Tuning of resonant Zener tunneling by vapor diffusion and condensation in porous optical superlattices Mher Ghulinyan, 1 Zeno Gaburro, 1 Diederik S. Wiersma, 2 and Lorenzo Pavesi 1 1 Nanoscience Laboratory, Department of Physics, University of Trento, Trento, Italy 2 European Laboratory for Nonlinear Spectroscopy and INFM-MATIS, Sesto Fiorentino, Florence, Italy Received 21 April 2006; revised manuscript received 30 May 2006; published 20 July 2006 We study a vapor-controlled optical superlattice realized with a silicon-based dielectric mesoporous material. By flowing organic vapors through the nanometer-sized pores, the position dependent refractive index can be continuously tuned, resulting in a tilted photonic band structure. A careful design of pore size distribution, close to the critical radius of capillary condensation of vapor, makes the superlattice sensitive to the flow direction. We drive the optical superlattice to the resonant Zener tunneling condition, introducing an enhanced transmission channel through the photonic crystal. Our results show that vapor capillary condensation can be used to modify the properties of optical superlattices allowing, e.g., to realize fast gas sensing devices due to their advantage to respond to vapor flow fronts. DOI: 10.1103/PhysRevB.74.045118 PACS numbers: 42.70.Qs, 42.25.Dd, 73.21.Cd, 78.67.Pt I. INTRODUCTION The control of optical properties of photonic crystals is currently an active research topic. 1,2 This is especially impor- tant when it can be applied as a function of position inside the crystal, because in such case the photonic energy bands can be tilted or curved. 3,4 Dielectric photonic crystals are often fabricated by peri- odically alternating one or several materials with air voids. With this method effective photonic crystals can be realized within a small volume, potentially allowing integration over a large scale. 5 There is a second strategic aspect of air voids: they can be filled and emptied. From the point of view of the photonic properties of the structure, the effect of locally con- trolled fluid exchange is equivalent to a local tuning of the refractive index. The aim of this paper is to demonstrate an effective mechanism to modulate the band structure of pho- tonic crystals as a function of position, by filling and empty- ing air gaps with fluids, taking the advantage of capillary condensation. 6,7 The starting idea is to exchange, with the crystal scaffold, vapors close to their dew point. This leads to capillary con- densation of the liquid—and a consequent significant modu- lation of the refractive index n n / n  10 -2 —in all voids whose linear dimension is below a critical value r c , calcu- lated according to Kelvin-Laplace theory. 8 For typical sol- vents in the proximity of dew point, the critical radius of curvature of the liquid-vapor interface r c , is in the range of few tens of nanometers, i.e., significantly below the charac- teristic length in optical photonic crystals. This suggests to consider two levels of structuring. The first level—for the fluid exchange control—is a high-resolution structure, which leads to porous elementary building blocks. The pore size distribution, which can be fabricated as a function of posi- tion, locally determines the amount of capillary condensation and thus the quantitative shift of the effective refractive in- dex. The second level of structure for the photonic properties can be then independently designed at lower resolution usu- ally, of the order of one-quarter wavelength. In this paper, we show how the capillary condensation in fine porous struc- tures can be used to tailor the optical response of a photonic crystal by modifying locally the material refractive index. In particular, we propose a one-dimensional photonic Zener tunnel crystal, which is pushed in and out of resonance by exposing it to vapors of ethanol in proximity of the dew point. 9 Zener tunneling ZT of light waves has been studied and observed in various physical systems, such as optical lattices, 10 waveguide arrays 11 and two-dimensional photonic lattices. 12 Photons undergo ZT in a one-dimensional optical superlattice, in which two photonic minibands are tilted to be coupled resonantly. 4 An optical superlattice can be built by repeating a dielectric supercell “Mirror / C / Mirror / D” com- posed of two cavities C and D centered at different frequen- cies and coupled through dielectric mirrors. When a constant optical path is maintained through the structure, two flat high-transmission photonic minibands separated by a fre- quency minigap, form in the stop band of the optical super- lattice Fig. 1. The introduction of an optical path gradient  along the superlattice growth direction results in a tilted photonic band structure. 3,4 The optical path gradient, which turns the delocalized photonic bands into Wannier-Stark WS ladders 13 , acts in the same way as the electric field in the case of the electrical Zener diode. 14 In close analogy to the case of a semiconductor crystal, in an optical superlattice the light transmission strongly increases 15 at the ZT fre- quency  ZT when the photonic minibands couple resonantly at a critical band tilting. This can be seen as an intense point in Fig. 1, when two states of different minibands come to the same frequency and suffer an anticrossing at the critical op- tical path gradient successive anticrossings occur upon fur- ther increasing the band tilting. The photonic structure can be in condition of resonance Fig. 2a, left-hand panel or not right-hand panel, depending on the optical path gradi- ent. In the reported photonic ZT structures, the optical path gradient has been hitherto built-in as a fixed parameter, dur- ing fabrication. The paper is organized as follows. In Sec. II we describe the sample design and the preparation technique, followed by the description of the optical transmission measurement PHYSICAL REVIEW B 74, 045118 2006 1098-0121/2006/744/0451185 ©2006 The American Physical Society 045118-1