Thermo-optic epsilon-near-zero effects

Abstract

Nonlinear epsilon-near-zero (ENZ) nanodevices featuring vanishing permittivity and CMOS-compatibility are attractive solutions for large-scale-integrated systems-on-chips. Such confined systems with unavoidable heat generation impose critical challenges for semiconductor-based ENZ performances. While their optical properties are temperature-sensitive, there is no systematic analysis on such crucial dependence. Here, we experimentally report the linear and nonlinear thermo-optic ENZ effects in indium tin oxide. We characterize its temperature-dependent optical properties with ENZ frequencies covering the telecommunication O-band, C-band, and 2-μm-band. Depending on the ENZ frequency, it exhibits an unprecedented 70-93-THz-broadband 660-955% enhancement over the conventional thermo-optic effect. The ENZ-induced fast-varying large group velocity dispersion up to 0.03-0.18 fs²nm^-1 and its temperature dependence are also observed for the first time. Remarkably, the thermo-optic nonlinearity demonstrates a 1113-2866% enhancement, on par with its reported ENZ-enhanced Kerr nonlinearity. Our work provides references for packaged ENZ-enabled photonic integrated circuit designs, as well as a new platform for nonlinear photonic applications and emulations.

Fig. 1. Adapted grain-boundary barrier model in indium tin oxide at different temperature ranges.

a The energy levels of a degenerate semiconductor such as indium tin oxide. b Oxygen diffusion mechanism in the sub-annealing domain with increasing temperature. c Permanent structural change above the annealing threshold.

Fig. 2. Samples and their epsilon-near-zero (ENZ) frequency response.

a Indium tin oxide samples with ENZ frequency at O-band, C-band, 2-μm-band, and without ENZ effects. b The variation of ENZ frequency with temperature at different thermal phases of O-band (top), C-band (middle), and 2-μm-band (bottom) samples.

Fig. 3. Spectra of refractive index and the giant enhancement of thermo-optic effects in the epsilon-near-zero (ENZ) region.

a Full refractive index spectrum of the O-band, C-band, and 2-μm-band samples. IR stands for infrared, and UV is ultraviolet. NZI represents near-zero-index where n < 1. b–d The variations of refractive indices with temperature for these three sets of samples near the ENZ frequency, respectively. e the TOCs in ENZ region. The top panel of the diagram shows the values of thermo-optic effects of the O-band, C-band, 2-μm, and non-ENZ samples. The bottom panel of the diagram is the ENZ-induced thermo-optic effect enhancement with respect to the non-ENZ sample. The colored rectangles denote the full-width-at-half-maximum (FWHM) bandwidth (BW) of the corresponding curve. The colored vertical lines in a and e denote the corresponding ENZ frequencies.

Fig. 4. Spectra of group velocity dispersion (GVD) and absorption.

a Full GVD spectrum of the O-band, C-band, and 2-μm-band samples. b–d The variations of GVD with temperature for these three sets of samples near the epsilon-near-zero (ENZ) frequency, respectively. e Full absorption spectrum of the three sets of samples. f–h The corresponding absorption variations with temperature near the ENZ frequency. In a and e, the colored vertical lines indicate the exact ENZ frequencies of the corresponding curves.

Fig. 5. Thermo-optic nonlinearity near epsilon-near-zero (ENZ) region.

a The thermo-optic nonlinear-index coefficients of the O-band, C-band, 2-μm-band ENZ and non-ENZ samples. b The ENZ-induced enhancement of the thermo-optic nonlinearity. The colored vertical lines indicate the exact ENZ frequencies of the corresponding curves.