Exceptional Points in Hybrid-Plasmonic Quasiparticles for Ultracompact Modulators

TL;DR

This study leverages exceptional points (EPs) in non-Hermitian photonics to design ultracompact silicon-integrated modulators based on hybrid plasmonic–waveguide quasiparticles. By engineering a layered Si–SiO2–Al–Si platform and incorporating a low-loss phase-change material, the authors realize near-EP degeneracy between HP and HW modes at λ=1.55 μm, with electrical tuning enabling large modulation over sub-micron lengths. A two-level coupled-mode theory captures the EP condition, and full-wave 3D simulations confirm near-EP signatures and substantial loss-to-transmission changes, including Sb2S3- and Sb2Se3-based tuning. The results suggest practical pathways to gain-enabled loss compensation and exploration of alternative tunable materials for even more responsive, ultracompact photonic devices.

Abstract

Current progress in electro-optical modulation within silicon integrated photonics, driven by the unique capabilities of advanced functional materials, has led to significant improvements in device performance. However, inherent constraints in dimensionality and tunability still pose challenges for further innovation. In this work, we propose a strategy that exploits the principles of non-Hermitian physics--specifically, the concept of exceptional points (EPs)--to transcend these limitations and pave the way for the next generation of versatile, high-performance photonic devices. Our multilayer structure supports hybrid plasmonic waveguide modes that can manifest as various orders of quasiparticles. By judiciously setting spatial parameters, the system can be tuned to exhibit both weak and strong coupling regimes between the plasmonic and dielectric modes, leading to the controlled formation of EP degeneracies. Furthermore, the integration of low-loss phase-change materials (Sb2S3 and Sb2Se3) enables dynamic electrical tuning, resulting in pronounced modulation of propagation loss and transmission coefficients over sub-micron distances. This superior performance not only sets a new benchmark for device responsivity and compactness but also opens promising avenues for future research, including the incorporation of gain media for loss compensation at EPs and the exploration of alternative tunable materials for next-generation ultracompact photonic devices.

Figures (5)

• Figure 1: (a)–(b) The layered Si–SiO$_2$–Al–Si structure on an SiO$_2$ substrate, which supports both weak and strong coupling between plasmonic and waveguide modes. This coupling leads to the formation of various orders of waveguide–plasmon polariton quasiparticles that, for specific spatial parameters, exhibit exceptional point (EP) characteristics. (c)-(d) real and imaginary parts of the effective refractive indices, respectively, as functions of the layer width. The highlighted curves correspond to modes that couple strongly to form hybrid plasmonic–waveguide quasiparticles—eventually leading to EP degeneracy—while the grey curves represent uncoupled modes (in the highlighted curves, brighter regions indicate minimal mode overlap; darker regions show increased overlap). Notably, the hybrid plasmonic modes exhibit higher imaginary parts compared to their hybrid waveguide counterparts. (e) For better illustration we depict $E_z$ field distributions at EP and out of EP at selected parameter points: the first column shows field distribution predominantly out of metallic interfaces (characteristic of the waveguide mode), the third column reveals field localization mainly at the metal interfaces (typical of the plasmonic mode), and the middle column corresponds to the nearly degenerate mode at the EP, where the two modes merge.
• Figure 2: A coupled mode theory analysis is conducted to elucidate the interaction between the waveguide and plasmonic modes, resulting in the formation of hybrid waveguide and hybrid plasmonic modes. (a)-(b) and (c)-(d) The real and imaginary parts of the effective refractive index as functions of the ridge width and the top silicon height, respectively. The solid curves represent the predictions from coupled mode theory, while the dots denote the mode analysis results obtained from Lumerical simulations. Insets display the equivalent refractive indices of the uncoupled waveguide ($n_W$) and plasmonic ($n_P$) modes extracted via curve fitting, providing additional insight into the modal behavior underlying the hybridization process. At EP, the real part of $n_W$ and $n_P$ are identical while the difference of their imaginary parts are twice of their coupling value. Notably, at the exceptional point (EP), the real parts of $n_W$ and $n_P$ converge, while the difference in their imaginary parts equals twice the coupling value, which result in degeneration of both real and imaginary parts of the effective indices.
• Figure 3: To elucidate the dynamic power transfer induced by variations in the geometrical dimensions, the hybrid structure is partitioned into discrete regions (S$_1$–S$_6$) for detailed modal power fraction analysis. In the nearly decoupled regime, the hybrid waveguide (HW) mode primarily confines its energy below the metallic layer, whereas the hybrid plasmonic (HP) mode concentrates most of its power above the metal. As the system parameters are tuned toward the exceptional point (EP), the HW mode progressively shifts its power upward, and the HP mode correspondingly transfers power downward, ultimately achieving a balanced condition at the EP where the two modes degenerate with an overlap approaching unity. (a) The partitioning strategy used for the power calculations. (b) The overlap between the HP and HW modes, with a maximum observed at a structure width of 600 nm and height of 310 nm, corresponding to EP degeneracy. (c) and (d) The power transfer dynamics across regions S$_1$–S$_6$ for the HW and HP modes, respectively, highlighting the abrupt changes in modal power distribution as the geometry is varied.
• Figure 4: Frequency-dependent tunability of the hybrid structure is demonstrated through the effective index and transmission spectra as functions of the input wavelength over a propagation distance of 900 nm. (a) and (b) The real and imaginary parts of the effective refractive index, respectively, with an exceptional point (EP) established at 1550 nm. (c) The transmission spectrum, which mirrors the behavior of the imaginary index. (d)-(e) The electric field distributions in both the (d) longitudinal and (e) transverse views reveal that at the EP the field profiles of the two modes become nearly identical. Notably, the hybrid waveguide mode exhibits maximum loss at the EP, with its loss decreasing abruptly when moving away from this point, whereas the hybrid plasmonic mode shows a minimum loss at the EP that increases sharply outside the EP.
• Figure 5: A 40‐nm phase-change material (PCM) layer—either Sb$_2$S$_3$ or Sb$_2$Se$_3$—is interposed between the aluminum layer and top silicon layer to serve as a tunable element. Notably, the low‐loss PCM exhibits a refractive index nearly identical to that of silicon in its favorable phase (crystallized for Sb$_2$S$_3$ and amorphous for Sb$_2$Se$_3$). In the first configuration, the device incorporates Sb$_2$S$_3$ with the geometrical parameters adjusted to reach an exceptional point (EP) when the material is crystallized; switching to the amorphous state shifts the operation away from the EP. Conversely, in the second configuration, Sb$_2$Se$_3$ is employed with the structure optimized for EP conditions in its amorphous phase, while its crystallized phase moves the system out of the EP regime. (a) and (b) display the real and imaginary parts of the effective refractive index as functions of the Sb$_2$S$_3$ refractive index, confirming that the EP is achieved in the crystallized state and lost upon amorphization. (c) and (d) The effective index components versus the Sb$_2$Se$_3$ refractive index, where the EP occurs in the amorphous phase and is absent in the crystallized state. (e) The hybrid plasmonic waveguide schematic, highlighting the integration of the low‐loss PCM. (f) The longitudinal view of electric field distribution within the central region of the silica layer over a 900‐nm propagation length, evidencing the transmission characteristics and strong amplitude modulation.