Optomechanics of two- and three-dimensional soft photonic crystals

Soft photonic crystals are a class of periodic dielectric structures that undergo highly nonlinear deformation due to strain or other external stimulus such as temperature, pH etc. This can in turn dramatically affect optical properties such as light transmittance. Moreover certain classes of lithographically fabricated structures undergo some structural distortion due to the effects of processing, eventually affecting the optical properties of the final photonic crystal. In this work, we study the deformation mechanics of soft photonic crystal structures using realistic physics-based models and leverage that understanding to explain the optomechanics of actual 2-D and 3-D soft photonic crystals undergoing similar symmetry breaking nonlinear deformations. We first study the optomechanics of two classes of 3-D soft photonic crystals: (1) hydrogel and (2) elastomer based material systems. The hydrogel based inverse face-centered-cubic structure undergoes swelling with change in pH of the surrounding fluid. The inverse structure is a network of bulky domains with thin ligament-like connections, and it undergoes a pattern transformation from FCC to L11 as a result of swelling. A continuum scale poroelasticity based coupled fluid-diffusion FEM model is developed to accurately predict this mechanical behavior. Light transmittance simulation results qualitatively explain the experimentally observed trends in the optical behavior with pH change. The elastomer based, lithographically fabricated material experiences shrinkage induced distortion upon processing. This behavior is modeled using FEM with the material represented by a neo-Hookean constitutive law. The light transmittance calculations for normal incidence are carried out using the transfer matrix method and a good comparison is obtained for the positions of first and second order reflectance peaks. A unit cell based approach is taken to compute the photonic bandstructure to estimate light propagation through the structure for other angles of light incidence. To obtain a detailed picture of the change in optical properties due to a pattern transformation, we study simple 2-D elastomer photonic crystals which undergo an interesting structural pattern transformation from simple circular holes to alternately oriented ellipses in a square lattice due to uniaxial compression. The incident light does not have any effect on the properties of the elastomer material. A decomposition of the deformation gradient quickly shows that the pattern transformation is induced by alternating rotations of the interstitial regions and the bending of interconnecting ligaments. Numerical simulations of light transmittance using vector element based FEM analysis of Maxwells equations shows changes in the light energy localization within the material especially in the high energy/low wavelength regions of the spectra. Additionally, with bandstructure calculations on a unit cell of the structure, the optomechanical behavior is completely explained. Finally, computational evidence is provided for a hypothetical 2-D photonic crystal made of a light-sensitive material, which undergoes a structural pattern transformation primarily due to the effect of incident light. The model takes into account the order kinetics of optically induced isomerization (of trans to cis configuration) in the azobenzene-liquid crystal elastomer to compute the transformational strain. This strain, in turn, deforms the structure and hence changes its periodicity and dielectric properties and thus affects the manner in which light gets localized within the material system. This consequently changes the profile of the imposed transformational strain on the deformed structure. The macroscopic strain history shows that prior to the mechanical instability that causes the pattern transformation, there is a period of structural relaxation which initiates the pattern transformation. After the symmetry breaking pattern transformation, the photonic bandstructure is altered significantly. Light does not get localized in the spot regions anymore and stress relaxation dominates. Due to this, the compressive macroscopic strain of the pattern transformed structure starts to decrease indicating a possible cyclical behavior.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Krishnan, Dwarak

Contributors dc:contributor

• Johnson, Harley T.
• Braun, Paul V.
• Aluru, Narayana R.
• Jin, Jianming

• optomechanics
• polymers
• photonic crystals
• liquid crystal elastomer
• multiphysics
• hydrogel
• poroelasticity
• rubber physics

Statement dc:rights

• Copyright 2011 Dwarak Krishnan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/24005

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/24005