Here you can find more details about our current research and projects. If you are a researcher interested in collaboration or a student who would like to participate in our research, please reach out to any Singular Optics Group member. We are open to each of such initiatives.

Metrological applications of optical vortices

The vortex interferometer is based on the regular lattice of optical vortices generated by three beam interferometer [1, 2]. Areas of interferogram with phase singularities are considered as difficult for analysis. They are neglected or required special treatment. Contrary to this we have shown that vortex lattice can be used for determining the wavefront geometry, wavefront tilt against two axes with single measurements [3, 4], and parameters of birefringent media [5]  

The idea of using vortices in microscopy has over thirty years of history. There were a few projects for such a microscope including our own one: Optical Vortex Scanning Microscope (OVSM). In our system, the object can be scanned in two ways. Classical one and by Internal Scanning Method. The Internal Scanning Method means that the object is scanned by a vortex point while the focused laser beam stays in place [6-8]. As so far, we were able to image the topography of simple objects. The main problem here is finding a way for recomputing the system response to object topography. We have also shown that the OVSM can be used for precise interferometric measurements [9].

The important part of our research is finding the method for vortex points’ localization. The vortex point is a central part of each optical vortex, the point where the phase is undetermined (phase singular point). Our last achievements in this area are based on the application of the Laguerre-Gaussian transform [10] and neural networks [11].

The next metrological topic concerns the application of vortex beams (i.e., light beams carrying optical vortices) for laser beam positioning. We have shown that optical vortex can serve as a phase marker which enables precise evaluation of the laser beam deflection due to atmospheric turbulence [11,12]

Our theoretical works are focused on solving the vortex beam diffraction problems and also on cases when the vortex beam symmetry is broken. The problems with broken symmetry are difficult. Nevertheless, we were able to find some solutions which results in somehow surprising conclusions [13-15]. In particular, we have described analytically the Internal Scanning Method in our vortex microscopy system. We do also make some theoretical results concerning the vortex beam propagation and diffraction [16, 17].

[1] Jan Masajada, Bogusława Dubik, Optical vortex generation by three plane waves interference. Optics Communications, 198, 21-27, 2001

[2] Jan Masajada, Agnieszka Popiołek-Masajada, Monika Leniec, Creation of vortex lattices by a wavefront division, Optics Express, 15, 5196 -5207, 2007

[3] Jan Masajada, Agnieszka Popiołek Masajada, David M. Wieliczka, The interferometric system using optical vortices as phase markers, Optics Communications, 207, 85-9358, 2002

[4] Agnieszka Popiołek-Masajada, Monika Borwińska, Wojciech Frączek, Testing a new method for small-angle rotation measurements with the optical vortex interferometer. Measurement Science & Technology, 17, 653-658, 2006

[5] Monika Borwińska, Agnieszka Popiołek-Masajada, Piotr Kurzynowski, Measurements of birefringent media properties using optical vortex birefringence compensator. Applied Optics, 46, 6419-6426, 2007

[6] Jan Masajada, Monika Leniec, Ireneusz Augustyniak, Optical vortex scanning inside the Gaussian beam, Journal of Optics, 13,  035714-1 – 035714-7, 2011

[7] Ireneusz Augustyniak, Agnieszka Popiołek-Masajada, Jan Masajada, Sławomir Drobczyński, New scanning technique for the optical vortex microscope, Applied Optics, 51 C117-C124, 2012

[8] Jan Masajada, Ireneusz Augustyniak, Agnieszka Popiołek-Masajada, Optical vortex dynamics induced by vortex lens shift – optical system error analysis, Journal of Optics, 15, 044031, 2013

[9] Agnieszka Popiołek-Masajada, Jan Masajada, Weronika Lamperska, Phase recovery with the optical vortex microscope. Measurement Science and Technology, 30, art. 105202, s. 1-9, 2019

[10] Mateusz Szatkowski, Emilia Burnecka, Hanna Dyła and Jan Masajada, Optical vortex tracking algorithm based on the Laguerre-Gaussian transform, Opt. Express, 30, 17451- 17464, 2022

[11] Agnieszka Popiołek-Masajada, Ewa Frączek, Emilia Burnecka, Subpixel localization of optical vortices using artificial neural networks. Metrology and Measurement Systems, 28, 1-12, 2021

[12] Ewa Frączek, Wojciech Frączek, Agnieszka Popiołek-Masajada Laser beam positioning by using a broken-down optical vortex marker. Applied Sciences, 11, 7677, 2021

[13] Łukasz S. Płociniczak, Agnieszka Popiołek-Masajada, Mateusz Szatkowski, D. Wojnowski, Transformation of the vortex beam in the optical vortex scanning microscope, Optics and Laser Technology, 81, 127-136 2016

[14] Łukasz S. Płociniczak, Agnieszka Popiołek-Masajada, Jan Masajada, Mateusz Szatkowski, Analytical model of the optical vortex microscope, Applied Optics, 55, B20-B27, 2016

[15] Ireneusz Augustyniak, Weronika Lamperska, Jan Masajada, Łukasz S. Płociniczak, Agnieszka Popiołek-Masajada, Off-axis vortex beam propagation through classical optical system in terms of Kummer confluent hypergeometric function, Photonics, 7, 1-21, 2020

[16] Anna Khoroshun, Andrew Ryazantsev, Oleksandr I. Ryazantsev, Shunichi Sato, Yuichi Kozawa, Jan Masajada, Agnieszka Popiołek-Masajada, Mateusz Szatkowski, Aleksey Chernykh, Aleksandr Y. Bekshaev, Formation of an optical field with regular singular-skeleton structure by the double-phase-ramp converter, Journal of Optics, 22, 1-9, 2020

[17] Aleksandr Y. Bekshaev, Aleksey Chernykh, Anna Khoroshun, Jan Masajada, Agnieszka Popiołek-Masajada, Andrii O. Riazantsev, Controllable singular skeleton formation by means of the Kummer optical-vortex diffraction at a rectilinear phase step, Journal of Optics, 23, 1-11, 2021