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Title: What is the Brillouin zone of an anisotropic photonic crystal?

Journal Article · · Physical Review B
 [1];  [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
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The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest band gap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ—defined as the Wigner-Seitz cell in the reciprocal lattice—is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic two-dimensional PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. In conclusion, the concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.

Research Organization:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); Natural Sciences and Engineering Research Council of Canada (NSERC); National Science Foundation (NSF)
Grant/Contract Number:
SC0001299; FG02-09ER46577; CHE-1111557
OSTI ID:
1470240
Alternate ID(s):
OSTI ID: 1237502
Journal Information:
Physical Review B, Vol. 93, Issue 5; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

References (17)

Chemically assisted femtosecond laser machining for applications in LiNbO3 and LiTaO3 journal July 2013
Spontaneous Emission Enhancement of Quantum Dots in a Photonic Crystal Wire journal October 2005
High-Resolution, Low-Noise Imaging in THz Polaritonics journal May 2013
Direct experimental visualization of waves and band structure in 2D photonic crystal slabs journal May 2014
Large Absolute Band Gap in 2D Anisotropic Photonic Crystals journal September 1998
Anisotropic photonic crystals: Generalized plane wave method and dispersion symmetry properties journal November 2008
Spatiotemporal Coherent Control of Lattice Vibrational Waves journal January 2003
Spontaneous emission from a two-level atom in two-band anisotropic photonic crystals journal October 2003
Guided modes in photonic crystal slabs journal August 1999
Strong localization of photons in certain disordered dielectric superlattices journal June 1987
Temperature tuning of the stop band in transmission spectra of liquid-crystal infiltrated synthetic opal as tunable photonic crystal journal August 1999
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Terahertz polariton propagation in patterned materials journal September 2002
Terahertz Polaritonics journal August 2007
Symmetry properties of two-dimensional anisotropic photonic crystals journal January 2006
Group theoretical investigations of photonic band structures journal June 2003
Single quantum-dot Purcell factor and β factor in a photonic crystal waveguide journal May 2007

Cited By (1)

Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model journal May 2016

Figures / Tables (11)

FIG. 1(p. 3)figure FIG. 1
FIG. 1.(p. 3)figure FIG. 1.
FIG. 2(p. 4)figure FIG. 2
FIG. 2.(p. 4)figure FIG. 2.
FIG. 3(p. 5)figure FIG. 3
FIG. 3.(p. 5)figure FIG. 3.
FIG. 4(p. 6)figure FIG. 4
FIG. 5(p. 7)figure FIG. 5
FIG. 5.(p. 7)figure FIG. 5.
FIG. 6(p. 7)figure FIG. 6
FIG. 6.(p. 7)figure FIG. 6.

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