challenge of nanophotonics [178]. Different studies have been focusing on enhancing the spontaneous emission rate [179] of a quantum system via tailoring the LDOS [180], [181], a phenomenon known as the Purcell effect [182]. In order to enhance the Purcell factor and improve emission directionality, epitaxial quantum dots (QDs) were first coupled to dielectric cavities [183]. Integrating emitters into dielectric optical micro- and nano-cavities with high quality factors (Q-factors) and small mode volumes [184], [185] can enhance the emission rate of the emitters [186]โ[190]. However, due to the high quality factor of dielectric nanocavities, single QDs need to be positioned at the maximum field of the cavity so that the emission of the QDs can be spectrally tuned to match the cavity mode [191].
This issue can be resolved by incorporating the quantum emitters into plasmonic nanostructures owing to their relatively broad spectral responses.
The Purcell factor describing the enhancement of the LDOS in resonant cavities can be defined by:
๐๐น = 3
4๐2(๐
๐)3 ๐
๐ (5.1)
where ๐
๐ is the wavelength of light in the medium, ๐ is the quality factor of the resonance, and ๐ is the mode volume.
As can be seen in Eq. (5.1), obtaining micro- and nano-cavities with large values of Q/V that can result in an increased Purcell factor is a central theme in solid-state quantum optics.
In plasmonic structures, absorptions and radiative losses lead to small quality factors.
However, excitation of plasmonic modes in such structures enables the confinement of radiation to sub-wavelength dimensions. This strong field enhancement in the plasmonic nanostructures provides large values of Q/V. This results in a strongly modified Purcell factor. As a consequence, coupling quantum emitters to plasmonic cavities can profoundly enhance the emission decay rate [192]โ[194]. Along the same lines, plasmonic patch antennas consisting of emitters situated in a vertical gap between a metal disk and a metal plane have been employed to enhance the emission rates of emitters [195]โ[197].
Recent studies have shown large emission rate enhancements, high radiative efficiencies, and directional emissions by embedding emitters in well-controlled nanoscale gaps sandwiched between a colloidally synthesized silver nanocube and a metal film. By controlling the refractive index and thickness of the gap as well as the dimensions of the nanocube, the resonance wavelength of the nanoscale patch antenna could be tuned from 500 nm to 900 nm [198]โ[200]. In a recent study, an ultrafast and efficient source of spontaneous emission with a lifetime shorter than 11 ps and Purcell factor of up to 880 was demonstrated by integrating colloidal and photostable semiconductor QDs into plasmonic nanopatch antennas. Coupling colloidal QDs to a plasmonic nanocavity, resulting in a 540-fold increase of the emission decay rate and a simultaneous 1900-fold increase of total emission intensity was also demonstrated [201].
In another study, Cy5 fluorophores were embedded within the gap region between colloidally synthesized silver nanocubes and a silver film [202]. The plasmon resonance of the nanocubes was tuned by varying the nanocube size, leading to 30000-fold fluorescence enhancements accompanied by a 74-fold enhancement of the spontaneous emission rate.
5.2. Reconfigurable Purcell Enhancement of Spontaneous Emission by Metasurfaces
Despite notable progress in this field, most of the micro- and nano-cavities to which quantum emitters are coupled have fixed properties at the time of fabrication. This fixed photonic environment leads to a static spontaneous emission decay rate of the emitter, limiting the functionality of such passive devices. In conventional schemes, the radiation from quantum emitters can be controlled by altering the optical [203] or electrical [204] pump intensity within a fixed nanostructured environment.
On the other hand, coupling quantum emitter to nanostructures with tunable local environments and optical properties could result in dynamic control of the emitter decay rate at a constant optical pump power.
Based on Fermiโs golden rule, the spontaneous emission decay rate of a dipole is given by:
๐พ๐ ๐(๐) = 2๐
3โ๐0|๐|2๐(๐, ๐) + ๐พ๐๐๐ก0 (5.2)
where ๐ is the position, ๐ is the emission frequency, ๐0 is the permittivity of free space, ๐ is the transition dipole moment of the emitter, and ๐พ๐๐๐ก0 is the internal non-radiative decay rate of the emitter. The local density of optical states, ๐(๐, ๐), is given by:
๐(๐, ๐) = 6๐
๐๐2[๐ฬ๐. ๐ผ๐{๐ฎ(๐, ๐)}. ๐ฬ๐] (5.3)
where ๐ฬ๐ and ๐บ(๐, ๐) are the unit vector pointing in the direction of ๐ and the dyadic Greenโs function of the system, respectively.
The dyadic Greenโs function of a dipole is determined by the electric field within the environment in which the dipole is embedded. This electric field is a function of the properties of the structure. As a result, tailoring the properties of the nanostructure via application of an external stimulus will enable dynamic control of the dyadic Greenโs
function, and hence, will result in a reconfigurable spontaneous emission decay rate of the dipole.
Figure 5.1 is a schematic illustration of the relation between the spontaneous emission decay rate of a dipole to the properties of the environment in which the dipole is embedded. In Fig. 5.1, one can see a dipole being embedded within a homogenous medium (Fig. 5.1a), inhomogeneous medium with fixed properties (Fig. 5.1b), and inhomogeneous medium with tunable properties (Fig. 5.1c).
Figure 5.1: Schematic illustration of Fermiโs golden rule. Here a dipole is assumed to be embedded in a (a) homogenous medium, (b) inhomogeneous medium, and (c) voltage-tunable inhomogeneous medium.
As mentioned in the previous chapters, different modulation mechanisms have been proposed to modulate the optical response of nanostructures in different wavelength regimes. Dynamic control of the spontaneous emission rate of epitaxial QDs coupled to high quality factor photonic crystal cavities has been experimentally demonstrated [205], [206]. However, these experiments required a cryogenic temperature ambient, making them less amenable for immediate practical applications.
This limitation can be alleviated by using active plasmonic structures to tune the emission of broadband room-temperature solid-state emitters. Thanks to their small optical mode volumes and relatively low quality factors, tunable plasmonic structures can eliminate the necessity of careful alignment of the quantum emitters and the structure resonances.
In a recent study, LDOS of visible-emitting colloidal QDs was manipulated via field- effect-induced optical permittivity modulation of ultrathin degenerately doped TiN in a gated TiN/SiO2/Ag plasmonic heterostructure [98]. The heterostructure consisted of 80 nm-thick Ag and 9 nm-thick SiO2 layers in which indium phosphide (InP) QDs were
embedded, followed by a 7 nm layer of TiN(see Fig. 5.2a). In this study, degenerately doped n-type TiN was used because of its ENZ wavelength which is located in the visible range. Visible-emitting InP/ZnS core-shell colloidal QDs were embedded in the insulating SiO2 spacer with a filling factor of 9%. The involved QDs were heavy-metal- free, and hence of great application interest, accounting for health and environmental concerns.
The fabricated TiN films were n-type with carrier densities ranging from 5.9 ร 1020 to 4.1 ร 1022 cmโ3. Depending on the carrier density, the fabricated TiN films could be optically dielectric (Re(ษ)>0) or optically plasmonic (Re(ษ)<0). When a bias was applied between TiN and Ag, a charge depletion or accumulation layer was formed in TiN at the interface with SiO2, with tunable real and imaginary parts of the permittivity (see Fig. 5.2b, c). This resulted in a modulation of the complex refractive index of TiN, and consequently, tuning of the reflection from the heterostructure via changing the applied bias (see Fig. 5.2d).
The optical measurements performed on the TiN/SiO2/Ag heterostructures showed a reflectance increase from 67% to 82% at the QD emission wavelength of ฮป=630 nm, when the gate voltage was varied from โ1 V to 1 V, with a modulation speed of exceeding 20 MHz. Due to the modulation of the refractive index of the TiN in its active region, one could achieve precise control over the LDOS at the position of QDs embedded in the SiO2 layer (see Fig. 5.2e).
As a result of the Fermiโs golden rule, the LDOS modulation led to a voltage-tunable lifetime (see Fig. 5.2f) and photoluminescence (PL) (see Fig. 5.2g) of the QDs. The time-resolved PL intensity measurement of the InP QDs showed a 12% decrease of the QD lifetime when the gate voltage VG was increased from 0 V to +1โV, and an 18%
increase of the QD lifetime when VG was varied from 0 V to โ1โV, leading to a total amount of 30% modulation of the lifetime of QDs. Moreover, the device provided a 10% relative increase in the PL intensity when the gate voltage VG was varied from 0 V to +1โV, and a 5% relative decrease in the PL intensity when VG was varied from 0 V to โ1โV. In addition to the lifetime and PL intensity modulation, a 26% increment of the radiative decay rate was observed when changing the applied bias. This led to a 56% increase of the quantum yield as the gate voltage VG varied from โ1 V to 1โV (see Fig. 5.2h).
Figure 5.2: TiN/SiO2/Ag plasmonic heterostructure used for active control of spontaneous emission of QDs. (a) Schematic of the gated plasmonic heterostructure. Cross-sectional TEM image of the fabricated heterostructure (top left). The scale bar is 10 nm. High-resolution TEM image of InP QDs with a diameter of 4โ5 nm (top right). The scale bar is 5 nm. Measured (b) real and (c) imaginary parts of the complex dielectric permittivity of TiN films. The gray dotted line in (b) denotes Re(ษ) = 0. For comparison, the dielectric permittivity values for gold and silver [207] are plotted. (d) The measured reflectance spectrum of the gated plasmonic heterostructure for different applied voltages. The inset shows the heterostructure reflectance as a function of voltage at a wavelength of ฮป=630 nm. (e) Calculated LDOS enhancement spectra at the position of a QD (averaged over QD dipole orientations) for different carrier densities in a 1 nm-thick modulated TiN layer. The black curve corresponds to a homogeneous TiN film, which is in the ENZ region. The red curve corresponds to a TiN film with a 1 nm- thick modulated TiN layer that is plasmonic but far from the ENZ region. The top panels show the simulated spatial distribution of the electric field |E| radiated by a QD (ฮป=630 nm). (f) PL lifetime of QDs embedded in the gated heterostructure. The inset shows the PL intensity as a function of time for different gate voltages VG. (g) Modulation of the PL intensity of InP QDs embedded in the gated heterostructure at the wavelength of ฮป=630 nm. The inset shows the PL intensity spectra for different gate voltages. (h) Radiative decay rate (top panel) of InP QDs (normalized to radiative decay rate at zero bias) embedded in the plasmonic heterostructure as a function of gate voltage. Dynamically tunable quantum yield (bottom panel) of QDs (normalized to quantum yield at zero bias).
As could be seen, the described platform could provide a promising scheme for modulating the spontaneous emission decay rate of quantum dots and quantum emitters in the visible wavelength range.
In the near- and mid-infrared regimes, modulation mechanisms have been adopted to tune the near-infrared emission of erbium ions coupled to Salisbury-screen type heterostructure via optically induced phase transition in VO2 [208] and electrically controlling the Fermi energy of graphene sheets [209], [210]. However, very small enhancement of the spontaneous emission rate could be achieved in such planar structures.
To conquer this issue, using reconfigurable plasmonic metasurfaces seems to be a promising approach to achieve tunable emission control with a notable enhancement of the spontaneous emission rate of emitters. Tunable metasurfaces can provide unique electromagnetic environments leading to precise control of the constitutive properties of radiation. The ability to tune the optical resonances of active metasurfaces is a key element to engineer enhancement of emission decay rate at desired wavelengths.
In this chapter, we propose an active plasmonic metasurface platform to achieve a tunable enhancement of the spontaneous emission decay rate of quantum emitters. The tunable metasurface operates based on a field-effect-induced modulation of the charge carrier concentrations in an ITO layer when an external DC electric field is applied across the layer. Figure 5.3 shows the spatial distribution of the number of charge carrier concentrations (Fig. 5.3a), real (Fig. 5.3b), and imaginary (Fig. 5.3c) parts of the ITO permittivity when a DC bias is applied between the ITO layer and another gate with a gate dielectric between them. The bulk charge carrier concentration of the ITO layer is chosen to be Nb = 1๏ด1020 cm-3. The metal and the gate dielectric of the metal- insulator-semiconductor (MIS) heterostructure are picked to be gold (Au) and HAOL [34], respectively.
As can be seen in Fig. 5.3a, when altering the applied bias between the Au gate and the ITO layer, the number of charge carrier concentrations of the ITO layer is changed especially in a thin region close to the interface of the ITO and the gate dielectric (corresponding to the right-border position in Fig. 5.3). This will result in a modulation of the real and imaginary parts of the electric permittivity of ITO.
Figure 5.3: Field-effect modulation of charge carrier concentration density and permittivity of ITO. Spatial distribution of (a) number of charge carrier concentration, (b) real and (c) imaginary part of the ITO permittivity for different applied biases. The bulk carrier concentration of ITO is 1ร1020. The right border (z = 7 nm) presents the interface of the ITO and the gate dielectric.
As a consequence, when the mentioned tunable MIS heterostructure is incorporated into a metasurface, the field-effect-induced modulation of the electric permittivity of ITO enables an active tuning of the LDOS. This leads to a reconfigurable enhancement of the spontaneous decay rate of the quantum emitters embedded within such a photonic environment.
Figure 5.4 shows a schematic of the proposed active metasurface which is composed of an Au back reflector on top of which an Al2O3 layer with quantum emitters embedded within it is located. The Al2O3 layer is followed by an ITO layer on top of which a HAOL gate dielectric and then Au fishbone antennas are placed.
Figure 5.4: Schematic of the gate-tunable metasurface used for active control of spontaneous emission decay rate of quantum emitters via modulation of the local density of optical states. Schematic of the (a) unit cell (the inset shows the top view of the unit) and (b) periodic array of electro-optically tunable metasurface used for modulation of Purcell enhancement. The metasurface consists of a gold back reflector, on top of which a host material (Al2O3) doped by quantum emitters (Er3+ ions) is placed. An ITO layer followed by HAOL gate-dielectric and gold antennas is then placed on top of the Er-doped Al2O3 layer.
The fishbone nanoantennas are composed of patch antennas that are connected by Au stripes, which also serve as gate voltage control electrodes. As discussed in the previous chapters, such a structure is able to provide a magnetic dipole plasmon resonance. By coupling this resonance with the emission of the desired quantum emitters, one can enhance the spontaneous emission decay rate of the emitters.
In order to achieve a tunable modulation of spontaneous emission decay rate in the NIR wavelength range, Er3+ ion is chosen as the quantum emitter to be embedded in an Al2O3 host material. Such a quantum emitter shows emission at a wavelength of 1535 nm.