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Loss and Gain in a Plasmonic Nanolaser

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Loss and Gain in a Plasmonic Nanolaser Nanophotonics 2020; 9(10): 3403–3408 Research article Shao-Lei Wang, Suo Wang, Xing-Kun Man* and Ren-Min Ma* Loss and gain in a plasmonic nanolaser https://doi.org/10.1515/nanoph-2020-0117 new powerful tool for a variety of applications ranging Received February 14, 2020; accepted April 3, 2020; published online from on-chip optical interconnector, sensing and detec- May 23, 2020 tion, to biological labeling and tracking [1–7]. In the past decade, plasmonic nanolasers with different configura- Abstract: Plasmonic nanolasers are a new class of laser tions and field confinement capabilities have been devices which amplify surface plasmons instead of photons demonstrated including one dimensional confined devices by stimulated emission. A plasmonic nanolaser cavity can represented by metal-insulator-metal and metal-insulator- lower the total cavity loss by suppressing radiation loss via semiconductor gap mode nanolasers [8–15], two dimen- the plasmonic field confinement effect. However, laser size sional confined devices represented by plasmonic nano- miniaturization is inevitably accompanied with increasing wire lasers [16–28], and three dimensional confined total cavity loss. Here we reveal quantitatively the loss and devices represented by metallic-nanoparticle lasers and gain in a plasmonic nanolaser. We first obtain gain co- metallic-coated nanolasers [29–50]. Plasmonic nanolaser efficients at each pump power of a plasmonic nanolaser via arrays have also been demonstrated to control the emission analyses of spontaneous emission spectra and lasing directionality and wavelength [51–58]. emission wavelength shift. We then determine the gain An essential merit of plasmonic nanolasers is to lower material loss, metallic loss and radiation loss of the plas- the total cavity loss by suppressing radiation loss via the monic nanolaser. Last, we provide relationships between plasmonic field confinement effect [15, 59, 60]. However, quality factor, loss, gain, carrier density and lasing emission increasing of total cavity loss with cavity size miniaturi- wavelength. Our results provide guidance to the cavity and zation is inevitable: pure photonic cavities are plagued by gain material optimization of a plasmonic nanolaser, which radiation loss, plasmonic cavities by ohmic loss [15, 59]. In can lead to laser devices with ever smaller cavity size, lower this article, we provide a quantitative study of the loss and fi power consumption and faster modulation speed. gain in a plasmonic nanolaser. We rst obtain excited carrier concentrations at varied pump intensity from Keywords: gain; laser miniaturization; loss; plasmonic spontaneous emission spectra and lasing emission wave- nanolaser; semiconductor. length shift, which are used to calculate Fermi inversion factors and consequently gain coefficients at each pump intensity. We further determine the gain material loss, metallic loss and radiation loss of the plasmonic nanolaser. 1 Introduction Last, we give a correspondence between cavity quality factor, total cavity loss, carrier concentration, emission Plasmonic nanolasers are a new class of laser devices with wavelength and gain material loss. feature size comparable to electronic devices. They offer a 2 Main text *Corresponding authors: Ren-Min Ma, State Key Lab for Mesoscopic Physics, School of Physics, Peking University, Beijing, China; A plasmonic nanolaser consists of two basic materials of Frontiers Science Center for Nano-optoelectronics & Collaborative metal and gain materials. Figure 1(a) shows the schematic Innovation Center of Quantum Matter, Beijing, China, E-mail: [email protected]; and Xing-Kun Man, Center of Soft of a metal-insulator-semiconductor gap mode plasmonic Matter Physics and Its Applications, School of Physics, Beihang nanolaser, where the electric field is strongly confined at University, Beijing, China; [email protected]. https://orcid.org/ the metal-insulator-semiconductor interface [9, 16]. In 0000-0003-4199-5772 (R.-M. Ma) contrast to conventional photonic mode lasers where the Shao-Lei Wang: Center of Soft Matter Physics and Its Applications, loss mainly consists of gain material loss due to stimulated School of Physics, Beihang University, Beijing, China; State Key Lab for Mesoscopic Physics, School of Physics, Peking University, Beijing, China absorption and radiation loss, there is an additional Suo Wang: State Key Lab for Mesoscopic Physics, School of Physics, metallic loss in plasmonic nanolasers. Figure 1(b) shows Peking University, Beijing, China the loss and gain of a plasmonic nanolaser in a schematic Open Access. © 2020 Shao-Lei Wang et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. 3404 S.-L. Wang et al.: Loss and gain in a plasmonic nanolaser energy band diagram. To achieve lasing state, carriers need is the effective mass of electrons (holes) of CdSe, m0 is free to be pumped in the excited energy level to a certain den- electron mass. Since the photo-excited electrons and holes sity. However, not all the excited carriers contribute to are dominant carriers in the laser cavity, we can assume gain. For semiconductor gain materials, there is a trans- that ΔNe equals to ΔNh. Based on Equation (1), we can parency carrier density at which point the excited carriers obtain the change of carrier density under varied pump are used to compensate the gain material loss. The extra powers. excited carriers beyond transparency carrier density are We then calculate carrier concentrations at pump used to compensate the metallic loss and radiation loss. powers well below threshold by fitting spontaneous Note that the total carrier number at lasing state can be emission spectra. For a given carrier density, quasi-Fermi used to calculate the threshold pump power [61]. levels are determined for photon excited electrons and We first focus on a room-temperature plasmonic holes, which can be used to obtain Fermi inversion factor nanolaser constructed by a CdSe nanosquare on top of Au and then the gain spectrum. The gain spectrum is related to film separated by 5 nm MgF2 as we reported previously [62]. the spontaneous emission spectrum via Einstein coeffi- The nanolaser is optically pumped by a nanosecond pump cient relations on spontaneous emission and stimulated laser at 532 nm (repetition rate: 1 kHz, pulse length: 4.5 ns). emission. We utilize the relationship between the gain Figure 2(a) shows emission spectra evolution with the in- spectrum g(λ) and the spontaneous emission spectrum crease of the pump power. There is a clear resonant peak Psp(λ) [64]: blue shift below and around lasing threshold which results hcλ − ΔF from the decrease of the refractive index due to the free- g(λ) Aλ51 − exp P (λ) (2) k T sp carrier dispersion. The blue shift saturates above the lasing B threshold due to the gain clamping. The emission wave- where ΔF EFc − EFv is the difference of the conduction length (λ) is related to the real part of the refractive index by and valence band quasi-Fermi levels.A is a constant related nrL = mλ, where L is the optical round-trip path inside the to volume of the gain material, the ratio of the final cavity and m is the order of the mode. Based on the Drude– measured spontaneous emission power to the total spon- Lorentz equation, we can get the density of electrons (Ne) taneous emission power and also the confinement factor; and holes (Nh) to the change of refractive index [63]: hc/λ is the energy of the one photon, kB is the Boltzmann constant, T is the room temperature of ∼300 K. Figure 2(b) −e2λ2 ΔN ΔN Δn 0 e + h (1) shows the fitted results of the spontaneous emission r 8π2c2ε n m∗ m∗ 0 r ce ch spectra under pump power of 15 kW cm−2 and 30 kW cm−2 ∼ × 18 −3 where e is the electronic charge, λ0 is the peak emission which give carrier densities of 1.2 10 cm and ∼ × 18 −3 wavelength, c is the light speed in vacuum, ε0 is the 2.2 10 cm respectively. Based on above calculations, ∗ . ( ∗ . ) permittivity of free space, mce 0 13 m0 mch 0 45 m0 we obtain the carrier densities at all measured pump Figure 1: Schematic of loss and gain in a plasmonic nanolaser. (a) Schematic of a plasmonic nanolaser consisting of a semiconductor gain material on top of a metal/dielectric substrate. Red wavy lines represent free space radiation and surface plasmon polariton radiation. (b) Loss and gain of a plasmonic nanolaser in a schematic energy band diagram. To achieve lasing state, carriers need to be pumped in the excited energy level to a certain density, the radiation of which compensates gain material absorption loss, metallic loss and radiation loss. S.-L. Wang et al.: Loss and gain in a plasmonic nanolaser 3405 powers as shown in Figure 2(c). We can see that carrier is at ∼109 kW cm−2 corresponding to a gain coefficient of density increases with the pump power and gets saturated 12,600 cm−1. Thereby we can get the metallic loss and ra- above lasing threshold. diation loss to be 12,600 cm−1 and 2500 cm−1 respectively, Extracted carrier densities give the maximum gain which is consistent with our full wave simulation result. coefficients in the gain spectra at each pump power as Estimated from the quality factors of the cavity with and shown in Figure 3(a), which can be used to determine the without ohmic loss, the simulation gives a metallic loss and gain material loss, metallic loss and radiation loss of the radiation loss to be ∼12,500 cm−1 and ∼2600 cm−1 respec- plasmonic nanolaser. First, at the full lasing state, the gain tively. coefficient saturates at ∼15,100 cm−1 which approximately Quality factor characterizes the photon loss rate of a equals to the summation of metallic loss and radiation loss.
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