Spontaneous Emission and Fundamental Limitations on the Signal-to-Noise Ratio in Deep-Subwavelength Plasmonic Waveguide Structures with Gain

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Spontaneous Emission and Fundamental Limitations on the Signal-to-Noise Ratio in Deep-Subwavelength Plasmonic Waveguide Structures with Gain

Andrey A. Vyshnevyy and Dmitry Yu. Fedyanin

Phys. Rev. Applied 6, 064024 – Published 29 December 2016

Abstract

Incorporation of gain media in plasmonic nanostructures can give the possibility to compensate for high Ohmic losses in the metal and design truly nanoscale optical components for diverse applications ranging from biosensing to on-chip data communication. However, the process of stimulated emission in the gain medium is inevitably accompanied by spontaneous emission. This spontaneous emission greatly impacts the performance characteristics of deep-subwavelength active plasmonic devices and casts doubt on their practical use. Here we develop a theoretical framework to evaluate the influence of spontaneous emission, which can be applied to waveguide structures of any shape and level of mode confinement. In contrast to the previously developed theories, we take into account that the spectrum of spontaneous emission can be very broad and nonuniform, which is typical for deep-subwavelength structures, where a high optical gain (approximately $1000 {cm}^{- 1}$ ) in the active medium is required to compensate for strong absorption in the metal. We also present a detailed study of the spontaneous emission noise in metal-semiconductor active plasmonic nanowaveguides and demonstrate that by using both optical and electrical filtering techniques, it is possible to decrease the noise to a level sufficient for practical applications at telecom and midinfrared wavelengths.

Received 13 September 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.064024

Physics Subject Headings (PhySH)

Integrated optics Photonics Plasmonics Quantum fluctuations & noise Quantum optics Spontaneous emission Waveguides

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Andrey A. Vyshnevyy and Dmitry Yu. Fedyanin^*

Laboratory of Nanooptics and Plasmonics, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russian Federation

^*dmitry.fedyanin@phystech.edu

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Vol. 6, Iss. 6 — December 2016

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Images

Figure 1
(a) Schematic illustration of the plasmonic waveguide with gain, which connects the transmitter and receiver. (b) Qualitative dependence of the energy density of the SPP mode on the propagation coordinate in a passive waveguide (blue curve) in a sophisticated active plasmonic waveguide with full loss compensation (yellow curve) and in a real active plasmonic waveguide with full loss compensation (red curve). In the latter case, spontaneous emission can significantly contribute to the power of the SPP mode.
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Figure 2
(a) Schematic of the single-mode active dielectric loaded SPP waveguide based on copper as a metal and (InGa)As as an active semiconductor medium, where the population inversion can be created. Dimensions of the waveguide cross section are 7 times smaller than the signal wavelength ( $220 \times 220 {nm}^{2}$ for $λ_{0} = 1550 nm$ ). (b) Electric-field-intensity ( $| E |^{2}$ ) distribution of the SPP mode simulated at $λ_{0} = 1550 nm$ using the finite-element method.
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Figure 3
(a) Spectrum of the net SPP modal gain $G_{net} (h ν) = G (h ν) - α (h ν)$ in the deep-subwavelength active plasmonic waveguide [Fig. 2] in the regime of full loss compensation [ $G_{net} (h ν_{0}) = 0$ ] and curves for the spectral density of spontaneous emission. The length of the active plasmonic waveguide is as high as 1 mm, which is the typical size for chip-scale optical communication systems [27]. The green curve corresponds to the spontaneous emission that goes into the SPP mode, and the red curve corresponds to the spontaneous emission registered at the receiver. The blue curve shows the emission of the active semiconductor core in a homogeneous semiconductor medium. (b) Spectral density of spontaneous emission at the receiver for different lengths of the active plasmonic waveguide.
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Figure 4
(a) Power spectral density of noise at the photodetector as a function of the length of the active plasmonic waveguide shown in Fig. 2. The signal power is equal to $100 μ W$ , $λ_{0} = 1550 nm$ . (b) Power spectral density of noise at the photodetector versus signal power at a fixed waveguide length of 1 mm.
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Figure 5
(a) Normalized rms current noise at the photodetector as a function of the waveguide length, $P_{0} = 100 μ W$ . (b) Dependence of signal-to-noise ratio on the waveguide length for two different signal powers. In both panels, the solid curves correspond to the system with a narrow bandpass optical filter, and the dashed curves correspond to the systems without optical filters.
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Figure 6
Signal-to-noise ratio at the receiver as a function of the operation wavelength $λ_{0}$ and the length of the active plasmonic waveguides. The white curve corresponds to $SNR = 6$ , which separates the regions with $BER < 10^{- 9}$ (to the left of the curve) and $BER > 10^{- 9}$ (to the right of the curve).
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