On-Demand Design of Tunable Complete Photonic Band Gaps based on Bloch Mode Analysis

The fundamental property of photonic crystals is the band gap effect, which arises from the periodic dielectric modulation of electromagnetic waves and plays an indispensable role in manipulating light. Ever since the first photonic-bandgap structure was discovered, the ability to tune its bandgap across a wide wavelength range has been highly desirable. Therefore, obtaining photonic crystals possessing large on-demand bandgaps has been an ever-attractive study but has remained a challenge. Here we present an analytical design method for achieving high-order two-dimensional photonic crystals with tunable photonic band gaps on-demand. Based on the Bloch mode analysis for periodic structures, we are able to determine the geometric structure of the unit cell that will realize a nearly optimal photonic band gap for one polarization between the appointed adjacent bands. More importantly, this method generates a complete bandgap for all polarizations, with frequencies tuned by the number of photonic bands below the gap. The lowest dielectric contrast needed to generate a photonic band gap, as well as conditions for generating complete bandgaps, are investigated. Our work first highlights the systematic approach to complete photonic band gaps design based on Bloch mode analysis. The physical principles behind our work are then generalized to other photonic lattices.

[1]  Y. Kivshar,et al.  Bloch-mode analysis for retrieving effective parameters of metamaterials , 2010, 1011.2669.

[2]  B. Jia,et al.  Two-Photon Polymerization for Three-Dimensional Photonic Devices in Polymers and Nanocomposites , 2007 .

[3]  Sailing He,et al.  Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm , 2003 .

[4]  E. Thomas,et al.  Impact of geometry on the TM photonic band gaps of photonic crystals and quasicrystals. , 2011, Physical review letters.

[5]  Dirk Englund,et al.  Ultrafast photonic crystal nanocavity laser , 2006 .

[6]  P. Parrilo,et al.  Design of photonic crystals with multiple and combined band gaps. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Ole Sigmund,et al.  Geometric properties of optimal photonic crystals. , 2008, Physical review letters.

[8]  Philippe Boucaud,et al.  Two-dimensional photonic crystals with large complete photonic band gaps in both TE and TM polarizations. , 2008, Optics express.

[9]  R. McPhedran,et al.  Density of states functions for photonic crystals. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Torquato,et al.  Optimized structures for photonic quasicrystals. , 2008, Physical review letters.

[11]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light , 1995 .

[12]  Steven G. Johnson,et al.  Photonic Crystals: Molding the Flow of Light - Second Edition , 2008 .

[13]  Hod Lipson,et al.  Two-dimensional photonic crystals designed by evolutionary algorithms , 2005 .

[14]  Min Gu,et al.  Observation of multiple higher-order stopgaps from three-dimensional chalcogenide glass photonic crystals. , 2008, Optics letters.

[15]  Sailing He,et al.  Large complete band gap in two-dimensional photonic crystals with elliptic air holes , 1999 .

[16]  C. Kittel.  Introduction to solid state physics , 1954 .

[17]  Jianlin Zhao,et al.  Tuning of Bloch modes, diffraction, and refraction by two-dimensional lattice reconfiguration. , 2010, Optics letters.

[18]  S. Hughes,et al.  Role of Bloch mode reshaping and disorder correlation length on scattering losses in slow-light photonic crystal waveguides , 2015 .

[19]  Baohua Jia,et al.  Bi-directional evolutionary optimization for photonic band gap structures , 2015, J. Comput. Phys..

[20]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Continuum Structures: Methods and Applications , 2010 .

[21]  E. N. Economou,et al.  Tight-Binding Parametrization for Photonic Band Gap Materials , 1998 .

[22]  Complete bandgap arising from the effects of hollow, veins, and intersecting veins in a square lattice of square dielectric rods photonic crystal , 2011 .

[23]  Yang Zhao,et al.  High-sensitivity and high-Q-factor glass photonic crystal cavity and its applications as sensors. , 2015, Optics letters.