Pathway to Optical-Cycle Dynamic Photonics: Extreme Electron Temperatures in Transparent Conducting Oxides

TL;DR

The paper addresses achieving optical-cycle-scale refractive-index modulation in transparent conducting oxides by driving extreme electron temperatures $T_e$ under ultrafast optical pumping. It develops an inverse-designed epsilon-near-zero cavity with a 10 nm TCO absorber to reach high $T_e$ and drive oscillatory, sign-reversing dynamics in the refractive index $n$ and transmittance $\\mathcal{T}$ on ~20 fs timescales, using a two-temperature model that includes thermionic emission. To realize practical modulation of $n$, it introduces a bilayer TCO scheme with a 2 nm acceptor layer that injects hot carriers across the interface, achieving ~2% oscillations in $n$ with similar sub-20 fs cycles and tunability via carrier density and pump parameters. Collectively, the work provides a practical pathway to time-varying photonic media and photonic time crystals operating from the visible to infrared, leveraging thermionic carrier injection in TCOs to access optical-cycle dynamics.

Abstract

We find that transparent conducting oxides (TCOs) exhibit oscillatory (sign-reversing) dynamics on a few optical cycle timescale under extreme electron temperatures. We demonstrate a mechanism for such transient dynamics and present an inverse-designed multilayer cavity incorporating an ultrathin TCO layer that supports the oscillatory behavior. This approach yields transmittance oscillations with a period of ~20 fs, which corresponds to three optical cycles of the probe beam. To achieve a similar oscillatory modulation in the refractive index, we incorporate a TCO electron-acceptor layer on top of the inverse-designed cavity, enabling thermionic carrier injection at the TCO heterojunction. The resulting acceptor layer achieves a striking Δn response time as short as 9 fs, approaching a single optical cycle, and is further tunable to sub-cycle timescales. The findings not only clarify the elusive transient physics in TCOs but also demonstrate, for the first time, the critical role of electron temperatures in driving oscillatory dynamic responses. More broadly, we establish TCO-based thermionic carrier injection as a practical route to novel time-varying photonic media operating on the timescale of an optical cycle, enabling time-reflection, time-refraction, and related dynamic phenomena from the visible to the infrared.

Figures (5)

• Figure 1: Oscillatory dynamics in the inverse-designed cavity.a, Illustration of oscillatory dynamics at different peak electron temperature regimes. Higher peak electron temperature results in a dynamic response evolving into a more complex oscillatory behavior (see Fig. \ref{['fig:fig_2']}). b, Schematic of the inverse-designed cavity, optimized for maximizing the electron temperature in a 10 nm TCO layer. The multilayer stack is excited by 10 fs, $p$-polarized pump pulse centered at the ENZ wavelength (1425 nm), incident at 60$^\circ$, with a fluence of 1.5 mJ/cm$^2$. c, Simulated electron temperature evolution in the 10 nm TCO layer, revealing enhanced electron temperature in the inverse-designed cavity compared to a single TCO film on a glass substrate. d, Normalized refractive index modulation ($\Delta n$) dynamics in the TCO, comparing different geometry and chemical-potential models. The pump excitation conditions are identical to those used in panel b. Top: 10 nm single TCO/glass response under the Sommerfeld approximation. Middle: Oscillatory $\Delta n$ response in the cavity-integrated TCO film with the Sommerfeld approximation. Bottom: Single-peaked $\Delta n$ response of the cavity-integrated TCO film under a carrier-conserving model. The Sommerfeld response reveals the underlying mechanism responsible for the oscillatory dynamics. e, Illustration of the mechanism driving $\Delta n$ reversals in the high $T_\mathrm{e}$ Sommerfeld scenario. Simultaneous increase in $n_\mathrm{e}$ and $m^*$ shifts the plasma frequency in opposite directions, giving rise to an oscillatory $\Delta n$ response. Left: Fermi--Dirac distribution for Sommerfeld versus carrier-conserving models. Right: Normalized energy distribution of total carriers, highlighting a large high-energy carrier population and increased effective mass in the Sommerfeld case. f, Schematic of various electron injection pathways in TCOs to achieve dynamic carrier density modulation.
• Figure 2: Electron temperature-dependent $\Delta n$, $\Delta \mathcal{T}$ sign map.a, Sign map of $\Delta n$ as a function of electron temperature and probe wavelength. Red and blue indicate positive and negative regions, respectively. The arrows highlight the more complex $\Delta n$ oscillation in TCO under cavity-enhanced absorption, compared to the simpler behavior of a single TCO film reaching moderate electron temperature and exhibiting fewer boundary crossings. b, Sign map of $\Delta \mathcal{T}$, revealing two distinct sign change spectral regions and highlighting the emergence of a more complex transmittance response at high electron temperatures.
• Figure 3: Oscillatory transmittance dynamics of the inverse-designed cavity.a, Relative transmittance response as a function of pump–probe delay and probe wavelength, with dotted lines marking the near ($\sim$1425 nm) and off-ENZ ($\sim$1200--1300 nm) zero-crossing lines. The probe incident angle is $50^\circ$. b, Near-ENZ ($\sim$1425 nm) transmittance oscillations with three $\sim$20 fs modulation cycles, tunable via probe-angle variation. The red dotted line marks the maximum electron temperature ($\sim$45 fs), and the black dotted line denotes 20 fs, highlighting the modulation-cycle duration. c, Off-ENZ ($\sim$1200--1300 nm) transmittance oscillations exhibiting opposite sign behavior compared to the near-ENZ case. d, Normalized transmittance ($\mathcal{T}_{\rm \textit{mod}}$) near the ENZ probe wavelengths, highlighting different shapes of the sub-20 fs complex temporal features. The red dotted line denotes the point of maximum electron temperature ($\sim$45 fs), and the black dotted line marks the 25 fs region to highlight the sub-20 fs temporal features.
• Figure 4: $\Delta n$ oscillations in the TCO electron-acceptor layer.a, Illustration of the multilayer structure incorporating the bilayer TCO configuration. A 2 nm low-doped TCO electron-acceptor layer is placed on top of the TCO absorber layer. Except for the added acceptor layer, the geometry is identical to that of the inverse-designed cavity in Figure \ref{['fig:fig_1']}(b). The hot carriers generated in the absorber layer are transferred to the acceptor layer via thermionic injection. The absorber and acceptor layers are in direct contact in the actual structure. b, Conduction band alignment of the bilayer TCO structure, highlighting the low barrier height and narrow barrier width that facilitates efficient carrier injection into the acceptor layer upon intraband optical pumping. c, Simulated spatio-temporal evolution of electron temperature along the vertical axis of the multilayer cavity, showing a significant temperature rise in the acceptor layer. The line color indicates the delay time after pump excitation. d, $\Delta n/n$ of the acceptor layer, exhibiting an oscillatory response with three modulation cycles of $\sim$20 fs duration and a peak modulation amplitude of $\sim$2%. e, Two-dimensional map of $\Delta n/n$, highlighting the spectral range of oscillations within the telecom wavelengths.
• Figure 5: Broad spectral and temporal tunability of the $\Delta n$ oscillation.a, Zero-crossing boundaries of $\Delta n(T_\mathrm{e})/n$ for a range of acceptor layer initial carrier density $n_{acceptor}$, demonstrating a broad spectral tunability. b, Demonstration of $\Delta n/n$ tunability achieved by modifying the acceptor layer carrier density ($0.8 \times 10^{20}\,\mathrm{cm}^{-3}$) and peak electron temperature, resulting in four modulation cycles within 100 fs with sub-optical-cycle timescale features. c, $\Delta n/n$ for $n_{acceptor} = 0.4 \times 10^{20}\,\mathrm{cm}^{-3}$, and shortened pulse excitation (5 fs), highlighting further modulation speed enhancement capability.