Photonic Crystals at Near-Infrared and Optical Wavelengths
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Photonic Crystals at Near-Infrared and Optical Wavelengths Alexander Moroz Debye Institute, Utrecht University, P.O. Box 80000, 3508 TA Utrecht, The Netherlands http://www.amolf.nl/research/photonic materials theory/moroz/moroz.html ABSTRACT As demonstrated for the example of a diamond and zinc blende structure of dielectric spheres, small inclusions of a low absorbing metal with the volume fraction f m can have a dramatic effect on a complete photonic band gap (CPBG) between the 2nd-3rd bands. For example, in the case of silica coated silver spheres, the CPBG opens for f m ≈ 1.1% and exceeds 5% for fm ≈ 2.5%. Consequently, any dielectric material can be used to fabricate a photonic crystal with a sizeable and robust CPBG in three dimensions. Absorption in the CPBG of 5% remains very small (≤ 2.6% for λ ≥ 750 nm). The structure enjoys almost perfect scaling, enabling one to scale the CPBG from microwaves down to ultraviolet wavelengths.
INTRODUCTION Photonic crystals are structures with a periodically modulated dielectric constant [1]. In analogy to the case of an electron moving in a periodic potential, certain photon frequencies in a photonic crystal can become forbidden, independent of photon polarization and the direction of propagation - a complete photonic bandgap (CPBG) [1, 2, 3]. In the last decade, photonic crystals enjoyed a lot of interest in connection with their possibilities to guide light and to become a platform for the fabrication of photonic integrated circuits [4, 5]. Despite the research activities of a large number of experimental groups, achievement of a CPBG below infrared wavelengths for both two- and three-dimensional photonic structures is still elusive, mainly because the required dielectric contrast δ to open a CPBG is rather high. Even for the best geometries δ ≈ 5 is required [2, 6]. Already this threshold value of δ excludes the majority of semiconductors and other compounds and materials, such as (conducting) polymers, from many useful photonic crystal applications. However, the required δ is even higher. For applications one needs a sufficiently large CPBG to leave a margin for gap-edge distortions due to omnipresent defects. Let us define the relative gap width g w as the gap width-to-midgap frequency ratio, 4ω/ωc. Then in order to achieve gw larger than 5%, δ ≥ 9.8 and δ ≥ 12 is required for a diamond [6] and face-centered-cubic (fcc) structure [7], respectively. This leaves only a couple of materials for photonic crystals applications at near infrared and optical wavelengths [8]. Surprisingly enough, there is a way to create a sizeable and robust CPBG with just any dielectric material, be it silica glass or a polymer. A price to pay is to accept a small volume fraction fm of a low absorbing metal, the actual amount of which depends on an available material dielectric constant ε. Obviously, small
K7.5.1
Gap/midgap ratio [%]
14 12 10 8 6 4 2 0
2nd−3rd, fs=0.34 8th−9th, fs=0.34 8th−9th, fs=0.17
4
6
8 10 12 14 16 18 20 22 24 Dielectric contrast
Figure 1: Gap width to midgap
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