DOCSLIB.ORG

Redalyc.Bidimensional Dynamic Maps in Optical Resonators

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Redalyc.Bidimensional Dynamic Maps in Optical Resonators Revista Mexicana de Física ISSN: 0035-001X [email protected] Sociedad Mexicana de Física A.C. México Aboites, V.; Barmenkov, Y.; Kiryanov, A.; Wilson, M. Bidimensional dynamic maps in optical resonators Revista Mexicana de Física, vol. 60, núm. 1, enero-junio, 2014, pp. 13-23 Sociedad Mexicana de Física A.C. Distrito Federal, México Available in: http://www.redalyc.org/articulo.oa?id=57048160002 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative EDUCATION REVISTA MEXICANA DE FISICA´ 60 (2014) 13–23 JANUARY–JUNE 2014 Bidimensional dynamic maps in optical resonators V. Aboitesa, Y. Barmenkova, A. Kiryanova and M. Wilsonb aCentro de Investigaciones en Optica,´ Loma del Bosque 115, Leon,´ 37150 Mexico.´ e-mail: [email protected] bUniversite´ des Sciences et Technologies de Lille 1, CNRS UMR 8523-UFR de Physique-Batimentˆ P5, 59655 Villeneuve d’Ascq Cedex, France. Received 29 August 2012; accepted 24 February 2014 In this article an introduction to the dynamical behavior of a beam within a ring phase-conjugated optical resonator is presented and modeled using two dimensional iterative maps. Three well known iterative maps are described: Duffing, Tinkerbell and Henon,´ and are applied to the description of optical resonators. It is explicitly shown how the difference equations of these maps can be used to describe the dynamic behavior of what we call Tinkerbell, Duffing and Henon´ beams i.e. beams that behave according to these maps. The matrix of a map generating device are found in terms of the specific map parameters, the state variables and the resonator parameters for each of the three named maps. Keywords: Resonator; chaotic maps; phase conjugation. En este art´ıculo se presenta una introduccion´ al comportamiento dinamico´ de un haz dentro de un resonador optico´ de anillo de conjugacion´ de fase el cual es modelado usando mapas iterativos bidimensionales. Tres bien conocidos mapas iterativos son descritos: Duffing, Tinkerbell y Henon,´ y son utilizados para la descripcion´ de resonadores opticos.´ Se muestra expl´ıcitamente como´ las ecuaciones de diferencia de los mapeos anteriores pueden ser utilizados para describir el comportamiento dinamico´ de lo que llamamos, Haces de Tinkerbell, Duffing y Henon´ i.e. haces que se comportan siguiendo dichos mapas. La matriz de un dispositivo generador del mapeo se encuentra en terminos´ de los parametros´ espec´ıficos del mapa, de las variables de estado y de los parametros´ del resonador para cada uno de los tres mapas anteriores. Descriptores: Resonador; mapeo caotico;´ resonador de anillo. PACS: 42.15.-I; 42.60.Da; 42.65.Hw 1. Introduction tion areas: such as high-brightness laser oscillator/amplifier systems, cavity-less lasing devices, laser target-aiming sys- Recently, optical phase conjugation (OPC) has been an im- tems, aberration correction for coherent-light transmission portant research subject in the field of lasers and nonlin- and reflection through disturbing media, long distance op- ear optics. As it is known, OPC defines a link between tical fiber communications with ultra-high bit-rate, optical two coherent optical beams propagating in opposite direc- phase locking and coupling systems, and novel optical data tions with reversed wave front and identical transverse am- storage and processing systems (see Ref. 1 and references plitude distributions. The unique characteristic of a pair of therein). The power performance of a phase conjugated laser phase-conjugate beams is that the aberration influence im- oscillator can be significantly improved introducing intracav- posed on the forward beam passed through an inhomoge- ity nonlinear elements, e.g. Eichler et al., [2] and O’Connor neous or disturbing medium can be automatically removed et al., [3] showed that a stimulated-Brillouin-scattering (SBS) for the backward beam passed through the same disturbing phase conjugating cell placed inside the resonator of a solid- medium. There are three leading approaches that are effi- state laser reduces its optical coherence length, because each ciently able to generate the backward phase-conjugate beam. axial mode of the phase conjugated oscillator experiences a The first one is based on the degenerate (or partially de- frequency shift at every reflection by the SBS cell resulting generate) four-wave mixing processes (FWM), the second is in a multi-frequency lasing spectrum, that makes the laser in- based on a variety of backward simulated (e.g. Brillouin, sensitive to changing operating conditions such as pulse rep- Raman or Kerr) scattering processes, and the third is based etition frequency, pump energy, etc. This capacity is very on one-photon or multi-photon pumped backward stimulated important for many laser applications including ranging and emission (lasing) processes. Among these different methods, remote sensing. The intracavity cell is also able to compen- there is a common physical mechanism in generating a back- sate optical aberrations from the resonator and from thermal ward phase-conjugate beam, which is the formation of the effects in the active medium, resulting in near diffraction lim- induced holographic grating and the subsequent wave-front ited output [4], and eliminate the need for a conventional restoration via a backward reading beam. In most experi- Q-switch as well, because its intensity-dependent reflectiv- mental studies, certain types of resonance enhancements of ity acts as a passive Q-switch, typically producing a train of induced refractive-index changes are desirable for obtaining nanosecond pulses of diffraction limited beam quality. One higher grating-refraction efficiency. OPC-associated tech- more significant use of OPC is a so-called short hologram, niques can be effectively utilized in many different applica- 14 V. ABOITES, Y. BARMENKOV, A. KIRYANOV AND M. WILSON which does not exhibit in-depth diffraction deformation of and its angle with the same axis as y(z) and θ(z), when the the fine speckle pattern of the recording fields [5]. A thermal ray undergoes a transformation as it travels through an optical hologram in the output mirror was recorded by two speckle system represented by the matrix [A; B; C; D], the resultant waves produced as a result of this recording a ring Nd:YAG values of y and θ are given by [18]: laser [6]. Phase conjugation by SBS represents a fundamen- µ ¶ µ ¶ µ ¶ tally encouraging approach for achieving power scaling of y AB y n+1 = n : (1) solid-state lasers [7,8] and optical fibers [9]. There are several θn+1 CD θn theoretical models to describe OPC in resonators and lasers. One of them is to use the SBS reflection as one of the cavity For any optical system, one may obtain the total mirrors of a laser resonator to form a so-called linear phase [A; B; C; D] matrix, by carrying out the matrix product of conjugate resonator [10], however ring-phase conjugate res- the matrices describing each one of the optical elements in onators are also possible [11]. The theoretical model of an the system. OPC laser in transient operation [12] considers the temporal and spatial dynamic of the input field the Stokes field and the acoustic-wave amplitude in the SBS cell. On the other hand Constant ABCD elements the spatial mode analysis of a laser may be carried out using transfer matrices, also know as ABCD matrices, which are a In passive optical elements, such as lenses, interfaces be- useful mathematical tool when studying the propagation of tween two media, reflections, propagation, and many others, light rays through complex optical systems. They provide a the elements A, B, C, D are constants and the determinant simple way to obtain the final key characteristics (position Det[A; B; C; D] = nn/nn+1, where nn and nn+1 are the re- and angle) of the ray. As an important example we could fraction index before and after the optical element described mention that transfer matrices have been used to study self- by the matrix. Since typically nn and nn+1 are the same, it adaptive laser resonators where the laser oscillator is made holds that Det[A; B; C; D] = 1. out of a plane output coupler and an infinite nonlinear FWM medium in a self-intersecting loop geometry [13]. Non constant ABCD elements In this article we put forward an approach where the in- tracavity element is presented in the context of an iterative Nevertheless, for active or non-linear optical elements the A, map (e.g. Tinkerbell, Duffing and Henon)´ whose state is de- B, C, D matrix elements are not constant but may be func- termined by its previous state. It is shown that the behavior tions of various parameters. The following three examples of a beam within a ring optical resonator may be well de- are worth mentioning. scribed by a particular iterative map and the necessary con- ditions for its occurrence are discussed. In particular, it is shown that the introduction of a specific element within a ring Curved interface with a Kerr electro-optic material phase-conjugated resonator may produce beams described by a Duffing, Tinkerbell or Henon´ map, which we call “Tinker- Due to the electro-optic Kerr effect the refraction index of bell, Duffing or Henon´ beams”. an optical media n is a function of the electric field strength The idea of introducing map generating elements in opti- E [19]. The change of the refraction index is given by cal resonators from a mathematical viewpoint was originally ¢n = ¸KE2, where ¸ is the wavelength and K is the Kerr explored in [14-17] and due to its pedagogical purposes this constant of the media.
Load more

Recommended publications
  • Chaotic Multiobjective Evolutionary Algorithm Based on Decomposition for Test Task Scheduling Problem
    Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2014, Article ID 640764, 25 pages http://dx.doi.org/10.1155/2014/640764 Research Article Chaotic Multiobjective Evolutionary Algorithm Based on Decomposition for Test Task Scheduling Problem Hui Lu, Lijuan Yin, Xiaoteng Wang, Mengmeng Zhang, and Kefei Mao School of Electronic and Information Engineering, Beihang University, Beijing 100191, China Correspondence should be addressed to Hui Lu; [email protected] Received 13 March 2014; Revised 20 June 2014; Accepted 20 June 2014; Published 15 July 2014 Academic Editor: Jyh-Hong Chou Copyright © 2014 Hui Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Test task scheduling problem (TTSP) is a complex optimization problem and has many local optima. In this paper, a hybrid chaotic multiobjective evolutionary algorithm based on decomposition (CMOEA/D) is presented to avoid becoming trapped in local optima and to obtain high quality solutions. First, we propose an improving integrated encoding scheme (IES) to increase the efficiency. Then ten chaotic maps are applied into the multiobjective evolutionary algorithm based on decomposition (MOEA/D) in three phases, that is, initial population and crossover and mutation operators. To identify a good approach for hybrid MOEA/D and chaos and indicate the effectiveness of the improving IES several experiments are performed. The Pareto front and the statistical results demonstrate that different chaotic maps in different phases have different effects for solving the TTSP especially the circle map and ICMIC map.
    [Show full text]
  • Enhanced Multi Chaotic Systems Based Pixel Shuffling for Encryption
    A Major Project Report On Enhanced Multi Chaotic Systems Based Pixel Shuffling for Encryption Submitted in partial fulfilment of the requirements for the award of the degree of Master of Technology In Information Systems Submitted By: MUNAZZA NIZAM Roll No. 07/IS/2010 Under the Guidance of Prof. O. P. Verma (HOD, IT Department) Department of Information Technology DELHI TECHNOLOGICAL UNIVERSITY Bawana Road, Delhi-110042 2010-2012 CERTIFICATE This is to certify that Ms. Munazza Nizam (07/IS/2010) has carried out the major project titled “Enhanced Multi-Chaotic Systems Based Pixel Shuffling for Encryption” as a partial requirement for the award of Master of Technology degree in Information Systems by Delhi Technological University. The major project is a bonafide piece of work carried out and completed under my supervision and guidance during the academic session 2010-2012. The matter contained in this report has not been submitted elsewhere for the award of any other degree. Prof. O. P. Verma (Project Guide) Head of Department Department of Information Technology Delhi Technological University Bawana Road, Delhi-110042 i ACKNOWLEDGEMENT It’s true and proved that behind every success, there is certainly an unseen power of Almighty Allah, He is the grand operator of all projects. First of all, I thank my parents who have always motivated me and given their blessings for all my endeavors. I take this opportunity to express my profound sense of gratitude and respect to all those who helped me throughout the duration of this project. I would like to express my sincere gratitude to Prof. O.P.
    [Show full text]
  • Jensen-Shannon Complexity and Permutation Entropy Analysis Of
    RESEARCH ARTICLE Jensen-Shannon Complexity and Permutation Entropy 10.1029/2018JA026248 Analysis of Geomagnetic Auroral Currents Key Points: • Jensen-Shannon complexity plane is Adnane Osmane1 , Andrew P. Dimmock2, and Tuija I. Pulkkinen3,4 used for first time to analyze auroral geomagnetic indices 1Department of Physics, University of Helsinki, Helsinki, Finland, 2IRF Swedish Institute of Space Physics, Uppsala, • Auroral indices are shown to be Sweden, 3Department of Climate and Space Sciences, University of Michigan, Ann Arbor, MI, USA, 4School of inconsistent with low-dimensional chaotic processes Electrical Engineering, Aalto University, Espoo, Finland • Maximum in complexity occurs on time scales ranging between 10 and 40 min Abstract In this study we determine whether auroral westward currents can be characterized by low-dimensional chaotic attractors through the use of the complexity-entropy methodology developed Correspondence to: by Rosso et al. (2007, https://doi.org/10.1103/PhysRevLett.99.154102) and based on the permutation A. Osmane, entropy developed by Bandt and Pompe (2002, https://doi.org/10.1103/PhysRevLett.88.174102). Our [email protected] results indicate that geomagnetic auroral indices are indistinguishable from stochastic processes from time scales ranging from a few minutes to 10 hr and for embedded dimensions d < 8. Our results Citation: are inconsistent with earlier studies of Baker et al. (1990, https://doi.org/10.1029/GL017i001p00041), Osmane, A., Dimmock, A. P., & Pavlos et al. (1992), D. Roberts et al. (1991, https://doi.org/10.1029/ 91GL00021), D. A. Roberts (1991, Pulkkinen, T. I. (2019). Jensen-Shannon complexity and https://doi.org/10.1029/91JA01088), and Vassiliadis et al.
    [Show full text]
  • Improved Spiral Dynamics and Artificial Bee Colony Algorithms with Application to Engineering Problems
    Improved Spiral Dynamics and Artificial Bee Colony Algorithms with Application to Engineering Problems By Mohd Ruzaini Bin Hashim Thesis submitted to the University of Sheffield for the degree of Doctor of philosophy Department of Automatic Control and Systems Engineering The University of Sheffield United Kingdom April 2018 Abstract The main focus of this research is to develop improved version of spiral dynamic algorithm (SDA) and srtificial bee colony algorithm (ABC) for solving various kinds of optimization problems. There are eight new algorithms developed in this research based on ABC and SDA. The first modification is on the initial distributions based on chaotic maps trajectory, random and opposition based learning. This adaptive initial distribution is used in all proposed algorithms. Second modification is to use spiral radius and chaotic rotational angle in modified SDA. Furher modifications include proposition of three adaptive ABC algorithms based on the modification of step size using exponential, linear and combination of both linear and exponential functions. Investigations have shown that SDA is a fast and simple algorithm but is subject to getting trapped in local optima and it lacks diversity in the search, while ABC is able to get accurate output at the expense of high computational time and slow convergence. Thus, the research further embarks on hybridisation of SDA and ABC, taking advantage of capabilities of both algorithms and three hybrid algorithms are thus proposed. The performances of the proposed algorithms are evaluated and assessed in single objective, multi-objective type and in practical optimization problems. Statistical and significant tests are used in the evaluations.
    [Show full text]
  • Math Morphing Proximate and Evolutionary Mechanisms
    Curriculum Units by Fellows of the Yale-New Haven Teachers Institute 2009 Volume V: Evolutionary Medicine Math Morphing Proximate and Evolutionary Mechanisms Curriculum Unit 09.05.09 by Kenneth William Spinka Introduction Background Essential Questions Lesson Plans Website Student Resources Glossary Of Terms Bibliography Appendix Introduction An important theoretical development was Nikolaas Tinbergen's distinction made originally in ethology between evolutionary and proximate mechanisms; Randolph M. Nesse and George C. Williams summarize its relevance to medicine: All biological traits need two kinds of explanation: proximate and evolutionary. The proximate explanation for a disease describes what is wrong in the bodily mechanism of individuals affected Curriculum Unit 09.05.09 1 of 27 by it. An evolutionary explanation is completely different. Instead of explaining why people are different, it explains why we are all the same in ways that leave us vulnerable to disease. Why do we all have wisdom teeth, an appendix, and cells that if triggered can rampantly multiply out of control? [1] A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Beno?t Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion. http://www.kwsi.com/ynhti2009/image01.html A fractal often has the following features: 1. It has a fine structure at arbitrarily small scales.
    [Show full text]
  • Sustainability As "Psyclically" Defined -- /
    Alternative view of segmented documents via Kairos 22nd June 2007 | Draft Emergence of Cyclical Psycho-social Identity Sustainability as "psyclically" defined -- / -- Introduction Identity as expression of interlocking cycles Viability and sustainability: recycling Transforming "patterns of consumption" From "static" to "dynamic" to "cyclic" Emergence of new forms of identity and organization Embodiment of rhythm Generic understanding of "union of international associations" Three-dimensional "cycles"? Interlocking cycles as the key to identity Identity as a strange attractor Periodic table of cycles -- and of psyclic identity? Complementarity of four strategic initiatives Development of psyclic awareness Space-centric vs Time-centric: an unfruitful confrontation? Metaphorical vehicles: temples, cherubim and the Mandelbrot set Kairos -- the opportune moment for self-referential re-identification Governance as the management of strategic cycles Possible pointers to further reflection on psyclicity References Introduction The identity of individuals and collectivities (groups, organizations, etc) is typically associated with an entity bounded in physical space or virtual space. The boundary may be defined geographically (even with "virtual real estate") or by convention -- notably when a process of recognition is involved, as with a legal entity. Geopolitical boundaries may, for example, define nation states. The focus here is on the extent to which many such entities are also to some degree, if not in large measure, defined by cycles in time. For example many organizations are defined by the periodicity of the statutory meetings by which they are governed, or by their budget or production cycles. Communities may be uniquely defined by conference cycles, religious cycles or festival cycles (eg Oberammergau). Biologically at least, the health and viability of individuals is defined by a multiplicity of cycles of which respiration is the most obvious -- death may indeed be defined by absence of any respiratory cycle.
    [Show full text]
  • Download Vol 5, No 1&2, Year 2012
    The International Journal on Advances in Internet Technology is published by IARIA. ISSN: 1942-2652 journals site: http://www.iariajournals.org contact: [email protected] Responsibility for the contents rests upon the authors and not upon IARIA, nor on IARIA volunteers, staff, or contractors. IARIA is the owner of the publication and of editorial aspects. IARIA reserves the right to update the content for quality improvements. Abstracting is permitted with credit to the source. Libraries are permitted to photocopy or print, providing the reference is mentioned and that the resulting material is made available at no cost. Reference should mention: International Journal on Advances in Internet Technology, issn 1942-2652 vol. 5, no. 1 & 2, year 2012, http://www.iariajournals.org/internet_technology/ The copyright for each included paper belongs to the authors. Republishing of same material, by authors or persons or organizations, is not allowed. Reprint rights can be granted by IARIA or by the authors, and must include proper reference. Reference to an article in the journal is as follows: <Author list>, “<Article title>” International Journal on Advances in Internet Technology, issn 1942-2652 vol. 5, no. 1 & 2, year 2012, <start page>:<end page> , http://www.iariajournals.org/internet_technology/ IARIA journals are made available for free, proving the appropriate references are made when their content is used. Sponsored by IARIA www.iaria.org Copyright © 2012 IARIA International Journal on Advances in Internet Technology Volume 5, Number 1
    [Show full text]
  • Jensen-Shannon Complexity and Permutation Entropy Analysis Of
    manuscript submitted to JGR: Space Physics 1 Jensen-Shannon Complexity and Permutation Entropy 2 Analysis of Geomagnetic Auroral Currents 1 2 3,4 3 Adnane Osmane , Andrew P. Dimmock , Tuija I. Pulkkinen 1 4 Department of Physics, University of Helsinki, Helsinki, Finland 2 5 Swedish Institute of Space Physics, Uppsala University, Uppsala, Sweden 3 6 Department of Climate and Space Sciences, University of Michigan, Ann Arbor, MI, USA 4 7 Aalto University, School of Electrical Engineering, Espoo, Finland 8 Key Points: 9 • Jensen-Shannon complexity plane used to analyse auroral geomagnetic indices. 10 • Auroral indices are shown to be inconsistent with low-dimensional chaotic processes. 11 • Maximum in complexity occurs on timescales ranging between 10 and 40 minutes. This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1029/2018JA026248 Corresponding author: Adnane Osmane, [email protected] This article is protected by copyright.–1– All rights reserved. manuscript submitted to JGR: Space Physics 12 Abstract 13 In this study we determine whether auroral westward currents can be characterised by 14 low dimensional chaotic attractors through the use of the complexity-entropy method- 15 ology developed by Rosso, Larrondo, Martin, Plastino, and Fuentes (2007) and based 16 on the permutation entropy developed by Bandt and Pompe (2002). Our results indi- 17 cate that geomagnetic auroral indices are indistinguishable from stochastic processes from 18 timescales ranging from a few minutes to 10 hours and for embedded dimensions d < 19 8.
    [Show full text]
  • FPGA Design of Encryption Speech System Using Synchronized Fixed-Point Chaotic Maps Based Stream Ciphers
    International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-8 Issue-6, August 2019 FPGA Design of Encryption Speech system using Synchronized Fixed-Point Chaotic Maps Based Stream Ciphers Zahraa M. Alroubaie, Muneer A. Hashem, Fadhil S. Hasan Abstract: In this work, speech encryption using synchronized Nowadays, Unpredictable long-term assessment of fixed-point chaotic map-based stream ciphers (SFPCM-SC) is chaotic systems has been appeared, initial parameters suggested. Five chaotic maps named quadratic, henon, logistic, sensitivity and infinite period, that the usage make them lozi and duffing are synchronized by using master-slave suitable in pseudo random bit generator [10],[14] and synchronization technique and then used to generate the pseudo permutation [15]. Therefore, different researchers are random bit generator (PRBG) using fixed-point converter. The PRBG is then Xor-ed with digitized speech signal where the suggested the chaotic system in stream ciphers-based speech encrypted signal is created. In the other side, the same map is encryption system. In [1] Lorenz chaotic system and Henon synchronized with the master one and used to recover the map in hybrid discrete continuous chaotic system for real original speech signal. First this work is simulated by using time wireless speech encryption are used. In [16] the chaotic MATLAB and then built the design using Xilinx system system is synchronized using the same manner described in generator (XSG). Finally, the hardware co-simulation is applied chaotic masking system. Furthermore, the proposed cipher for the proposed system by using FPGA SP605 XC6SLX45T speech system is implemented using FPGA Virtex-II device.
    [Show full text]
  • Noise Versus Chaos in a Causal Fisher-Shannon Plane
    Papers in Physics, vol. 7, art. 070006 (2015) www.papersinphysics.org Received: 20 November 2014, Accepted: 1 April 2015 Edited by: C. A. Condat, G. J. Sibona Licence: Creative Commons Attribution 3.0 DOI: http://dx.doi.org/10.4279/PIP.070006 ISSN 1852-4249 Noise versus chaos in a causal Fisher-Shannon plane Osvaldo A. Rosso,1, 2∗ Felipe Olivares,3 Angelo Plastino4 We revisit the Fisher-Shannon representation plane H × F, evaluated using the Bandt and Pompe recipe to assign a probability distribution to a time series. Several stochastic dynamical (noises with f −k, k ≥ 0, power spectrum) and chaotic processes (27 chaotic maps) are analyzed so as to illustrate the approach. Our main achievement is uncovering the informational properties of the planar location. I. Introduction quantifiers. Chaotic systems display \sensitivity to ini- Temporal sequences of measurements (or observa- tial conditions" and lead to non-periodic motion tions), that is, time-series (TS), are the basic ele- (chaotic time series). Long-term unpredictability ments for investigating natural phenomena. From arises despite the deterministic character of the tra- TS, one should judiciously extract information on jectories (two neighboring points in the phase space dynamical systems. Those TS arising from chaotic move away exponentially rapidly). Let x (t) and systems share with those generated by stochastic 1 x2(t) be two such points, located within a ball of processes several properties that make them very radius R at time t. Further, assume that these two similar: (1) a wide-band power spectrum (PS), (2) points cannot be resolved within the ball due to a delta-like autocorrelation function, (3) irregular poor instrumental resolution.
    [Show full text]
  • Empirical Analysis of Robust Chaotic Maps for Image Encryption
    International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-9 Issue-11, September 2020 Empirical Analysis of Robust Chaotic Maps for Image Encryption Sonal Ayyappan, C Lakshmi Abstract: The rate of transferring data in the form of text, image, video or audio over an open network has drastically increased. As these are carried out in highly sophisticated fields of medicine, military and banking, security becomes important. In- order to enhance security for transmission, encryption algorithms play a vital role. So as to enhance the proficiency of the existing Images are represented as 2-dimensional arrays of encryption methods and for stronger anti attack abilities, chaotic data. Hence to apply encryption algorithms it must be based cryptography is essential. Chaotic based encryption has considered as one-dimensional array of data[3]. One- advantages of being sensitive to initial conditions and control parameters. Images have features like bulk data capacity and high dimensional image array consumes more space when inter pixel correlation. Transmission of such medical data should compared to one dimensional text data which leads to be highly confidential, integral and authorized. Hence chaos-based compression. It results in reduced space and reduced time for image encryption is an efficient way of fast and high-quality image transmission. But this may cause loss of some data which encryption. It has features like good speed, complexity, highly may be agreeable for general images but may be costly for secure, reasonable computational overhead and power. In this medical images. This results to wrong diagnosis of these paper a comprehensive analysis and an evaluation regarding the medical images [4].
    [Show full text]
  • Generalized Chaotic Maps and Elementary Functions Between Analysis and Implementation
    GENERALIZED CHAOTIC MAPS AND ELEMENTARY FUNCTIONS BETWEEN ANALYSIS AND IMPLEMENTATION By Wafaa Saber AbdelHalim Sayed A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in Mathematical Engineering FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2015 GENERALIZED CHAOTIC MAPS AND ELEMENTARY FUNCTIONS BETWEEN ANALYSIS AND IMPLEMENTATION By Wafaa Saber AbdelHalim Sayed A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in Mathematical Engineering Under the Supervision of Prof. Abdel-Latif E. Hussien Prof. Hossam A. H. Fahmy Professor Professor Engineering Mathematics and Physics Department Electronics and Communication Engineering Department Faculty of Engineering, Cairo University Faculty of Engineering, Cairo University Assoc. Prof. Ahmed G. Radwan Associate Professor Engineering Mathematics and Physics Department Faculty of Engineering, Cairo University FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2015 GENERALIZED CHAOTIC MAPS AND ELEMENTARY FUNCTIONS BETWEEN ANALYSIS AND IMPLEMENTATION By Wafaa Saber AbdelHalim Sayed A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in Mathematical Engineering Approved by the Examining Committee: Prof. Abdel-Latif E. Hussien, Thesis Main Advisor Prof. Hossam A. H. Fahmy, Member Assoc. Prof. Ahmed G. Radwan, Member Prof. Salwa K. Abd-El-Hafiz, Internal Examiner Prof. Nasser H. Sweilam, External Examiner Professor, Faculty of Science, Cairo University FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT 2015 Engineer’s Name: Wafaa Saber AbdelHalim Sayed Date of Birth: 20/3/1991 Nationality: Egyptian E-mail: [email protected] Registration Date: 1/10/2013 Awarding Date: –/–/2015 Degree: Master of Science Department: Engineering Mathematics and Physics Supervisors: Prof.
    [Show full text]