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Improving security in terahertz wireless links using beam symmetry of vortex and Gaussian beams

Tinkara Troha, Tomáš Ostatnický, and Petr Kužel

Open Access Open Access

Abstract

We present an effective way to improve the security of a point-to-point terahertz wireless link on a physical layer supported by numerical calculations in the frame of Fourier optics. The improvement is based on original countermeasures which exploit three independent degrees of freedom of the carrier wave: its intensity and azimuthal and radial symmetry. When the transmission line is intercepted, the light beam is subject to changes in either of the three degrees of freedom. We propose a strategy to measure these changes and they are quantified by a single eavesdropping parameter that is shown to be correlated to the secrecy capacity of the transmission. Consequently, its excessive value serves as an indication of the beam interception. We consider the carrier wave in the form of Gaussian and vortex beams. Comparison between the two reveals that vortex beam ensures a even higher level of security.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Supplementary Material (1)

NameDescription
Supplement 1       Supplement to the manuscript nr. 433606

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)
Fig. 1.
Fig. 1. Sketch of eavesdropping geometry. Alice sends the signal in a direct line towards Bob. Eve inserts a metallic object into the beam path and locates her detector somewhere outside the beam path.

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Fig. 2.
Fig. 2. Light intensity profile at Bob’s detector for freely propagating (a) Gaussian and (b) vortex beam. The vacuum wavelength of radiation is $\lambda = 1\; \textrm{mm}$, the beam waist radius is ${w_0} = 20\, \textrm{cm}$ and Bob’s detector is at $d = 50\; \textrm{m}$ away from the waist. (c) Changes in the Gaussian beam profile and (d) vortex beam profile when intercepted with a circular mirror positioned off-axis. In this example, the mirror with radius a = 8 cm is placed inside the beam in the waist position at an angle of 45° with respect to the beam propagation direction (x-axis). The mirror is displaced from the beam center in y-direction by 7.5 cm; (e) The intensity profile as a function of the azimuthal angle $\theta $, defined as $\tan \theta = y/z$ with the fixed radial component $R = \sqrt {{y^2} + {z^2}} $. For Gaussian beam, RG = 12.6 cm, and (f) for vortex beam, RV = 15.2 cm.

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Fig. 3.
Fig. 3. Bob’s detection configuration; light intensity is measured at six equidistant positions lying on a circle around a beam center (denoted by red circles) and in the beam center (blue circle). The distance from the center of the detector to each point is R; for Gaussian beam RG = 12.6 cm, and for vortex beam it is RV = 15.2 cm.

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Fig. 4.
Fig. 4. Definition of the geometry and of the coordinate system. (a) The light propagates in the x-direction and it is polarized in the z-direction. Bob’s detector lies in the yz-plane. Eve puts a circular mirror into the beam waist. (b) View from above: The center of the mirror is displaced from the beam axis in the y-direction by a variable distance s and it is oriented at 45° with respect to the beam propagation direction.

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Fig. 5.
Fig. 5. Eavesdropping parameter p (filled circles) and secrecy capacity ${c_s}$ (empty circles) as a function of the displacement s of the mirror from the beam axis. Mirror radius is (a) a = 6 cm, (b) a = 7 cm, (c) a = 8 cm, (d) a = 12 cm, and (e) a = 13 cm. Red color corresponds to the Gaussian beam and blue to the vortex beam. The intervals where Eve can successfully eavesdrop, i.e., she is not revealed by Bob’s countermeasures with the selected threshold (${c_s} < 0.5$ and $p < 0.5$), are labeled light red (for the Gaussian beam) or light blue (for the vortex beam). (f) A metallic cylinder with radius a = 5 cm is considered as an intercepting object.

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Fig. 6.
Fig. 6. Behavior of individual countermeasure parameters that contribute to the overall eavesdropping parameter p (black circles) as a function of the interception object displacement s. Blue triangles: blockage b; red squares: angular symmetry breaking parameter η; green diamonds: radial symmetry breaking parameter η0. Interceptions objects: circular mirror with the radius a = 13 cm in a Gaussian beam (a) and vortex beam (b); metallic cylinder with radius a = 5 cm, in a Gaussian beam (c) and vortex beam (d).

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Equations (7)

Equations on this page are rendered with MathJax. Learn more.

c s = 1 − log ⁡ ( 1 + SN R Eve ) log ⁡ ( 1 + SN R Bob ) .
b = 1 − SNR Bob object SNR Bob no\; object
b = 1 − ave(SN R k ) SN R ref .
η = 1 − min ( SN R k ) max ( SN R k ) ,
η 0 , Gauss = | 1 − 2 ave ( SN R k ) SN R 0 | ,
η 0 , vortex = SN R 0 SN R 0 + 4 ,
p ( n ) = ρ ( n ) 3 ( 2 n − 1 ) + 2 3 ( 2 n − 1 ) + 2 n + 1 ρ ( n ) n n .
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