Profile thickness synthesis of thin-film waveguide Luneburg lens

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Abstract

In the work the link between the focusing inhomogeneity of the effective refractive index of waveguide Luneburg lens and the irregularity of the waveguide layer thickness generating this inhomogeneity is demonstrated. For the dispersion relation of irregular thin-film waveguide in the model of adiabatic waveguide modes the problem of mathematical synthesis and computer-aided design of the waveguide layer thickness profile for the Luneburg thin-film generalized waveguide lens with a given focal length is being solved. The calculations are carried out in normalized (in a special way) coordinates to adapt the used relations to computer calculations. The obtained solution is compared with the same solution within the cross-section’s method. The performance of the algorithm implemented in Delphi, was demonstrated by plotting the dispersion curves and plotting a family of dispersion curves, demonstrating a critical convergence. As an additional result, the thickness profiles of additional (irregular in thickness) waveguide layer, forming a thin film generalized waveguide Luneburg lens were synthesized. This result generalizes Southwell’s results.

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1. Model of adiabatic waveguide modes Using the example of a thin film generalized waveguide Luneburg (TGWL) lens (see figure 1), which performs a two-dimensional Fourier transform with a finite aperture, the application of the adiabatic mode model is demonstrated. The inverse problem of synthesizing a thin film generalized waveguide Luneburg (TGWL) lens is solved within the framework of the model of adiabatic waveguide modes. Figure 1. Cross section of the TGWL under consideration Solutions of the Maxwell’s equations for adiabatic waveguide modes are sought in the form [1]: {E(
×

About the authors

Konstantin P. Lovetskiy

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: lovetskiy-kp@rudn.ru
ORCID iD: 0000-0002-3645-1060

Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Anton L. Sevastianov

Higher School of Economics (HSE University)

Email: alsevastyanov@gmail.com
ORCID iD: 0000-0002-0280-485X

Candidate of Physical and Mathematical Sciences, Deputy Head of Department of Education digitalization

11, Pokrovsky Bulvar, Moscow, 109028, Russian Federation

Alexander V. Zorin

Peoples’ Friendship University of Russia (RUDN University)

Email: zorin-av@rudn.ru
ORCID iD: 0000-0002-5721-4558

Doctor of Physical and Mathematical Sciences, Assistant Professor of Department of Applied Probability and Informatics

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

References

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Copyright (c) 2022 Lovetskiy K.P., Sevastianov A.L., Zorin A.V.

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