Bessel-Gaussian Beams and Physical-Layer Security in a Free-Space Optical Channel

Physical-layer security in free-space optical communications channels can be compromised when an eavesdropper performs optical beam-splitting attacks over an atmospheric channel. In this scenario the free-space optical communications channel is referred to as an optical wiretap channel, which is an extension of Wyner’s wiretap channel model. For secure communications, Shannon's classical solution requires the transmitter and receiver to share a common secret key of length greater than or equal to the message length. This can become intractable as the message length grows in size. On the other hand the wiretap channel model proposed by Wyner is based on the premise that secrecy can be obtained even without a shared key if the noisy and degraded channel conditions experienced by the eavesdropper can be exploited. The primary metric to analyze physical-layer security is secrecy capacity, the highest data capacity at which the eavesdropper is unable to obtain information sent from the transmitter to the receiver. Positive secrecy capacity is possible when the main channel to the receiver is of better quality than the channel to the eavesdropper in the sense of signal-to-noise ratio. In this thesis we study how transmitting data using orbital angular momentum modes such as Laguerre-Gaussian and Bessel-Gaussian beams can achieve higher secrecy capacities compared to that of ordinary Gaussian beams within the turbulent conditions of an optical channel. Using computer simulations and experiments with spatial light modulators we demonstrate that Bessel- Gaussian beams provide 10 to 30 bits/sec/Hz higher secrecy capacity over their corresponding Laguerre-Gaussian counterparts in the weak to medium turbulence regimes, indicating a better resilience to atmospheric turbulence effects. We follow this with another experiment exclusively conducted with Bessel-Gaussian beams onto which we encode a pseudo-random binary sequence to emulate data transmission over an optical wiretap channel. Bit-error rate curves for the intended receiver and the eavesdropper are calculated from which estimates of secrecy capacity are derived. We demonstrate that the bit-error rate curves for the eavesdropper are consistently worse than those of the intended receiver under several turbulence conditions and find further evidence of an error floor even when the eavesdropper uses an optical amplifier. While these results show promise for secure communications further research will be needed to optimize the quality of these beams to help realize a practical system