I NTRODUCTION
1.2 Outline of the Thesis
inside a nonlinear directional coupler [48]. Also, for an all-optical switching device with lower critical power and shorter device length, the requirement of ultrashort pulse con- sequently necessitates the inclusion of third-order dispersion. Additionally, a nonlinear directional coupler, made of two fibers coupled together or a fiber with dual core, acts as a bimodal device which supports a linear combination of symmetric and antisymmetric modes, each with different propagation constants. The different group delay between these two modes during propagation along the coupler length leads to intermodal disper- sion. In the coupled mode theory, this group delay between the modes is analogous to the coupling-coefficient dispersion. Previously it has been reported that both third-order dispersion and intermodal dispersion have no effect on dark soliton [48,49,50] but they have considerable influence on bright soliton propagation inside a conventional coupler [51,52,53,54,55,56]. In the presence of such dispersive coupling, a new kind of dark soliton has been introduced in a dual-core coupler [57]. Intrigued by the steady nature of the dark soliton, in this thesis, we study the steering dynamics of the dark soliton in P T-symmetric couplers and investigate if P T symmetry amplifies the effect of third-order and intermodal dispersions.
1.2 Outline of the Thesis
In the following, we present a more elaborate plan of the thesis by including a description of the various problems that have been addressed, in the form of different chapters of the thesis. There are a total of six chapters.
Chapter 1: already provides the introduction to the thesis, where the background and motivation for the work is outlined. It also contains the literature review and report of the recent developments in the field ofP T symmetry in optics.
Chapter 2:This chapter is devoted to familarise the readers with relevant concepts related to research problems discussed in this thesis. Here, we discuss the concept of parity-time symmetry in the context of an optical system. This is followed by a brief discussion on solitons and physics behind soliton switching.
Chapter 3: In this chapter, we investigate the soliton steering dynamics in a P T-
symmetric directional coupler in the femtosecond domain in great detail. We first ex- plore the effects of individual higher-order perturbations (higher-order dispersions, self-steepening and intrapulse Raman scattering) on switching dynamics. Following that, we investigate the cumulative combined effects of all perturbations, which result in a significant improvement in the stability and switching of fs soliton against individual perturbations as well as unperturbed cases. With a high gain/loss, the combined effect of perturbations is found to stabilize the soliton pulse evolution in the coupler from the chaotic behavior of unperturbed evolution. This work demonstrates that it is possible to achieve efficient soliton steering, even in the femtosecond regime, at very low criti- cal power at a relatively higher gain/loss coefficient in theP T-symmetric directional coupler. It has been previously reported that in the context of conventional couplers intrapulse Raman scattering restabilizes the symmetric solitons at sufficiently large en- ergies. However, in the case of aP T-symmetric coupler, we show that a partly radiating solitons caused by high gain/loss values (although the pulse is low energy fundamental soliton) are stabilised in the presence of higher-order perturbations. This finding is new in the context of ultrafast soliton steering in aP T-symmetric coupler, paving the way for stable and efficient fs all-optical switching at low energy than the conventional one.
Chapter 4: In connection with the all-optical switching devices, in this chapter, we concentrate on the steering dynamics in aP T-symmetric saturable nonlinear coupler.
We first obtain the exact soliton solution which can propagate through such a medium and then observe the transmission characteristics of that pulse for theP T-symmetric coupler and solve the corresponding equation considering the device length to be half-beat length. The corresponding theoretical model along with a discussion on the numerical finding of soliton solution which can propagate in a saturating nonlinear medium has been demonstrated. The bistable solitons in the context ofP T-symmetric coupler with saturable nonlinearity has been studied. The spatiotemporal characteristics of solitons are illustrated and the phase-controlled soliton switching behavior is demonstrated.
Chapter 5: In this chapter we demonstrate steering dynamics of dark soliton in a P T-symmetric nonlinear directional coupler in the presence of third-order dispersion and intermodal dispersions. A complete switching with an excellent efficiency at a very low critical power, even lower as compared to the bright soliton switching has been observed. The numerical results showing that both the dispersions have no effect on
1.2 Outline of the Thesis
soliton steering inP T-symmetric couplers which makes the dark solitons to be a stable solution under dispersive effects. Additionally, we have studied the switching dynamics of the dark soliton by controlling the phase of a weaker signal inP T couplers with two different coupling lengths and demonstrated its advantage over the power-controlled one.
Chapter6:This chapter concludes the thesis with a summary of the major findings of the research works carried out, and a brief outline on the scope for future studies.