Study on the evolution of Airy beam in PT symmetric medium

Wen Bing; Deng Yangbao; Zhang Saiwen; Wei Jiamou; Deng Shuguang; Zhang Guangfu

doi:10.3788/IRLA20200165

Volume 49 Issue S1

Sep. 2020

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Wen Bing, Deng Yangbao, Zhang Saiwen, Wei Jiamou, Deng Shuguang, Zhang Guangfu. Study on the evolution of Airy beam in PT symmetric medium[J]. Infrared and Laser Engineering, 2020, 49(S1): 20200165. doi: 10.3788/IRLA20200165

Citation:

Wen Bing, Deng Yangbao, Zhang Saiwen, Wei Jiamou, Deng Shuguang, Zhang Guangfu. Study on the evolution of Airy beam in PT symmetric medium[J]. Infrared and Laser Engineering, 2020, 49(S1): 20200165. doi: 10.3788/IRLA20200165

Study on the evolution of Airy beam in PT symmetric medium

doi: 10.3788/IRLA20200165

1. All-Solid-State Energy Storage Materials and Devices Key Laboratory of Hunan Province, College of Information and Electronic Engineering, Hunan City University, Yiyang 413002, China;
2. Key Laboratory for Micro-/Nano-Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China

Received Date: 2020-05-01
Rev Recd Date: 2020-06-14
Publish Date: 2020-09-22

Abstract

The evolution characteristics of an Airy beam in PT symmetric medium by using split-step Fourier method was investigated. Then the impact of truncation width, modulation depth, and modulation width on the propagation properties of soliton generated from an Airy beam was discussed in detail. The results illustrate that when an Airy beam propagates in a PT symmetric medium, a soliton with periodic variation is shedded at the main peak position and a lateral offset is generated. Moreover, it is demonstrated that with decreasing truncation width a, increasing modulation depth P and modulation factor w, the peak-to-average power ratio of a soliton from Airy beam increases, which causes the beam interference and beam distortion become more and more. With decrement of modulation depth P and increment of modulation factor w, the peak intensity and peak-to-average power ratio of a soliton from an Airy beam jump obviously, leading to decreasing propagation stability of a soliton. However, the shedding soliton can still propagates stably in a long distance.
- Airy beam,
- PT symmetric,
- shedding soliton,
- evolution

References

[1]	Zhang L F, Zhong H Z. Modulation instability of finite energy Airy pulse in optical fiber[J]. Opt Express, 2014, 22:17107-17115.
[2]	Wu Z K, Wang Z P, Guo H, et al. Self-accelerating Airy Laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium[J]. Opt Express, 2017, 25:30468-30478.
[3]	Banerjee A, Roy S. Self-healing dynamics and absolute temporal focusing of a truncated Airy pulse under higher-order phase modulations[J]. J Opt Soc Am B, 2018, 35:878-885.
[4]	Imran M, Li R J, Jiang Y Y, et al. Airy beams on two dimensional materials[J]. Opt Commun, 2018, 414:40-44.
[5]	Cheng K, Zhong X Q, Xiang A. Propagation dynamics and optical trapping of a radial Airy array beam[J]. Optik, 2014, 125:3966-3971.
[6]	Shi X, Tan C, Bai Y, et al. Dressed dynamics of two time reversed shapes of Airy pulses in a relaxing nonlinear medium[J]. J Opt Soc Am B, 2015, 32:1816-1823.[1] Deng Z X, Chen Y, Liu J, et al. Graded-index breathing solitons from Airy pulses in multimode fibers[J]. Opt Express, 2019, 27:483-493.
[7]	Peng X, Peng Y L, Zhang L P, et al. Reversed Airy Gaussian and Airy Gaussian vortex light bullets in harmonic potential[J]. Laser Phys Lett, 2017, 14:055002.
[8]	Ke X Z, Wang S. Evolution of the intensity of partially coherent Airy Beam in Atmospheric turbulence[J]. Acta Photonica Sinica, 2017, 46(7):0710001. (in Chinese)
[9]	Zhu L, Wang J. Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element[J]. Optics Express, 2015, 23(20):26221-26233.
[10]	Zhu L, Wang J. Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode[J]. Optics Letters, 2015, 40(23):5463-5466.
[11]	Carl M Bender, Stefan Boettcher. Real spectra in Non-Hermitian Hamiltonians having PT symmetry[J]. Physical Review Letters, 1998, 80(24):5243-5246.
[12]	El-Ganainy R, Makris K G, Christodoulides D N, et al. Theory of coupled optical PT-symmetric structures[J]. Optics Letters, 2007, 32(17):2632-2634.
[13]	Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, et al. Parity-time synthetic photonic lattices[J]. Nature, 2012, 488(7410):167-171.
[14]	Makris K G, El-Ganainy R, Christodoulides D N. Beam dynamics in PT symmetric optical lattices[J]. Phys Rev Lett, 2008, 100:103904.
[15]	Nixon S, Zhu Y, Yang J. Nonlinear dynamics of wave packets in parity-time symmetric optical lattices near the phase transition point[J]. Opt Lett, 2012, 37:4874-4876.
[16]	Cole J T, Makris K G, Musslimani Z H, et al. Two fold PT-symmetry in doubly exponential optical lattices[J]. Phy Rev A, 2016, 93:013803.
[17]	Huang C, Zeng J. Solitons stabilization in PT-symmetric potentials through modulation the shape of imaginary component[J]. Opt Laser Technol, 2017, 88:104-110.
[18]	Nixon S, Ge L, Yang J. Stability analysis for solitons in PT-symmetric optical lattice[J]. Phy Rev A, 2012, 85:023822.
[19]	He Y, Zhu X, Dumitru M, et al. Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices[J]. Phy Rev A, 2012, 85:013831.
[20]	Hao R. Optical soliton control in inhomogeneous nonlinear media with the parity time symmetric potentials[J]. Opt Communications, 2015, 338:265-268.
[21]	Flach S, Willis C R. Discrete breathers[J]. Phys Rep, 1998, 295(5):181-264.
[22]	Chabchoub A, Hoffmann N P, Akhmediev N. Rogue wave observation in a water wave tank[J]. Phys Rev Lett, 2011, 106(20):204502.
[23]	Dudley J M, Dias F, Erkintalo M, et al. Instabilities, breathers and rogue waves in optics[J]. Nat Photonics, 2014, 8(10):755-764.
[24]	Deng Yangbao, Deng Shuguang, Tan Chao, et al. Study on propagation characteristics of temporal soliton in Scarff Ⅱ PT-symmetric potential based on intensity moments[J]. Opt Laser Technol, 2016, 79:32-38.
[25]	Wright L G, Renninger W H, Christodoulides D N, et al. Spatiotemporal dynamics of multimode optical solitons[J]. Opt Express, 2015, 23(3):3492-3506.
[26]	Renninger W H, Wise F W. Optical solitons in graded-index multimode fibres[J]. Nat Commun, 2013, 4(1):1719.
[27]	Wen Bing, Deng Yangbao, Shi Xiaohui, et al. Evolution of finite-energy Airy pulse interaction with high-power soliton pulse in optical fiber with higher-order effects[J]. Optik, 2018, 152:61-68.
[28]	Hu S, Ma X, Lu D, et al. Solitons supported by complex PT-ymmetric Gaussian potentials[J]. Phys Rev A, 2011, 84:043818.

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

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Study on the evolution of Airy beam in PT symmetric medium

1. All-Solid-State Energy Storage Materials and Devices Key Laboratory of Hunan Province, College of Information and Electronic Engineering, Hunan City University, Yiyang 413002, China;

2. Key Laboratory for Micro-/Nano-Optoelectronic Devices of Ministry of Education, School of Physics and Electronics, Hunan University, Changsha 410082, China

Received Date: 2020-05-01

Rev Recd Date: 2020-06-14

Publish Date: 2020-09-22

Key words:

Abstract: The evolution characteristics of an Airy beam in PT symmetric medium by using split-step Fourier method was investigated. Then the impact of truncation width, modulation depth, and modulation width on the propagation properties of soliton generated from an Airy beam was discussed in detail. The results illustrate that when an Airy beam propagates in a PT symmetric medium, a soliton with periodic variation is shedded at the main peak position and a lateral offset is generated. Moreover, it is demonstrated that with decreasing truncation width a, increasing modulation depth P and modulation factor w, the peak-to-average power ratio of a soliton from Airy beam increases, which causes the beam interference and beam distortion become more and more. With decrement of modulation depth P and increment of modulation factor w, the peak intensity and peak-to-average power ratio of a soliton from an Airy beam jump obviously, leading to decreasing propagation stability of a soliton. However, the shedding soliton can still propagates stably in a long distance.

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Reference (28)

[1]	Zhang L F, Zhong H Z. Modulation instability of finite energy Airy pulse in optical fiber[J]. Opt Express, 2014, 22:17107-17115.
[2]	Wu Z K, Wang Z P, Guo H, et al. Self-accelerating Airy Laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium[J]. Opt Express, 2017, 25:30468-30478.
[3]	Banerjee A, Roy S. Self-healing dynamics and absolute temporal focusing of a truncated Airy pulse under higher-order phase modulations[J]. J Opt Soc Am B, 2018, 35:878-885.
[4]	Imran M, Li R J, Jiang Y Y, et al. Airy beams on two dimensional materials[J]. Opt Commun, 2018, 414:40-44.
[5]	Cheng K, Zhong X Q, Xiang A. Propagation dynamics and optical trapping of a radial Airy array beam[J]. Optik, 2014, 125:3966-3971.
[6]	Shi X, Tan C, Bai Y, et al. Dressed dynamics of two time reversed shapes of Airy pulses in a relaxing nonlinear medium[J]. J Opt Soc Am B, 2015, 32:1816-1823.[1] Deng Z X, Chen Y, Liu J, et al. Graded-index breathing solitons from Airy pulses in multimode fibers[J]. Opt Express, 2019, 27:483-493.
[7]	Peng X, Peng Y L, Zhang L P, et al. Reversed Airy Gaussian and Airy Gaussian vortex light bullets in harmonic potential[J]. Laser Phys Lett, 2017, 14:055002.
[8]	Ke X Z, Wang S. Evolution of the intensity of partially coherent Airy Beam in Atmospheric turbulence[J]. Acta Photonica Sinica, 2017, 46(7):0710001. (in Chinese)
[9]	Zhu L, Wang J. Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element[J]. Optics Express, 2015, 23(20):26221-26233.
[10]	Zhu L, Wang J. Demonstration of obstruction-free data-carrying N-fold Bessel modes multicasting from a single Gaussian mode[J]. Optics Letters, 2015, 40(23):5463-5466.
[11]	Carl M Bender, Stefan Boettcher. Real spectra in Non-Hermitian Hamiltonians having PT symmetry[J]. Physical Review Letters, 1998, 80(24):5243-5246.
[12]	El-Ganainy R, Makris K G, Christodoulides D N, et al. Theory of coupled optical PT-symmetric structures[J]. Optics Letters, 2007, 32(17):2632-2634.
[13]	Alois Regensburger, Christoph Bersch, Mohammad-Ali Miri, et al. Parity-time synthetic photonic lattices[J]. Nature, 2012, 488(7410):167-171.
[14]	Makris K G, El-Ganainy R, Christodoulides D N. Beam dynamics in PT symmetric optical lattices[J]. Phys Rev Lett, 2008, 100:103904.
[15]	Nixon S, Zhu Y, Yang J. Nonlinear dynamics of wave packets in parity-time symmetric optical lattices near the phase transition point[J]. Opt Lett, 2012, 37:4874-4876.
[16]	Cole J T, Makris K G, Musslimani Z H, et al. Two fold PT-symmetry in doubly exponential optical lattices[J]. Phy Rev A, 2016, 93:013803.
[17]	Huang C, Zeng J. Solitons stabilization in PT-symmetric potentials through modulation the shape of imaginary component[J]. Opt Laser Technol, 2017, 88:104-110.
[18]	Nixon S, Ge L, Yang J. Stability analysis for solitons in PT-symmetric optical lattice[J]. Phy Rev A, 2012, 85:023822.
[19]	He Y, Zhu X, Dumitru M, et al. Lattice solitons in PT-symmetric mixed linear-nonlinear optical lattices[J]. Phy Rev A, 2012, 85:013831.
[20]	Hao R. Optical soliton control in inhomogeneous nonlinear media with the parity time symmetric potentials[J]. Opt Communications, 2015, 338:265-268.
[21]	Flach S, Willis C R. Discrete breathers[J]. Phys Rep, 1998, 295(5):181-264.
[22]	Chabchoub A, Hoffmann N P, Akhmediev N. Rogue wave observation in a water wave tank[J]. Phys Rev Lett, 2011, 106(20):204502.
[23]	Dudley J M, Dias F, Erkintalo M, et al. Instabilities, breathers and rogue waves in optics[J]. Nat Photonics, 2014, 8(10):755-764.
[24]	Deng Yangbao, Deng Shuguang, Tan Chao, et al. Study on propagation characteristics of temporal soliton in Scarff Ⅱ PT-symmetric potential based on intensity moments[J]. Opt Laser Technol, 2016, 79:32-38.
[25]	Wright L G, Renninger W H, Christodoulides D N, et al. Spatiotemporal dynamics of multimode optical solitons[J]. Opt Express, 2015, 23(3):3492-3506.
[26]	Renninger W H, Wise F W. Optical solitons in graded-index multimode fibres[J]. Nat Commun, 2013, 4(1):1719.
[27]	Wen Bing, Deng Yangbao, Shi Xiaohui, et al. Evolution of finite-energy Airy pulse interaction with high-power soliton pulse in optical fiber with higher-order effects[J]. Optik, 2018, 152:61-68.
[28]	Hu S, Ma X, Lu D, et al. Solitons supported by complex PT-ymmetric Gaussian potentials[J]. Phys Rev A, 2011, 84:043818.

Study on the evolution of Airy beam in PT symmetric medium

doi: 10.3788/IRLA20200165

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References

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