Fully Programmable Plasmonic PT-Symmetric Dimer with Epsilon Near Zero and Phase-Change Materials for Integrated Photonics

TL;DR

The work tackles the challenge of independently tuning optical losses and resonant frequencies in nanoscale photonics while remaining CMOS-compatible. It introduces a fully programmable photonic dimer built from a hybrid plasmonic waveguide that combines epsilon-near-zero (ENZ) material ITO for loss control with a low-loss phase-change material $Sb_2S_3$ for frequency tuning, enabling navigation of Exceptional Points (EPs) in a PT-symmetric system. Key contributions include a CHPW-based dimer design with two tuning schemes, a coupled-mode theory framework for complex frequencies $\Omega_{1,2}=f_{1,2}+i\gamma_{1,2}$ and coupling $\kappa$, and demonstration of at least $16$ programmable states with robust EP access and fabrication error compensation. The approach yields deep subwavelength confinement, low energy operation (e.g., $U\approx3.39$ fJ for ITO modulation at $2$ V) and CMOS-compatible manufacturability, offering significant impact for on-chip reconfigurable photonics in communications, sensing, and quantum information processing. The methodology opens avenues for scalable, high-dimensional photonic networks with AI-assisted EP control and multi-resonator architectures.

Abstract

As photonic systems progress toward enhanced miniaturization, dynamic reconfigurability, and improved energy efficiency, a central challenge endures: the accurate and independent control of optical losses and resonant properties on scalable, CMOS-compatible platforms. To address this challenge, we present a hybrid plasmonic dimer that functions in a non-Hermitian regime, capitalizing on the synergistic interplay between Epsilon Near Zero (ENZ) materials and phase-change materials (PCMs) to achieve superior reconfigurability through electrical modulation. Our approach harnesses non-Hermitian physics by precisely modulating the loss differential among coupled modes alongside their resonant frequencies, thereby steering the system to an Exceptional Point (EP) characterized by emergent phenomena and enhanced perturbation sensitivity. By integrating ENZ materials to control dissipation with PCMs to fine-tune resonant frequencies, our structure achieves robust programmability, delivering at least 16 distinct operational states for coupled resonators. This capability supports deep subwavelength confinement and transitions between EP and non-EP regimes, while the inherently low power consumption of ENZ materials and PCMs under deep-subwavelength confinement offers significant advantages even in high-dimensional configurations. We believe that this work outlines a significant route for next-generation programmable photonics, delivering subwavelength confinement, energy-efficient operation, and high-dimensional optical reconfigurability within an integrated, scalable, and manufacturable platform.

Figures (5)

• Figure 1: Programmable Photonic Dimer Enabled by Epsilon-Near-Zero and Phase-Change Materials for High-Dimensional Tunability. (a) The design incorporates CHPW ring resonators constructed from thin layers of low-index material and metal that are embedded within high-index layers. To achieve a fully programmable dimer, the standard low-index materials are replaced with epsilon-near-zero (ENZ) materials and phase-change materials (PCMs). In this configuration, the ENZ materials permit loss modulation through the application of voltage, while the PCMs alter the resonant frequencies by switching between their amorphous and crystalline states. As a result, each resonator within the dimer can function in at least four distinct states, defined by the voltage applied to the ENZ layer and the phase of the PCM. (b) The dimer system’s transmission characteristics reveal at least 16 distinct programmable states, significantly increasing its configuration options and enabling high-dimensional programmability. The digits in the figure correspond to the states of $V_{1}^{PCM},V_{1}^{ITO},V_{2}^{PCM},V_{2}^{ITO}$ representing whether they are on or off, respectively. For instance, $0110$ is associated to $V_{1}^{PCM}:off,\ V_{1}^{ITO}:on,\ V_{2}^{PCM}:on,\ V_{2}^{ITO}:off$. The transmission is calculated from coupled mode theory (CMT) in which ${{f}_{1,2}}\left( V_{1,2}^{PCM}:off \right)=196.7$ THZ, ${{f}_{1,2}}\left( V_{1,2}^{PCM}:on \right)=195.6$ THZ, ${{\gamma }_{1,2}}\left( V_{1,2}^{ITO}:off \right)=0.4$ THZ, ${{\gamma }_{1,2}}\left( V_{1,2}^{ITO}:on \right)=1.6$ THZ.
• Figure 2: Eigenvalues of CHPW Ring Resonator (a) The initial dimensions of the CHPW ring resonator layers were established using eigenvalue analysis in COMSOL to ensure the desired resonant frequency and dissipation characteristics. In this structure, silicon (Si) serves as the high-index material, silicon dioxide (SiO$_2$) as the low-index material, and aluminum (Al) as the metallic layer. The SiO$_2$ and Al layers have thicknesses of 20 nm and 10 nm, respectively, with the silicon layer at the base being 220 nm thick. Additionally, both the ridge width and the radial difference between the outer and inner edges of the ring resonator are set at 200 nm. (b) To enable tunability, the thin SiO$_2$ layer was substituted with tunable materials. In the first configuration, indium tin oxide (ITO) was used, while in the second, a combination of ITO and phase-change material (PCM) was employed. Finite-difference time-domain (FDTD) simulations in Lumerical were then performed to evaluate the system's performance. (c)-(h) The eigenvalue analysis investigates variations in the resonator’s outer radius $R_{out}$ and the thickness of the top silicon layer $h_{Si}$. A minimized-loss mode (ring 1) is achieved with $h_{Si}= 185$ nm $R_{out}=1500$, corresponding to a whispering gallery mode (WGM) with $m=10$. A lossy mode (ring 2) occurs with $h_{Si}=123$ nm and $R_{out}=1625$ nm, corresponding to a WGM with $m=9$. The $|E_z|$ component for the minimized-loss and lossy modes is illustrated in (c) and (d), respectively. The real and imaginary parts of the eigenvalues for WGMs with $m=10$ are shown in (e)-(f), and for $m=9$ in (g)-(h).
• Figure 3: Inhomogeneous Field Distribution in the ITO Layer (a) The real and imaginary parts of the ITO refractive index are plotted across its thickness, for varying applied voltages. The epsilon-near-zero (ENZ) region, where the real and imaginary components are nearly equal, initially forms near the ITO/TiO$_2$ interface and shifts further away as the voltage increases. (b) The effective index of the CHPW structure with ITO is shown as a function of the applied voltage. The imaginary part of the effective index ($\kappa_{eff}$) rises with voltage, saturating at approximately 2 V. The real part ($n_{eff}$) slightly decreases up to 1 V before gradually returning to its initial value. These findings indicate that voltage application around 2 V primarily enhances loss without significantly altering the resonant frequency. (c)-(f) The electric field intensity peaks within the ENZ region and shifts further from the interface with increasing voltage. For $V=0.5$ V (c) and $V=1$ V (d), where the ENZ region cannot form, the field distribution remains nearly homogeneous across the ITO layer. However, at higher voltages, such as $V=1.5$ V (e) and $V=2$ V (f), the field intensity becomes concentrated within the ENZ region, which moves further away from the interface.
• Figure 4: Scheme 1: Transmission spectra and eigenvalue analysis. (a) Transmission spectra of the through port for coupled resonators are shown. The low-index layer consists of 10 nm thick ITO/TiO$_2$ layers, while the metallic thin layer is aluminum (Al) with a thickness of 10 nm. The ring dimensions are optimized to achieve EP conditions: $\left( {{h}_{Si,1}}=185\ \text{nm},\ {{R}_{out,1}}=1500\ \text{nm} \right)$ and $\left( {{h}_{Si,2}}=127\ \text{nm},\ {{R}_{out,2}}=1630\ \text{nm} \right)$. The dissipation of the first resonator is adjusted by applying a voltage to the ITO layer. The blue and red curves correspond to the ITO layer being voltage-off and voltage-on, respectively. dotted lines represent results from Lumerical simulations, while solid lines show outcomes from coupled-mode theory (CMT) analysis. (b)-(c) Coupled-mode and eigenvalue analyses are used to estimate the complex frequencies of the resonators as $f_1+i\gamma_1=197.2+i0.8$ THz and $f_2+i\gamma_2=197.3+i2.2$ THz, with a coupling constant $\kappa=0.8$ THz. These values satisfy the EP conditions ($f_1=f_2$ and $\gamma_2-\gamma_1=2\kappa$). When voltage is applied to the ITO layer in the first ring, its complex frequency changes to $f_1+i\gamma_1=197.5+i2.2$ THz, showing that the real part of the frequency remains nearly the same while the imaginary part increases to match that of the second ring. The complex, resonant eigenfrequency of the second ring and the coupling constant remain unaffected. Schematic illustrations of the proposed photonic modulation schemes. (d) Scheme 1: ITO/TiO$_2$/Al layers sandwiched between Si layers, where voltage is applied between the ITO and Al layers to modulate the ITO layer. (e) Scheme 2: ITO/PCM/Al layers sandwiched between Si layers, with a graphene layer introduced between ITO and PCM as a common ground.Voltage is applied between ITO and graphene to modulate the ITO and between graphene and Al to modulate the PCM.
• Figure 5: Scheme 2: Transmission spectra and eigenvalue analysis. (a)-(f) In the first scenario, identical coupled resonators are analyzed. In the second scenario, a voltage is applied to the ITO layer of the second resonator, tuning the system to EP conditions. (g)-(l) In the third scenario, the system is already at EP due to the applied voltage on the second resonator's ITO layer. Additional voltage is then applied to the PCM of the first resonator, causing the system to move away from the EP. Finally, in the fourth scenario, the radius of the first resonator is adjusted, restoring the system back to EP conditions. The complex frequency of the resonators in different states are as following. State 1 (lower band): $f_1+i\gamma_1 = 189 + i0.6$ THz, $f_2 +i\gamma_2= 189 + i0.6$ THz, $\kappa = 0.8$ THz. State 2 (lower band): $f_1+i\gamma_1 = 189 + i0.6$ THz, $f_2+i\gamma_2 = 189 + i1.4$ THz, $\kappa = 0.8$ THz. State 1 (upper band): $f_1+i\gamma_1=196.7+ i0.4$ THz, $f_2+i\gamma_2= 196.7+ i0.4$ THz, $\kappa = 0.63$ THz. State 2 (Upper band (EP)): $f_1+i\gamma_1 = 196.7 + i0.4$, $f_2+i\gamma_2 = 196.7 + i1.6$, $\kappa = 0.63$ THz. State 3 (lower band): $f_1+i\gamma_1=188.1 + i0.6$ THz, $f_2 +i\gamma_2= 189 + i1.4$ THz, $\kappa = 0.8$ THz. State 4 (lower band): $f_1+i\gamma_1=189+i0.6$ THz, $f_2 +i\gamma_2= 189 + i1.4$ THz, $\kappa = 0.8$ THz. State 3 (upper band): $f_1+i\gamma_1 = 195.6 + i0.4$ THz, $f_2+i\gamma_2 = 196.7 + i1.6$ THz, $\kappa = 0.63$. State 4 (upper band (EP)): $f_1+i\gamma_1=196.7+i0.4$ THz, $f_2+i\gamma_2 = 196.7 + i1.6$ THz, $\kappa = 0.63$ THz.