Chinese Optics Letters, Volume. 20, Issue 9, 092501(2022)

Generation of Lommel beams through highly scattering media

Shijie Tu1, Qiannan Lei1, Yangjian Cai1,2,*, and Qian Zhao1,**
Author Affiliations
  • 1Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Jinan 250358, China
  • 2School of Physical Science and Technology, Soochow University, Suzhou 215006, China
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    Lommel beams have been potential candidates for optical communication and optical manipulation, due to their adjustable symmetry of transverse intensity distribution and continuously variable orbital angular momentum. However, the wavefront of the Lommel beam is scrambled when it transmits through highly scattering media. Here, we explore the construction of Lommel beams through highly scattering media with a transmission matrix-based point spread function engineering method. Experimentally, various Lommel beams with different parameters were generated through a ZnO scattering layer by use of a digital micromirror device. The construction of Lommel beams under high scattering is expected to benefit the optical applications behind highly scattering media.


    1. Introduction

    In recent years, nondiffracting beams have attracted much attention due to their peculiar properties[1,2]. Such beams are able to keep their transverse intensity distribution over a long distance in free space and quickly reestablish their structures when encountering barriers[3]. Since the pioneering work of Durnin et al., Bessel beams, which are the exact solution of the Helmholtz wave equation in circular cylindrical coordinates, were presented[4] and have shown outstanding performance in the fields of optical trapping[5,6], optical microscopy[7,8], material processing[9], and so on. Apart from Bessel beams, plane waves[10], Mathieu beams[11], and Weber beams[12] are the families of propagation invariant beams, which are, respectively, the nonparaxial solutions of the Helmholtz equation under Cartesian coordinates, elliptic cylindrical coordinates, and parabolic cylindrical coordinates. In particular, a family of nondiffracting beams forms a set of complete orthogonal solutions. In this case, any linear superposition of the same type of diffraction-free modes with the same radial wave vector keeps the nondiffracting properties[13]. Recently, Kovalev et al. presented a linear superposition of Bessel modes, whose complex amplitude can be expressed in terms of Lommel functions of two variables. Hence, such a beam is called Lommel beam[14]. Compared to Bessel beam whose transverse intensity profile is radial symmetry, the Lommel beam has a reflective symmetry with respect to both Cartesian coordinate axes[15]. In addition, a Lommel beam has an adjustable symmetrical transverse intensity pattern and continuously variable orbital angular momentum (OAM), which can benefit optical manipulation[16,17] and optical information encoding[18,19].


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    Shijie Tu, Qiannan Lei, Yangjian Cai, Qian Zhao. Generation of Lommel beams through highly scattering media[J]. Chinese Optics Letters, 2022, 20(9): 092501

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    Paper Information

    Category: Optoelectronics

    Received: Mar. 4, 2022

    Accepted: May. 10, 2022

    Published Online: Jun. 16, 2022

    The Author Email: Yangjian Cai (, Qian Zhao (



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