Chirp-dispersion management inducing regeneration of truncated Airypulses in fiber optics links
Crépin Heuteu, Lucien Mandeng Mandeng, Clément Tchawoua
Abstract
In this paper, we introduce another technique of Airy pulse regeneration in fiber links using the interaction between group velocity dispersion (GVD) and the initial value of frequency chirp. This technique of regeneration consists of managing the product of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> <mml:mi mathvariant="normal">D</mml:mi> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">c</mml:mi> <mml:mi mathvariant="normal">h</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:math> over each piece <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>…</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> of fiber line having <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> pieces in the case of zero-third-order dispersion (TOD) systems. This work follows [ Phys. Rev. A 89 , 043817 ( 2014 ) PLRAAN 1050-2947 10.1103/PhysRevA.89.043817 ], which studied the nonzero-TOD system. Three models are considered: the first consists of alternation of the GVD with the chirp being constant, the second consists of alternation of the chirp with a constant GVD, and the third consists of the alternation of both parameters. Through the numerical results obtained in the linear optical system, we show that the first model with an initial condition corresponding to the asymmetric inversion (A.I.) mechanism, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">V</mml:mi> <mml:mi mathvariant="normal">D</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">c</mml:mi> <mml:mi mathvariant="normal">h</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:mrow> <mml:mo><</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0</mml:mn> </mml:mrow> </mml:mrow> </mml:math> , is the best at yielding interesting regeneration for both a single finite energy Airy pulse (FEAP) and for the symmetric FEAPs previously defined in [ Opt. Commun. 399 , 16 ( 2017 ) OPCOB8 0030-4018 10.1016/j.optcom.2017.04.064 ]. There is a need to achieve the A.I. mechanism on each piece of fiber through the condition <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>s</mml:mi> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>C</mml:mi> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> </mml:msup> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> </mml:math> , where the GVD sign <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>s</mml:mi> </mml:math> alternates and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>C</mml:mi> <mml:mi class="MJX-variant" mathvariant="normal">′</mml:mi> </mml:msup> </mml:math> is the intrinsic chirp developed by the pulse itself within the current piece <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:mrow> </mml:math> before its injection into the next piece <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>i</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . The main parameter that is beneficial for this kind of chirp-dispersion management (CDM) regeneration of FEAPs in fiber links is found to be the initial chirp whose dimensionless optimal absolute value is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>C</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>1</mml:mn> <mml:mo>;</mml:mo> <mml:mn>3</mml:mn> <mml:mo stretchy="false">]</mml:mo> </mml:math> in order to combine the quality and good intensity. In contrast, the temporal gap <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>τ</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:mrow> </mml:math> and nonlinearity have a deleterious impact on regeneration. Moreover, the noise in the regeneration originates from the alternation of the chirp, the simultaneous alternation of both the GVD and the chirp, the drastic increase in chirp, and nonlinearity.