|
Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions |
JOSA B, Vol. 28, Issue 8, pp. 1951-1958 (2011)
http://dx.doi.org/10.1364/JOSAB.28.001951
Enhanced HTML 
Acrobat PDF (8838 KB)
Abstract
Wannier function expansions are well suited for the description of photonic-crystal-based defect structures, but constructing maximally localized Wannier functions by optimizing the phase degree of freedom of the Bloch modes is crucial for the efficiency of the approach. We systematically analyze different locality criteria for maximally localized Wannier functions in two-dimensional square and triangular lattice photonic crystals, employing (local) conjugate-gradient as well as (global) genetic-algorithm-based stochastic methods. Besides the commonly used second moment (SM) locality measure, we introduce a new locality measure, namely, the integrated modulus (IM) of the Wannier function. We show numerically that, in contrast to the SM criterion, the IM criterion leads to an optimization problem with a single extremum, thus allowing for fast and efficient construction of maximally localized Wannier functions using local optimization techniques. We also present an analytical formula for the initial choice of Bloch phases, which, under certain conditions, represents the global maximum of the IM criterion and, thus, further increases the optimization efficiency in the general case.
© 2011 Optical Society of America
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(230.3120) Optical devices : Integrated optics devices
(250.5300) Optoelectronics : Photonic integrated circuits
(230.5298) Optical devices : Photonic crystals
ToC Category:
Optical Devices
History
Original Manuscript: March 28, 2011
Revised Manuscript: June 8, 2011
Manuscript Accepted: June 21, 2011
Published: July 18, 2011
Citation
Tobias Stollenwerk, Dmitry N. Chigrin, and Johann Kroha, "Efficient construction of maximally localized photonic Wannier functions: locality criterion and initial conditions," J. Opt. Soc. Am. B 28, 1951-1958 (2011)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-28-8-1951
You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Log in to access OSA Member Subscription
Related Journal Articles 
- New Taylor-expansion method for solving a general class of wave equations (JOSAA)
- Demonstration of an Optical Isolator by Use of a Nonreciprocal Phase Shift (AO)
- Vertical antiresonant reflecting optical waveguide coupler for three-dimensional optical interconnects: optimum design for large tolerance, high coupling efficiency, and short coupling length (AO)
- Design of Compact Optical Bends with a Trench by use of Finite-Element and Beam-Propagation Methods (AO)
- Demonstration of an Optical Isolator with a Semiconductor Guiding Layer that was Obtained by Use of a Nonreciprocal Phase Shift (AO)
Related Conference Papers
- Integration Techniques for InP-Based High-Functionality Photonic Integrated Circuits
- Nano-taper mode-size converter
- A New Simple Process for Optical Mode Converter Integration with Active and Passive Waveguides in InGaAsP/InP
- Design of a bent-waveguide-based multimode interference demultiplexer using the full-vectorial BPM
- Hollow optical waveguide with thin film coating for micromachined photonic integrated circuits
« Previous Article | Next Article »
OSA is a member of 