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Abstract
The control of fluorescent properties of single-photon sources in solid-state host systems via optically resonant nanostructures is a key issue in quantum nanophotonics. Here we propose a design of a resonant metal-dielectric nanoantenna for the Purcell factor and radiation pattern control of a quantum emitter placed in the gap between metal and dielectric components of the nanostructure. We demonstrate that large Purcell factor, considerable field enhancement in the gap as well as high directivity can be achieved. The developed nanosystem can be utilized for different solid-state host systems from nanocrystals to 2D materials.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Development of nanoscale single-photon emitters (SPEs) operating on-demand is a challenging task in photonic quantum technologies. At present, a plenty of systems like color centers in diamond, 2D materials, quantum dots(QDs), etc. are considered as promising platforms for SPEs creation [1–3]. But for these systems the problems of efficient photons collection, control of emission lifetime (i.e. Purcell enhancement) as well as directivity still exist. A way to overcome these difficulties is integration of SPEs with resonant optical nanostructures [2,4].
Among of nanophotonic structures plasmonic ones attract high interest since in these nanosystems a high value of the Purcell factor(PF) can be achieved [5,6]. Moreover, the localization of the electromagnetic field on the surface leads to efficient coupling of a SPE placed near a plasmonic nanostructure [7,8]. But metallic structures have high losses which lead to decaying of the excitation and heating of the nanostructure. Despite losses can be decreased by utilization of complex fabrication methods (e.g. creation of mono-crystalline silver nanostructures [9]), the application of plasmonic nanosctructures for the SPEs control is limited.
On the other side, dielectric nanostructures have low losses and provide control of radiation directivity in a single resonant nanopaticle [10,11]. The opportunity to achieve emission enhancement through Purcell factor control in such nanoantennas is also demonstrated, but obtained PF values are lower compared to plasmonic nanostructures even in case if an emitter is placed inside of a dielectric nanostructure [12–14].
To combine remarkable optical properties of plasmonic and dielectric materials (low losses, high value of the PF, directivity control) the hybrid nanosystems comprised of metal and dielectric components have been proposed recently [15–18]. These nanostructures have attracted high attention induced by coupling of plasmonic and Mie resonance, or the unification of a resonant dielectric nanoparticle with plasmonic substrate. Thus, they exhibit extraordinary optical properties including broadband photoluminescence (PL) enhancement [17,18], optical switching [19], unidirectional scattering [20,21], near-field tuning [22,23] high-efficiency harmonic generation [24], enhancement of Raman scattering signal [25], etc.
In this paper, we propose a design of a resonant hybrid metal-dielecric nanostructure for the emission control of a single-photon emitter. We numerically investigate the PF enhancement, electromagnetic field distribution and opportunity for the spatial distribution of radiation control in this nanosystem.
2. Results and discussion
Figure 1 schematically shows the configuration of the proposed hybrid nanoantenna consisting of a gold sphere placed on the top of a crystalline silicon truncated cone, while a quantum source, varying from single atom layer to dozens of nanometers occupies the gap between the plasmonic sphere and dielectric cone. The hybrid metal-dielectric nanostructure is located on a glass substrate. As follows from the figure, different single-photon sources covering wide range from ultraviolet to infrared under the excitation of green laser (532 nm) can be coupled with this nanoantenna. Table 1 summarized the optical characteristics (conductor type, band gaps, zero-phonon-line wavelength (ZPL), second-order correlation function ($g^{(2)}(0$)) and operation temperature) of the promising solid-state single-photon emitters, laying a foundation of future studies of each system. Here $g^{(2)} (0)$ quantitatively yields the single-photon purity (multi-photon probability), $g^{(2)} (0)$ $<$ 0.5 indicates a single-photon emitter, while $g^{(2)} (0)$ $>$ 0.5 corresponds to the multiple photon emission.
Fig. 1. Schematic illustration of the proposed hybrid nanoantenna coupled with a quantum source. The different host medium (e.g. 2D material) are pumped by a green laser (532 nm) and emit single-photons of different wavelengths from ultraviolet to infrared. Left insets show the achieved high Purcell factor and radiation pattern at 518 nm when the dipole is directed horizontally.
Table 1. Solid State single-photon emitters
Integration of single-photon sources with nanoantennas could strongly modify the spontaneous emission, i.e. Purcell factor. The Purcell factor plays an important role in designing of the optical devices. Therefore optimizing the Purcell factor for the hybrid nanoantenna is of great importance.
To study the Purcell factor, radiation pattern and field enhancement the hybrid nanoantenna provides, numerical simulations are carried out by the CST Microwave Studio. The bottom diameter of the silicon cone is $D$ = 190 nm, which is twice that of the upper diameter. Besides, the upper diameter is identical to the diameter of sphere, i.e., $D$/2 = 95 nm. The size of monolayer 2D materials may only contain a few angstroms, such as hexagonal Boron Nitride (hBN) ($\sim$ 0.32 nm). Typical dimensions of carbon nanotube (CNT) and QDs are within the range of 10 nm. With regard to colour centers in diamond and compound semiconductors, the studied magnitude is approaching the vicinity of 50 nm. In addition, detonation nanodiamond with a diameter around 5 nm is also extensively investigated. On the other hand, perovskites possess complex composition and various dimensions. On the basis of this notion, the simulations are conducted at a range of 6 $\sim$ 45 nm. Quantum emitter has been simplified as a 5 nm discrete dipole with horizontal or vertical orientation, as the host media for the quantum source a nanodiamond has taken ($\epsilon = 2.4$). In our case, we calculated Purcell factor [43] according to:
where $R_{in}$ and $R_{0, in}$ represent the radiation impedances of the equivalent dipole in presence of the proposed hybrid nanoantenna and free space, respectively; Re $Z_{in}$ and Re $Z_{0, in}$ are the real parts of the corresponding input impedances of the nanodiamond with and without the presence of the hybrid nanoantenna, which can be exported from CST directly and thus depicted in Fig. 2.Fig. 2. Purcell factor configuration (log-scale) of the hybrid nanoantenna coupled to quantum sources at the range of 6-45 nm for horizontal (a) and vertical (b) dipole orientation. The identical peaks at $\lambda$ = 637 nm and a broadband resonance centered at $\lambda$ = 518 nm are observed. Insets show the dipole orientation relative to the symmetry axis of the hybrid nanostructures. (c) average radiative Purcell factor for the resonance 518 and 637 nm. Radiative pattern for 518 nm (d-e) and 637 nm (f-g) for both dipole orientations.
Figures 2a and 2b illustrate the log-scale Purcell factor pattern as a function of the operation wavelength and distance between the gold sphere and the silicon cone when the dipole is oriented horizontally and vertically to the symmetry axis of the hybrid nanoantenna, as indicated in the insets. Qualitatively speaking, the Purcell factor decays exponentially with the increase of the gap (0-45 nm) for both horizontal and vertical dipole orientations. Quantitatively speaking, the ultrahigh Purcell factor values are achieved, exceeding of 10$^{3.5}$ for horizontal orientation and 10$^{6.5}$ for vertical orientation. Besides, we have tuned the prominent resonance to the ZPL (637 nm) of negatively charged nitrogen-vacancy (NV$^{-}$) centers in diamond for both dipole orientations. This high-quality resonance can strongly enhance the photoluminescence(PL) of the NV-center in a nanodiamond. In fact, by adjusting the parameters of the spheres and cones, the resonance of the Purcell factor can be easily shifted to the ZPL of other single-photon source from the Table 1 in the visible range. In addition, the neighboring broadband resonance (500-550 nm) in Figs. 2(a)–2(b) is promising for highly strengthening the PL of hBN, QDs, colour centers in compound semiconductors as well as perovskites. It should be noted that as the thickness of 2D materials is relatively thin, essentially the discrete dipole could exclusively orientated horizontally [3]. Regarding NV center nanodiamond, it could be difficult to estimate the exact orientation. In this situation, the average Purcell factor are supposed to describe the modification of nanodiamonds’ decay rate, namely $F_{average} = 2/3 F_{hor} + 1/3 F_{ver}$. Therefore the average radiative Purcell factor at $\lambda = 518$ nm and $\lambda = 637$ nm is calculated and depicted in Fig. 2(c).
Except for the Purcell factor control, radiation directivity is another key element for single-photon emission. Thus the radiation pattern for different dipole orientations at $\lambda = 518$ nm and $\lambda = 637$ nm are presented in Figs. 2(d)–2(g). As it can be seen from Fig. 2(d), the center of the broadband resonance (518 nm) in Fig. 2(a) approximately radiates unidirectionally when the dipole orientated horizontally. This guarantees the maximum signal could be detected and utilized along the symmetric axis of the hybrid nanoantenna. The broadband Purcell factor achieved above alongside with high directivity make the proposed hybrid nanostructure promising for effective control of the single-photon emission and other applications.
Apart from Purcell factor and radiation directivity, electric field confinement also plays an important role in single-photon emission enhancement. Fig. 3(a) represents the electric near-field enhancement (E$\_$enhancement) achieved at the center of the gap between the metal sphere and the dielectric cone as a function of the gap width for the arrangement of the probe shown in the inset at the operation wavelength of 637 nm. Note that the calculations for $\lambda$ = 518 nm are omitted since obtained in this case spectra are almost overlapped the spectra for $\lambda$ = 637 nm. The hybrid nanoantenna is illuminated with TE/TM-polarized electromagnetic waves along the negative z-axis (i.e. the symmetry axis of the hybrid nanoantenna) under oblique incidence of 68 degrees. The E$\_$enhancement monotonically decreases starting from the gap size of 19 nm for the TM polarization and remains extremely low for the TE polarization. This can be explained by the corresponding near-field distribution patterns taking the dipole length $l$ equals to 10 nm. As indicated in Fig. 3c, the plasmonic resonance is excited in the case of the electric vector oscillates in the incident plane (TM polarization), and thus the electric energy has been localized in the gap. In the same time, a magnetic resonance is also observed inside the silicon cone. This high E$\_$enhancement makes the hybrid nanoantenna promising for effective pumping of a single-photon emitter as well as for field-enhanced spectroscopy. Additionally, we notice the occurrence of a magnetic quadrupole resonance under the excitation of the TE polarization, observing at the wavelength of $\lambda$ = 518 nm.
Fig. 3. (a) Dependence of the electric field enhancement as a function of the gap width as $\lambda$ = 637 nm for TE/TM polarization. Electric and magnetic near-field patterns calculated for TE (b) and TM (c) polarization distributed at $\lambda$ = 637 nm and $\lambda$ = 518 nm. The gap equals to 10 nm.
Metallic nanostructures normally contribute to high Purcell factor and field enhancement due to their ability to confine the electric field [44]. On the other hand, typical plasmonic nanostructures, such as spheres and disks, only exhibit electric resonances, leading to the difficulty to control the radiation direction. Conversely, all-dielectric nanostructures show their advantage for directivity manipulation via coupling magnetic and plasmonic modes [10,45]. As a result, hybrid metal/dielectric nanosystems combine the unique properties of both materials and present high directivity, Purcell factor as well as field enhancement simultaneously [16,46]. Table 2 summarized the above performance of existing all-dielectric, metallic and hybrid nanoresonators and systems and compared with the proposed scheme calculated at gap = 6 nm.
Table 2. Comparison of various dielectric and metallic nanosystems performance
3. Conclusion
We have proposed a hybrid metal-dielectric nanoantenna coupled with a single-photon quantum emitter in a host media. This kind of hybrid nanostructures can be easily fabricated by combination of nanolithography and “Pick-and-place” technique. Three main factors: Purcell factor, directivity and field confinement to control single-photon emission are studied. Ultrahigh Purcell factor values($\sim 10^{3.5}$ for horizontal and $\sim 10^{6.5}$ for vertical dipole orientation) are achieved. Besides, simulations demonstrate the high electric energy localization between the metal sphere and dielectric cone at the Purcell factor resonances (518 nm and 637 nm) under TM-polarized excitation. Indeed, the corresponding near-field patterns show the simultaneously observed electric and magnetic resonances, especially the magnetic quadrupole resonance at 518 nm. We believe that proposed hybrid platform unified with single-photon systems will enable effective radiation control, high-efficient PL and can be applied for quantum optical chips as well as field-enhanced spectroscopy.
Funding
Ministry of Education and Science of the Russian Federation (19-19-00691).
Acknowledgments
The studies of the Purcell factor enhancement, radiation pattern and electric field enhancement were supported by the Russian Scientific Foundation (Project 19-19-00691). The electric and magnetic near-field patterns were calculated with the support of the Ministry of Education and Science of the Russian Federation (Project 14.Y26.31.0010).
Disclosures
The authors declare no conflicts of interest.
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