Ball lens reflections by direct solution of Maxwell’s equations

Ratowsky, R. P.; Yang, Ligang; Deri, Robert J.; Kallman, J S; Trott, G.R.

doi:10.1364/ol.20.002048

Cited by 8 publications

(2 citation statements)

References 5 publications

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“…As mentioned before, the cusp catastrophe can be caused by such an aberrated focus. Relatively large ball-lenses have been intensively studied for optical-fiber communication systems [6][7][8]. Its characteristics are well studied by geometric optics under paraxial approximation [5].…”

Section: Introductionmentioning

confidence: 99%

Refraction limit of miniaturized optical systems: a ball-lens example

et al. 2016

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Abstract:We study experimentally and theoretically the electromagnetic field in amplitude and phase behind ball-lenses across a wide range of diameters, ranging from a millimeter scale down to a micrometer. Based on the observation, we study the transition between the refraction and diffraction regime. The former regime is dominated by observables for which it is sufficient to use a ray-optical picture for an explanation, e.g., a cusp catastrophe and caustics. A wave-optical picture, i.e. Mie theory, is required to explain the features, e.g., photonic nanojets, in the latter regime. The vanishing of the cusp catastrophe and the emergence of the photonic nanojet is here understood as the refraction limit. Three different criteria are used to identify the limit: focal length, spot size, and amount of crosspolarization generated in the scattering process. We identify at a wavelength of 642 nm and while considering ordinary glass as the ball-lens material, a diameter of approximately 10 µm as the refraction limit. With our study, we shed new light on the means necessary to describe micro-optical system. This is useful when designing optical devices for imaging or illumination.

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Section: Introductionmentioning

confidence: 99%

Refraction limit of miniaturized optical systems: a ball-lens example

et al. 2016

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“…Increasing ball lens mode converter performance through a more reliable design has been discussed by many researchers using theoretical or experimental methods. Correctly predicting the refractions from a ball lens into an SMF [1] and accurately calculating the coupling efficiency from an LD into an optical fiber through a ball lens using the exact solution to Maxwell's equations for the beam scattering from a sphere have been accomplished [2]. Maxwell's equations compared to a conventional method using geometrical and diffraction analysis have also revealed that the optimum coupling efficiency depends on sufficiently fine discretization of the distances between the source and fiber from the ball lens [3].…”

Section: Introductionmentioning

confidence: 99%

Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers

Yang

Chao

Lin

et al. 2003

J. Micromech. Microeng.

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This paper presents a mathematical model to design and fabricate micro-ball lens array using thermal reflow in two polymer layers. The experimental results showed that micro-ball lens arrays were fabricated and integrated onto a planar substrate. Two polymer layers were coated onto a silicon substrate. The upper layer was a photoresist. The lower layer was a polyimide material. The polyimide was expected to form a pedestal to sustain the ball lens after the heat reflow process. Once the patterned polymer is heated above its glass transition temperature, the melting polymer surface will change into a spherical profile for minimizing its surface energy. A successful micro-ball array was formed in the photoresist through the different glass transition temperatures between two polymer materials. The interactive force between two material interfaces caused by surface tension causes the upper profile to form a spherical profile. This also forms the polyimide pedestal into a trapezoid with arc sides. The error in the fabricated micro-ball lens characteristics was 8% between the theoretical models used to predict the photoresist pattern thickness. This model is feasible for fabricating various sized micro-ball lens arrays.

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Micro-ball lens array fabrication in photoresist using PTFE hydrophobic effect

et al. 2006

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This paper presents a simple method for fabricating a micro-ball lens and its array. The core technology involves the hydrophobic characteristics of polyterafluoroethylene (PTFE) substrate. High contact angle between the melted photoresist pattern and PTFE generates the micro-ball lens and array. The PTFE thin film is spun onto a silicon wafer and oven dried. Photoresist AZ4620 is used to pattern micro-columns with various diameters; 60, 70 and 80 mu m. A thermal reflow process is then applied to melt these micro-column patterns into a micro-ball lens array. The achieved micro-ball lens array has a diameter of 98 mu m fabricated using 80 mu m diameter patterns. This method provides a simple fabrication process and low material cost

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Ball lens reflections by direct solution of Maxwell’s equations

Abstract: Thisisa preprintof apaperintended forpublicationina journalorproceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

Cited by 8 publications

References 5 publications

Refraction limit of miniaturized optical systems: a ball-lens example

Refraction limit of miniaturized optical systems: a ball-lens example

Micro-ball lens array modeling and fabrication using thermal reflow in two polymer layers

Micro-ball lens array fabrication in photoresist using PTFE hydrophobic effect

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