Topological protection of photonic mid-gap cavity modes (1611.02373v1)

Abstract: Defect modes in two-dimensional periodic photonic structures have found use in a highly diverse set of optical devices. For example, photonic crystal cavities confine optical modes to subwavelength volumes and can be used for Purcell enhancement of nonlinearity, lasing, and cavity quantum electrodynamics. Photonic crystal fiber defect cores allow for supercontinuum generation and endlessly-single-mode fibers with large cores. However, these modes are notoriously fragile: small changes in the structure can lead to significant detuning of resonance frequency and mode volume. Here, we show that a photonic topological crystalline insulator structure can be used to topologically protect the resonance frequency to be in the middle of the band gap, and therefore minimize the mode volume of a two-dimensional photonic defect mode. We experimentally demonstrate this in a femtosecond-laser-written waveguide array, a geometry akin to a photonic crystal fiber. The topological defect modes are determined by a topological invariant that protects zero-dimensional states (defect modes) embedded in a two-dimensional environment; a novel form of topological protection that has not been previously demonstrated.

• The paper presents a novel experimental model using femtosecond-laser-written waveguide arrays to demonstrate topological protection of mid-gap cavity modes.
• The paper establishes that a non-trivial topological invariant in BDI class systems with C6 symmetry robustly secures defect states against structural imperfections.
• The paper confirms that topological protection maintains stable resonance frequency and confined mode volume, improving photonic device performance.

Overview of Topological Protection of Photonic Mid-Gap Cavity Modes

This paper by Jiho Noh et al. presents a paper on the topological protection of photonic mid-gap cavity modes within two-dimensional periodic photonic structures, specifically employing a photonic topology in crystalline structures. The research addresses a significant problem in photonic devices: the vulnerability of defect modes to structural changes, which often results in detuning of resonance frequencies and alterations in mode volumes. To mitigate this issue, the authors utilize a photonic topological crystalline insulator (PTCI) to offer topological protection, ensuring the resonance frequency is centrally located within the band gap, thus minimizing mode volume.

Key Contributions

1. Experimental Model and Setup: The paper utilizes a femtosecond-laser-written waveguide array, analogous to a photonic crystal fiber, for experimental validation. The geometry chosen is directly related to that introduced in prior theoretical frameworks, such as Benalcazar et al. (2014) and Wu et al. (2015), but shifts focus onto the defect states, a novel domain not previously demonstrated.
2. Topological Protection Mechanism: The innovation hinges on a topological invariant that secures zero-dimensional states (defect modes) in the two-dimensional context. This ensures the defect modes are robust against minor structural imperfections without drifting away from the optimal mid-gap resonance frequency.
3. Topological Invariant Application: The authors theoretically ground their model in the classification system for BDI class systems supplemented with $C_6$ symmetry. They identify that such class structures exhibit band inversions indicating a non-trivial topology, characterized by an integer-valued topological invariant, [M].
4. Practical Implications: This work suggests that topological protection can safeguard photonic devices from inaccuracies introduced by inevitable parasitic scattering during manufacturing. Furthermore, it implies that cavity modes in photonic crystal slabs and fibers can achieve more stable frequencies and allow tighter confinement, enhancing the applicability in optical communications and quantum information processing.

Numerical Results and Experiments

• The authors present simulations and experimental data showing the confinement of light in the trivial, critical, and non-trivial phases of the photonic lattice. In the non-trivial phase, light is localized at the input corner across the wavelength range, confirming the presence of topologically protected modes.
• An in-depth eigenmode analysis reveals the spectral separation between trivial defect modes and topological modes, with significant fluctuations in light intensity profiles confirming such theoretical predictions. The measured data firmly aligns with the anticipated behavior, showcasing the mode protection ensuring mid-gap residence despite structural variances and disorder.

Implications and Future Directions

The documented results not only testify to the potential robustness of photonic devices through topological frameworks but also extend the understanding of topological protection in higher dimensions and diverse material contexts. The implications include improved efficiency and reliability of photonic crystal cavities and enhanced nonlinear optical effects due to assured mid-gap mode presence. Future developments may explore broader material configurations and strive towards scalable solutions exploiting these findings in practical applications, such as single-mode fibers and quantum dot enhancements.

In conclusion, the paper solidifies the technological significance of topological invariants in photonic systems, leaving a substantial footprint for subsequent investigations into topologically enhanced photonic and related emergent materials.