Optical system design for orthosymplectic transformations in phase space

Rodrigo, José A.; Alieva, Tatiana; Calvo, M. L.

doi:10.1364/josaa.23.002494

Cited by 51 publications

(50 citation statements)

References 18 publications

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“…The 2D-NS-LCT can represent a wide variety of non-orthogonal, non-axially symmetric and anamorphic systems [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] . Among its special cases are the FT, FRT, and FST, gyrator transform, chirp transform, homogeous coordinate/affine transform (including e.g.…”

Section: An Overview Of 2d-ns-lctmentioning

confidence: 99%

“…It however is widely accepted that the security of any encryption system depends on the keys used and therefore the larger the key-space the more the security will be 5 . In addition to these approaches, in this paper, for the first time, a novel 2D-NS-LCT [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] based optical DRPE system is proposed. This proposed system offers encrypting information in multiple (10) degrees of freedom (see Table 1).…”

Section: Introductionmentioning

confidence: 99%

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2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

et al. 2017

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Section: An Overview Of 2d-ns-lctmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

et al. 2017

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“…This decomposition is a special case of the Iwasawa decomposition [34][35][36]. (For a discussion of the implications of this decomposition on the propagation of light through first-order optical systems, see [19,37].…”

Section: Quadratic-phase Systemsmentioning

confidence: 99%

Phase-space window and degrees of freedom of optical systems with multiple apertures

Özaktaş

Oktem

2013

J. Opt. Soc. Am. A

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We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its spacefrequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.

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“…Based on the matrix formalism, flexible optical setups have been designed [17], with which an antisymmetric fractional FT R T f ͑␥,−␥͒ , a gyrator R T g ͑␥͒ , and a rotator R T r ͑␥͒ (with /2ഛ ␥ ഛ 3 / 2) can be realized, and which can be used for controlled geometric phase accumulation.…”

Section: ͑5͒mentioning

confidence: 99%

Dynamic and geometric phase accumulation by Gaussian-type modes in first-order optical systems

Alieva

Bastiaans

2008

Opt. Lett.

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Based on the ray transformation matrix formalism, we propose a simple method for the identification of the dynamic and geometric parts of the Gouy phase, acquired by an appropriate Gaussian-type beam while propagating through a first-order optical system. © 2008 Optical Society of America OCIS codes: 070.2575, 070.2580, 070.2590, 070.3185, 070.4690, 080.2468 A transversal mode with a Gaussian envelope, undergoing a cycle of transformations while propagating through a paraxial optical system, accumulates Gouy phase, usually divided into two parts: A dynamic part and a geometric part [1][2][3][4]. The identification of the Gouy phase is important in resonator theory [5], in optical trapping [6], and in possible applications of its geometric part for quantum computation [7]. The physical origin of the geometric phase, its calculation in parametric space [2,3], and its experimental measurement [4] have been discussed in a series of publications.In this Letter we propose a simple method for the determination of the Gouy phase-and in particular its dynamic and geometric parts-accumulated by an appropriate Gaussian-type mode during its propagation through a first-order optical system. It is based on the analysis of the eigenvalues of the ray transformation matrix associated with the first-order optical system.Strictly speaking, a coherent beam of light ⌿͑r͒, propagating through an optical system described by an operator R, accumulates a phase shift only if it is an eigenfunction of R with a unimodular eigenvalue exp͑i͒: R͓⌿͑r i ͔͒͑r o ͒ = exp͑i͒⌿͑r o ͒. Therefore we need to identify a system where phase accumulation is possible and determine the corresponding beams.Beam propagation through a lossless first-order optical system is described by the canonical integral transformation R T [8,9], whose kernel is parameterized by the real symplectic ray transformation matrix T, which relates the (properly normalized) position r = ͑x , y͒ t and direction p = ͑p x , p y ͒ t of an incoming ray to those of the outgoing ray. Using the modified Iwasawa decomposition [10] the (normalized) ray transformation matrix T can be written as a product of three symplectic matrices,where the first matrix T L represents a lens described by the symmetric matrix G =−͑CA t + DB t ͒͑AA t + BB t ͒ −1 , the second matrix T S corresponds to a scaler described by the positive definite symmetric matrix S = ͑AA t + BB t ͒ 1/2 , and the third matrix T O is orthogonal and can be described by the unitary matrix U = X + iY = ͑AA t + BB t ͒ −1/2 ͑A + iB͒. A simple example of Gouy phase accumulation is the propagation of the well-known HermiteGaussian (HG) modes H m,n ͑r͒ = H m ͑x͒H n ͑y͒, where H n ͑x͒ =2

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Optical system design for orthosymplectic transformations in phase space

Cited by 51 publications

References 18 publications

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

2D non-separable linear canonical transform (2D-NS-LCT) based cryptography

Phase-space window and degrees of freedom of optical systems with multiple apertures

Dynamic and geometric phase accumulation by Gaussian-type modes in first-order optical systems

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