Nonlinear nonuniform PT -symmetric Bragg grating structures

Low-power optical bistability in $\mathcal{PT}$-symmetric chirped Bragg gratings with four-wave mixing

“…This clearly explains that the combination of self-focusing nonlinearity along with self-focusing nonlinear modulation term is not the preferable regime for realizing all-optical switches. In our previous work, we have already demonstrated that any sign mismatch between the type of nonlinearity and chirping parameter will result in switching at higher powers [46]. This conclusion holds good in the presence of modulation of Kerr nonlinearity term (γ K ) also as shown in Fig.…”

“…This proves that a judicious selection of the operating parameters is an inevitable component to avoid numerical instabilities. Exotic light dynamics like the existence of ramp-like stable states were discovered during our studies in the broken P T -symmetric regime [45,46]. The question that arises here is that whether the ramp-like stable states can continue to evolve in the company of perturbations in the form of modulation of the Kerr nonlinearity (γ K ) and chirping (C).…”

“…The high value of nonlinearity alongside the gain supplied to the system may lead to instability under some specific values of system parameters [16]. But, if the excitation source is a high power continuous wave laser and the system parameters are kept at optimal values, it is possible to obtain stable states in the broken P T -symmetric regime of the nonlinear uniform [45] and nonuniform [46] PTFBGs. This proves that a judicious selection of the operating parameters is an inevitable component to avoid numerical instabilities.…”

“…This notion would have remained as an unrealistic subject in real physical settings forever if not for the fact that the fundamental postulates of P T -symmetry can be translated from quantum mechanics to optics [26,37,38]. As far as FBGs are concerned, P T -symmetric structures reveal some atypical light propagation characteristics such as direction-dependent (linear) [29,[39][40][41][42][43][44], nonreciprocal (nonlinear) [45][46][47], and unidirectional [39] wave transport provided that the mathematical condition n(z) = n * (−z) for the refractive index is fulfilled by the structure via a precise equilibrium between gain and loss regions. Also, it is proven that different kinds of nonlinearity including Kerr modulation could essentially suppress the instability in certain P T -symmetric systems with equal amount of gain and loss [48,49].…”

“…To cite a few, time domain and time-independent models of PTFBG with Kerr nonlinearity [50], a combination of third-order nonlinearity with dispersive and saturable gain and loss profiles [17,51,52], PTFBGs with modulated Kerr nonlinearity [16], and higher-order nonlinearities [45] are some of the important works in the literature, as of now. Subsequently, three of the present authors with Mahalingam came up with a theoretical modeling of a low power switch involving a nonlinear PTFBG with a chirping nonuniformity [46].…”