Porous Silicon Gradient Refractive Index Micro-Optics.

The emergence and growth of transformation optics over the past decade has revitalized interest in how a gradient refractive index (GRIN) can be used to control light propagation. Two-dimensional demonstrations with lithographically defined silicon (Si) have displayed the power of GRIN optics and also represent a promising opportunity for integrating compact optical elements within Si photonic integrated circuits. Here, we demonstrate the fabrication of three-dimensional Si-based GRIN micro-optics through the shape-defined formation of porous Si (PSi). Conventional microfabrication creates Si square microcolumns (SMCs) that can be electrochemically etched into PSi elements with nanoscale porosity along the shape-defined etching pathway, which imparts the geometry with structural birefringence. Free-space characterization of the transmitted intensity distribution through a homogeneously etched PSi SMC exhibits polarization splitting behavior resembling that of dielectric metasurfaces that require considerably more laborious fabrication. Coupled birefringence/GRIN effects are studied by way of PSi SMCs etched with a linear (increasing from edge to center) GRIN profile. The transmitted intensity distribution shows polarization-selective focusing behavior with one polarization focused to a diffraction-limited spot and the orthogonal polarization focused into two laterally displaced foci. Optical thickness-based analysis readily predicts the experimentally observed phenomena, which strongly match finite-element electromagnetic simulations.

[1]  L. Canham.  Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers , 1990 .

[2]  X. Zhang,et al.  Dielectric Optical Cloak , 2009, 0904.3602.

[3]  G. Parish,et al.  Pulsed Anodization for Control of Porosity Gradients and Interface Roughness in Porous Silicon , 2009 .

[4]  L. Christophorou.  Science , 2018, Emerging Dynamics: Science, Energy, Society and Values.

[5]  Grégory Vincent,et al.  Optical properties of porous silicon superlattices , 1994 .

[6]  U. Leonhardt,et al.  Luneburg lens in silicon photonics. , 2011, Optics express.

[7]  X. G. Zhang.  Morphology and Formation Mechanisms of Porous Silicon , 2004 .

[8]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[9]  David S. Barth,et al.  Macroscale Transformation Optics Enabled by Photoelectrochemical Etching , 2015, Advanced materials.

[10]  M. Breese,et al.  Fabrication of three dimensional porous silicon distributed Bragg reflectors , 2008 .

[11]  J. Sipe,et al.  Nanoscale porous silicon waveguide for label-free DNA sensing. , 2008, Biosensors & bioelectronics.

[12]  M. Lipson,et al.  Silicon nanostructure cloak operating at optical frequencies , 2009, 0904.3508.

[13]  Michael J. Sailor,et al.  Painting a rainbow on silicon – a simple method to generate a porous silicon band filter gradient , 2005 .

[14]  M. Ghadiri,et al.  A porous silicon-based optical interferometric biosensor. , 1997, Science.

[15]  David R. Smith,et al.  Planar, flattened Luneburg lens at infrared wavelengths. , 2012, Optics express.

[16]  D. S. Bradshaw,et al.  Photonics , 2023, 2023 International Conference on Electrical Engineering and Photonics (EExPolytech).

[17]  K. Stetson,et al.  Progress in optics , 1980, IEEE Journal of Quantum Electronics.

[18]  Thomas J. Kempa,et al.  High-throughput patterning of photonic structures with tunable periodicity , 2015, Proceedings of the National Academy of Sciences.

[19]  Stephan Frohnhoff,et al.  Porous silicon superlattices , 1994 .

[20]  M. Fujii,et al.  Dichroic rugate filters based on birefringent porous silicon. , 2008, Optics express.

[21]  G. Bartal,et al.  An optical cloak made of dielectrics. , 2009, Nature materials.

[22]  K. Imai.  A new dielectric isolation method using porous silicon , 1981 .

[23]  Z. Gaburro,et al.  Free-standing porous silicon single and multiple optical cavities , 2003 .

[24]  A. Danner,et al.  Controlling birefringence in dielectrics , 2011 .

[25]  Michael J Sailor,et al.  Smart dust: Self-assembling, self-orienting photonic crystals of porous Si , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[26]  X. Zhang,et al.  An Optical “Janus” Device for Integrated Photonics , 2010, Advanced materials.

[27]  Wenqi Zhu,et al.  Efficient polarization beam splitter pixels based on a dielectric metasurface , 2015 .

[28]  Peter J. Reece,et al.  Porous silicon: a versatile optical material , 2004, SPIE Micro + Nano Materials, Devices, and Applications.

[29]  Michal Lipson,et al.  Integrated Luneburg Lens via Ultra-strong Index Gradient on Silicon References and Links , 2022 .

[30]  Lorenzo Pavesi,et al.  Porous silicon microcavities as optical chemical sensors , 2000 .

[31]  Focusing light in a curved-space , 2010, CLEO/QELS: 2010 Laser Science to Photonic Applications.

[32]  Topological Control of Porous Silicon Photonic Crystals by Microcontact Printing , 2013 .

[33]  Leonid A. Golovan,et al.  Photonic bandgap materials and birefringent layers based on anisotropically nanostructured silicon , 2002 .

[34]  Volker Lehmann,et al.  Porous silicon formation: A quantum wire effect , 1991 .

[35]  S. D. Collins,et al.  Porous silicon formation mechanisms , 1992 .

[36]  M. Gal,et al.  Gradient refractive index planar microlens in Si using porous silicon , 2006 .

[37]  Michael J. Sailor,et al.  Determining Protein Size Using an Electrochemically Machined Pore Gradient in Silicon , 2002 .