18% and 3 % 
for pulse durations
100
fs


,
50
fs


and, 
20
fs


correspondingly. Our numerical 
approach was based on the Runge- Kutta method of the 4
th
order and the fast Fourier 
transform method. The last one was used to analyze the influence of the dispersion of the 
medium, while the Runge-Kutta method – second and third order nonlinear coupling of the 
wave interactions. To keep high accuracy of the numerical method of calculation, a method of 
the symmetric scheme of the steps along the nonlinear and linear parts of the Maxell equations 
was used.