Obstacle run for light: liquid crystals to help

The creation of any technology or material is associated with the fact of its imperfections. Anyway there will be flaws. Sometimes significant, strongly influencing the work of a particular system, and, accordingly, requiring a lot of time and effort to refine. And sometimes the shortcomings may be such that we can put up with. But should they? I think no. To perfect something is never too late. This is what today's heroes think about - scientists who decide to improve photonic crystals. Today we will learn how topological insulators, particle scattering, liquid crystals and light waves will be combined in the study. Go.

Lyrical (theoretical) retreat

For a start, it is worth paying a little attention to the theory (although a little, do not be afraid).

I mentioned “photonic crystals” in the prologue, but what is it? This is a very unusual material, the main feature of which is the periodicity of changes in the coefficient (index) of refraction in its structure. By digging deeper, you can supplement this thesis by the fact that, due to its peculiarity, photonic crystals make it possible to obtain allowed and forbidden zones for photon energies. These zones are familiar to us thanks to semiconductors, where they already “work” in a team with the energy of charge carriers — particles that carry an electric charge.


Photonic crystals are present in the wings of butterflies (diffraction gratings).

In the case of photonic crystals, everything depends on the length of the light wave. If a photon with a wavelength corresponding to the forbidden zone is incident on the crystal, then the photon does not spread and is reflected back. Conversely, if the energy of a photon incident on a crystal is "equal" to the allowed zone, then the photon propagates in the crystal.

It turns out that the photonic crystal has non-standard conductive properties. And this brings us to another concept - topological insulators.

Such insulators are like a sandwich (or a sandwich, if someone prefers anglicisms). That is, outside the structure of such a material is an insulator, and inside - a conductor. In, so to speak, classical topological insulators, one of the problems is particle scattering. Particles - the guys are mobile and a bit tactless, because during the movement they love to push, which is the reason for changing their original trajectory. Such processes cause certain losses, which is naturally bad.


The dependence of the energy on the pulse: a is a common insulator, b is a topological one.

Scientists, whose work we are talking about today, believe that these problems can be solved by combining photonic crystals and silicon photonic technologies. Vaguely somehow, don't you think? But scientists quickly clarify exactly what they decided to use - liquid crystals. But this phrase already really makes raise the eyebrow. How can a crystal be liquid? But, as in physics often happens, not everything should be understood at 100% literally. Liquid crystals are a state into which certain substances are transferred under extreme conditions. In this case, these substances can simultaneously possess the properties of liquids and crystals (fluidity and anisotropy). You have probably met liquid crystals at some time in your life (electronic watches, LCD TVs, cell phones, etc.).


The types of liquid crystals in phases: a - nematic, b - smectic, c - cholesteric.

In order for the liquid crystals to play their role, it is necessary to gain control over the topological boundary states. This can be achieved through manipulations with the refractive index of the liquid crystal.

Interesting work in which boundary states are affected.

The basis of the study

The structure created by the researchers is a photonic crystal of silicon columns (columns) immersed in a liquid crystal medium between conducting electrodes (image 1a ).


Image №1

The structure consists of two main areas: with a trivial topology and with a non-trivial topology. Smaller areas are represented as hexagonal grids with six columns each. Each such grid is a meta-molecule (exaggerated, a set of molecules), which may have the characteristics of a trivial or nontrivial topology of the zones, depending on the distance between the columns.

Due to the fact that the photonic crystal is immersed in a liquid crystal medium, scientists can manipulate with the index of refraction. In this case, the amplitude of the controlled change of this parameter can be quite large. Control and manipulation are achieved due to the external electric field received from two electrodes, “limiting” the structure from below and from above.

The average liquid crystal has a refractive index of 1.5, and the birefringence (when the light beam is split in two) is of the order of 0.2. In this study, a liquid crystal of the nematic type E7 was used: the absolute refractive index was 1.51, the extraordinary refractive index * was 1.69.

Extraordinary refractive index * - when the light has a parallel polarization about the optical axis.

Figure 1b shows how liquid crystal molecules line up in parallel along the silicon columns (ON mode) when the structure is affected by an external electric field. In such a situation, the light rather effectively follows the rhomboid path, while the boundary state is located in the volume forbidden zone (image 1c ).

The second “mode” of the structure - OFF is the state of the structure without the influence of an electric field. In this case, the molecules are perpendicular to the silicon pillars (image 1d). Thus, the topological characteristics of the structure do not change, however, the position of the forbidden zone changes. The light begins to spread throughout the structure. That is, the light does not pass along the necessary path, and there are large losses in the process. This is shown in image 1e .

According to the researchers, custom topological edge states are a very promising basis for many technologies. Obtaining the ability to conduct light along a given path with minimal losses (ideally, of course, without loss) can be provided precisely by manipulating the edge states.

In the structure under study, edge states are formed between topological and trivial photonic crystals. The lattices of both crystals, independently of each other, have a type of symmetry C6, which is broken in the space between these two fundamentals of the structure. The violation of symmetry leads to the appearance of degeneracy between spin states, and this allows them to interact near the point Γ. As a result of this interaction, a small zone appears (“gap”). But, despite the fact that the edge states are not devoid of such zones, they allow you to create a system for transmitting light along a given path without loss.

Losses in the path can occur for a number of reasons: sharp turns of the path, defects in the structure or crystal in particular. Thus, the structure should work so that, despite such barriers, the light passes the path without loss. First of all, it is necessary to have edge states at a given frequency.


Image number 2

Scientists decided to analyze the ribbon photonic crystal in order to confirm the presence of non-trivial edge states in its structure. The analysis showed the presence of both boundary and bulk states. And this is a problem. Since the presence of at least one volume state, even in the presence of edge states, will lead to the fact that any obstacle in the path of the light will cause its dispersion in the volume of the structure, that is, to losses (image 2). As a conclusion - you need to get rid of bulk states.

For example, use the Z-shaped path of light. Such a path is associated with losses, due to its non-direct path. So, there are two options to carry the light along such an unusual path without loss. The first is to use metal electrodes that will “hold back” the light inside the structure of the photonic crystal. This method, unfortunately, has its drawbacks: the losses will still be there, but already at the level of optical frequencies. The second option is much more attractive - to place the electrodes at some distance from the structure of the photonic crystal. The resulting free space can be filled with a liquid crystal, which has a significantly lower refractive index in comparison with the main structure.

Also, researchers have discovered a limiting range of frequencies at which neither the desired boundary states nor undesired volume states will arise. This is due to the desire to avoid intersections of the edge states, which may occur due to violation of C6 symmetry.

The refractive index also affects the size and location of the bandgap structure. For example, in the image 2c it is shown that with the exponent in 1.51 the forbidden zone covers the range of normalized frequencies 0.441 ... 0.462. But with an indicator of 1.69, the range changes - 0.433 ... 0.447 (image 2g ).


Image No. 3

For further analysis, the scientists decided to choose a frequency of 0.433. On image 3a (refractive index 1.51) and 3d(refractive index 1.69) shows how light travels at such a frequency.

When the refractive index is 1.51, the necessary boundary states do not arise, which is why the light does not focus, so to speak, and begins to diffuse throughout the structure. Let's return to the image №2, more precisely to d and g , for clarification. The normalized frequency of 0.433 is located below the band gap of the trivial (red curves) and topological (green curves) regions of the photonic crystal. If the refractive index is 1.69, then the frequency 0.433 falls just in the forbidden zone of both regions.

Also, scientists conducted an experiment with different refractive indices simultaneously. This was achieved by separating the external electric field into the trivial and topological regions separately. The electrodes are separated by a thin film of the insulator. The gap analysis in this experiment is shown in images 2e and 2f . And the propagation of light along the path with a rhombic defect is shown in 3b and 3c . In this experiment, the light again spreads through the structure. As a consequence, both regions of the structure, topological and trivial, must have the same refractive index.

You can get acquainted with the details of the study, in particular with the calculations, byreport research group .

Epilogue

The researchers managed to create a system in which light can be conducted along a complex (non-linear) path without losses, using manipulations with the refractive indices of the constituent elements of the structure. The necessary conditions for obtaining a similar result were noted: the presence of nontrivial topological boundary states and the absence of bulk states. The researchers also noted that the difference in the refractive index between the trivial and topological regions adversely affects the light transmission, leading to scattering of light and, consequently, to losses.

The use of liquid crystals in conjunction with silicon allowed us to control, modify and manipulate certain characteristics of the structure, thereby setting it up to the desired result.

This study once again shows the incredible potential of liquid crystals as an integral part of improving data transmission technologies, as well as their processing. This technology is not new, but not all variations of its application have been discovered. The more ways scientists find, the easier it is to develop technologies. And even if the open path will not be used in the future, it can serve as an impetus for other researchers to find their way. Competition is useful not only in economics, but also in research.

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