Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Mahmut Bağcı

doi:10.33187/jmsm.1012850

EN

Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response

Abstract

Vortex solitons in parity-time ($\mathcal{PT}$) symmetric and partially $\mathcal{PT}$ (p$\mathcal{PT}$) symmetric azimuthal lattices are demonstrated for a media with quadratic nonlinear response. Stability properties of the vortices are investigated comprehensively by linear spectra and nonlinear evolution of the governing equations, and it is shown that, although the existence domain of the $\mathcal{PT}$-symmetric and p$\mathcal{PT}$-symmetric lattices are identical, the stability region of $\mathcal{PT}$-symmetric lattice is narrower than that of the p$\mathcal{PT}$-symmetric lattice. It is also observed that deeper real part in the azimuthal potentials supports stability of vortex solitons, whereas deeper imaginary part and strong quadratic electro-optic effects impoverish stability properties of the vortices. Moreover, it is shown that there are different stability properties of vortices in p$\mathcal{PT}$-symmetric azimuthal potentials for different vorticity values, while there is no such difference for vortices in $\mathcal{PT}$-symmetric potentials.

Keywords

Partially parity-time-symmetric, Quadratic nonlinear media, Vortex solitons

References

[1] M. J. Ablowitz, N. Antar, ˙I. Bakırtas¸, B. Ilan, Band-gap boundaries and fundamental solitons in complex two-dimensional nonlinear lattices, Phys. Rev. A., 81(3) (2010), 033834.
[2] M. J. Ablowitz, N. Antar, ˙I. Bakırtas¸, B. Ilan, Vortex and dipole solitons in complex two-dimensional nonlinear lattices, Phys. Rev. A., 86(3) (2012), 033804.
[3] M. J. Ablowitz, B. Ilan, E. Schonbrun, R. Piestun, Solitons in two-dimensional lattices possessing defects, dislocations, and quasicrystal structures, Phys. Rev. E., 74(3) (2006), 035601.
[4] G. Burlak, B. A. Malomed, Matter-wave solitons with the minimum number of particles in two-dimensional quasiperiodic potentials, Phys. Rev. E., 85(5) (2012), 057601.
[5] M. Ba˘gcı, ˙I. Bakırtas¸, N. Antar, Vortex and dipole solitons in lattices possessing defects and dislocations, Opt. Commun., 331 (2014), 204-218.
[6] J. Yang, Necessity of pt symmetry for soliton families in one-dimensional complex potentials, Phys. Lett. A., 378(4) (2014), 367-373.
[7] D. N. Christodoulides, J. Yang, Parity-Time Symmetry and Its Applications, Singapore, Springer, 2018.
[8] C. M. Bender, S. Boettcher, Real spectra in non-hermitian hamiltonians having PT symmetry, Phys. Rev. Lett., 80(24) (1998), 5243-5246.
[9] K. G. Makris, R. El-Ganainy, D. N. Christodoulides, Z. H. Musslimani, Beam dynamics in PT symmetric optical lattices, Phys. Rev. Lett., 100(10) (2008), 103904.
[10] C. E. R¨uter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, D. Kip, Observation of parity-time symmetry in optics, Nat. Phys., 6(3) (2010), 192-195.

[11] A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, U. Peschel, Parity-time synthetic photonic lattices, Nature, 488 (2012), 167-171.
[12] L. Feng, R. El-Ganainy, L. Ge, Non-hermitian photonics based on parity-time symmetry, Nat. Photon, 11(12) (2017), 752-762.
[13] J. Yang, Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials, Opt. Lett., 39(19) (2014), 5547-5550.
[14] ˙I. G¨oksel, N. Antar, ˙I. Bakırtas¸, Solitons of (1+1)d cubic-quintic nonlinear Schr¨odinger equation with pt-symmetric potentials, Opt. Commun., 354 (2015), 277-285.
[15] Q. Zhou,, A. Biswas, Optical solitons in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity, Superlattices and Microstructures, 109 (2017), 588-598.
[16] M. Ba˘gcı, ˙I. Bakırtas¸, N. Antar, Fundamental solitons in parity-time symmetric lattice with a vacancy defect, Opt. Commun., 356 (2015), 472-481.
[17] ˙I. G¨oksel, N. Antar, ˙I. Bakırtas¸, Two-dimensional solitons in PT-symmetric optical media with competing nonlinearity, Optik., 156 (2018), 470-478.
[18] ˙I. G¨oksel, N. Antar, ˙I. Bakırtas¸, Two-dimensional solitons in cubic-saturable media with PT-symmetric lattices, Chaos Solitons Fractals., 109 (2018), 83-89
[19] J. Yang, Symmetry breaking of solitons in two-dimensional complex potentials, Phys. Rev. E., 91(2) (2015), 023201.
[20] J. Yang, Partially PT symmetric optical potentials with all-real spectra and soliton families in multidimensions, Opt. Lett., 39(5) (2014), 1133-1136.
[21] Y. V. Kartashov, V. V. Konotop, L. Torner, Topological states in partially-PT -symmetric azimuthal potentials, Phys. Rev. Lett., 115(19) (2015), 193902.
[22] L. C. Crasovan, J. P. Torres, D. Mihalache, L. Torner, Arresting wave collapse by wave self- rectification, Phys. Rev. Lett., 91(6) (2003), 063904.
[23] R. Schiek, T. Pertsch,Absolute measurement of the quadratic nonlinear susceptibility of lithium niobate in waveguides, Opt. Mater. Express., 2(2) (2012), 126-139.
[24] M. J. Ablowitz, G. Biondini, S. Blair, Localized multi-dimensional optical pulses in non-resonant quadratic materials, Math. Comput. Simul., 56 (2001), 511-519.
[25] M. Ba˘gcı, J. N. Kutz, Spatiotemporal mode locking in quadratic nonlinear media, Phys. Rev. E., 102(2) (2020), 022205.
[26] D. J. Benney, G. J. Roskes, Wave instabilities, Stud. in App. Math., 48 (1969), 377-385.
[27] A. Davey, K. Stewartson, On three-dimensional packets of surface waves, Proc. of the Royal Soc. of London. Series A, Math. and Phys. Sci., 338 (1974), 101-110.
[28] M. J. Ablowitz, G. Biondini, S. Blair, Multi- dimensional pulse propagation in non-resonant c(2) materials, Phys.Lett. A., 236(5) (1997), 520-524.
[29] M. J. Ablowitz, G. Biondini, S. Blair, Nonlinear Schr¨odinger equations with mean terms in nonresonant multidimensional quadratic materials, Phys. Rev. E., 63(4) (2001), 046605.
[30] M. J. Ablowitz, ˙I. Bakırtas¸, B. Ilan, Wave collapse in a class of nonlocal nonlinear Schr¨odinger equations, Physica D: Nonlinear Phenomena, 207(3) (2005), 230-253.
[31] M. Ba˘gcı, ˙I. Bakırtas¸, N. Antar, Lattice solitons in nonlinear Schr¨odinger equation with coupling-to-a-mean-term, Opt. Commun., 383 (2017), 330-340.
[32] M. Ba˘gcı, Soliton dynamics in quadratic nonlinear media with two-dimensional pythagorean aperiodic lattices, J. Opt. Soc. Am. B., 38(4) (2021), 1276-1282.
[33] M. Ba˘gcı, Partially PT -symmetric lattice solitons in quadratic nonlinear media, Phys. Rev. A., 103(2) (2021), 023530.
[34] J. Yang, T. I. Lakoba, Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations, Stud. in App. Math., 118(2) (2007), 153-197.
[35] J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, SIAM, Philadelphia, 2010.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mahmut Bağcı ^*
0000-0001-6931-6837
Türkiye

Publication Date

December 27, 2021

Submission Date

October 21, 2021

Acceptance Date

November 16, 2021

Published in Issue

Year 2021 Volume: 4 Number: 3

DOI

https://doi.org/10.33187/jmsm.1012850

IZ

https://izlik.org/JA54CF95AB

APA

Bağcı, M. (2021). Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response. Journal of Mathematical Sciences and Modelling, 4(3), 117-125. https://doi.org/10.33187/jmsm.1012850

AMA

1.Bağcı M. Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response. Journal of Mathematical Sciences and Modelling. 2021;4(3):117-125. doi:10.33187/jmsm.1012850

Chicago

Bağcı, Mahmut. 2021. “Vortex Solitons on Partially $\mathcal{PT}$-Symmetric Azimuthal Lattices in a Medium With Quadratic Nonlinear Response”. Journal of Mathematical Sciences and Modelling 4 (3): 117-25. https://doi.org/10.33187/jmsm.1012850.

EndNote

Bağcı M (December 1, 2021) Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response. Journal of Mathematical Sciences and Modelling 4 3 117–125.

IEEE

[1]M. Bağcı, “Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response”, Journal of Mathematical Sciences and Modelling, vol. 4, no. 3, pp. 117–125, Dec. 2021, doi: 10.33187/jmsm.1012850.

ISNAD

Bağcı, Mahmut. “Vortex Solitons on Partially $\mathcal{PT}$-Symmetric Azimuthal Lattices in a Medium With Quadratic Nonlinear Response”. Journal of Mathematical Sciences and Modelling 4/3 (December 1, 2021): 117-125. https://doi.org/10.33187/jmsm.1012850.

JAMA

1.Bağcı M. Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response. Journal of Mathematical Sciences and Modelling. 2021;4:117–125.

MLA

Bağcı, Mahmut. “Vortex Solitons on Partially $\mathcal{PT}$-Symmetric Azimuthal Lattices in a Medium With Quadratic Nonlinear Response”. Journal of Mathematical Sciences and Modelling, vol. 4, no. 3, Dec. 2021, pp. 117-25, doi:10.33187/jmsm.1012850.

Vancouver

1.Mahmut Bağcı. Vortex Solitons on Partially $\mathcal{PT}$-symmetric Azimuthal Lattices in a Medium with Quadratic Nonlinear Response. Journal of Mathematical Sciences and Modelling. 2021 Dec. 1;4(3):117-25. doi:10.33187/jmsm.1012850