Symmetry’s End: Engineering High-Q Resonances with Topological Quasibound States

by

Author: Denis Avetisyan

Breaking mirror symmetry in plasmonic crystals provides a novel pathway to transition between bound states in the continuum and high-quality quasi-bound states, enabling precise control over light-matter interactions.

This review details how σh symmetry breaking induces a topological phase transition and creates tunable, high-Q resonances in plasmonic lattices via the formation of quasi-bound states in the continuum.

Conventional approaches to realizing high-quality resonances typically rely on manipulating in-plane symmetry, often overlooking the potential of out-of-plane asymmetry. This work, titled ‘σh-Broken Induced Topological quasi-BIC’, demonstrates that breaking \sigma_h symmetry in plasmonic lattices induces a transition from bound states in the continuum (BICs) to quasi-BICs, accompanied by a topological phase transition characterized by a Zak phase inversion. This mechanism not only enables controlled radiation coupling but also establishes a defect-immune regime for high-Q resonances. Could this approach pave the way for the design of topologically robust and highly efficient plasmonic cavities with tailored optical properties?

The Illusion of Control: Harnessing Light’s Boundaries

Photonic crystals represent a revolutionary approach to light management, achieving control over electromagnetic waves at the nanoscale previously considered impossible. These structures, characterized by a periodic arrangement of materials with differing refractive indices, create ‘photonic band gaps’ – ranges of wavelengths that cannot propagate through the material, analogous to the electronic band gaps in semiconductors. This precise manipulation isn’t simply about blocking light; it allows for the creation of waveguides, resonators, and filters with extraordinary precision, enabling the slowing, bending, and even trapping of light. The implications extend to a vast range of applications, from highly efficient solar cells and advanced optical sensors to novel laser designs and the potential for all-optical computing – promising a future where light, rather than electrons, powers information technology.

Bound States in the Continuum (BICs) represent a counterintuitive phenomenon within photonic crystals where light can be trapped within a structure despite possessing the energy to radiate into free space. These states arise from specific configurations that effectively cancel out any leakage of light, leading to extraordinarily high quality (Q) factors – a measure of how long light remains confined. Unlike typical resonant states, BICs are not dictated by the material properties alone, but rather by the precise geometry of the photonic crystal itself. This geometric control allows for the tailoring of resonant wavelengths and intensities at the nanoscale, opening doors for applications ranging from highly sensitive sensors and efficient lasers to novel optical filters and enhanced light-matter interactions. The potential for manipulating light in this way, without material absorption, offers a pathway toward realizing compact and energy-efficient photonic devices with unprecedented performance characteristics.

The full potential of Bound States in the Continuum (BICs) within photonic crystals is currently hampered by a critical challenge: their extreme sensitivity to even minor imperfections in fabrication or operation. Traditional BIC designs rely on precise symmetry and parameter tuning to trap light, but any deviation – a slight asymmetry, a change in refractive index, or even nanoscale roughness – can destroy the BIC, leading to significant losses and a diminished quality factor. This fragility hinders the development of robust photonic devices, as real-world fabrication processes are inherently imperfect. Researchers are actively exploring novel designs and materials that can create ‘protected’ BICs, less susceptible to these perturbations, by engineering topological protection or utilizing symmetry-protected modes, ultimately paving the way for reliable and scalable photonic technologies.

Symmetry’s Embrace, and its Deliberate Fracture

Bound states in the continuum (BICs) traditionally require strict symmetry protection, limiting design flexibility. Introducing asymmetry into photonic crystal structures, and specifically breaking mirror symmetry about the plane defined by σh, provides a controlled mechanism to transition from these symmetry-protected BICs to quasi-BICs (qBICs). This symmetry breaking perturbs the perfect confinement of the BIC, allowing for a small degree of radiative loss. The resultant qBICs, while not perfectly confined, exhibit a finite quality factor and represent a significant improvement in practicality for applications compared to true BICs, as the symmetry requirement is relaxed allowing for greater design freedom.

Introducing asymmetry perpendicular to the photonic crystal plane – termed out-of-plane asymmetry – provides a mechanism for transitioning from Bound States in the Continuum (BICs) to quasi-BICs. This is achieved by intentionally disrupting the symmetry of the structure, allowing for manipulation of the resonance properties. Specifically, controlled deviations from the original symmetric design enable fine-tuning of the resonant wavelength, linewidth, and radiation characteristics. The degree of asymmetry directly correlates with the extent of the BIC perturbation, and thus, the Q-factor and radiative decay rate of the resulting quasi-BIC resonance can be precisely controlled through geometric parameter adjustments during fabrication or post-processing.

The introduction of asymmetry into photonic crystal structures, specifically the breaking of \sigma_h symmetry, results in the emergence of a Zak Phase. This Zak Phase is a topological invariant, a quantity that remains constant under continuous deformations, and directly reflects a shift in the material’s band structure. Quantitatively, the Zak Phase is defined as the Berry phase accumulated around the Brillouin zone and can be calculated as the line integral of the Berry connection. Its presence confirms the transition from a Bound State in the Continuum (BIC) – characterized by an infinite Q-factor – to a quasi-BIC (qBIC) possessing a finite, though exceptionally high, Q-factor. The magnitude of the Zak Phase is directly correlated with the degree of symmetry breaking and serves as a robust indicator of the qBIC formation process.

The introduction of asymmetry into photonic crystal designs results in quasi-bound states in the continuum (qBICs) characterized by a finite quality factor (Q). Unlike the infinite Q-factor theoretically predicted for perfect BICs, these qBICs demonstrate a Q exceeding 10⁴. This finite, yet exceptionally high, Q-factor is crucial for practical device implementation, as it allows for resonant energy confinement without the limitations imposed by a truly non-radiative, infinitely sharp resonance. The measurable decay rate associated with a finite Q enables efficient coupling to external systems and facilitates the utilization of qBICs in applications such as high-sensitivity sensing, nonlinear optics, and laser development where energy transfer and light-matter interaction are essential.

The Unveiling: How Distorted Symmetry Reshapes Resonance

The introduction of asymmetry into a photonic crystal structure fundamentally changes the interaction between dipole and quadrupole resonant modes. In symmetrical structures, these modes typically exhibit predictable coupling behavior, resulting in specific field distributions and resonant frequencies. However, asymmetry disrupts this balance, leading to hybridization and significant modifications in mode characteristics. Specifically, the symmetry-breaking induces a shift in the resonant wavelengths and alters the spatial distribution of electromagnetic fields associated with both dipole and quadrupole excitations. This altered interplay is a direct consequence of the modified boundary conditions and the disruption of translational symmetry within the photonic crystal lattice, influencing the overall photonic response of the material.

The introduction of asymmetry to a photonic crystal structure directly impacts its dispersion relation, resulting in shifts to resonant frequencies and alterations in the spatial distribution of electromagnetic fields. The dispersion relation, which mathematically describes the relationship between frequency and wavevector k, is fundamentally altered when symmetry is broken. This modification manifests as a deviation from the expected band structure and leads to changes in the wavelengths of light that can propagate through the material. Consequently, the electric and magnetic field distributions associated with resonant modes are no longer symmetrical and can become highly localized or exhibit more complex spatial patterns, influencing the material’s interaction with light at specific frequencies.

Finite Element Method (FEM) simulations reveal a direct correlation between the geometry and dielectric properties of the photonic crystal structure and the resulting mode characteristics. These simulations demonstrate that alterations to the constituent building blocks-specifically, changes in shape and material composition-directly impact the resonant frequencies, Q-factor, and field distribution of the photonic modes. The FEM allows precise control over geometric parameters and material properties within the simulation environment, enabling detailed analysis of how these factors influence the electromagnetic response of the structure. The method facilitates the prediction and optimization of mode characteristics by solving Maxwell’s equations numerically within the defined geometry and material constraints.

Transitioning from metallic cylinder building blocks to metallic cones introduces geometric asymmetry that significantly impacts the photonic response of the structure. Finite Element Method analysis reveals a critical threshold at a cone angle of tan(\theta) = 0.768 . Beyond this angle, a substantial decrease in the Q-factor is observed, indicating a reduction in resonance sharpness and an increased rate of energy dissipation. This suggests that the cone angle directly influences the confinement and lifetime of the photonic modes within the structure, with higher angles promoting faster decay of the resonant field.

Beyond the Horizon: Implications and Future Delusions

The research establishes a clear route toward fabricating advanced photonic devices with precisely tailored properties. By manipulating the symmetry of photonic structures to create quasi-bound states in the continuum, engineers can develop robust and highly sensitive sensors capable of detecting minute changes in their environment. Furthermore, this approach allows for the creation of optical filters that selectively transmit or block specific wavelengths of light, and opens doors to nonlinear optical elements – crucial components for technologies like optical computing and advanced imaging. The tunability inherent in this design methodology-achieved through control over structural parameters-offers the potential to dynamically adjust device characteristics, leading to adaptable and reconfigurable photonic systems with broad applications in telecommunications, environmental monitoring, and biomedical diagnostics.

The intentional disruption of symmetry within photonic structures presents a powerful strategy for manipulating light at the nanoscale and intensifying light-matter interactions. This approach, centered on engineering quasi-bound states in the continuum (quasi-BICs), allows for the confinement of light within a very small volume, dramatically increasing the density of optical energy. Such concentrated fields enhance the interaction between light and materials, proving critical for applications like highly sensitive sensing, efficient nonlinear optics, and advanced light harvesting. By precisely controlling the degree of symmetry breaking – introducing subtle asymmetries into the structure – researchers can tune the properties of these quasi-BICs, effectively tailoring the strength and nature of these enhanced interactions for specific functionalities and enabling the creation of novel photonic devices with unprecedented performance.

Investigating in-plane asymmetry represents a significant frontier in manipulating light at the nanoscale. By intentionally disrupting the symmetry within a material’s structure or its dielectric properties – its permittivity – researchers anticipate unlocking unprecedented control over light behavior. Subtle alterations to these parameters allow for the precise tailoring of optical resonances, enabling the creation of photonic devices with highly customizable characteristics. This approach moves beyond simple symmetry breaking to nuanced control, promising a broader range of achievable optical responses and functionalities, ultimately leading to more versatile and efficient devices for applications like sensing, filtering, and advanced optical signal processing.

The principles demonstrated with dielectric metasurfaces extend promisingly to plasmonic lattices, offering a route towards dramatically miniaturized and highly efficient photonic components. Investigations into these lattices reveal the potential for exceptional performance characteristics; for instance, related designs have already achieved quality factors – a measure of resonant energy storage – exceeding 2,663 at visible light frequencies. Furthermore, these structures can be engineered to exhibit near-unity circular dichroism – a property crucial for manipulating light polarization – with values reaching 0.93 in specifically designed, slant resonant metasurfaces. These achievements suggest that leveraging plasmonic lattices, guided by the principles of symmetry breaking and quasi-bound states in the continuum, holds substantial promise for advancing a new generation of compact and versatile optical devices.

The investigation into symmetry breaking within plasmonic crystals reveals a profound interplay between fundamental physical laws and emergent phenomena. The transition from bound states in the continuum to quasi-BICs, facilitated by σh symmetry breaking, underscores the limitations of relying solely on established theoretical frameworks. As Pierre Curie observed, “One never obtains one hundred percent of anything.” This sentiment resonates with the findings; the pursuit of perfect bound states is perpetually constrained by real-world imperfections and the subtle nuances of symmetry. The observed topological phase transition highlights that even within seemingly well-defined systems, the boundaries of predictability remain ever-present, mirroring the inherent incompleteness of any physical model.

Where Do We Go From Here?

The demonstrated transition from bound states in the continuum to quasi-BICs via σh symmetry breaking, while conceptually satisfying, reveals the inherent fragility of any constructed order. Any model simplification, particularly concerning topological photonics and plasmonic crystals, requires strict mathematical formalization to avoid the inevitable decay toward a less-defined state. The observed band inversion, and the manipulation of the Zak phase, are merely points on a landscape of possible configurations-configurations that, ultimately, exist only within the limits of the chosen theoretical framework.

Future investigations must address the limitations of current perturbative methods when dealing with strongly interacting systems. The high-Q resonance engineering enabled by these quasi-BICs offers promise, yet true control necessitates a deeper understanding of loss mechanisms and the effects of imperfections-factors that are always present, like background noise in a silent room.

The field now faces the task of moving beyond simply creating these states to truly understanding their fundamental nature. Each advance in topological photonics feels less like a discovery and more like a temporary reprieve from the inevitable-a momentary glimpse of order before the system succumbs to the entropic pull beyond the event horizon of complexity.

Original article: https://arxiv.org/pdf/2601.15569.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

See also:

2026-01-25 22:08