Finite barrier bound state

Area of Science:

• Condensed Matter Physics
• Photonics
• Wave Phenomena

Background:

• Boundary modes in finite lattices typically exhibit tunneling to the opposite side, leading to unwanted couplings.
• Tunneling probability is conventionally understood to decay exponentially with system size, necessitating large lattices for negligible coupling.

Purpose of the Study:

• To investigate the possibility of trapping boundary modes within a finite number of lattice sites.
• To explore mechanisms that allow boundary modes to be completely localized, irrespective of conventional tunneling behavior.

Main Methods:

• Theoretical analysis of boundary mode behavior in finite lattices.
• Experimental validation using dielectric photonic crystals at microwave frequencies.
• Investigation of specific wavevectors where tunneling probability vanishes.

Main Results:

• Demonstrated that tunneling probability for certain boundary modes can vanish at specific wavevectors.
• Observed complete trapping of boundary modes within very few lattice sites, even without a well-defined bulk bandgap.
• Found that the number of trapped states corresponds to the number of lattice sites normal to the boundary.

Conclusions:

• Introduced a novel phenomenon of finite barrier-bound states, analogous to bound states in the continuum.
• Provided experimental evidence for this peculiar trapping mechanism in photonic crystals.
• Highlighted the potential for flexible control over light coupling and manipulation.