Polarization Stop Bands in Chiral Polymeric Three-Dimensional Photonic Crystals

Chiral 3D photonic crystals are an interesting subclass of 3D photonic crystals. For example, large complete 3D photonic bandgaps have been predicted for high-index-contrast silicon square-spiral structures; corresponding experiments using glancing-incidence deposition, interference lithography, or direct laser writing have been published. In addition to complete gaps or stop bands, theory also predicts polarization stop bands, i.e., stop bands for just one of the two circular polarizations. Such polarization stop bands can give rise to strong circular dichroism, which can potentially be used for constructing compact “thin-film” optical diodes. In this report, we fabricate high-quality polymeric 3D spiral photonic crystals via direct laser writing. The measured transmittance spectra of these low-index-contrast structures reveal spectral regions where the transmittance is below 5 % for one circular incident polarization and above 95 % for the other—for just eight lattice constants along the propagation direction. The experimental data are compared with scattering-matrix calculations for the actual finite structures, leading to good agreement. For what conditions do we expect strong circular dichroism? For circular polarization of light, the tip of the electricfield vector simply follows a spiral. The pitch of this spiral is just the material wavelength k. Thus, intuitively, we expect a chiral resonance from spiral photonic crystals if the pitch of circularly polarized light matches the pitch of the dielectric spirals, i.e., the lattice constant az. This condition, k/az = 1, corresponds to the edge of the second Brillouin zone, i.e., to a wave number kz = 2p/k= 2p/az. Recall that the edge of the first Brillouin zone is at kz = p/az. Thus, one does not anticipate a strong chiral response around and below the fundamental stop band (or bandgap), but rather at higher frequencies. Theory for high-index silicon-based structures confirms this intuitive reasoning. We have repeated similar calculations for low-index-contrast polymeric structures, revealing essentially the same trends. The parameters of the 3D spiral photonic crystals to be discussed below are the result of an optimization with respect to circular dichroism. The samples in our experiments are made by direct laser writing, which essentially allows for the fabrication of almost arbitrarily shaped 3D photoresist structures. Details of our process based on the commercial thick-film resist SU-8 can be found in the Experimental section and in earlier work. Our structures are mechanically supported by a 2D network of bars at, or close to, the top of the 3D crystal. As the spirals are not at all mechanically connected to their neighbors, very unstable low-quality structures would result without this grid. Furthermore, all the structures for optical experiments are surrounded by a thick massive wall (see Fig. 1a), which aims at reducing the effects of strain on the 2D grid caused by photoresist shrinkage during development. Here, we use a round (rather than a rectangular) wall in order to evenly distribute strain inside the wall. Through numerical calculations (see below), we have confirmed that the distortion of the optical properties by the 2D network is only marginal. Most importantly, the network does not introduce any chirality. A small gallery of selected electron microscopy images is shown in Figure 1, which gives first evidence that the sample quality is very good. Figure 1a gives an overview of the sample to be optically characterized below. The sample parameters are: in-plane lattice constant axy = 1.3 lm, pitch az = 1.3 lm, spiral diameter d = 0.78 lm, volume filling fraction 34.7 %, lateral diameter of the spiral arms darm = 380 nm, ratio between the axial and the lateral diameter 2.7, and N = 8 lattice constants along the z-direction. These parameters were extracted from the close-up cross-sectional view in Figure 1a. To demonstrate the versatility of our approach, Figure 1b exhibits a cut of a structure with axy = 1.5 lm, az = 1.5 lm, and N = 4. Because the focused-ion-beam cut was stopped in between two rows of spirals, the stabilizing network mentioned C O M M U N IC A IO N