Reflectivity of three-dimensional GaAs photonic band-gap crystals of finite thickness

Cornelis A M Harteveld,Willem L Vos,Shun Takahashi,Takeyoshi Tajiri,Yasuhiko Arakawa,Satoshi Iwamoto

doi:10.1103/physrevb.101.235303

Abstract

We study the optical reflectivity of three-dimensional (3D) photonic band gap crystals with increasing thickness. The crystals consist of GaAs plates with nanorod arrays that are assembled by an advanced stacking method into high-quality 3D woodpile structures. We observe intense and broad reflectivity peak with stop bands that correspond to a broad gap in the photonic band structures. The maximum reflectivity quickly reaches high values even for a few crystal layers. Remarkably, the bandwidth of the stop bands hardly decreases with increasing crystal thickness, in good agreement with FDTD simulations. This behavior differs remarkably from the large changes observed earlier in weakly interacting 3D photonic crystals. The nearly constant bandwidth and high reflectivity are rationalized by multiple Bragg interference that occurs in strongly interacting photonic band gap crystals, whereby the incident light scatters from multiple reciprocal lattice vectors simultaneously, in particular from oblique ones that are parallel to a longer crystal dimension and thus experience hardly any finite size effects. Our new insights have favorable consequences for the application of 3D photonic band gap crystals, notably since even thin structures reveal the full band gap functionality, including devices that shield quantum bits from vacuum fluctuations.

Highlights

There is a worldwide interest in three-dimensional (3D) photonic crystals that radically control both the propagation and the emission of light [1,2,3,4,5,6,7,8]
The 3D photonic crystal reveals an intense and broad reflectivity stop band at frequencies between 6000 and 10 000 cm−1 that corresponds to the Z stop gap in the band structures
The stop band is slightly broader for the thinnest crystal thickness of L = 2d002, and the bandwidth only slightly decreases with increasing thickness

Summary

Introduction

There is a worldwide interest in three-dimensional (3D) photonic crystals that radically control both the propagation and the emission of light [1,2,3,4,5,6,7,8]. When the frequency of light lies in a gap in the dispersion relations for a certain wave vector tending from the origin to the Brillouin zone boundary, light cannot propagate in the corresponding direction as a result of Bragg diffraction [9]. Such a directional gap or stop gap is usually probed with reflection or transmission experiments where a reflectivity peak or transmission trough occurs, known as a stop band [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. Applications of 3D photonic band-gap crystals range from dielectric reflectors for antennae [33] and for efficient photovoltaic cells [34,35,36], via white-light-emitting diodes [37,38], to elaborate 3D waveguides [39] for 3D photonic integrated circuits [40,41,42], and to low-threshold miniature lasers [43] and devices to control quantum noise for quantum measurement, amplification, and information processing [29,44,45]

Methods

Results

Discussion

Conclusion