Lasing Conditions of Transverse Electromagnetic Modes in Metallic-Coated Micro- and Nanotubes

Abstract

In this work, we study the lasing conditions of the transverse electric (TE) modes of micro-and nanotubes coated internally with a thin metallic layer. This geometry may tackle some of the problems of nanolasers and spasers as it allows the recycling of the active medium while providing a tunable plasmonic cavity. The system presents two types of TE modes: cavity modes (CMs) and whispering-gallery modes (WGMs). On the one hand, we show that the lasing of WGM is only possible in nanoscale tubes. On the other hand, for tubes of some micrometers of diameter, we found that the system presents a large number of CMs with lasing frequencies within the visible and near-infrared spectrum and very low gain thresholds. Moreover, the lasing frequencies of CMs can be accurately described by a simple one-parameter model. Our results may be useful in the design of micro-and nanolasers for "lab-on-chip" devices, ultra-dense data storage, nanolithography, or sensing.

Spaser and optical amplification conditions in graphene-coated active wires

“…As shown, for example, in Ref. [26], under the appropriate conditions, this approximation provides reliable results for the gain thresholds.…”

“…[25,30]. The gain-loss compensation condition discussed in our work, also referenced as the gain threshold [26], does not necessarily mean that most emitted photons are the result of stimulated (coherent) emission, since, as calculations including saturation show, spontaneous (incoherent) emission can still be very important (especially if Purcell effects are relevant in the system studied). Requiring that most emitted photons come from spontaneous emission is a more strict condition that demands larger gain values than the ones informed here [32,33].…”

“…This is not a problem in principle if one is only interested in finding lasing conditions and not the intensity of the electromagnetic fields. Indeed, this property can be used for finding gain thresholds as divergences of properties such as the scattering coefficient [26,31]. Instead, here, we use another strategy, which is to find the critical value of the imaginary part of ε 1 , for which the modal eigenfrequency ω n is real [24][25][26].…”

“…Indeed, this property can be used for finding gain thresholds as divergences of properties such as the scattering coefficient [26,31]. Instead, here, we use another strategy, which is to find the critical value of the imaginary part of ε 1 , for which the modal eigenfrequency ω n is real [24][25][26]. Despite its limitations, the strategy used in the present work is still useful to correctly predict the mode that will be lasing (or spasing) and the frequency at which this occurs.…”

“…In a first stage, we use the eigenmode approach [22], particularly well-suited for finding the criticalgain values [Imε 1 ] c of the imaginary part of the permittivity of the active medium where the spaser condition is fulfilled. In the context of the eigenmode approach, these critical-gain values can be rigorously obtained by requiring simply that the imaginary part of a modal frequency be zero [24][25][26]. To do so, we use fully retarded methods in all of the examples presented here.…”