The anisotropic plasmons properties of black phosphorus allow for realizing direction-dependent plasmonics devices. Here, we theoretically investigated the hybridization between graphene surface plasmons (GSP) and anisotropic black phosphorus localized surface plasmons (BPLSP) in the strong coupling regime. By dynamically adjusting the Fermi level of graphene, we show that the strong coherent GSP-BPLSP coupling can be achieved in both armchair and zigzag directions, which is attributed to the anisotropic black phosphorus with different in-plane effective electron masses along the two crystal axes. The strong coupling is quantitatively described by calculating the dispersion of the hybrid modes using a coupled oscillator model. Mode splitting energy of 26.5 meV and 19 meV are determined for the GSP-BPLSP hybridization along armchair and zigzag direction, respectively. We also find that the coupling strength can be strongly affected by the distance between graphene sheet and black phosphorus nanoribbons. Our work may provide the building blocks to construct future highly compact anisotropic plasmonics devices based on two-dimensional materials at infrared and terahertz frequencies.

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THz focusing and imaging include bulky dielectric refractive lenses and parabolic mirrors. Due to the diffraction effect, the resolution of conventional optics is limited by the Abbe diffraction limit (DL) of 0.5λ/NA, [5] where λ and NA are working wavelength and numerical aperture (NA), respectively. Recently, there has been a growing interest in developing far-field super-resolution optical devices, which can achieve point-spread-function (PSF) of size smaller than the Abbe DL without evanescent waves [6] at a distance far beyond the near-field regime. [7,8] Based on the concept of superoscillation, [9-11] a variety of sub-diffraction or super-resolution optical devices have been demonstrated either theoretically or experimentally, including scalar super-resolution metalenses [12-22] and vector super-resolution metalenses. [23-33] Such super-resolution devices have been successfully shown great potential in labelfree super-resolution microscopy [13,21,34,35] and super-resolution telescope. [36] However, most previously reported super-resolution metalenses only work at one single wavelength [37] or several designed discrete wavelengths, [38,39] while broadband achromatic metalenses working in the visible [40-42] and nearinfrared spectrum [43-46] as well as THz regime [47] are restricted by the Abbe DL. To achieve a broadband super-resolution imaging, recently, a broadband super-resolution scheme was proposed and experimentally demonstrated by adopting the combination of a super-oscillatory binary phase filter and a conventional bulk achromatic refractive convex lens. [48] Up to now, it is still a great challenge to realize a sub-diffraction achromatic metalens with a continuous broad bandwidth. To achieve broadband achromatic super-resolution focusing, similar to the conventional optics, dispersion compensation is required to ensure that the wave of different wavelengths is focused at the same focal point. In addition, wave front engineering is also required to achieve the super-resolution PSF. Recent fast development of metasurfaces [49-54] provides effective ways to manipulate the amplitude, [55,56] phase, [57-61] polarization [30,33,62-66] and dispersion properties [67,68] of light waves. To achieve wave front shaping without influences on dispersion, one possible way is to realize broadband achromatic super-resolution by adopting amplitude modulation. Conventionally, pupil filters [69-78] can be used to achieve super-resolution in traditional optical systems. Recently, there are growing interests in developing super-resolution metalenses for applications of focusing and imaging. On one hand, various sub-diffraction metalenses have been demonstrated; however, most of them only work at a single wavelength or multiple discrete wavelengths. On the other hand, the previously reported broadband achromatic metalenses are diffraction-limited, or their focal spots are larger than the corresponding Abbe diffraction limit, 0.5λ/NA, where λ and NA are the lens working wavelength and numerical aperture. In the present wo...

Aluminum nitride offers unique material advantages for the realization of ultrahigh-frequency acoustic devices attributed to its high ratio of stiffness to density, compatibility with harsh environments, and superior thermal properties. Although, to date, aluminum nitride thin films have been widely investigated regarding their electrical and mechanical characteristics under alternating small signal excitation, their ultrathin nature under large bias may also provide novel and useful properties. Here, we present a comprehensive investigation of electric field stiffening effect in c-oriented aluminum nitride piezoelectric thin films. By analyzing resonance characteristics in a 2.5 GHz aluminum nitride-based film bulk acoustic resonator, we demonstrate an up to 10% linear variation in the equivalent stiffness of aluminum nitride piezoelectric thin films when an electric field was applied from -150 to 150 MV/m along the c-axis. Moreover, for the first time, an atomic interaction mechanism is proposed to reveal the nature of electric field stiffening effect, suggesting that the nonlinear variation of the interatomic force induced by electric field modulation is the intrinsic reason for this phenomenon in aluminum nitride piezoelectric thin films. Our work provides vital experimental data and effective theoretical foundation for electric field stiffening effect in aluminum nitride piezoelectric thin films, indicating the huge potential in tunable ultrahigh-frequency microwave devices.