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Optics Communications

Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms

Orhan Aytür, Haldun M. Özaktaş

Published Oct 1, 1995• 44 citations
Publisher
DOI
10.1016/0030-4018(95)00452-e

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In this paper, a dual optics paths optical image cryptosystem based on tilt Fresnel diffraction and a phase modulation in extend fractional Fourier transform (eFrFT) domain is presented. The tilt Fresnel is designed by using a non-spherical mirror. A part of data from the original image is modulated by the mirror, while the other part is encoded by an expanded fractional Fourier transform. Besides, the random data of the dual channels is combined for forming the encrypted image. The structure parameters in designing the optical hardware system and the random phase can be regarded as decryption keys. Various potential attack experiments are implemented to check the validity of the proposed cryptographic system.
From the perspective of optical information security, we demonstrate that conventional phase retrieval algorithms, such as the Gerchberg–Saxton algorithm, can be still valid when extended from the Fourier transform domain into the fractional Fourier transform (FRFT) domain. Based on this extension, we propose a method of known-plaintext attack (KPA) on double random phase encoding in the fractional Fourier transform domain (DRPE-FRFT). With this attack, an opponent can access two encryption phase keys with the help of the phase retrieval algorithm in the FRFT domain, and meanwhile obtain the two FRFT order keys by using an exhaustive search. This indicates that the optical encryption scheme based on the DRPE-FRFT scheme is vulnerable to KPA due to the nature of the linearity of FRFT. The validity of this attack is verified by numerical simulations.
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing, and computing. In this Letter, we present the experimental realization of the fractional Fourier transform in the time-frequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing, and superresolved parameter estimation.