Two-plasmon spontaneous emission from a degenerately-doped nonlocal epsilon-near-zero material

The large field confinement and slow-light effect near the epsilon-near-zero (ENZ) frequency of the light-emitting material itself is combined with plasmonic cavities, to greatly enhance the “forbidden” two-plasmon spontaneous emission (2PSE) process.

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Plasmonics is a vibrant field of research exploiting the light-matter interaction in metallic nanostructures. Plasmonic cavities can provide deep subwavelength light confinement, opening up new avenues for enhancing the spontaneous emission process towards both classical and quantum optical applications. Conventionally, light cannot be directly emitted from the plasmonic metal itself, remaining a grand challenge to generate single- or entangled-surface plasmon polaritons (SPPs) directly from the plasmonic metal.

Two-photon emission (TPE) refers to the simultaneous emission of two photons during a radiative transition process. Recent researches suggest TPE rate may be selectively enhanced by the Purcell effect, as a promising approach to generate entangled photon pairs in semiconductors (for it emits two photons with intrinsic energy conservation and time concurrence) [1, 2]. Here, researchers propose a scheme to achieve efficient two-plasmon spontaneous emission (2PSE), by employing a degenerately doped semiconductor ENZ thin film that simultaneously serves as the light-emitting medium and the plasmonic cavity, as illustrated in Fig. 1. The proposed structure consists of a 50-nm-thick degenerately doped InSb film sandwiched between two AlSb layers, which are known to support SPP modes in the mid- and far-infrared.

Fig. 1
Figure 1. a Schematics of the proposed structure that supports surface plasmon polaritons (SPPs). b Schematics of the one-photon emission process in a semiconductor with a degenerate doping level. The dashed line marks the Fermi level EF. Yellow arrows represent the thermalization of photoexcited carriers. ω0 represents the angular frequency of the photon emitted during one-photon emission. ωENZ is the angular frequency where the permittivity of InSb approaches zero. k is the electron wavevector. c Schematics of the two-plasmon spontaneous emission process in a semiconductor with a degenerate doping level. ω1 and ω2 represent the angular frequencies of the two plasmons emitted in the spontaneous emission process, respectively.

The performance of the resultant devices are summarized as Fig. 2 (see the original article & its supplementary info &  for details). In conclusion, ultrafast and tunable 2PSE is theoretically shown to be potentially realized in a nonlocal ENZ film [3, 4], by spatially and spectrally matching 2PSE with highly confined SPP modes. Similar concepts can be extended to other semiconductors, 2D materials, and superconductors supporting Josephson plasmons. The 2PSE lifetime could be reduced from tens of milliseconds to several nanoseconds, comparable to the one-photon emission rate. Furthermore, we show that the optical nonlocality may largely govern the optical response of the ultrathin ENZ film. Efficient 2PSE from a doped semiconductor film may provide a pathway towards on-chip entangled light sources, with an emission wavelength and bandwidth widely tunable in the mid-infrared.

Fig. 2
Figure 2. ab The q-resolved Purcell factors f as a function of the in-plane momentum q and the energy ω for both in-plane (||) and out-of-plane () dipole orientations at z = 3 nm. cd The q-resolved Purcell factors f as a function of q and ω for both dipole orientations at z = 25 nm. ef The Purcell factor F as a function of ω for both dipole orientations. The gray dashed line represents the epsilon-near-zero (ENZ) energy. g Two-plasmon spontaneous emission through the Cn-HHn transition. Here, C represents the conduction subband and HH represents the heavy-hole subband. k|| is the the in-plane electron wavevector. The blue arrow represents the transition excited by the in-plane polarization Ex-yh Two-plasmon spontaneous emission through the Cn+/-1-HHn transition. The blue arrow represents the transition excited by Ex-y. The red arrow represents the transition excited by the out-of-plane polarization Ezi The one-photon emission (OPE) and the two-plasmon spontaneous emission (2PSE) rates R(ω) in the InSb film averaged over the z-position at an operation temperature T = 77 K.


[1] Rivera, N. et al. Shrinking light to allow forbidden transitions on the atomic scale. Science 353, 263–269 (2016).

[2] Goncalves, P. et al. Plasmon–emitter interactions at the nanoscale. Nature Communications 11, 366 (2020).

[3] Hu, F. et al. High-contrast optical switching using an epsilon-near-zero material coupled to a Bragg microcavity. Optics Express 27, 26405 (2019).

[4] Yang, Y. et al. High-harmonic generation from an epsilon-near-zero material. Nature Physics 15, 1022–1026 (2019).

Article info:

Two-plasmon spontaneous emission from a nonlocal epsilon-near-zero material, Communications Physics, 4, 84 (2021).

DOI: 10.1038/s42005-021-00586-4


Yuan Meng

PhD, Tsinghua University