Purcell Effect in the Stimulated and Spontaneous Emission Rates of Nanoscale Semiconductor Lasers

Abstract

Nanoscale semiconductor lasers have been developed recently using either metal, metallo-dielectric or photonic crystal nanocavities. While the technology of nanolasers is steadily being deployed, their expected performance for on-chip optical interconnects is still largely unknown due to a limited understanding of some of their key features. Specifically, as the cavity size is reduced with respect to the emission wavelength, the stimulated and the spontaneous emission rates are modified, which is known as the Purcell effect in the context of cavity quantum electrodynamics. This effect is expected to have a major impact in the 'threshold-less' behavior of nanolasers and in their modulation speed, but its role is poorly understood in practical laser structures, characterized by significant homogeneous and inhomogeneous broadening and by a complex spatial distribution of the active material and cavity field. In this work, we investigate the role of Purcell effect in the stimulated and spontaneous emission rates of semiconductor lasers taking into account the carriers' spatial distribution in the volume of the active region over a wide range of cavity dimensions and emitter/cavity linewidths, enabling the detailed modeling of the static and dynamic characteristics of either micro-or nano-scale lasers using single-mode rate-equations analysis. The ultimate limits of scaling down these nanoscale light sources in terms of Purcell enhancement and modulation speed are also discussed showing that the ultrafast modulation properties predicted in nanolasers are a direct consequence of the enhancement of the stimulated emission rate via reduction of the mode volume.

Rate equation description of quantum noise in nanolasers with few emitters

“…For inhomogeneously broadened systems, such as quantum dots with more levels and wetting layer transitions, b will in general depend on the total carrier density. 15,20 Notice that the pump-blocking term c p (n 0 À n e ) ensures that only a finite number of emitters (n 0 ) are considered.…”

Parametric optimization of visible wavelength gold lattice geometries for improved plasmon-enhanced fluorescence spectroscopy

“…The parameters contained in (62) are the quality factor (Q), the mode volume (V), and the wavelength in the material (λ) [62,[74][75]79]. The quality factor of the cavity mode is defined as:…”

“…power loss at an angular frequency (ω0) at which stored energy and power loss are measured. Note that a low Q delineates an overdamped system with a high Q delineating an underdamped system [79,109]. Furthermore, τ is directly proportional to Q.…”

“…Above, Rl is the emission rate per unit time into other modes [79]. It can be observed that that β can be enhanced substantially by ensuring Rl is suppressed, even in the case where Rsp,cav = Rbulk (without any Purcell enhancmenet).…”

“…The parameter ⃗ is the dipole operator, is the upper level wavefunction of the atom, and is the lower level wavefunction of the atom [79].…”