Multifaceted dynamics and gap solitons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric periodic structures

Raja, S. Vignesh; Govindarajan, A.; Mahalingam, A.; Lakshmanan, M.

doi:10.1103/physreva.100.033838

Cited by 22 publications

(19 citation statements)

References 68 publications

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“…3(a) and 4(a), we arrive at a conclusion that the inclusion of modulation of Kerr nonlinearity (FWM) term (γ K ) is beneficial only if it is assumed to be of self-defocusing type. The thumb rule to realize an all-optical switch with low switching powers is to use a material with a high value of nonlinearity in magnitude and not in sign (γ nl ) [45] and this is confirmed from Fig. 4(b).…”

Section: A2 Type Of Nonlinearity: Self-defocusing (γmentioning

confidence: 59%

“…3(c) and we infer that with increase in the value of γ nl the intensity required to switch between the states decreases. We would like to note that the value of the length of the device (L) and the coupling coefficient (κ) should be chosen carefully so that the feedback to the system is sufficient without which the optical bistability phenomenon cannot occur [45]. Through a series of numerical experiments we found that if the value of L is too large (L > 5) and the coupling coefficient (κ) is comparatively less than L [L >> k], the system produces undesirable bistable states which indicate the onset of instability.…”

Section: A1 Type Of Nonlinearity: Self-focusing (γmentioning

confidence: 99%

“…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.…”

Section: B Broken P T -Symmetric Regimementioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

“…In the context of uniform P T -symmetric FBGs (PTFBGs), quite a good number of nonlinear models have been proposed so far to realize all-optical switches. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Sudhakar,

Raja,

Govindarajan

et al. 2022

Preprint

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The central theme of this article is the analysis of the usefulness of introducing four-wave mixing or modulation of Kerr nonlinearity in a nonuniform grating structure with gain and loss. To do so, we propose an inhomogeneous system in which the nonlinearity of the P T -symmetric grating is modulated. It is proven that the proposed scheme can be fruitful only if the nonlinearity and its associated modulation terms are assumed to be self-defocusing ones. In order to cut down the intensity required for the steering, the sign of chirping is taken to be negative and the wavelength of operating light is considered to be higher than the Bragg wavelength. Alongside these settings, launching the light from the rear end of the device dramatically reduces the critical intensity to a value of 0.015 (approximately) which must be the lowest switching intensity ever reported in the context of nonlinear P T -symmetric gratings. The ramplike stable states in the broken P T -symmetric regime prevail even in the company of modulation in the nonlinearity index for both of the light incident directions.

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Section: A2 Type Of Nonlinearity: Self-defocusing (γmentioning

confidence: 59%

Section: A1 Type Of Nonlinearity: Self-focusing (γmentioning

confidence: 99%

Section: B Broken P T -Symmetric Regimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sudhakar,

Raja,

Govindarajan

et al. 2022

Preprint

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Multifaceted nonlinear dynamics in $$\mathcal {PT}$$-symmetric coupled Liénard oscillators

et al. 2020

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We propose a generalized parity-time (PT ) -symmetric Liénard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of Jacobian and evaluate the stability threshold thereafter. In the first order nonlinear damping model, we discover that the temporal evolution of both gain and lossy oscillators attains a complete convergence towards the stable stationary state leading to the emergence of oscillation and amplitude deaths. Also, the system displays a remarkable manifestation of transient chaos in the lossy oscillator while the gain counterpart exhibits blow-up dynamics for certain choice of initial conditions and control parameters. Employing an external driving force on the loss oscillator, we find that the blow-up dynamics can be controlled and a pure aperiodic state is achievable. On the other hand, the second order nonlinear damping model yields a completely different dynamics on contrary to the first order where the former reveals a conventional quasi-periodic route to chaos upon decreasing the natural frequency of both gain and loss oscillators. An electronic circuit scheme for the experimental realization of the proposed system has also been put forward.

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Propagation of dissipative simple vortex-, necklace- and azimuthon-shaped beams in Kerr and non-Kerr negative-refractive-index materials beyond the slowly varying envelope approximation

Megne,

Tabi,

Otsobo

et al. 2023

Nonlinear Dyn

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Multifaceted dynamics and gap solitons inPT-symmetric periodic structures

Cited by 22 publications

References 68 publications

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

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

Multifaceted nonlinear dynamics in $$\mathcal {PT}$$-symmetric coupled Liénard oscillators

Propagation of dissipative simple vortex-, necklace- and azimuthon-shaped beams in Kerr and non-Kerr negative-refractive-index materials beyond the slowly varying envelope approximation

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