Algorithmic design of diffractive optical systems for information processing

Müller-Quade, Jörn; Aagedal, Harald; Beth, Thomas; Schmid, M.

doi:10.1016/s0167-2789(98)00055-4

Cited by 19 publications

(17 citation statements)

References 2 publications

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“…As shown constructively in [12,14], diffractive optical systems obtained in this manner yields the whole C n×n . (See also the related paper [1].)…”

Section: And Beam Combinersmentioning

confidence: 74%

“…Building on the linear algebraic framework for numerical wave optics proposed in [12], products of circulant and diagonal matrices are taken to model diffractive optical systems. As shown constructively in [12,14], diffractive optical systems obtained in this manner yields the whole C n×n .…”

Section: And Beam Combinersmentioning

confidence: 99%

“…Because of its nonlinearity, computationally the problem gets very challenging as soon as there are more than two factors. In [12] a substitution scheme is proposed for finding the factors of A that is known to be an exact product of two circulants and a diagonal matrix. In [7] an algorithm is devised to approximate with three factors an energy preserving diffractive optical system.…”

Section: And Beam Combinersmentioning

confidence: 99%

“…This gives rise to a 4 f system once a diffractive optical element is placed between two 2 f systems. After discretizations, a single 4 f system is represented in [12] by…”

Section: Representing Ideal Diffractive Optical Systemsmentioning

confidence: 99%

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Approximating ideal diffractive optical systems

Huhtanen

2008

Journal of Mathematical Analysis and Applications

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In numerical wave optics involving diffractive optical elements one is required, at some point, to form a multiplicative matrix factorization. This paper is concerned with such representations and related approximations of ideal diffractive optical systems. Various simple diffractive optical elements are used. The basic factoring problem being highly nonlinear, a minor parallelism in terms of beam splitters and beam combiners makes the task computationally much more tractable and versatile. This gives rise to several matrix nearness problems of geometric nature.

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“…As shown constructively in [12,14], diffractive optical systems obtained in this manner yields the whole C n×n . (See also the related paper [1].)…”

Section: And Beam Combinersmentioning

confidence: 74%

Section: And Beam Combinersmentioning

confidence: 99%

Section: And Beam Combinersmentioning

confidence: 99%

“…This gives rise to a 4 f system once a diffractive optical element is placed between two 2 f systems. After discretizations, a single 4 f system is represented in [12] by…”

Section: Representing Ideal Diffractive Optical Systemsmentioning

confidence: 99%

See 2 more Smart Citations

Approximating ideal diffractive optical systems

Huhtanen

2008

Journal of Mathematical Analysis and Applications

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“…(For the splitting (1.1), see [1].) Our most recent interest in factorization problems originates from the algorithmic construction of diffractive optical systems, where matrices of particular type have a direct physical interpretation [10,9]. Then, somewhat unconventionally in numerical linear algebra, one may need to have all the possible factorizations available for singling out one with most desirable properties.…”

Section: Introductionmentioning

confidence: 99%

Factoring matrices into the product of two matrices

Huhtanen

2007

Bit Numer Math

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Linear algebra of factoring a matrix into the product of two matrices with special properties is developed. This is accomplished in terms of the so-called inverse of a matrix subspace which yields an extended notion for the invertibility of a matrix. The product of two matrix subspaces gives rise to a natural generalization of the concept of matrix subspace. Extensions of these ideas are outlined. Several examples on factoring are presented. (2000): 15A23, 65F30. AMS subject classificationKey words: matrix factorization, inverse of a matrix subspace, product of matrix subspaces.

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Universal Metasurfaces for Complete Linear Control of Coherent Light Transmission

et al. 2022

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Recent advances in metasurfaces and optical nanostructures have enabled complex control of incident light with optically thin devices. However, it has thus far been unclear whether it is possible to achieve complete linear control of coherent light transmission, that is, independent control of polarization, amplitude, and phase for both input polarization states, with just a single, thin nanostructure array. Here, it is proved possible, and a universal metasurface is proposed, a bilayer array of high‐index elliptic cylinders that possesses a complete degree of optical freedom with fully designable chirality and anisotropy. The completeness of achievable light control is mathematically shown with corresponding Jones matrices, new types of 3D holographic schemes that were formerly impossible are experimentally demonstrated, and a systematic way of realizing any input‐state‐sensitive vector linear optical device is presented. The results unlock previously inaccessible degrees of freedom in light transmission control.

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Algorithmic design of diffractive optical systems for information processing

Cited by 19 publications

References 2 publications

Approximating ideal diffractive optical systems

Approximating ideal diffractive optical systems

Factoring matrices into the product of two matrices

Universal Metasurfaces for Complete Linear Control of Coherent Light Transmission

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