title: Porous Silicon Gradient Refractive Index Micro-Optics.
abstract: 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.
authors: Department of Materials Science and Engineering, Department of Chemistry, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: Neil A
authors: NA
authors: Krueger
authors: Geballe Laboratory for Advanced Materials, Stanford University , Stanford, California 94305, United States.
authors: Aaron L
authors: AL
authors: Holsteen
authors: Department of Materials Science and Engineering, Department of Chemistry, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: Seung-Kyun
authors: SK
authors: Kang
authors: Department of Materials Science and Engineering, Department of Chemistry, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: Christian R
authors: CR
authors: Ocier
authors: The Dow Chemical Company, 2301 N. Brazosport Boulevard, B-1470, Freeport, Texas 77541, United States.
authors: Weijun
authors: W
authors: Zhou
authors: Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: Glennys
authors: G
authors: Mensing
authors: Department of Materials Science and Engineering, Department of Chemistry, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: John A
authors: JA
authors: Rogers
authors: Geballe Laboratory for Advanced Materials, Stanford University , Stanford, California 94305, United States.
authors: Mark L
authors: ML
authors: Brongersma
authors: Department of Materials Science and Engineering, Department of Chemistry, Frederick Seitz Materials Research Laboratory, and Beckman Institute, University of Illinois at Urbana-Champaign , Urbana, Illinois 61801, United States.
authors: Paul V
authors: PV
authors: Braun
keywords: Microlenses; birefringence; silicon photonics; transformation optics