Non-Hermitian systems exhibiting parity-time (PT) symmetry demonstrate a unique coalescence of eigenvalues and eigenstates at exceptional points (EPs). The study of EPs and their associated non-Hermitian physics has been facilitated by the introduction of tailored gain and loss in various photonic systems, including microcavities, coupled waveguides, gratings, and photonic crystals. The topological characteristics of EPs, forming a self-intersecting Riemann surface, lead to phenomena like loss-induced transmission enhancement, enhanced sensitivity, unidirectional invisibility, and single-mode lasing, enabling novel technologies. Recent research has shown that non-adiabatic transitions (NATs) during dynamic EP encirclement can create strong directional responses and chiral state evolution. Chiral mode switching has been experimentally and theoretically verified by mapping Hamiltonian parameters onto coupled waveguide structures. Clockwise (CW) or anticlockwise (ACW) encirclement of EPs results in different output modes, with the final output mode independent of the input mode for a given handedness. However, conventional chiral mode converters based on this principle suffer from low transmission efficiency due to energy dissipation near EPs, with a maximum experimental efficiency of only 46%. Theoretical studies have shown that high-efficiency chiral mode transmission is possible using discontinuous encircling protocols via Hamiltonian hopping, but this approach introduces mode crosstalk due to mode mismatch. This paper presents a novel approach that leverages fast adiabatic parametric evolution along the Hamiltonian parameter space boundary to achieve high-efficiency chiral mode transmission with a compact footprint. This approach addresses the limitations of previous methods by minimizing energy dissipation and reducing modal crosstalk.

The study of exceptional points (EPs) in non-Hermitian systems has gained significant traction, driven by their potential for applications in various fields. Early works demonstrated the observation of PT-symmetry breaking in complex optical potentials and the breakdown of adiabatic light transfer in waveguides with absorption. Subsequently, research focused on dynamically encircling EPs for asymmetric mode switching, both theoretically and experimentally. These studies utilized different approaches, including mapping Hamiltonian parameters onto coupled waveguide structures, and explored the effects of adiabatic and non-adiabatic transitions. However, achieving high efficiency in chiral mode conversion remained a challenge due to energy dissipation near the EPs. Previous attempts to improve efficiency, such as the use of discontinuous encircling protocols via Hamiltonian hopping, introduced additional mode crosstalk. This paper builds upon this existing research, offering a novel method to overcome the limitations of these previous approaches.

To demonstrate chiral mode transmission with fast parametric evolution, the researchers constructed a system of double-coupled silicon waveguides (DSWs). The system is fabricated on a silicon-on-isolator (SOI) wafer, with a chromium layer of varying widths placed on one waveguide to introduce position-dependent loss. Full-wave simulations using finite-difference time-domain methods were used to model the system's behavior. The chiral mode switching is analyzed using the evolution equation dψ/dz = iHψ, where ψ(z) = [a₁(z), a₂(z)] represents the eigenfunction, a₁(z) and a₂(z) are the mode amplitudes, and H(z) is the Hamiltonian matrix containing parameters β(z), γ(z), and κ(z) representing detuning, loss rate, and coupling strength. The eigenvalues and eigenstates are derived from the Hamiltonian, revealing an EP at (β/κ, γ/κ) = (0, 1). The degree of adiabaticity, U, is defined and related to the parameter evolution rate and eigenstate variations. The analysis shows that along the parameter space boundary, one eigenstate exhibits extremely low energy dissipation, while the other converges to [0,1] or [1,0]. The researchers mapped the required Hamiltonian parameters onto the DSWs, achieving near-unity efficiency with low crosstalk. The dynamic evolution path of the Hamiltonian for CW and ACW loops was simulated and visualized on the Riemann surfaces formed by the real and imaginary parts of the energy spectra. Experimental verification involved fabricating DSWs with carefully chosen geometrical parameters based on a mapping database linking structural and Hamiltonian parameters. TE₀ and TE₁ modes in the silicon bus waveguide represent [1, 1]ᵀ and [1, -1]ᵀ respectively. Light propagation direction determines the evolution (CW or ACW). Transmission measurements were performed using a tunable laser, grating couplers, and an optical power meter, with results compared to simulations. The fabrication process involved three-step electron-beam lithography (EBL), inductively coupled plasma (ICP) etching, electron-beam evaporation (EBE), and plasma-enhanced chemical vapor deposition (PECVD).

The study's key findings demonstrate that high-efficiency chiral mode switching can be achieved using fast parametric evolution along the Hamiltonian parameter space boundary. This contrasts with conventional methods requiring slow, adiabatic evolution. The researchers experimentally demonstrated this principle in a 57 µm-long double-coupled silicon waveguide system, achieving near-unity transmission efficiency (~-1 dB) at 1550 nm with a crosstalk of approximately -16 dB. The simulated transmittance spectra showed excellent agreement with the experimental results. The high efficiency and compact device size represent significant improvements over previous methods. Specifically, the efficiency is significantly higher than previously reported values (46%), and the device length is much shorter than previous designs, ranging from millimeters to 1.25 meters. The mode crosstalk is also substantially lower. The researchers also investigated shorter device lengths, finding that a 30 µm device is feasible, although this pushes the limits of current fabrication capabilities. The analysis shows that the adiabaticity condition is satisfied even with fast parametric evolution along the parameter space boundary due to the extremely low energy dissipation rate of one eigenstate in this region. The system exhibits chiral response, with distinct output states for CW and ACW encirclement, regardless of the input state. The output state's crosstalk is primarily determined by the transition from the parameter space boundary back to the starting point. The study's results offer a new perspective on non-Hermitian dynamics and provide a pathway towards highly integrated, high-efficiency optical devices.

The findings of this research significantly advance the field of chiral mode converters by demonstrating that high efficiency is achievable without the need for slow, adiabatic parameter evolution. The proposed method using fast parametric evolution along the Hamiltonian parameter space boundary offers a practical route toward realizing compact and efficient devices. The experimental validation with near-unity transmission efficiency at telecommunication wavelengths and low crosstalk underscores the potential of this approach for practical applications. The ability to shorten the device length while maintaining high efficiency is crucial for integrated photonics. The demonstrated principle is not limited to the specific system used in the study and can be extended to other (anti-)PT-symmetric systems with gain and/or loss in various domains. Future research could explore the integration of nonlinear systems for optical isolation or the application of the input-independent output states in phase-locked laser technology. The work contributes to developing smaller, more efficient optical devices on a chip.

This study has demonstrated that high-efficiency chiral mode switching can be achieved through fast parametric evolution along the Hamiltonian parameter space boundary, significantly relaxing the adiabaticity constraints of previous methods. A 57 µm-long double-coupled silicon waveguide device experimentally achieved near-unity transmission efficiency and low crosstalk at 1550 nm, surpassing previous results in both efficiency and compactness. This approach holds promise for creating compact, high-performance optical devices in integrated photonic systems. Future work may explore the integration of this method with nonlinear systems or its application in other fields such as acoustics and quantum mechanics.

While the study demonstrates high efficiency and compactness, limitations exist. The shortest achievable device length (30 µm) is challenging to fabricate with current technologies, requiring advanced fabrication techniques to achieve the necessary feature sizes and precision. Minor discrepancies between simulation and experimental results may be attributed to imperfections in the fabrication process, such as variations in grating couplers and asymmetric directional couplers. Further optimization of the fabrication process is needed to fully realize the potential of the proposed method.