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Volume holographic optical encryption and decryption in photorefractive LiNbO3:Fe crystal

OPTICS COMMUNICATIONS 2019年 437卷 95-103页

作者： Kwak, Chong Hoon Kim, Gun Yeup Javidi, Bahram Yeungnam Univ Dept Phys Kyongsan 712749 South Korea Univ Connecticut Dept Elect & Comp Engn Storrs CT 06269 USA

We present general volume holographic encryption and decryption system by means of two wave mixing process that can apply to variety of diffraction domains, including the conventional Fourier hologram domain (using 4f -optical processor), the Fresnel hologram domain, and fractional Fourier hologram domain. A rigorous theory for volume holographic encryption and decryption is developed and presented under the framework of Collins diffraction integral formalism. The ability for volume holographic encryption and decryption are successfully demonstrated in a photorefractive LiNbO3:Fe crystal. We also demonstrate a robustness test of our holographic decryption system with respect to misalignment of the phase key in both longitudinal and transversal directions away from the original position and blind decryption without knowledge of the correct key.

关键词： Optical security and encryption Volume gratings abcd transforms Real-time holography Photorefractive materials Two-wave mixing

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A fast numerical algorithm for the 2D non-separable linear canonical transform based on a decomposition of the abcd matrix 6

A fast numerical algorithm for the 2D non-separable linear c...

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Conference on Holography - Advances and Modern Trends VI

作者： Zhao, Liang Wan, Min Li, Qing Liu, Sannuya Sheridan, John T. Healy, John J. Cent China Normal Univ NERCEL NELEBD Wuhan Hubei Peoples R China Univ Coll Dublin Sch Elect & Elect Engn Lab IoE2 Dublin 4 Ireland

ISBN: (数字)9781510627277

ISBN: (纸本)9781510627277

The two-dimensional non-separable linear canonical transform (2D-NS-LCT) can model a wide range of paraxial optical systems. Digital algorithms to calculate the 2D-NS-LCTs are of great interested in both light propagation modeling and digital signal processing. We have previously reported that the transform of a 2D image with rectangular sampling grid generally results in a parallelogram output sampling grid, thus complicating further calculations. One possible solution is to use interpolation techniques. However, it usually leads to poor calculation speed and reduced accuracy. To alleviate this problem, we previously proposed a unitary algorithm by choosing an advantageous sampling rate related to the system parameters. In this paper, a fast algorithm is further proposed based on a novel matrix decomposition, which can significantly improve the efficiency of the numerical approximations.

关键词： Digital holography abcd transforms Numerical approximation and analysis Discrete optical signal processing

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Convolution theorems for the linear canonical transforms 6

Convolution theorems for the linear canonical transforms

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Conference on Holography - Advances and Modern Trends VI

作者： Healy, John J. Li, Xiaolin Wan, Min Zhao, Liang Univ Coll Dublin Sch Elect & Elect Engn Dublin 4 Ireland Cent China Normal Univ Natl Engn Res Ctr E Learning Wuhan Hubei Peoples R China

ISBN: (数字)9781510627277

ISBN: (纸本)9781510627277

The linear canonical transforms (LCTs) are a Lie group of transforms including the Fresnel and Fourier transforms that describe scalar wave propagation in quadratic phase systems. As such, they are useful in system analysis and design, and their discretisations are important for opto-numerical systems, e.g. numerical reconstruction algorithms in digital holography. An important topic in the literature is therefore the generalization of Fourier transform properties for the LCTs. A number of authors have proposed convolution theorems for the linear canonical transform, with different goals in mind. In this paper, we compare those methods, with particular attention being paid to the consequences of discretization. In a similar way to how discrete convolution associated with the DFT differs from that associated with the Fourier transform, we must take the chirp-periodic nature of discrete LCTs into account when determining the discrete convolution associated with LCTs. This work is of significance for the simulation of VanderLugt correlators, which have been used for optical implementations of neural networks, and for optical filtering operations and coherent optical signal processing in general.

关键词： abcd transforms Fourier optics linear canonical transforms correlation convolution

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Propagation properties of hypergeometric-Gaussian type-II beams through the quadratic-index medium

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APPLIED OPTICS 2018年第17期57卷 4735-4742页

作者： Bian, Lirong Tang, Bin Changzhou Univ Sch Math & Phys Changzhou 213164 Peoples R China Shanghai Jiao Tong Univ State Key Lab Adv Opt Commun Syst & Networks Shanghai Peoples R China

The analytical expressions of hypergeometric-Gaussian type-II (HyGG-II) beams propagating in the quadratic-index medium are deduced based on the abcd optical transformation matrix method. The propagation properties of HyGG-II beams in the quadratic-index medium are numerically and theoretically analyzed in detail. The intensity distribution and the second-order moment-based beam width vary periodically when the HyGG-II beams pass through the quadratic-index medium. The interactions of two HyGG-II beams are also discussed graphically. (C) 2018 Optical Society of America

关键词： abcd transforms Fractional Fourier transforms Matrix methods Numerical simulation Optical fields Spatial solitons

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Fast and accurate computation of normalized Bargmann transform

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2017年第1期34卷 18-26页

作者： Pei, Soo-Chang Huang, Shih-Gu Natl Taiwan Univ Dept Elect Engn Taipei 10617 Taiwan Natl Taiwan Univ Grad Inst Commun Engn Taipei 10617 Taiwan

The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex LCT. In this paper, we normalize the Bargmann transform such that it can be bounded near infinity. We derive the relationships of the normalized Bargmann transform to Gabor transform, Hermite-Gaussian functions, gyrator transform, and 2D nonseparable LCT. Several kinds of fast and accurate computational methods of the normalized Bargmann transform and its inverse are proposed based on these relationships. (C) 2016 Optical Society of America

关键词： Fourier optics and signal processing Paraxial wave optics abcd transforms Fractional Fourier transforms Quantum optics

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Propagation of an Airy-Gaussian-Vortex beam in a chiral medium

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OPTICS COMMUNICATIONS 2017年 388卷 29-37页

作者： Hua, Sen Liu, Youwen Zhang, Huijie Tang, Liangzun Feng, Yunxcai Nanjing Univ Aeronaut & Astronaut Dept Appl Phys Nanjing 210016 Jiangsu Peoples R China

Based on the Huygens diffraction integral, the analytical expressions of electric field distribution of the Airy-Gaussian-Vortex (AiGV) beam in a chiral medium are derived, and its propagation properties are investigated. With increasing the value of chiral parameter., the parabolic deflection of the LCP light increases and the RCP light decreases respectively. For the first-order AiGV beam with only one positive or negative optical vortex (OV), a half-moon-shaped intensity profile can be observed because of overlap of the OV and the Airy main lobe, and then the main lobe will be reconstructed and the vortex could be recovered after the overlap position. The intensity distribution of AiGV beam, the deflection trajectories of central positions of Airy beam and OV under different competing parameters between Gaussian and Airy terms have been studied. Furthermore, for the second-order counterrotating AiGV beam with positive and negative vortexes, it could be considered the superposition of two first-order AiGV beams with respective positive and negative vortexes. Two vortexes can regenerate during propagation and the intensity distribution the AiGV beam in the far zone can be controlled by adjusting the coordinates of two vortexes.

关键词： Airy Gaussian beam Optical vortex Chiral medium abcd transforms

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Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform 5

Constraints to solve parallelogram grid problems in 2D non s...

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Conference on Holography - Advances and Modern Trends V

作者： Zhao, Liang Healy, John J. Muniraj, Inbarasan Cui, Xiao-Guang Malallah, Ra'ed Ryle, James P. Sheridan, John T. Univ Coll Dublin Insight Ctr Data Analyt Dublin 4 Ireland Univ Coll Dublin Coll Engn & Architecture SFI Strateg Res Cluster Solar Energy Convers Sch Elect & Elect EngnLab IoE2 Dublin 4 Ireland Chinese Acad Sci Inst Automat 95 East Zhong Guan Cun Rd Beijing 100190 Peoples R China Univ Basrah Fac Sci Phys Dept Garmat Ali Basrah Iraq

ISBN: (数字)9781510609686

ISBN: (纸本)9781510609679;9781510609686

The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques;however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.

关键词： Digital holography abcd transforms Numerical approximation and analysis Discrete optical signal processing

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Influence of the eigenmode polarization deviation on the output Sagnac frequency difference in nonplanar ring resonators

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APPLIED OPTICS 2016年第3期55卷 473-478页

作者： Li, Dong Bi, Chao Jiang, Yajun Zhao, Jianlin Northwestern Polytech Univ Minist Educ Key Lab Space Appl Phys & Chem Xian 710072 Peoples R China Northwestern Polytech Univ Sch Sci Shaanxi Key Lab Opt Informat Technol Xian 710072 Peoples R China

We present a theoretical model to quantitatively analyze the influence of the eigenmode polarization deviation (described with ellipticity parameter) on the output Sagnac frequency difference in two nonplanar ring resonators with different mirror arrangements. The theoretical and numerical analysis results prove that the deviation of the eigenmode polarization from the ideally circular polarized state will produce a drop of the output Sagnac frequency difference. Furthermore, for the identical ellipticity parameter and incident angles, the decline values along the rotation axis A(2) is more obvious than that along axis A(1). In other words, these results show that the output Sagnac frequency difference can be improved effectively by restraining the eigenmode polarization deviation quantitatively and that these analysis findings are useful for designing and optimizing the structure of laser gyroscopes with super-high precision. (C) 2016 Optical Society of America

关键词： abcd transforms Sagnac effect Lasers Lasers ring Polarization

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Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2016年第6期33卷 1025-1031页

作者： Zhao, Ruihuang Deng, Fu Yu, Weihao Huang, Jiayao Deng, Dongmei S China Normal Univ Guangdong Prov Key Lab Nanophoton Funct Mat & Dev Guangzhou 510631 Guangdong Peoples R China Univ Sci Technol China Chinese Acad Sci CAS Key Lab Geospace Environm Hefei 230026 Peoples R China

Propagation of Airy-Gaussian vortex (AiGV) beams through the gradient-index medium is investigated analytically and numerically with the transfer matrix method. Deriving the analytic expression of the AiGV beams based on the Huygens diffraction integral formula, we obtain the propagate path, intensity and phase distributions, and the Poynting vector of the first-and second-order AiGV beams, which propagate through the paraxial abcd system. The ballistic trajectory is no longer conventional parabolic but trigonometric shapes in the gradient-index medium. Especially, the AiGV beams represent the singular behavior at the propagation path and the light intensity distribution. The phase distribution and the Poynting vector exhibit in reverse when the AiGV beams through the singularity. As the order increases, the main lobe of the AiGV beams is gradually overlapped by the vortex core. Further, the sidelobe weakens when the AiGV beams propagate nearly to the singularity. Additionally, the figure of the Poynting vector of the AiGV beams proves the direction of energy flow corresponding to the intensity distribution. The vortex of the second-order AiGV beams is larger, and the propagation velocity is faster than that of the first order. (C) 2016 Optical Society of America

关键词： Laser beam transmission Phase shift Optical vortices Paraxial wave optics abcd transforms Materials and process characterization

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Unified matrix approach to the description of phase-space rotators

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APPLIED OPTICS 2016年第7期55卷 1530-1536页

作者： Gitin, Andrey V. Tech Univ Berlin Inst Opt & Atomare Phys Sekr ER 1-1Str 17 Juni 135 D-10623 Berlin Germany

In optics, the rotation of a phase-space can be realized via light propagation through both an inhomogeneous medium with a radial gradient of refractive index and two special kinds of mirror-symmetrical optical systems suggested by Lohmann. Although light propagation through Lohmann's systems is described in terms of matrix optics, light propagation through the gradient-index medium is traditionally described as a solution of the wave equation. The difference in these descriptions hinders the understanding of the phase-space rotators. Fortunately, there is a matrix description of light propagation through a gradient-index medium too. A general description of the phase-space rotators is presented, which can be used to treat light propagation through both Lohmann's systems and the gradient-index medium in a unified matrix manner. (C) 2016 Optical Society of America

关键词： Fiber optics abcd transforms Matrix methods in paraxial optics Propagation

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