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Topology-Enabled Switchable Unidirectional Radiative Band in a Bilayer Photonic Crystal

This paper proposes a robust, switchable unidirectional radiative band in a bilayer photonic crystal, achieved through non-Hermitian hybridization of interlayer resonances and controlled by a topological vortex that enables reversible emission direction tuning via refractive index modulation.

Original authors: Zhiyi Yuan, Vytautas Valuckas, Yuhao Wang, Thi Thu Ha Do, Ningyuan Nie, Yu-Cheng Chen, Hai Son Nguyen, Cuong Dang, Son Tung Ha

Published 2026-02-16

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CC BY 4.0

Original authors: Zhiyi Yuan, Vytautas Valuckas, Yuhao Wang, Thi Thu Ha Do, Ningyuan Nie, Yu-Cheng Chen, Hai Son Nguyen, Cuong Dang, Son Tung Ha

Original paper licensed under CC BY 4.0 (http://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 you have a light bulb that usually shines in all directions, like a candle in a dark room. Now, imagine you want to build a light bulb that only shines forward, never backward, and you want to be able to flip a switch to make it shine only backward instead.

Usually, to do this, you need a mirror behind the bulb to block the backward light. But mirrors are bulky, and if you move the light source slightly, the mirror might not work anymore.

This paper describes a new, "magic" way to build a light source that does this without any mirrors. It uses a special sandwich of materials to trick light into going only one way, and it can be flipped back and forth just by changing the liquid surrounding it.

Here is the breakdown of how they did it, using simple analogies:

1. The Two-Layer Sandwich (The Hetero-Bilayer)

Think of the device as a two-layer sandwich:

Top Layer: A thin sheet of silicon with tiny holes punched in it (like a cookie cutter).
Bottom Layer: A similar sheet made of a different material (Titanium Dioxide), also with holes.
The Filling: A tiny gap of glass (Silicon Dioxide) separates them.

Individually, each layer is like a drum. If you hit it, it vibrates and sends sound (or light) out in all directions. But when you stack them very close together, they start to "talk" to each other.

2. The "Dance" of Light (Non-Hermitian Hybridization)

When the two layers are close, the light waves trapped inside them start to dance together. This is called hybridization.

Sometimes they dance in sync (the "Bonding" mode).
Sometimes they dance in opposition (the "Antibonding" mode).

The scientists engineered this dance so perfectly that for one specific rhythm, the light waves cancel each other out on one side of the sandwich but add up on the other side.

Analogy: Imagine two people shouting. If they shout at the exact same time and volume, the sound is loud. But if one shouts while the other whispers, or if they time it so their voices cancel out in one direction, the sound only travels the other way.
In this device, the "cancellation" is so perfect that zero light leaks out the back, and 100% of the light shoots out the front.

3. The "Magic Vortex" (Topology)

Why is this so special? Usually, if you nudge the sandwich slightly (change the temperature or make a tiny manufacturing error), the perfect cancellation breaks, and light starts leaking backward.

But this team used a concept called Topology.

Analogy: Think of a whirlpool in a bathtub. No matter how you swirl the water around the drain, the drain (the center of the vortex) stays exactly where it is. The water flows around it, but the center point is "locked" by the shape of the flow.
In their device, the "direction of the light" is locked by a mathematical vortex. Even if you wiggle the device a bit, the light keeps going in the same direction because the "vortex" protects it. This makes the device robust (tough against mistakes).

4. The "Remote Control" (Switching the Direction)

The coolest part is the switch. How do you make the light go backward instead of forward?

The Trick: They changed the liquid surrounding the sandwich.
The Analogy: Imagine the sandwich is a boat floating in water. If you change the water from fresh water to salt water, the boat sits slightly differently in the water.
In the experiment, they dipped the device in two different liquids (one with a lower "refractive index," like a thin oil, and one with a higher index).
The Result: When they switched the liquid, the "vortex" moved just enough to flip the switch. The light that was previously shooting UP suddenly started shooting DOWN.

Why Does This Matter?

This is a big deal for the future of technology:

Better Lasers: You can make lasers that shoot light in only one direction without needing bulky mirrors.
Super Sensors: Because the light direction flips so easily when the liquid changes, you could use this to detect tiny amounts of chemicals or viruses in a liquid. If the light suddenly flips direction, you know something is in the water.
Tiny Computers: This could help build smaller, more efficient optical chips for computers that use light instead of electricity.

In a nutshell: They built a light-sandwich where the layers dance together to block light in one direction. They proved that this dance is protected by a "mathematical shield" (topology), making it unbreakable by small errors, and they found a way to flip the dance direction just by changing the liquid around it.

1. Problem Statement

Controlling how open photonic systems exchange energy with their environment, specifically achieving unidirectional radiation (emission predominantly in one direction), is a fundamental challenge in non-Hermitian wave physics.

Limitations of Existing Solutions: Previous approaches, such as Unidirectional Guided Resonances (UGRs) in single-layer or bilayer metasurfaces, suffer from three main drawbacks:
1. Low Quality Factors (Q): They rely on leaky resonances, leading to intrinsic radiative losses.
2. Lack of Reversibility: Once fabricated, the emission direction is fixed and cannot be easily switched.
3. Angular Constraints: Directionality is often restricted to oblique angles rather than near-normal emission, limiting their utility in high-performance integrated devices.

2. Methodology

The authors propose a novel mechanism based on non-Hermitian hybridization of resonances in a hetero-bilayer photonic crystal (PhC).

Structure: The system consists of two vertically stacked PhC slabs made of different materials (Amorphous Silicon and Titanium Dioxide) separated by a subwavelength Silicon Dioxide gap. Each slab supports symmetry-protected Bound States in the Continuum (BICs) derived from electric-quadrupole (EQ) modes.
Theoretical Framework:
- The system is modeled using Temporal Coupled-Mode Theory (TCMT) with an effective non-Hermitian Hamiltonian ( $H$ ).
- The Hamiltonian accounts for:
  - Resonance frequencies ( $\omega_U, \omega_L$ ) and radiative decay rates ( $\gamma_U, \gamma_L$ ) of individual layers.
  - Near-field coupling ( $W$ ): Evanescent coupling across the gap.
  - Radiative coupling: Interference between the upward and downward radiation channels mediated by the continuum.
- Key Mechanism: By tuning the interlayer gap and slab thicknesses, the system creates hybrid "bonding" and "antibonding" modes. The authors demonstrate that these modes can satisfy the Friedrich–Wintgen (FW) interference condition, leading to a specific type of BIC where radiation is completely suppressed on one side while remaining strong on the other.
Topological Analysis: The radiation asymmetry is characterized by a pseudo-polarization vector defined by the front ( $S_F$ ) and back ( $S_B$ ) field amplitudes. The phase of this vector forms a topological vortex (singularity) in the parameter space (defined by phase delays $\Phi$ and $\Phi_U - \Phi_L$ ).

3. Key Contributions

High-Q Unidirectional Bands: Unlike previous UGRs that are restricted to single momentum points or suffer from low Q-factors, this work achieves unidirectional emission across a broad spectral and momentum range while maintaining high Q-factors derived from BICs.
Topological Robustness: The unidirectionality is not just a result of fine-tuned interference but is organized by a topological singularity (a vortex in the radiation-asymmetry pseudo-polarization field). This ensures the directionality is robust against structural perturbations.
Reversible Switching: The authors demonstrate that the emission direction can be reversibly switched by tuning the surrounding refractive index (RI). This moves the topological singularity in parameter space, flipping the system from front-emitting to back-emitting (or vice versa) without altering the physical geometry.

4. Results

Numerical Simulations:
- Analytical models and Finite Element Method (FEM) simulations confirmed that the bonding mode of the hetero-bilayer exhibits near-unity radiation asymmetry ( $F_{asy} \approx \pm 1$ ) over a wide range of in-plane wavevectors.
- A "four-quadrant" pattern of the asymmetry factor was observed around the FW-BIC point, confirming the topological nature of the singularity.
Experimental Demonstration:
- Fabrication: Two samples (Sample A and Sample B) were fabricated with specific thicknesses ( $t_{Si}$ , $t_{gap}$ ) designed to target opposite emission directions.
- Measurements: Angle-resolved photoluminescence (PL) measurements showed that Sample A emitted almost exclusively to the back, while Sample B emitted almost exclusively to the front. The measured Radiation Asymmetry factor approached $\pm 1$ , matching theoretical predictions.
- Switching: A third sample (Sample C) was immersed in liquids with different refractive indices (PMMA, $n=1.47$ $n = 1.47$ vs. Oil, $n=1.6$ $n = 1.6$ ).
  - In PMMA, the sample exhibited negative asymmetry (back emission).
  - In Oil, the emission direction switched to positive asymmetry (front emission).
  - The experimental switching was confirmed by a change in the RA factor from $F_{asy} \approx -0.5$ to $F_{asy} \approx 0.65$ .

5. Significance and Impact

New Design Paradigm: This work establishes a general route to robust, reconfigurable, high-Q directional emission based on topological singularities in synthetic parameter spaces, rather than relying on geometric asymmetry.
Applications:
- Reconfigurable Light Sources: Enables switchable unidirectional lasers and LEDs.
- Topological Photonic Sensing: Provides a sensing mechanism based on intensity imbalance (directional switching) rather than spectral shifts. This offers higher robustness and simpler readout compared to conventional refractive index sensors that require high spectral resolution.
- Integrated Nanophotonics: The ability to engineer vertical emission directionality in a compact bilayer platform is crucial for on-chip optical interconnects and vertical cavity devices.

In summary, the paper successfully bridges the gap between topological photonics and non-Hermitian engineering, demonstrating a scalable platform for high-performance, switchable unidirectional emitters.