Milliwatt terahertz harmonic generation from topological insulator metamaterials

Abstract

Achieving efficient, high-power harmonic generation in the terahertz spectral domain has technological applications, for example, in sixth generation (6G) communication networks. Massless Dirac fermions possess extremely large terahertz nonlinear susceptibilities and harmonic conversion efficiencies. However, the observed maximum generated harmonic power is limited, because of saturation effects at increasing incident powers, as shown recently for graphene. Here, we demonstrate room-temperature terahertz harmonic generation in a Bi2Se3 topological insulator and topological-insulator-grating metamaterial structures with surface-selective terahertz field enhancement. We obtain a third-harmonic power approaching the milliwatt range for an incident power of 75 mW—an improvement by two orders of magnitude compared to a benchmarked graphene sample. We establish a framework in which this exceptional performance is the result of thermodynamic harmonic generation by the massless topological surface states, benefiting from ultrafast dissipation of electronic heat via surface-bulk Coulomb interactions. These results are an important step towards on-chip terahertz (opto)electronic applications.

Observation of terahertz second harmonic generation from surface states in the topological insulator Bi$_2$Se$_3$

“…And since only the surface of Bi 2 Se 3 breaks inversion symmetry and two-fold rotation symmetry as required for a second order process, the 1.0 THz peak is found to be thickness independent, as dictated by the symmetry and shown in Fig 2 .d. This clear THz-SHG response from Bi 2 Se 3 , which reaches a high conversion efficiency of ∼ 0.005% (accounting for the SHG-specific filters), is consistent with HG studies outside of the THz regime [49][50][51][52][53][54][55], but contrasts sharply with the previous THz studies [40,44,45] of bismuth chalcogenides, which failed to report THz-SHG.…”

“…Since its first demonstration [9], THz third harmonic generation (THG) has rapidly become a standard tool for characterizing the Higgs mode [9][10][11][12][13] and other nonlinear optical processes [14][15][16][17][18][19][20][21][22][23][24][25][26] in a variety of superconductors [27][28][29][30][31][32][33][34]. Yet more recently, odd-order THz-HG has been reported in doped Si [35,36] and materials hosting Dirac fermions, namely graphene [37][38][39][40], Cd 3 As 2 [41][42][43], and the bismuth chalcogenide family of topological insulators [40,44,45]. The latest studies have explored controlling and optimizing THz-HG, demonstrating that the nonlinear process can be effectively tuned via gating [38] and metasurfacing [39,40].…”

“…Yet more recently, odd-order THz-HG has been reported in doped Si [35,36] and materials hosting Dirac fermions, namely graphene [37][38][39][40], Cd 3 As 2 [41][42][43], and the bismuth chalcogenide family of topological insulators [40,44,45]. The latest studies have explored controlling and optimizing THz-HG, demonstrating that the nonlinear process can be effectively tuned via gating [38] and metasurfacing [39,40].…”

“…Most strikingly, intrinsic even-order THz harmonics, which are only generated in systems that break inversion symmetry, have never been demonstrated in an equilibrium material, having been observed only in superconductors with a net propagating supercurrent [46,47] or in carefully engineered devices [48]. The lack of THz second harmonic generation (SHG) in the studies of the bismuth chalcogenides [40,44,45] is of particular note, as SHG-and even-order HG in general-originating from the surface has been a well-established feature of the nonlinear optical response outside of the THz regime [49][50][51][52][53][54][55]. Furthermore, as the bismuth chalcogenides are prototypical topological insulators [56][57][58][59] with a centrosymmetric bulk and inversion symmetry-breaking surfaces, the second-order optical response of THz-SHG offers a pathway to measuring the properties of the topological surface state while intrinsically avoiding the properties of the bulk band, without resorting to doping [45].…”

Topological Insulator Films for Terahertz Photonics

“…To estimate the pump intensity, where the conversion efficiency of Bi 2 Se 3 and BSTS would reach that of graphene, we extrapolated the pure cubic dependence for Bi 2 Se 3 and BSTS to higher fields. The validity of such an extrapolation is also supported by recent experiments by the Kovalev group [ 52 ], in which the cubic dependence is confirmed over the wide range of pump intensities. To approximate the saturating dependence of the third harmonic field strength in graphene, we use the empirical expected expression , where is the saturation strength of the cubic susceptibility.…”