Enhancement of the spontaneous emission in subwavelength quasi-two-dimensional waveguides and resonators

We consider a quantum-electrodynamic problem of the spontaneous emission from a two-dimensional (2D) emitter, such as a quantum well or a 2D semiconductor, placed in a quasi-2D waveguide or cavity with subwavelength confinement in one direction. We apply the Heisenberg-Langevin approach, which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. The Langevin noise operators that we introduce do not depend on any particular model of dissipative reservoir and can be applied to any dissipation mechanism. Moreover, our approach is applicable to nonequilibrium electron systems, e.g., in the presence of pumping, beyond the applicability of the standard fluctuation-dissipation theorem. We derive analytic results for simple but practically important geometries: strip lines and rectangular cavities. Our results show that a significant enhancement of the spontaneous emission, by a factor of order 100 or higher, is possible for quantum wells and other 2D emitters in a subwavelength cavity.

Figure 1

Sketch of a nanocavity with thickness $L_z$ much smaller than wavelength. An active layer of 2D emitters is shown in dark blue. The profile of the electric field of the fundamental ${\mathrm{TE}}_{011}$ mode is sketched on the sides. The radiation can be outcoupled through the gratings or cavity edges.

Figure 2

Normalized effective $Q$ factor as a function of the normalized cavity linewidth ${\mathrm{\Gamma }}_r/{\gamma }_{21}$ at exact resonance ${\omega }_{21}={\omega }_{\nu }$. Four curves correspond to four different values of the total intracavity absorption rate $({\mathrm{\Gamma }}_{\sigma }+\gamma )/{\gamma }_{21}$: 0.01, 0.1, 1, and 10, from top to bottom curve.

Figure 3

Normalized effective $Q$ factor as a function of frequency detuning at ${\mathrm{\Gamma }}_r={\gamma }_{21}$. Three curves correspond to three different values of the total intracavity absorption rate $({\mathrm{\Gamma }}_{\sigma }+\gamma )/{\gamma }_{21}$: 0.01, 0.1, and 1, from top to bottom curve. They are plotted for the values of the normalized cavity linewidth ${\mathrm{\Gamma }}_r/{\gamma }_{21}=0.1$, 0.3, and 1, respectively, which correspond to the maximum $Q_{\mathrm{eff}}$ in Fig. 2.