Engineering Advances

Downloads: 25812 Total View: 271267
Frequency: bimonthly ISSN Online: 2768-7961 CODEN: EANDDL

Analytic Theory of the Evolution of Circle Pearcey Beam

Minghan Liu*, Gouhua Fu

Hainan Hanrbor & Shipping Holding Co., Ltd., Haikou, Hainan, China.

*Corresponding author: Minghan Liu

Published: September 11,2023


With the research of abrupt autofocusing beams deeper than ever before, the application of that turns wider, such as the particle manipulation, biomedicine, optical communication, vortex beams and so on, arousing scientists’ interest further. However, the analytical solution of circle Pearcey beams (CPBs) in paraxial propagation has not yet been proposed so far. In this work, we first propose the analytical solution of circle Pearcey beams (CPBs) transmitting on axi, and obtain semi-analytical solution of which transmitting off axis under paraxial condition. Particularly, the complex amplitude and analytical expressions of the circle Pearcey beam (CPB) at any point in the free space under the paraxial approximation are obtained by means of the stationed phase method, the asymptotic theory and decouple theory–separation variable method, which contains separation variable method. It’s fantastic that the analytical solution we acquire is well consistent with the numerical solution gained by three-step Fourier algorithm. Furthermore, compared with the three-step method, we theoretically get the self-focusing distance of circle Pearcey beams (CPBs), expounding the phenomena of autofocusing and the law of spatial evolution under paraxial approximation.


[1] M. A. Alonso and R. Borghi. Complete far-field asymptotic series for free fields. Opt. Lett., 31 (2006), pp. 3028-3030.

[2] M. Berry and C. Upstill. Iv catastrophe optics: Morphologies of caustics and their diffraction patterns. Progress in Optics, Elsevier, vol. 18, 1980, pp. 257-346.

[3] M. V. Berry and C. J. Howls. Hyperasymptotics for integrals with saddles. Proceedings Mathematical Physical Sciences, 434 (1991), pp. 657-675.

[4] R. Borghi. Evaluation of diffraction catastrophes by using weniger transformation. Opt. Lett., 32 (2007), pp. 226-228.

[5] R Borghi. On the numerical evaluation of cuspoid diffraction catastrophes. J. Opt. Soc. Am. A, 25 (2008), pp. 1682-1690.

[6] R. Borghi and M. Santarsiero. Summing lax series for nonparaxial beam propagation. Opt. Lett., 28 (2003), pp. 774-776.

[7] X. Chen, D. Deng, J. Zhuang, X. Peng, D. Li, L. Zhang, F. Zhao, X. Yang, H. Liu, and G. Wang. Focusing properties of circle pearcey beams. Opt. Lett., 43 (2018), pp. 3626-3629.

[8] X. Chen, D. Deng, J. Zhuang, X. Yang, H. Liu, and G. Wang. Nonparaxial propagation of abruptly autofocusing circular pearcey gaussian beams. Appl. Opt., 57 (2018), pp. 8418-8423.

[9] I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Fourier-space generation of abruptly autofocusing beams and optical bottle beams, Opt. Lett., 36 (2011), pp. 3675-3677.

[10] J. Connor. Catastrophes and molecular collisions. Molecular Physics, 31 (1976), pp. 33-55.

[11] M. Howls. Hyperasymptotics. Proceedings Mathematical Physical Sciences, 430 (1990), pp. 653-668.

[12] Max Born and Emil Wolf. With contributions by Principles of Optics. Principles of Optics, 1999.

[13] J. F. Nye. Natural focusing and fine structure of light: caustics and wave dislocations, Natural focusing and fine structure of light: caustics and wave dislocations by J.F. Nye. Bristol; Philadelphia: Institute of Physics Pub, (1999).

[14] P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis. Sharply autofocused ring-airy beams transforming into non-linear intense light bullets. Nature Communications, 2013, 2622(2013).

[15] D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis. Observation of abruptly autofocusing waves. Opt. Lett., 36 (2011), pp. 1842-1844.

[16] Wenzhi Y, Amin P, Yi C, et al. Transient heat transfer analysis of a cracked strip irradiated by ultrafast Gaussian laser beam using dual-phase-lag theory [J]. International Journal of Heat and Mass Transfer, 2023, 203.

[17] K.R. S, Rajneesh J, Bhaskar K. Erratum to “Mueller-matrix for non-ideal beam-splitters to ease the analysis of vectorial optical fields” [Opt. Laser Technol. 154 (2022) 108288] [J]. Optics and Laser Technology, 2023, 161.

[18] Salma C, Abdelmajid B. Analyzing the spreading properties of vortex beam in turbulent biological tissues [J]. Optical and Quantum Electronics, 2022, 55(1).

[19] D. M T, Jerome K, E. M B, et al. BioSAXS at European Synchrotron Radiation Facility—Extremely Brilliant Source: BM29 with an upgraded source, detector, robot, sample environment, data collection and analysis software [J]. Journal of Synchrotron Radiation, 2022, 30(1).

[20] A. Y, B. G, C. C, et al. OD31 - Detector selection impact on small-field dosimetry of collecting beam data measurements among Elekta Versa HD 6MV FFF Beams: a multi-institutional variability analysis [J]. Physica Medica, 2021, 92(S).

How to cite this paper

Analytic Theory of the Evolution of Circle Pearcey Beam

How to cite this paper: Minghan Liu, Gouhua Fu. (2023). Analytic Theory of the Evolution of Circle Pearcey Beam. Engineering Advances3(4), 363-368.