PHYSICAL REVIEW B 100, 045424 (2019) Scattering of surface plasmons on graphene by abrupt free-carrier generation A. V. Shirokova, A. V. Maslov, and M.I. Bakunov * Department of Radiophysics, University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia (Received 1 April 2019; published 30 July 2019) We explore the temporal dynamics of a surface plasmon on a graphene sheet after an abrupt increase of graphene’s carrier density. The plasmon is transformed into two frequency-upshifted surface plasmons propagating in the forward and backward directions, transient free-space radiation, and two-stream dc motion of carriers. The two-stream carrier motion carries zero net electric current and therefore does not generate any magnetic field. Nevertheless, it can consume a substantial fraction, up to a half, of the initial plasmon energy in the form of the kinetic energy of the carriers. We revisit the recent claim in the literature that graphene’s nonstationarity can amplify plasmons. DOI: 10.1103/PhysRevB.100.045424 I. INTRODUCTION Graphene appears to be a promising plasmonic material for the terahertz and infrared frequency ranges due to its capability of supporting low loss and highly confined surface plasmons that can be dynamically tuned by varying the car- rier density via electrical gating or optical excitation. These advantages over plasmons in metals make graphene plasmons attractive for a wide range of photonic applications, such as surface-enhanced infrared absorption spectroscopy [1,2], infrared and terahertz photodetectors [3,4], sources [5,6], and modulators [7–9]. The tunability of graphene plasmons is vital for developing graphene-based active plasmonics [10]. By temporally vary- ing the graphene conductivity, one can change the dispersion properties of graphene plasmons and by this means modulate their frequency. Frequency manipulation of optical signals is important, for example, for the wavelength division multi- plexing technology in all-optical signal processing [11,12]. Dynamic frequency conversion of light confined in silicon- based photonic structures, both cavities and waveguides, have been experimentally demonstrated by photogeneration of free carriers in silicon [13–18]. For developing high-speed op- toelectronic devices, rapid variations of graphene properties are of considerable interest. In particular, ultrafast optical excitation of free carriers in graphene on the scale of a few tens of femtoseconds has been demonstrated [19–21]. The ultrafast dynamics of graphene plasmons after a photoexcita- tion of carriers has been revealed [22]. Elucidating the role of electron-hole pair creation and hot carrier dynamics on sub-100-fs time scales is currently a subject of intensive study [23,24]. Theoretical understanding of plasmon transformation on a time-varying graphene requires a careful consideration on the basis of nonstationary constitutive relations. Previously, the theory of wave transformation in time-varying media has been mainly developed for the waves in bulk materials, such as * bakunov@rf.unn.ru dielectrics or plasmas [25–29]. The transformation of surface waves was investigated in the geometries of plasma half-space [30–32] or plasma layers [31,33], both for slow [31] and rapid [30,32,33] plasma density variations. It was found that medium nonstationarity can give rise to specific effects such as frequency shifting, reflection at the temporal boundaries, temporal scattering of surface waves to bulk radiation, and generation of self-consistent distributions of static magnetic field and dc currents (the so-called free-streaming modes) in plasma. These effects, however, were not considered for the waves guided by two-dimensional structures, such as graphene sheets. The problem of graphene plasmon transformation by time modulation of graphene’s free-carrier density was addressed very recently in Refs. [34] and [35]. The most salient pre- diction of these works is that nonstationarity can amplify plasmons by imparting energy to them. In Ref. [34], the plasmon amplification occurs if the carrier density abruptly decreases. In Ref. [35], on the contrary, the amplification was predicted for a carrier density increase. In a more recent paper [36], however, the claim of plasmon amplification, made in Ref. [34] for the carrier density de- crease, was refuted and the origin of the mistake was pointed out. Namely, the approach of Ref. [34] is based on the conti- nuity of the plasmon’s magnetic field and its time derivative at the temporal discontinuity and on a simultaneous neglect of the transient bulk radiation. The transient radiation is indeed negligible in the quasistatic regime studied in Ref. [34]. The plasmon’s magnetic field, however, is also negligible, and using the continuity of this field and its derivative without including transient radiation is incorrect. For a correct consid- eration, one should use the initial conditions for the dominant components of the plasmon, i.e., its in-plane electric field and surface current [36]. In Ref. [35], the consideration is also limited by the qua- sistatic approximation but, unlike Ref. [34], other initial con- ditions, namely, the continuity of the plasmon’s electric and magnetic fields at the temporal discontinuity, are used without any justification. Due to different initial conditions, the results of Refs. [34] and [35] contradict each other. Moreover, as was 2469-9950/2019/100(4)/045424(7) 045424-1 ©2019 American Physical Society