Stable localized modes in asymmetric waveguides with gain and loss

Tsoy, Eduard N.; Allayarov, Izzatjon; Abdullaev, F. Kh.

doi:10.1364/ol.39.004215

Cited by 67 publications

(92 citation statements)

References 19 publications

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“…Regarding the first question, we recognize that in the absence of PT symmetry, the existence of a constant of motion in the stationary soliton equation plays a crucial role in the existence of soliton families. Assuming this constant of motion for complex potentials is a continuous deformation of one that exists in the NLS equation without a potential, we show that the only complex potentials which admit a constant of motion are those of the form reported in [22,23], that is, V (x) = g 2 (x) + ig (x), where g(x) is an arbitrary real function. This strongly suggests that potentials of the above form are the only one-dimensional non-PT -symmetric complex potentials that admit soliton families.…”

Section: Introductionmentioning

confidence: 87%

“…However, in non‐

scriptPT

‐symmetric potentials, soliton families are generically forbidden . Surprisingly, it was reported recently through numerical examples that in complex potentials of the special form

V (x) = g^{2} (x) + i g^{'} (x),

where

g (x)

is an arbitrary real function, soliton families can still bifurcate out from linear modes even when

V (x)

is non‐

scriptPT

‐symmetric (i.e., when

g (x)

is not even) . This result is very unintuitive.…”

Section: Preliminariesmentioning

confidence: 98%

“…In dissipative and non‐

scriptPT

‐symmetric systems, the expectation is that any solitons will be isolated with discrete energy values, as seen in typical dissipative systems . However, exceptions were reported numerically in for the NLS equation with a non‐

scriptPT

‐symmetric complex potential of special form, where families of solitons with continuous energy values can bifurcate out from the linear modes of the potential. This finding is very surprising in view of the lack of

scriptPT

symmetry here.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials

Nixon

Yang

2016

Stud Appl Math

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Continuous families of solitons in the nonlinear Schrödinger equation with non‐scriptPT‐symmetric complex potentials and general forms of nonlinearity are studied analytically. Under a weak assumption, it is shown that stationary equations for solitons admit a constant of motion if and only if the complex potential is of a special form g2(x)+ig′(x), where g(x) is an arbitrary real function. Using this constant of motion, the second‐order complex soliton equation is reduced to a new second‐order real equation for the amplitude of the soliton. From this real soliton equation, a novel perturbation technique is employed to show that continuous families of solitons bifurcate out from linear discrete modes in these non‐scriptPT‐symmetric complex potentials. All analytical results are corroborated by numerical examples.

show abstract

Section: Introductionmentioning

confidence: 87%

“…However, in non‐

scriptPT

‐symmetric potentials, soliton families are generically forbidden . Surprisingly, it was reported recently through numerical examples that in complex potentials of the special form

V (x) = g^{2} (x) + i g^{'} (x),

where

g (x)

is an arbitrary real function, soliton families can still bifurcate out from linear modes even when

V (x)

is non‐

scriptPT

‐symmetric (i.e., when

g (x)

is not even) . This result is very unintuitive.…”

Section: Preliminariesmentioning

confidence: 98%

“…In dissipative and non‐

scriptPT

scriptPT

scriptPT

symmetry here.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials

Nixon

Yang

2016

Stud Appl Math

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show abstract

“…A class of potentials introduced by Wadati [100] of the special form W 2 (x) − idW (x)/dx, where W (x) is a real-valued function, is attracting increasing attention in context of PT-symmetric nonlinear systems [101][102][103]. The PT-symmetric Wadati potentials have a unique feature of supporting continuous families of asymmetric solitons, in contrast to other PT-symmetric potentials [81,104].…”

Section: Solitons In Localized Potentialsmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

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One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

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“…It is demonstrated below that the nonlinearity creates solitons in the present system. In this connection, it is relevant to mention recently introduced nonlinear models with alternating gain and loss, which do not obey the condition of the V T symmetry, but nevertheless support stable solitons [48][49][50], A solution to the linear version of Eqs. (1) and (2) …”

Section: A the System: Phenomenological Formulationmentioning

confidence: 99%

CPsymmetry in optical systems

2015

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We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.

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Stable localized modes in asymmetric waveguides with gain and loss

Cited by 67 publications

References 19 publications

Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials

Bifurcation of Soliton Families from Linear Modes in Non‐‐Symmetric Complex Potentials

Nonlinear switching and solitons in PT‐symmetric photonic systems

CPsymmetry in optical systems

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