@article{zhou2010average,
	title={Average intensity and spreading of a Lorentz-Gauss beam in turbulent atmosphere},
	author={Zhou, Guoquan and Chu, Xiuxiang},
	journal={Optics express},
	volume={18},
	number={2},
	pages={726--731},
	year={2010},
	publisher={Optica Publishing Group}
}

@article{zhao2010paraxial,
	title={Paraxial propagation of Lorentz and Lorentz--Gauss beams in uniaxial crystals orthogonal to the optical axis},
	author={Zhao, Chengliang and Cai, Yangjian},
	journal={Journal of Modern Optics},
	volume={57},
	number={5},
	pages={375--384},
	year={2010},
	publisher={Taylor \& Francis}
}
@article{zheng2013self,
	title={Self-focusing Dynamics of Lorentz-Gaussian Beams in Kerr Media.},
	author={ZHENG, H-P and CHEN, R-P and Ooi, Chong Heng Raymond},
	journal={Lasers in Engineering (Old City Publishing)},
	volume={24},
	year={2013}
}

@article{guo2021,
	title={Propagation of partially coherent vortex beams in gain media},
	author={Guo, Xin and Yang, Chen and Duan, Meiling and Guo, Miaojun and Wang, Jing and Li, Jinhong},
	journal={Optik},
	volume={243},
	pages={167361},
	year={2021},
	publisher={Elsevier}
}

@article{liu2017propagation,
	title={Propagation properties of a partially coherent Lorentz beam in uniaxial crystal orthogonal to the optical axis},
	author={Liu, Dajun and Yin, Hongming and Wang, Guiqiu and Wang, Yaochuan},
	journal={JOSA A},
	volume={34},
	number={6},
	pages={953--960},
	year={2017},
	publisher={Optica Publishing Group}
}

@book{dalgac2021propagation,
	title={The Propagation of Vortex Beams in Random Mediums},
	author={Dalgac, Sekip and Elmabruk, Kholoud},
	number={article 101061},
	year={2021},
	publisher={IntechOpen}
}


@article{ni2013propagation,
	title={Propagation of a Lorentz--Gauss vortex beam through a paraxial ABCD optical system},
	author={Ni, Yongzhou and Zhou, Guoquan},
	journal={Optics Communications},
	volume={291},
	pages={19--25},
	year={2013},
	publisher={Elsevier}
}

@article{liu2017propagation2,
	title={Propagation of partially coherent Lorentz--Gauss vortex beam through oceanic turbulence},
	author={Liu, Dajun and Yin, Hongming and Wang, Guiqiu and Wang, Yaochuan},
	journal={Applied optics},
	volume={56},
	number={31},
	pages={8785--8792},
	year={2017},
	publisher={Optica Publishing Group}
}

@article{liu2018evolution,
	title={Evolution properties of a radial phased-locked partially coherent Lorentz-Gauss array beam in oceanic turbulence},
	author={Liu, Dajun and Wang, Yaochuan},
	journal={Optics \& Laser Technology},
	volume={103},
	pages={33--41},
	year={2018},
	publisher={Elsevier}
}

@article{dong2020propagation,
	title={Propagation properties of partially coherent modified Bessel--Gauss beams through the gradient-index medium},
	author={Dong, Miao and Bai, Yihua and Yao, Jun and Zhao, Qi and Yang, Yuanjie},
	journal={Applied Optics},
	volume={59},
	number={26},
	pages={8023--8028},
	year={2020},
	publisher={Optica Publishing Group}
}

@article{zhou2013propagation,
	title={Propagation of a Lorentz-Gauss vortex beam in a turbulent atmosphere},
	author={Zhou, Guoquan and Ru, Guoyun},
	journal={Progress In Electromagnetics Research},
	volume={143},
	pages={143--163},
	year={2013},
	publisher={EMW Publishing}
}


@article{zhou2010pclginABCD,
	title={Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system},
	author={Zhou, Guoquan},
	journal={Optics Express},
	volume={18},
	number={5},
	pages={4637--4643},
	year={2010},
	publisher={Optica Publishing Group}
}

@article{liu2017propagation3,
	title={Propagation of partially coherent Lorentz--Gauss vortex beam through oceanic turbulence},
	author={Liu, Dajun and Yin, Hongming and Wang, Guiqiu and Wang, Yaochuan},
	journal={Applied optics},
	volume={56},
	number={31},
	pages={8785--8792},
	year={2017},
	publisher={Optica Publishing Group}
}

@article{liu2018average,
	title={Average intensity and coherence properties of a partially coherent Lorentz-Gauss beam propagating through oceanic turbulence},
	author={Liu, Dajun and Wang, Guiqiu and Wang, Yaochuan},
	journal={Optics \& Laser Technology},
	volume={98},
	pages={309--317},
	year={2018},
	publisher={Elsevier}
}

@book{jeffrey2008handbook,
	title={Handbook of mathematical formulas and integrals},
	author={Jeffrey, Alan and Dai, Hui Hui},
	year={2008},
	publisher={Elsevier}
}

@article{Liu,
	title={Propagation of partially coherent Lorentz--Gauss vortex beam through oceanic turbulence},
	author={Liu, Dajun and Yin, Hongming and Wang, Guiqiu and Wang, Yaochuan},
	journal={Applied optics},
	volume={56},
	number={31},
	pages={8785--8792},
	year={2017},
	publisher={Optica Publishing Group}
}

@article{dong2020propagation2,
	title={Propagation properties of partially coherent modified Bessel--Gauss beams through the gradient-index medium},
	author={Dong, Miao and Bai, Yihua and Yao, Jun and Zhao, Qi and Yang, Yuanjie},
	journal={Applied Optics},
	volume={59},
	number={26},
	pages={8023--8028},
	year={2020},
	publisher={Optica Publishing Group}
}

@article{yang2020propagation,
	title={Propagation properties of Gaussian vortex beams through the gradient-index medium},
	author={Yang, Shuai and Wang, Jing and Guo, Miaojun and Qin, Zhenxing and Li, Jinhong},
	journal={Optics Communications},
	volume={465},
	pages={125559},
	year={2020},
	publisher={Elsevier}
} 

@book{jeffrey2008handbook2,
	title={Handbook of mathematical formulas and integrals},
	author={Jeffrey, Alan and Dai, Hui Hui},
	year={2008},
	publisher={Elsevier}
}


@book{tablemath,
	title={Table of integrals, series, and products},
	author={Gradshteyn, Izrail Solomonovich and Ryzhik, Iosif Moiseevich},
	year={2014},
	publisher={Academic press}
}

@article{zhou2010propagation,
	title={Propagation of a partially coherent Lorentz-Gauss beam through a paraxial ABCD optical system},
	author={Zhou, Guoquan},
	journal={Optics Express},
	volume={18},
	number={5},
	pages={4637--4643},
	year={2010},
	publisher={Optica Publishing Group}
}

@article{alkelly2021coherence,
	title={Coherence Properties and Intensity Distribution of a Partially Coherent Lorentz--Gauss Beam Emerging from the Axicon},
	author={Alkelly, Abdu A and Hassan, Labiba F},
	journal={International Journal of Optics},
	volume={2021},
	pages={1--11},
	year={2021},
	publisher={Hindawi Limited}
}

@article{qusailah2023propagation,
	title={The propagation properties of a lorentz--gauss vortex beam in a gradient-index medium},
	author={Qusailah, Mohammed S and Alkelly, Abdu A and Al-Bahry, Wafa’a A and others},
	journal={International Journal of Optics},
	volume={2023},
	year={2023},
	publisher={Hindawi}
}

@article{lazrek2022propagation,
	title={Propagation of vortex Hermite-cosh-Gaussian beams in a gradient-index medium},
	author={Lazrek, M and Hricha, Z and Belafhal, A},
	journal={Optical and Quantum Electronics},
	volume={54},
	number={1},
	pages={67},
	year={2022},
	publisher={Springer}
}

@article{zhao2016propagation,
	title={Propagation properties of Airy--Gaussian vortex beams through the gradient-index medium},
	author={Zhao, Ruihuang and Deng, Fu and Yu, Weihao and Huang, Jiayao and Deng, Dongmei},
	journal={JOSA A},
	volume={33},
	number={6},
	pages={1025--1031},
	year={2016},
	publisher={Optica Publishing Group}
}

@article{cao2018propagation,
	title={Propagation of on-axis and off-axis Bessel beams in a gradient-index medium},
	author={Cao, Zhaolou and Zhai, Chunjie and Xu, Shanshan and Chen, Yunyun},
	journal={JOSA A},
	volume={35},
	number={2},
	pages={230--235},
	year={2018},
	publisher={Optica Publishing Group}
}


@article{al2023effective,
	title={The effective beam width of a partially coherent rectangular mul-ti-gaussian schell-model vortex beam propagating in a turbulent plasma},
	author={AL-Nadary, HO and Alkelly, Abdu Ahmed and Khaled, MAH and Hassan, Labiba F},
	journal={Sana'a University Journal of Applied Sciences and Technology},
	volume={1},
	number={3},
	year={2023}
}

@article{morone2015influence,
	title={Influence maximization in complex networks through optimal percolation},
	author={Morone, Flaviano and Makse, Hern{\'a}n A},
	journal={Nature},
	volume={524},
	number={7563},
	pages={65--68},
	year={2015},
	publisher={Nature Research}
}

@article{hirsch2005index,
	title={An index to quantify an individual's scientific research output},
	author={Hirsch, Jorge E},
	journal={Proceedings of the National academy of Sciences of the United States of America},
	pages={16569--16572},
	year={2005},
	publisher={JSTOR}
}

@article{dangalchev2006residual,
	title={Residual closeness in networks},
	author={Dangalchev, Chavdar},
	journal={Physica A: Statistical Mechanics and its Applications},
	volume={365},
	number={2},
	pages={556--564},
	year={2006},
	publisher={Elsevier}
}

@article{garg2015brief,
	title={A Brief Survey of Various Ranking Algorithms for Web Page Retrieval in Web Structure Mining},
	author={Garg, Yogita and Jain, Mr Vinod},
	journal={International Journal of Engineering Trends and Technology},
	volume={21},
	number={3},
	pages={168--172},
	year={2015}
}

@phdthesis{testthesis,
  author={R.S. McKay},
  title={X-ray crystallography},
  school={Princeton University},
  year={1982}
}


@article{Zhang:14,
author = {Yaxin Zhang and Shen Qiao and Linlin Sun and Qi Wu Shi and Wanxia Huang and Ling Li and Ziqiang Yang},
journal = {Optics Express},
keywords = {Modulators; Metamaterials; Spectroscopy, teraherz ; Thin film devices and applications},
number = {9},
pages = {11070--11078},
publisher = {Optica},
title = {Photoinduced active terahertz metamaterials with nanostructured vanadium dioxide film deposited by sol-gel method},
volume = {22},
month = {May},
year = {2014},
url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-22-9-11070},
doi = {10.1364/OE.22.011070},
}

@misc{OPTICA,
author = {{Optica Publishing Group}},
title = {{Optica}},
howpublished = {\url{https://opg.optica.org}},
}

@INCOLLECTION{FORSTER2007,
author={P Forster and V Ramaswamy and P Artaxo and T Bernsten and R Betts and D Fahey and J Haywood and J Lean and D Lowe and G Myhre and J Nganga and R Prinn and G Raga and M Schulz and R V Dorland},
title={Changes in atmospheric consituents and in radiative forcing},
booktitle={Climate Change 2007: The Physical Science Basis. Contribution of Working Group 1 to the Fourth assesment report of Intergovernmental Panel on Climate Change},
editor={S Solomon and D Qin and M Manning and Z Chen and M Marquis and K B Averyt and M Tignor and H L Miler},
year={2007},
publisher={Cambridge University Press}
}

@article{manga_rao_single_2007,
	title = {Single quantum-dot {Purcell} factor and $\beta$ factor in a photonic crystal waveguide},
	volume = {75},
	issn = {1098-0121, 1550-235X},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.75.205437},
	doi = {10.1103/PhysRevB.75.205437},
	language = {en},
	number = {20},
	urldate = {2018-06-05},
	journal = {Physical Review B},
	author = {Manga Rao, V. S. C. and Hughes, S.},
	month = may,
	year = {2007},
}