Plasmonic Purcell factor and coupling efficiency to surface plasmons. Implications for addressing and controlling optical nanosources

Abstract

Abstract. The Purcell factor Fp is a key quantity in cavity quantum electrodynamics (cQED) that quantifies the coupling rate between a dipolar emitter and a cavity mode. Its simple form Fp ∝ Q/V unravels the possible strategies to enhance and control light-matter interaction. Practically, efficient light-matter interaction is achieved thanks to either i) high quality factor Q at the basis of cQED or ii) low modal volume V at the basis of nanophotonics and plasmonics. In the last decade, strong efforts have been done to derive a plasmonic Purcell factor in order to transpose cQED concepts to the nanocale, in a scale-law approach. In this work, we discuss the plasmonic Purcell factor for both delocalized (SPP) and localized (LSP) surface-plasmon-polaritons and briefly summarize the expected applications for nanophotonics. On the basis of the SPP resonance shape (Lorentzian or Fano profile), we derive closed form expression for the coupling rate to delocalized plasmons. The quality factor factor and modal confinement of both SPP and LSP are quantified, demonstrating their strongly subwavelength behaviour.

Design and simulation of a germanium multiple quantum well metal strip nanocavity plasmon laser

“…Purcell factor as can be expressed in (4) specifies the possible strategies to enhance and control light-matter interaction. [18] Efficient light-matter interaction is achieved by means of either high quality factor "Q" or low modal volume "V", which is the basis of plasmonic cavity quantum electrodynamics (PCQED). [19] Where "λ" is free-space wavelength, "n" is the refractive index of gain medium and Q is the quality factor for the plasmonic resonator.…”

Nanoscale Plasmon Sources: Physical Principles and Novel Structures

“…However, applications of plasmons as a tool for nanoscale manipulation of light has gained significant attention with the paper by H. Atwater in 2007 named "Promise of plasmonics" [21]. In the past two decades, plasmonics has been developed both in theoretical and experimental aspects, and many different devices like switches [22], detectors [23], routers [24], amplifiers [25], and sources [17] have been introduced.…”

“…It can be calculated by Fermi's golden rule in a two-level atomic system and expressed by Eq. (10) [24]. (10) In which "Γ cav " is the decay rate in the cavity, "Γ 0 " is the decay rate in the free space, "n 1 " is the refractive index of the propagation medium, "λ em " and "ω em " are the emission wavelength of the medium, "ω c " is the cavity resonance frequency, "Q" is the quality factor of the cavity, "V eff " is the effective mode volume of the propagating mode in the cavity, and the dot product of the nominator corresponds to the mismatch between directions of transition dipole and the field.…”

“…(11) which results in a large Purcell factor which is crucial for the nanolaser operation. Moreover, since the emission rate is proportional to the LDOS, the higher Purcell factor means the higher local density of optical states [24]. where "ε(r)" is the permittivity as a function of position inside the resonator volume in which the integral is calculated and "E(r)" is the electrical field related to the propagating mode.…”

“…In a homogenous medium, spontaneous emission rate "A" is equal to "1/τ sp0 " and "τ sp0 " is the spontaneous emission lifetime of the material. However, in a nanocavity, Purcell effect [24] modifies the spontaneous emission rate via "A=F p A 0 ," where "F p " is the Purcell factor and "A 0 " is the natural spontaneous emission rate in a homogenous medium. "n 0 " is the excited state population of carriers in transparency, "v s " is surface recombination velocity at the sidewalls of the resonator, and "S a " and "V a " are the area of sidewalls of the resonator and volume of the gain medium, respectively.…”