Two-dimensional photonic crystals with anisotropic unit cells
imprinted from PDMS membranes under elastic deformation
Xuelian Zhu
a
, Ying Zhang
a
, Dinesh Chandra
a
, Shih-Chieh Cheng
a
, James M. Kikkawa
b
, Shu Yang
*a
a
Department of Materials Science & Engineering, University of Pennsylvania, 3231 Walnut Street,
Philadelphia, PA 19104;
b
Department of Physics and Astronomy, University of Pennsylvania, 209
South 33rd Street, Philadelphia, PA 19104.
ABSTRACT
We study structural symmetries of two-dimensional (2D) photonic crystals with anisotropic unit cells, including square-
and rectangular-lattices with orientationally modulated elliptic motifs, a compound structure consisting of circles with 6-
fold rotational symmetry and elliptical lines with 2-fold symmetry, and a rectangular lattice of aligned ovals, which are
created through elastic deformation of an elastomeric membrane with circular pores. We then investigate the photonic
bandgap (PBG) properties of the corresponding 2D Si posts, and their tolerance to the structural deviation. We find that
in the compound structure the overall PBGs are dominated by the sublattice with a higher symmetry, while the total
symmetry is determined by the one with a lower symmetry.
Keywords: photonic bandgap materials, crystal symmetry, crystallographic aspects of phase transformations, surface
strain, elastic deformation, polymer swelling, elastomers, complex nanostructures.
1. INTRODUCTION
Photonic crystals (PCs) with periodically modulated refractive-index are of interest for potential applications in large-
scale optical integrated circuits, including micro-wave scale, single-mode waveguides with sharp bends[1, 2], high-Q
resonant cavities[3], distributed feedback lasers[4], superprisms[5], and perfect lenses[6]. In comparison to three-
dimensional (3D) PCs, two-dimensional (2D) PC slabs could confine light in 3D by a combination of 2D photonic
bandgap (PBG) effect for the in-plane direction and total internal reflection for the vertical direction. Therefore, 2D PC
slabs offer an efficient alternative of the 3D PCs, which can retain or approximate many of the desirable properties of 3D
PCs and be mass-produced over a large area with submicron resolution[7, 8]. The most widely studied 2D PCs are
square and triangular lattices with isotropic circular-shaped unit cells[3, 7-10]. However, there have been comparatively
few studies of 2D PCs with anisotropic unit cells except recent work demonstrating control of the polarization modes of
the emitted light[11].
2D PC slabs are typically fabricated by conventional photolithography, electron beam lithography, and focused ion
beam techniques, which require expensive tools and sometimes are only applicable to limited areas. Recently, we and
others have demonstrated a simple yet robust method to produce orientationally modulated 2D patterns via pattern
transformation triggered by elastomeric deformation[12-14]. Solvent-induced swelling instabilities of a single
poly(dimethylsiloxane) (PDMS) membrane with a square lattice of micrometer-scale circular holes yield a library of 2D
patterns with submicron resolution, including square- or rectangular-lattices with orientationally modulated elliptical-
shaped motifs (i.e. diamond plate), compound structures consisting of circles and elliptical lines, and a rectangular lattice
of aligned ovals[13]. By imposing an external elastic force that competes with internal stresses and manipulating the
volume expansion ratio of the PDMS membrane using different swelling agents (e.g. organic solvents vs. monomers),
we can fine-tune the structural details of the 2D patterns. The resulting patterns can then be used as etch masks to
transfer the transformed patterns to semiconductors (e.g. Si), metals (e.g. Au), and polymer films.
In this report, we study the PBGs of the corresponding 2D Si PCs as a function of the structural symmetries of the
resulting patterns, and their tolerance to structural deviation during fabrication. In a diamond plate structure with fatter
ellipses, where the transformed pattern is imprinted from poly(ethylene glycol dimethacrylate) (PEGDMA), we find that
the lowest transverse magnetic (TM) bandgap exhibits a high PBG quality, and in contrast to the square lattice with
*
shuyang@seas.upenn.edu; phone 1-215-898-9645; fax: 1-215-573-2128
Photonic and Phononic Crystal Materials and Devices IX,
edited by Ali Adibi, Shawn-Yu Lin, Axel Scherer, Proc. of SPIE Vol. 7223,
72231C · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.809275
Proc. of SPIE Vol. 7223 72231C-1