Optics

Download Field guide to digital micro-optics by Bernard C. Kress PDF

By Bernard C. Kress

Conventional macro-optics could be designed with out complicated layout software program instruments. even though, electronic optics, specifically wafer-scale micro-optics, require particular software program and instruments. there's frequently no analytical answer, and hence advanced iterative optimization algorithms should be required. This ebook covers refractive and diffractive micro-optics, the iterative optimization technique, and modeling and fabrication recommendations an important to this box. the facility to create hybrid structures able to generating analog and electronic performance can also be addressed

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In many cases, a more-complex phase profile might be required to address specific aberration corrections. A general aspheric phase profile can be described through the sag equation and an astigmatic polynomial series: ! XN 2p Cr2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ C r2i uðrÞ ¼ i¼1 i l 1 þ 1 À ðA þ 1Þr2 C 2 where A is the conic constant, and C is the curvature at the vertex. Note that these phase profiles are described over a target surface that is then converted into a real surface-relief profile as a function of the index and/or the design wavelength.

This is not the case for diffractives, at least when they are fabricated via microlithography. For diffractives, a general polynomial (X/Y cross-linked terms) may bear the same lithographic fabrication burden as the fabrication of simpler linear or spherical surfaces. While designing such aspheric surfaces, care must be taken when unleashing higher-order coefficients in the optimization process (in CAD tools): this may not necessarily yield fewer aberrations if the cost function has not been designed to prevent the divergence of higher aspheric polynomial coefficients.

The Fresnel rings can also be considered as slices of 2p cut from the continuous phase profile. The following figure shows how a continuous phase profile is sliced into 2p slices and reset on the same surface to form the Fresnel rings. The phase profile is expressed over a planar or curved surface and is not a refractive profile. The phase profile is imprinted on the wavefront at that surface (at least in the fundamental diffraction order). 2π 2π 2π 2π 2π Field Guide to Digital Micro-Optics 32 Diffractive Micro-Optics Diffractive Lens Profile Descriptions 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !

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