Atomically thin semiconductors as nonlinear mirrors

Abstract

We show that a transition metal dichalcogenide monolayer with a radiatively broadened exciton resonance would exhibit perfect extinction of a transmitted field. This result holds for s-or p-polarized weak resonant light fields at any incidence angle, due to the conservation of in-plane momentum of excitons and photons in a flat defect-free two dimensional crystal. In contrast to extinction experiments with single quantum emitters, exciton-exciton interactions lead to an enhancement of reflection with increasing power for incident fields that are blue detuned with respect to the exciton resonance. We show that the interactions limit the maximum reflection that can be achieved by depleting the incoming coherent state into an outgoing two-mode squeezed state. In this Letter we show that a TMD monolayer acts as a perfect atomically-thin mirror for radiation that is resonant with radiatively broadened excitonic resonances. In the limit of weak resonant incident laser field, destructive interference between the transmitted field and the field generated by the TMD excitons leads to perfect extinction. In-plane momentum conservation ensures that the transmitted field vanishes for any incidence angle as long as the generated 2D excitons have a perfect overlap with the incident field polarization: this is the case for an incident s-polarized field. Remarkably, p-polarized fields also yield perfect extinction since the generated longitudinally-polarized exciton couples exclusively to ppolarized outgoing radiation. On the other hand, any superposition of s-and p-polarized fields will have finite transmission: this is a consequence of finite energy splitting of the transverse and longitudinal exciton resonances induced by the electron-hole exchange interaction [7]. MonolayersThe exciton-exciton interactions ensure that there will be a non-zero transmitted field as the intensity of the field is increased: this is the analog of saturation induced reduction in extinction observed in resonantly driven single quantum emitters. Unlike the latter however, strong extinction of the mean transmitted field is possible in the TMD case by tuning the incident field to blue (red) side of the resonance for repulsive (attractive) exciton-exciton interactions. We find that for laser detunings and intensities where the exciton system approaches bistability, the extinction of the mean field is only limited by the deple -FIG. 1: (a) The schematic of the experimental setup. A collimated coherent laser field is incident on a transition metal dichalcogenide (TMD) monolayer. In addition to coherent transmitted and reflected fields, a two-mode squeezed-state (TMSS) is generated due to exciton-exciton interactions. Unlike the coherent fields, the TMSS is emitted into a large solid-angle. Electromagnetic field can be characterized as consisting of right (left) propagating input rin (lin) and output rout (lout) modes. (b) The reflection from the 2D TMD layer for weak near resonant drive. Destructive interference between the directly transmitted field an...

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using MonolayerMoSe2

“…S6 [18] shows that the extinction remains unchanged as we vary the incident intensity by 4 orders of magnitude from 0.5 to 400 W=cm 2 . Verification of the theoretically predicted unusual saturation characteristics of TMD mirrors is likely to require pulsed laser excitation [13].…”

“…These narrow linewidths have a dominant contribution from radiative decay of ∼1.5 meV for MoSe 2 [11,12]. Motivated by these developments, we previously analyzed the optical response of a monolayer TMD theoretically [13] and showed that it realizes an atomically thin mirror [13][14][15].…”

“…The outgoing right-propagating electric field mode E r out ðωÞ [ Fig. 1(b)] can be expressed in terms of the incident field modes E r in ðωÞ and E l in ðωÞ [13] E r out ðωÞ ¼…”

Large Excitonic Reflectivity of MonolayerMoSe2Encapsulated in Hexagonal Boron Nitride

“…Their miniaturization is fundamentally limited by the optical wavelength in the case of dielectric mirrors and photonic crystals (1) or by the skin depth for metallic mirrors (2). Recently, resonant scattering has emerged as a method for overcoming these limitations and for controlling light at the atomic scale (3)(4)(5)(6)(7)(8)(9)(10)(11). For instance, highly reflective mirrors based on individual quantum emitters have been demonstrated by coupling them to optical cavities and nanophotonic waveguides (3)(4)(5)(6)(7)(8).…”

“…Such resonant mirrors feature very unusual properties due to their extraordinary nonlinearity down to the single-photon level (3)(4)(5)(6)(7)(8). A two-dimensional (2D) layer of emitters, such as atomic lattices or excitons (9)(10)(11), has also been predicted to act as an efficient mirror when the incident light is resonant with the resonance frequency of the system. Such atomically thin mirrors represent the ultimate miniaturization limit of a reflective surface, and could enable unique applications ranging from quantum nonlinear optics (9-11) to topological photonics (12,13).…”