Threshold conditions for transversal modes of tunable plasmonic nanolasers shaped as single and twin graphene-covered circular quantum wires

Abstract

We implement the Lasing Eigenvalue Problem (LEP) approach to study the electromagnetic field in the presence of a circular quantum wire (QW) made of a gain material and wrapped in graphene cover and a dimer of two identical graphene-covered QWs, at the threshold of stationary emission. LEP delivers the mode-specific eigenvalue pairs, namely the frequencies and the threshold values of the QW gain index for the plasmon and the wire modes of such nanolasers. In our analysis, we use quantum Kubo formalism for the graphene conductivity and classical Maxwell boundary-value problem for the field functions. The technique involves the resistive boundary conditions, the separation of variables in the local coordinates, and, for the dimer, the addition theorem for the cylindrical functions. For single-wire plasmonic laser, we derive approximate engineering expressions for the lasing frequencies and threshold values of the gain index that complement the full-wave computations. For the dimer, we derive separate determinantal equations for four different classes of symmetry of the lasing supermodes and solve them numerically. Our investigation of the mode frequencies and thresholds versus the graphene and QW parameters shows that plasmon modes or, for the dimer, plasmon supermodes have lower frequencies and thresholds than the wire modes provided that the QW radius is smaller than 10 μm, however in thicker wires they are comparable. Only the plasmon-mode characteristics are well-tunable using the graphene chemical potential. In the dimer, all lasing supermodes form closely located quartets, however, they quickly approach the single-wire case if the inter-wire separation becomes comparable to the radius. These results open a way for building essentially single-mode plasmonic nanolasers and their arrays and suggests certain engineering rules for their design.

Wave Diffraction from a Bicone Conjoined with an Open-Ended Conical Cavity

“…Here, we use the orthogonality properties of the associated Legendre functions P 1 z n −1/2 (− cos θ) over the interval γ 1 ≤ θ ≤ π to obtain these expressions [46]. It is worth noting that series (39) and ( 40) are formal because the asymptotic behaviour of the moduli of their terms decays as n −1 if n → ∞. Therefore, we substitute series (39) and ( 40) into the right-hand side of Equations ( 21) and ( 22), taking into account the finite numbers of their terms.…”

“…It is worth noting that series (39) and ( 40) are formal because the asymptotic behaviour of the moduli of their terms decays as n −1 if n → ∞. Therefore, we substitute series (39) and ( 40) into the right-hand side of Equations ( 21) and ( 22), taking into account the finite numbers of their terms. Then, let us form the homogeneous series equations concerning kernel functions P 1 z n −1/2 (− cos θ) and equate the coefficients to zero.…”

“…This technique has also been applied to analyse open-ended cylindrical and spherical cavities [33][34][35]. Various directions of analytical regularization methods are developed in [36][37][38][39], and references therein.…”

Tunability of Radiation Pattern of the H-Polarized Natural Waves of Dielectric Waveguide with Infinite Graphene Plane and Finite Number of Graphene Strips at THz

“…Together with the extraordinary hardness and flexibility of graphene, these properties open up wide opportunities for its inclusion in the construction of tunable antennas, absorbers, sensors, polarizers, lasers, etc. [6][7][8][9][10][11]. In [12], dynamic single-and dual-channel graphene Q-switching in an Yb:YAG waveguide with controlled power-splitting ratios for application in lasers is demonstrated.…”

“…10 show normalized radiation patterns (in amplitude) for different value of the chemical potential of graphene. For clarity, in Figure10, we also show the pola plot.…”