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Chiral Selection of Purely Localized and Delocalized States in Non-Hermitian Photonic Waveguide Arrays

This paper presents a non-Hermitian quasiperiodic mosaic waveguide array that utilizes exceptional-point encircling dynamics to deterministically select between purely localized and delocalized output states, a mechanism experimentally validated via femtosecond laser direct writing in glass.

Original authors: Yan Li, Ruiqi Wang, Yuliang Tang, Qihuang Gong

Published 2026-06-30

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CC BY 4.0

Original authors: Yan Li, Ruiqi Wang, Yuliang Tang, Qihuang Gong

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a busy highway system for light, where the "cars" are beams of light traveling through tiny glass tunnels called waveguides. Usually, engineers want to control where these cars go: sometimes they want all the cars to merge into a single lane (concentration), and other times they want them to spread out across many lanes (distribution).

This paper describes a new, clever way to control this traffic using a special kind of "one-way street" rule based on the direction you drive. The researchers built a device that acts like a chiral (handed) traffic switch: if you drive your light beam clockwise, it forces all the light to merge into a single, tight spot. If you drive it counter-clockwise, it forces the light to spread out evenly across the whole system.

Here is how they did it, broken down into simple concepts:

1. The Problem: Mixing vs. Choosing

In the past, scientists could build systems where light could either stay in one spot or spread out. However, they couldn't easily force the light to choose one or the other just by changing the direction of travel. It was like having a road with two possible destinations, but no sign telling the driver which way to go; the car would just end up in a mix of both.

2. The Solution: The "Exceptional Point" Trap

The researchers used a concept from physics called an Exceptional Point (EP). Think of an EP as a special, invisible whirlpool in the energy landscape of the light.

In normal physics, if you drive around a hill, you end up exactly where you started.
In this special "non-Hermitian" physics, if you drive around this whirlpool (the EP), the rules change. The path you take determines your final destination, regardless of where you started.

3. The Design: A Quasiperiodic Maze

To create this effect, they built a specific pattern of glass waveguides (a "quasiperiodic mosaic").

The Localized State: Imagine a car getting stuck in a single garage. This is "localized" light.
The Delocalized State: Imagine a car driving freely down a long, open highway. This is "delocalized" light.

The researchers engineered the glass so that the "whirlpool" (the Exceptional Point) sits exactly between these two states.

4. The Magic Trick: Driving Around the Loop

The core of their discovery is the direction of travel.

Clockwise Drive: The researchers designed the path so that if the light travels clockwise around the whirlpool, it gets "funneled" into the single garage (the localized state). No matter which lane the light started in, it ends up squeezed into one spot.
Counter-Clockwise Drive: If the light travels the opposite way, the path guides it to spread out across the highway (the delocalized state).

This is called Chiral Selection. The "handedness" (direction) of the loop decides the outcome.

5. The Experiment: Laser-Written Glass

To prove this works, the team didn't just simulate it on a computer; they built it.

They used a high-powered femtosecond laser (an ultra-fast laser) to "write" these tiny glass tunnels directly inside a block of glass.
They created a 5-lane system.
The Result: When they shone light into the system and guided it clockwise, the light exited only from the center lane (a "combiner"). When they guided it counter-clockwise, the light exited from the two outer lanes, splitting the beam (a "splitter").

Why This Matters (According to the Paper)

The paper claims this is a new way to control light on computer chips. It allows for deterministic routing:

Optical Funneling: Collecting signals from many sources into one.
Optical Routing: Distributing a single signal to many places.

The key takeaway is that by simply changing the direction of the light's path around a specific point, you can force the light to either concentrate or spread out, without needing to change the hardware itself. It's like having a traffic light that changes the entire road layout based solely on which way the cars are turning.

Technical Summary: Chiral Selection of Purely Localized and Delocalized States in Non-Hermitian Photonic Waveguide Arrays

Problem Statement
Integrated photonic systems require precise control over light transport, specifically the ability to switch between spatially concentrated (localized) and distributed (delocalized) optical signals for functions such as optical funneling and routing. While systems with mobility edges (MEs) naturally host coexisting localized and delocalized states, they lack a mechanism for deterministic chiral selection between these two distinct output forms. Existing non-Hermitian approaches utilizing dissipation can drive systems toward steady states dominated by either localized or delocalized components, but these typically result in mixed steady states and do not offer directional selection based on propagation direction. Furthermore, implementing the required phase-engineered Lindblad dissipation in integrated waveguide arrays presents practical challenges.

Methodology
The authors propose and realize a non-Hermitian quasiperiodic mosaic waveguide array that integrates the coexistence of localized and delocalized states with Dynamically Encircling Exceptional Points (DEEPs).

Theoretical Model: The study extends the one-dimensional quasiperiodic mosaic lattice (an exactly solvable model hosting MEs) into the non-Hermitian regime by introducing a non-Hermitian quasiperiodic onsite potential. This potential includes a quasiperiodic amplitude, a phase offset, and distinct intrinsic loss terms ( $\gamma_q$ and $\gamma_z$ ) for sites with and without the potential.
Dissipative Coupling: The system employs dissipative coupling ($C = iJ$) rather than conservative coupling. This induces multiple pairs of exceptional points (EPs) in the energy spectrum. Crucially, unlike conventional PT- or anti-PT-symmetric systems where eigenstates on different branches share the same inverse participation ratio (IPR), the engineered dissipative coupling creates spectral branches where eigenstates exhibit distinct spatial localization profiles (one localized, one delocalized) on the lowest-loss energy surface.
Chiral Selection Mechanism: A closed-loop trajectory is designed in the two-dimensional parameter space spanned by coupling strength ( $J$ ) and relative dissipation ( $\gamma = \gamma_q - \gamma_z$ ). This loop encircles the EPs. Due to non-adiabatic transitions inherent in DEEPs, the final state is determined by the direction of encircling (clockwise vs. counterclockwise) rather than the initial state. The trajectory is specifically configured so that the two segments extending from the start point traverse regions of the lowest-loss surface corresponding to high-IPR (localized) and low-IPR (delocalized) states, respectively.
Experimental Realization: The authors fabricated a chiral beam splitter-combiner using femtosecond laser direct writing in borosilicate glass. To implement the required dissipative coupling, which is difficult to achieve directly, they utilized a five-waveguide system with auxiliary lossy modes. By adiabatically eliminating these auxiliary modes, the system effectively realizes the target three-state Hamiltonian. Loss was introduced into specific waveguides (WG2 and WG4) via discrete scatterers created by focused laser pulses.

Key Results

Theoretical Simulation: Simulations for small systems ( $N=3$ $N = 3$ ) and larger systems ( $N=13$ $N = 13$ ) confirmed that the encircling direction deterministically selects the output state.
- Clockwise (CW) encircling: The system evolves into a purely localized state (IPR $\approx$ 1), regardless of the initial excitation.
- Counterclockwise (CCW) encircling: The system evolves into a delocalized state (IPR $\approx$ 0.1 for $N=13$ , fitting a double-Gaussian profile), regardless of the initial excitation.
Experimental Demonstration: The fabricated five-waveguide device successfully demonstrated chiral mode conversion at 785 nm.
- Under CW propagation, the device functioned as an optical combiner, consistently outputting through the central waveguide (WG3).
- Under CCW propagation, the device functioned as a beam splitter, distributing the output nearly equally between the outer waveguides (WG1 and WG5).
Performance: The experimentally measured transmission efficiency was 59.4%, with the discrepancy from the simulated 78.1% attributed to fabrication imperfections in the discrete scatterer loss implementation leading to nonuniform loss. Numerical simulations confirmed the system's robustness against local random perturbations in coupling and loss parameters.

Significance and Claims
The paper claims to provide a novel approach for controlling on-chip light transport by combining non-Hermitian encircling dynamics with localization physics. The primary significance lies in achieving deterministic chiral selection between purely localized and purely delocalized states, a functionality previously unavailable in integrated photonic systems.

The authors assert that this mechanism enables:

Direction-Controlled Switching: The ability to switch between signal collection (funneling) and distribution (routing) solely by reversing the propagation direction.
Experimental Validation: The successful fabrication of a chiral beam splitter-combiner that physically validates the theoretical mechanism.
Generalizability: While demonstrated in photonics, the underlying mechanism is claimed to be generalizable to other physical settings, including atomic and electronic systems.
Future Extensions: The authors suggest that with suitable gain media, this mechanism could be extended to active platforms for reconfigurable on-chip lasers, allowing the switching between laser supermodes with distinct spatial profiles.

The work is presented as a step toward enriched mode control and new information-processing functionalities in integrated photonic platforms, without claiming immediate commercial deployment or applications beyond the demonstrated optical funneling and routing concepts.