The Mathematical Theory of Laser Beam-Splitting Gratings

Romero, Louis A.; Dickey, Fred M.

doi:10.1016/s0079-6638(10)05411-9

Cited by 39 publications

(49 citation statements)

References 30 publications

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“…In the absence of fabrication errors and using a thin grating approximation, the transmitted phase in air of a beam at position x is changed by an amount ( ) ( )2 ( 1) / , x h x n φ π λ = − (1) where n is the grating material refractive index and λ is the wavelength of light. If there are multiplicative fabrication errors Δ, the accumulated phase has a total phase transmission (1 + Δ)φ(x).…”

Section: Theorymentioning

confidence: 99%

“…It is often desirable to split one laser beam into multiple beams with equal energy for applications such as laser machining and material processing in parallel, sensor systems, interferometry, communication systems, and image processing and gathering systems [1]. The authors require multiple beams with equal energy for a scanning array confocal microscope [2].…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

et al. 2015

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A method to design one-dimensional beam-spitting phase gratings with low sensitivity to fabrication errors is described. The method optimizes the phase function of a grating by minimizing the integrated variance of the energy of each output beam over a range of fabrication errors. Numerical results for three 1x9 beam splitting phase gratings are given. Two optimized gratings with low sensitivity to fabrication errors were compared with a grating designed for optimal efficiency. These three gratings were fabricated using gray-scale photolithography. The standard deviation of the 9 outgoing beam energies in the optimized gratings were 2.3 and 3.4 times lower than the optimal efficiency grating.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

et al. 2015

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“…However, as the topological charge of the vortex beam increases, the diameter of the generated doughnut diffraction order also increases. Therefore, a diffraction grating with equal energy in the various orders does not generate equally intense doughnut beams because their diameters are different and the energy is distributed across a wider area.In this Letter, we produce a variation on previous approaches [10] for producing high efficiency grating beam splitters, where the energies of the output beams have a predefined nonuniform distribution. As an example, we use this method to produce a vortex-generating grating where the intensities of the doughnut beams at each different orders are all equal, in opposition to what happens in those reported in [13][14][15].…”

mentioning

confidence: 99%

“…In this Letter, we produce a variation on previous approaches [10] for producing high efficiency grating beam splitters, where the energies of the output beams have a predefined nonuniform distribution. As an example, we use this method to produce a vortex-generating grating where the intensities of the doughnut beams at each different orders are all equal, in opposition to what happens in those reported in [13][14][15].…”

mentioning

confidence: 99%

“…However, optimal efficient diffraction grating fan-out elements can be analytically solved using a single equation with a limited set of parameters. For instance, Gori et al solved the optimal triplicator in [9], and Romero and Dickey further extended the technique to an arbitrary number of target diffraction orders in [10]. However, one can barely find experimental realizations of this last kind of gratings in the literature due to the difficulties in reproducing the derived continuous phase profiles [11].…”

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confidence: 99%

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Generalized phase diffraction gratings with tailored intensity

et al. 2012

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We report the generation of continuous phase masks designed to generate a set of target diffraction orders with defined relative intensity weights. We apply a previously reported analytic calculation that requires resolving a single equation with a set of parameters defining the target diffraction orders. Then the same phase map is extended to other phase patterns such as vortex generating/sensing gratings. Results are demonstrated experimentally with a parallel-aligned spatial light modulator.

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Energy‐Tailorable Spin‐Selective Multifunctional Metasurfaces with Full Fourier Components

Liu

et al. 2019

Advanced Materials

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investigated at different wavebands, such as microwave, [1] terahertz, [2,3] and infrared [4] regions. Artificial metasurfaces composed of customized planar nanostructures have been a research hot spot to manipulate EM waves, which provide a wide platform for deep light-matter interactions at the subwavelength scale. [5][6][7][8][9][10] Taking advantage of the abundant resonances generated from nanostructures composed of different materials, such as metallic, [11] dielectric, [12,13] and 2D materials, [14] various kinds of metasurfaces have been proposed in the applications of electromagnetically induced transparency, [15] zero-index responses, [16,17] asymmetric spin-orbit interaction, [18,19] structural colors, [20][21][22][23] surface waves, [24] topological photonics, [25,26] and so on. Metasurfaces are also a sophisticated and versatile tool to control optical amplitude, [27] phase, [28] polarization, [29] and the combination of these optical dimensions. [30][31][32][33] Compared with single-layer metasurfaces, few-layer metasurfaces with two or more overlapping structure layers significantly increase the effective light-matter interaction distances and exploit the integrated functionalities of metasurfaces. [34][35][36][37][38][39] However, to date the integration of arbitrary optical functionalities onto one single metasurface is still challenging due to the limitation of theoretical design and the absence of full control for multidimensional optical fields.Recently, integrated multifunctional metasurfaces that can deal with concurrent tasks have drawn much attention of the scientific community. [40][41][42][43] One of the designs to realize multifunctional metasurfaces is to divide the device into several areas, and each area serves as one functionality. [44,45] Such designs usually suffer from low information capacity and strong noises originated from channels mixing. [46] Another design utilizes harmonic analysis to distribute all the functionality channels to each nanostructures, which has been widely investigated to achieve polarization-controllable multichannel vortex beams generation. [47][48][49] Jiang et al. proposed a broadband multipole vortex beams generation for centimeter waves, and opened up the possibilities for multichannel informational gigahertz modulation. [50] However, the abovementioned designs employ intensity-or phase-only manipulation to control the optical fields, which suffer from unavoidable noises for multifunctional optical devices. Especially for the phase-only design, [51] one usually needs to perform complex optimizations Compact integrated multifunctional metasurface that can deal with concurrent tasks represent one of the most profound research fields in modern optics. Such integration is expected to have a striking impact on minimized optical systems in applications such as optical communication and computation. However, arbitrary multifunctional spin-selective design with precise energy configuration in each channel is still a challenge, and suffers from intrinsic noise...

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The Mathematical Theory of Laser Beam-Splitting Gratings

Cited by 39 publications

References 30 publications

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings

Generalized phase diffraction gratings with tailored intensity

Energy‐Tailorable Spin‐Selective Multifunctional Metasurfaces with Full Fourier Components

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