Polarization‑Insensitive Plasmonic Electro‑Absorption Modulator Using Epsilon‑Near‑Zero Indium Tin Oxide

Background

Photonic integrated circuits have experienced rapid advancement, driven by applications in optical communication, sensing, and imaging. Reducing device footprint and power consumption remains a primary goal for future high‑speed on‑chip interconnects. Silicon waveguide modulators traditionally rely on altering either the refractive index or absorption of a material; however, silicon’s weak plasma‑dispersion effect and the diffraction limit of conventional waveguides lead to large footprints (≈10^3–10^4 µm²) for Mach‑Zehnder interferometers, and even ring modulators with high Q resonance suffer from limited bandwidth and temperature sensitivity.

Plasmonics offers a path to sub‑diffraction‑limited miniaturization. Recent work has explored CMOS‑compatible slot modulators and plasmonic structures that use silicon as the active medium, but performance is still constrained by silicon’s modest carrier dispersion. Transparent conductive oxides (TCOs), such as indium tin oxide (ITO), aluminum‑zinc oxide, and gallium‑zinc oxide, present a compelling alternative because their permittivity can be tuned electrically. Carrier accumulation in the ITO layer under bias can produce refractive index changes of Δn = 0.092 and absorption changes of Δk = 0.27 at 1310 nm, and when the real part of the permittivity approaches zero—known as the epsilon‑near‑zero (ENZ) state—absorption peaks due to extreme field confinement.

Previous plasmonic modulators have predominantly supported only TM modes because surface charge generation requires an electric field normal to the metal‑dielectric interface, and slot waveguides confine TE modes in low‑index regions. In fiber‑based systems, the random polarization of incoming light leads to significant polarization‑dependent loss unless a polarization‑diversity component (e.g., a rotator) is added, which typically introduces additional coupling loss. Although some ITO‑based designs support both TE and TM modes, the extinction‑ratio difference (ΔER) can still reach 0.9 dB/µm, corresponding to a 4 % efficiency penalty. Therefore, a plasmonic modulator that delivers minimal ΔER while maintaining high extinction and low insertion loss is essential for polarization‑insensitive PICs.

In this study, we investigate a silicon waveguide clad with an Au/SiO₂/ITO multilayer using numerical simulation. The hybrid surface plasmon polariton (HSPP) mode is excited along the low‑index SiO₂/ITO interface, either at the top or sidewalls, depending on the input polarization. By tuning the carrier concentration in the ITO layer via the MOS capacitor, we demonstrate extinction ratios exceeding 1.43 dB/µm with ΔER below 0.01 dB/µm, a record low that markedly reduces polarization‑dependent loss.

Methods

We employ ITO as the active material, exploiting its strong carrier‑accumulation response to achieve high‑speed electro‑absorption. The permittivity of ITO is described by the Drude model:

Here, ε∞ is the high‑frequency permittivity, Γ the electron damping factor, ω the angular frequency, NITO the electron concentration, m* the effective mass, e the elementary charge, and ε0 the vacuum permittivity. The electron density peaks at the ITO/oxide interface and decays rapidly with distance, ensuring strong field confinement in the accumulation layer.

The real part (ε1) and imaginary part (ε2) of ITO’s permittivity versus wavelength for various electron concentrations. The ENZ point is identified where ε1 crosses zero.

To support both TE and TM modes, the waveguide incorporates two orthogonal metal‑dielectric interfaces. The proposed structure consists of a silicon core (width WSi, height HSi), an ITO layer (thickness DITO), a SiO₂ intermediate layer (width Wp, height Hp), and a 100 nm Au cladding. The device is fabricated using standard e‑beam lithography, DRIE, PLD, and PECVD—methods compatible with CMOS back‑end processing. The hybrid plasmonic mode propagates in the low‑index region between SiO₂ and ITO, minimizing insertion loss while maintaining strong field overlap with the active layer.

a 3‑D view and b cross‑section of the EA plasmonic modulator integrated with a stripe dielectric waveguide.

We used a non‑uniform FDTD mesh with a minimum cell size of 0.2 nm and perfectly matched layers (PML) to suppress reflections. The simulation wavelength was set to 1.55 µm, with refractive indices nSi = 3.48, nSiO₂ = 1.44, and Au dielectric constant −116.62 + 11.46i. The MIS waveguide supports both polarizations with minimal propagation‑constant disparity, enabling efficient modulation.

Results and discussion

Figure 3 illustrates the electric field distribution for TE and TM modes under low‑bias (“ON”) and high‑bias (“OFF”) conditions. In the ON state, the TE field concentrates at the sidewalls of the SiO₂ layer, while the TM field resides at the top of the SiO₂. In the OFF state, increased carrier density reduces the real part of the ITO permittivity, pulling the field into the accumulation layers and increasing absorption. This shift peaks at the ENZ point, maximizing loss in the OFF state.

Electric field profiles for the TE mode (a, c) and TM mode (b, d) in ON and OFF states. Insets show the field density in the ITO layer during OFF. Parameters: WSi = 310 nm, HSi = 340 nm, Hp = 20 nm, Wp = 25 nm.

Extinction ratio (ER) and insertion loss (IL) are defined as:

The propagation loss α is calculated from the imaginary part of the effective index: α = 4πκ/λ. α is largely determined by absorption in the accumulation layers, which is influenced by the SiO₂ dimensions. Figure 4 shows that increasing Wp reduces the overlap between the guided mode and the accumulation layer, lowering ER, while ΔER reaches a minimum when Wp slightly exceeds Hp.

ER and ΔER versus Wp for Hp = 20 nm and 30 nm.

Figure 5 explores ER and ΔER across wavelength for different NITO values. Both metrics peak near the ENZ point and then decline. For NITO = 6.0×10^20 cm^−3, the maximum ERs are 1.65 dB/µm (TE) and 1.56 dB/µm (TM) at 1.50 µm, while ΔER reaches a minimum of 0.009 dB/µm at the operating wavelength of 1.55 µm—ideal for a polarization‑insensitive device.

ER and ΔER as functions of wavelength for (a) NITO = 5.6×10^20 cm^−3 and (b) NITO = 6.0×10^20 cm^−3.

Increasing NITO enhances absorption until the ENZ point, beyond which further carrier addition increases κ, reducing ER. Figure 6 confirms that ER peaks near the ENZ value, while ΔER remains below 0.01 dB/µm, demonstrating strong polarization immunity.

ERs and ΔER versus NITO for the EA modulator (HSi = 340 nm, WSi = 310 nm, Hp = 20 nm, Wp = 25 nm, DITO = 10 nm, HAu = 100 nm).

To evaluate practical performance, we simulated a 14‑µm‑long modulator excited with 1.55‑µm light in both TE and TM polarizations. Figures 7a–d display the transverse electric and magnetic field distributions for ON and OFF states, confirming that the ΔER of 0.009 dB/µm balances the output intensities over the device length.

Field distributions of E_x for TE (a,b) and E_y for TM (c,d) across the Si waveguide center for ON and OFF states. Parameters: HSi = 340 nm, WSi = 310 nm, Hp = 20 nm, Wp = 25 nm, DITO = 10 nm, HAu = 100 nm.

Coupling efficiency between the plasmonic waveguide and a silicon stripe was assessed by varying the Si waveguide width. Figure 8 shows the coupling efficiency (CE) for both polarizations. While mode mismatch introduces some reflected light, the ΔCE remains below 6 % at the optimal width, yielding CE of 80.46 % (TE) and 74.83 % (TM) in the ON state.

CE between the plasmonic waveguide (Hp = 20 nm, Wp = 25 nm) and the Si waveguide versus width for TE and TM modes in ON and OFF states (HSi = 340 nm, WSi = 310 nm, DITO = 10 nm, HAu = 100 nm).

Conclusions

We have demonstrated, through detailed simulation, an electro‑absorption modulator that is intrinsically polarization‑insensitive. By integrating a hybrid plasmonic waveguide in both the x‑ and y‑directions, the device supports dual‑polarization modes and forms a MOS capacitor that induces carrier accumulation at the dielectric‑ITO interfaces. Tuning the carrier density yields an extinction‑ratio difference of only 0.009 dB/µm at 1.55 µm, a record low that eliminates polarization‑dependent loss. Coupling efficiencies exceeding 74 % for both TE and TM polarizations are achieved using a silicon feeding waveguide. These ITO‑based plasmonic modulators represent a compact, CMOS‑compatible building block for high‑performance PICs. Future work will focus on optimizing the asymmetric coating geometry to increase fabrication tolerance without compromising performance.