PhD Thesis

Artificial Piezoelectricity in Silicon Phononic Crystals
Available Online:

Errata:

1.) Electric polarization unit should be C/m^2, in Table 2.1, 2.2 and 2.3.

2.) World complimentary should be complementary in p.88.

Brief overview:

We develop a new class of metamaterials designed to achieve artificial piezoelectricity in centrosymmetric materials.  Our focus is on silicon, a centrosymmetric material that lacks natural piezoelectric properties, which is crucial for various silicon-based on-chip applications.  We demonstrate how heterogeneous metal-on-silicon phononic crystals can induce artificial piezoelectricity in silicon.  Our structure(s) introduce a comprehensive analytical framework for one- and two-dimensional meta-atom structures that replicate piezoelectric behaviors.  We derive constitutive relations for the direct and converse piezoelectric effects and the electromechanical coupling factor.  We designate the 1D structure as a piezorope and the quasi-2D structure as a piezosheet.  By applying a DC bias to create dipoles in sub-units of simple geometric silicon structures, we configure these sub-units back-to-back to form a phononic crystal.  One application of this artificial piezoelectricity is an electrically tunable mechanical filter in silicon.  

We found that near unity electromechanical coupling factor can in principle be achieved by driving the system near resonance, with the added advantage of low voltage operation.  Moreover, our structure permits scalable frequency operation up to tens of giga hertz (GHz).  We have also designed and simulated realistic 2D metal-on-silicon phononic crystal structures on the Silicon-on-Insulator (SOI) platform and demonstrated artificial piezoelectricity by numerical experiment.  By tailoring both the electromagnetic and phononic band structures of these periodic structures, efficient excitation of coherent phononic modes can be achieved, which can potentially have novel applications in acousto-optics, acousto-electromagnetics, transducers, and quantum phononics.

Scientific papers

• Golam Kibria Chowdhury, "Realizing Piezoelectric-Like Behavior in Silicon Phononic Crystals using a DC Biased Electrostriction Technique" In-review. Since it is in-review, I am not sharing the pdf copy here.

Brief Overview:

Traditional microscopic techniques, such as confocal microscopy, use ballistic photons and can image only tens of micrometers in depth, smaller than 1 transport mean free path (TMFP) which is typically < 1 mm.  Diffuse optical tomography can be used to image deeper than microscopy, typically > 1 cm, depths larger than 10 TMFP, but the resolution is poor (currently mm-cm resolutions for diffuse optical tomography).  Photo-acoustic imaging is playing a role to bridge this gap.  In optical-resolution photo-acoustics microscopy (PAM), optical focusing of light inside tissue determines the lateral resolution, whereas in acoustic-resolution PAM, the ultrasonic focusing dictates the lateral resolution.  In both cases, the axial resolution is determined by bandwidth of the transducer.  However, the photo-acoustic sensitivity is typically at micro-molar to milli-molar range. This is several orders of magnitude weaker than fluorescence methods, which is typically in the nano-molar range.  The higher the fluorescence quantum yield the less the photo-acoustic effect, in fact, it is (1 - fluorescence quantum yield). We illustrate the potential of unprecedented resolution fluorescence molecular tomography in the transport regime using reflection-mode illumination and detection.

• Golam Kibria Chowdhury and Roger J. Zemp, “Transport-Regime Fluorescence Molecular Tomography,” In-review. Since it is in-review, I am not sharing the pdf copy here.

• Golam Kibria Chowdhury and Roger J. Zemp, “Molecular Fluorescence Imaging in the Transport Regime using Exact and Efficient PN Solution of the Radiative Transport,” In-review. Since it is in-review, I am not sharing the pdf copy here.

• Golam Kibria Chowdhury and Roger J. Zemp, “Sparse Super-Localization Reconstruction in Transport-Regime Fluorescence Molecular Tomography,” In-review. Since it is in-review, I am not sharing the pdf copy here.

• Golam Kibria Chowdhury, André Liemert, Roger J. Zemp, "Sparse Super-Localization Reconstruction in Transport-Regime Fluorescence Molecular Tomography," Talk, SPIE BiOS, San Francisco, California, United States, 31 January 2018.

• David Egolf, Ryan Chee, Golam Chowdhury, Roger Zemp, "Super-resolution photoacoustic imaging of sparse absorbers using L1-norm minimization," Conference Presentation, SPIE BiOS, San Francisco, California, United States, 15 March 2018.

• Golam Kibria Chowdhury, André Liemert, Roger J. Zemp, "Computationally-efficient and analytical radiative transport Jacobian models for transport-regime fluorescence mesoscopic tomography," Poster Presentation, SPIE BiOS, San Francisco, California, United States, 31 January 2017.

Master Thesis

Locally Divergence-free Elements for Discontinuous Galerkin Method

Brief Overview:

The discontinuous Galerkin method is a powerful numerical technique to accurately solve partial differential equations such as Maxwell's equations.  Our existing implementation uses a nodal scheme, which is efficient and offers great flexibility.  Unfortunately, it does not allow to strongly enforce the divergence equations which are part of Maxwell's equations.  In this thesis, a different formulation of the discontinuous Galerkin approach should be implemented, which (at least locally) enforces the appropriate divergence conditions.

In the nodal discontinuous Galerkin approach, the computational domain is split into finite elements (typically triangles in two dimensions) and the physical fields are then expanded into polynomials on each element.  For efficiency, it makes sense to employ a so-called nodal basis, where the expansion coefficients are actual field values on certain nodes.  In-between those points, Lagrange polynomials are used to interpolate the fields.  For Maxwell's equations, this expansion is not ideal, since it allows solutions which do not fulfill the divergence conditions. While measures can be taken so that those unphysical solutions do not contaminate our numerical solutions, we still waste a certain number of unknowns.

In B. Cockburn (2004) and coworkers proposed to use a modal expansion basis, where the modes are already divergence-free. This approach leads to a significant reduction of the number of unknowns for a fixed polynomial expansion order. On the other hand, the advantages of a nodal basis are lost, which might lead to a reduction in performance. The aim of this thesis is to implement the technique proposed in B. Cockburn (2004) and to investigate its influence on the performance and accuracy of the method.

Available Online

Scientific papers

• C. Schmidt, A. Chipouline, T. Kasebier, G. K. Chowdhury, E.-B. Kley, A. Tunnermann, L. Deych, and T. Pertsch, "Nonlinear effects in silica and hybrid silica/silicon disc micro resonators," IEEE/LEOS Winter Topicals Meeting Series, 12-14 Jan. 2009

• G. K. Chowdhury, A. Chipouline, C. Schmidt, T. Pertsch, "Extraction of statistical parameters of micro-resonator from digitized images using dynamic slicing," OpSciTech Summer Workshop sponsored by the European Union, Friedrich Schiller University of Jena, Germany, 7-11 July 2008

• Golam Kibria Chowdhury, "Cultural Integration in EU:A lever for socio-economic prosperity", Jean Monnet Circle Seminar: European Integration and Institutional Seminar, Karlsruhe Institute of Technology, 2010

• Golam Kibria Chowdhury, "Business Negotiation with the Dragons", Transcultural Management, Karlsruhe Institute of Technology, 2009

• Golam Kibria Chowdhury, "Optical Mirrors – Science, Technology, Entrepreneurial Spirit, and International Trade," Mini-Conference on Selected Topics in Modern Optics, Faculty for Physics and Astronomy, Friedrich Schiller University of Jena, Germany, 16 February 2008