Light Localization in Local Isomorphism Classes of Quasicrystals

Area of Science:

• Condensed matter physics
• Materials science
• Photonics

Background:

• Photonic quasicrystals offer unique wave manipulation properties.
• Local isomorphism (LI) classes provide a framework for classifying quasicrystal structures.
• Understanding structure-property relationships is crucial for designing advanced optical materials.

Purpose of the Study:

• To investigate a continuum of photonic quasicrystal heterostructures derived from pentagonal quasicrystal tilings.
• To determine how different local isomorphism (LI) classes affect the electronic and optical properties of these heterostructures.
• To explore the relationship between pattern properties and state localization.

Main Methods:

• Generating quasicrystal tilings via direct projection from a five-dimensional hypercubic lattice.
• Analyzing the resulting heterostructures for degenerate and localized states.
• Relating localization phenomena to the mathematical concept of 'restorability' in tiling patterns.

Main Results:

• Most LI classes, excluding the Penrose class, yield degenerate, localized states in photonic quasicrystal heterostructures.
• The properties of these localized states, including frequencies and densities, are precisely predictable and tunable.
• Localization and tunability are mathematically linked to the 'restorability' property of the quasicrystal pattern.

Conclusions:

• The choice of local isomorphism (LI) class significantly dictates the localization and tunability of photonic quasicrystal heterostructures.
• The 'restorability' property offers a predictive tool for designing quasicrystal-based photonic devices with tailored properties.
• This research opens avenues for novel photonic applications leveraging engineered quasicrystal designs.