Taking advantage of imperfections to focus light in photonic crystals inside the stop gap

[R. Uppu et al., arxiv, 2007.11104v1 (2020)]

Photonic crystals have the ability to forbid the entrance of light for certain ranges of frequencies, that is even the usual reason why we build them. Within the spatial frequency range for which the stop band of a given photonic crystal exists, modulation of the input wavefront should not dramatically modify the penetration of light, which exhibits an exponential decay. In this paper, R. Uppu and collaborators from the University of Twente demonstrate that it is indeed possible to drastically change the penetration properties of light inside a photonic crystal by optimizing the wavefront taking advantage of unavoidable sources of disorder. They experimentally show the focusing of light inside such crystal beyond the expected maximal penetration length - the Bragg length.

Optical media typically shows a mix of ordered and disordered properties. At one end of the spectrum, we have ideally random scattering media, that show little order behaviors (well, you always have some, for instance, the finite size of the particles creates short-range order due to the presence of a minimum distance possible between the centers of the particles). The opposite asymptotic case concerns ideal photonic crystals, due to the periodicity of the structure. The existence of symmetries decreases the number of degrees of freedom one can control using wavefront shaping. Indeed, an excitation pattern shifted at different places should lead to the same properties, and rotating a plane wave around any vector normal to the surface should not change anything. It is then the boring case of wavefront shaping when very little could be achieved, the exact opposite to random scattering media where the lack of symmetries offers a great number of degrees of freedom one can play with.

However, real photonic crystals are not free of any source of randomness, in particular due to the fabrication. The authors show that, while a photonic crystal exhibits the properties expected from an ordered photonic crystal, the randomness offers enough degrees of freedom to still control light propagation inside the structure. The schematic of the experiment is presented in Figure 1., a wavefront shaping apparatus is used to modulate the incident wavefront on a photonic crystal at a wavelength inside the stop gap. The intensity inside the structure of the crystal is probed using a camera that images the out-of-plane scattering of the 2d structure.

Figure 1. Schematic of the experiment presented in [R. Uppu et al., arxiv, 2007.11104v1 (2020)]

R. Uppu and coauthors then run a sequential optimization of the wavefront where the phase of 340 elements is controlled. The optimization target is the intensity of the scattered light at a point at a chosen depth inside the crystal. Figure 2. shows the results of the optimization for a target 10 microns deep, about 5 times the Bragg length, with an intensity enhancement of about 65 compared to an unoptimized wavefront. They also show the possibility to focus light significantly at depths up to 8 times the Bragg length.

Figure 2. Intensity scattered inside the photonic crystal before (left) and after (right) wavefront shaping optimization.

In the paper, the authors also developed a matrix model that shows that the system behaves, for the focusing experiment, as a scattering medium with attenuation due to the out-of-plane scattering.