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Chaos waves in microluminal crystals determined by Bloch’s theorem


Guide

Recently, the team of Professor Moon Jip Park of the Institute of Basic Science in Daejeon City, South Korea, together with the team of Professor Hee Chul Park of the Department of Physics, Pukyung National University, Busan, South Korea, successfully generalized the wave chaos theory to microcavity crystals, and discovered the “locking” effect of crystal momentum and internal cavity dynamics. This technique contributes to a better understanding of optical behavior within microluminal crystals and provides the basis for future microstructured light control techniques.

Research background

Optical microcavity is an optical resonant cavity with high-quality factors, which plays a fundamental and extremely important role in quantum optics, quantum information processing, sensors and other fields. In optical microcavities, photons are reflected in the inside of the microcavity and are affected by factors such as the shape of the microcavity boundary. This effect can lead to changes in energy transfer and coherence in fluctuating systems and cause chaotic phenomena.

Traditional optical microcavity chaos theory mainly focuses on chaotic phenomena in a single microcavity or microcavity array with aperiodic structure, and adjusts optical behavior, such as coherence, polarization, and transmission, by changing the shape of the microcavity echo boundary. Experimenters usually study chaotic phenomena by measuring parameters such as intensity distribution and frequency distribution of photons at different locations and times.

However, in practical applications, once the optical microcavity is manufactured, its boundary shape can no longer be arbitrarily changed, so it is difficult to obtain convenient and high-precision optical control in experiments.

Innovative research

This paper innovatively uses the cavity-momentum locking effect to overcome the above difficulties. By adjusting the incidence amplitude and direction of light, the propagation of light in the cavity and lattice can be controlled without changing the shape of the cavity. Specifically, the authors designed cavities with deformed structures and formed these cavities into a two-dimensional cavity array with a quad structure (see Figure 1). Among them, the authors focused on analyzing two cavity modes: “scar mode” and “bow tie mode”. They found that Bloch waves exhibit chaotic behavior due to the presence of microlumen crystals. This chaotic phenomenon is caused by the coupling of the Bloch vector of the crystal and the intraluminal dynamics. This phenomenon of “cavity-wave vector locking” replaces the original boundary deformation theory and becomes the main reason for the chaos of light waves in the cavity. In addition, by studying the Q-function of scar states in phase space, the authors found that the presence of periodic lattice structures also leads to phase space reconfiguration, thereby inducing a dynamic localization shift (see Figure 2).

In addition, the conditions for maximum coupling are discussed in detail. When the intracavity mode density is high and the momentum matching conditions are met, the maximum momentum coupling can be obtained. Because of the above properties, lattice chaotic waves have become a new experimental platform to study the chaotic phenomena of various waves. In addition, if a high- or low-energy state is involved, this state triggers momentum-induced dynamic tunneling. This will be a future research topic.

On the other hand, the authors note that there are topological effects in the system, and this topological effect is not exactly the same as the paradigm of traditional topological photonics. Topological photonics is dominated by Rayleigh scattering, while the scattering of dominant chaos is dominated by Michaotic scattering. Michael’s scattering is mainly described by semiclassical theory. For the first time, it was proposed that Mie-scattering would also accumulate the Bailey phase. And use this Bailey curvature to realize the possibility of transportation. This work can also be extended to other different lattice platforms, such as the Lieb lattice, the kagome lattice, etc.

Figure 1: (a) Schematic diagram of a cavity array photonic crystal. The array consists of a designed deformation cavity. (b) Schematic diagram of a quad lattice with lattice constant a. (c) The eigenfrequency real part in a single cavity is a function of cavity deformation. (d) The energy characteristic value in the cavity array lattice is a function of the deformation when the lattice momentum is 0.

Figure 2: The Husimi function of the mode in the cavity lattice is superimposed in the ray dynamics phase space at the Birkhoff coordinate. where q/L is the length normalized by the cavity circumference L and is the angle of incidence of the ray. The small figures on the left and right sides represent the two degenerate modes in the cavity.

Figure 3: (a) Schematic diagram of a pseudospin orbiting a crystal zero-momentum space. The upper and lower figures (b)-(e) represent the modulo square|ψ|2 of the wave function corresponding to i-iv in figure (a) and the real part Re(ψ).

The article was recently published in Light: Science & Applications in the top international academic journal “Bloch Theorem Dictated Wave Chaos in Microcavity Crystals”. Chang-Hwan Yi is the first author of the paper, and Hee Chul Park and Moon Jip Park are the corresponding authors of the paper. (Source: LightScience Applications WeChat public account)

Related paper information:https://www.nature.com/articles/s41377‍-023-0‍1156-9

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