A cavity-based optical antenna for color centers in diamond

In the past few years, color centers in diamond involving a substitutional atom from group IV of the periodic table and a nearby vacancy (group IV vacancy centers¹) have gained strong interest for applications in quantum technologies;² among them are the negatively charged silicon (SiV⁻),^3,4 germanium (GeV⁻),^5,6 and more recently also tin^7,8 (SnV⁻) and lead (PbV⁻) vacancy centers.^8,9 Their emission into the zero-phonon line (ZPL) exceeds that of the well-studied negatively charged nitrogen-vacancy center (NV⁻) by one order of magnitude at room temperature.¹⁰ Moreover, group IV vacancy centers possess an optically accessible electron spin,^7,11–15 rendering them well-suited building blocks for spin–photon interfaces.² 

However, the high refractive index of diamond at visible wavelengths (n = 2.414 at 620 nm¹⁶) induces a severe limitation on the photon extraction efficiency. Because of total internal reflection, refraction, and reflection at the diamond–air interface, only around 2% of the emission of color centers in bulk {100}-polished diamond can be collected with a standard air objective (e.g., NA = 0.8). This is a well-known problem¹⁷ also in competing systems, such as semiconductor quantum dots, or in classical light sources, such as light emitting diodes (LEDs),¹⁸ where the refractive index of the host materials is typically even higher. Consequently, there have been many proposals to increase the collectible photon rate from quantum emitters out of high index materials, most of them trying to shape the dielectric environment to circumvent total internal reflection. For color centers in diamond, non-resonant structures, such as nanowires^19–21 or solid immersion lenses,^22–25 have been shown to be a feasible solution, yet they enhance the collectible photon rate only by one order of magnitude to around 30% of the total emission rate and for only a small fraction of emitters with the matching position and orientation. More sophisticated approaches involve resonant cavities, channeling the emission into one spatial and spectral mode and additionally enhancing the emission rate beyond the bulk emission rate via the Purcell effect.²⁶ This includes fiber-based Fabry–Pérot type cavities^27–31 and a plethora of integrated micro- and nanophotonic approaches.^17,32 Generally speaking, interfaces between solid-state emitters and freely propagating photons may be summarized as optical antennas:³³ An optical antenna is defined as a device that not only enhances the collectible photon rate from an emitter but vice versa also enhances the coupling of external light to the emitter. Whereas optical antennas have been realized with a multitude of designs,³⁴ the simplest structure may consist of a planar stack of dielectric layers as proposed by Lee et al.³⁵ This approach has been demonstrated to be a promising option to enhance photon extraction for many emitters in the same structure, achieving outstanding collection efficiencies well above 95% for single molecules.³⁵ The need for oil immersion microscopy to avoid total internal reflection, however, limits its applications to room temperature. Circumventing this limitation has yet been shown to be possible: For color centers in a diamond membrane, a purely dielectric design for the extraction of the emitted photons can be achieved by placing a material with a higher refractive index in contact with the diamond.²⁴ The diamond membrane thereby forms a leaky slab waveguide, directing the emission toward the higher index material, comparable to the design presented by Lee et al. The need for oil immersion can further be avoided by tailoring the higher index material as a macroscopic solid immersion lens.²⁴ For an ideal functionality, however, the color centers in the diamond membrane need to be placed centered with respect to the solid immersion lens. A similar design has also been demonstrated for quantum dots.³⁶ 

In this work, we overcome the limitations of the designs mentioned above and return to an entirely planar design consisting of a dielectric slab with metal coatings. A comparable approach has recently been implemented by Checcucci et al.,³⁷ estimating collection efficiencies well above 50% for the emission of single molecules embedded in a crystalline matrix. It is based on two gold mirrors that are directly coated onto the host layer, yielding an intrinsic mechanical stability. The thickness of the host layer and mirrors is chosen to enhance the beaming of the emission of molecules into a narrow lobe in the far field. Recently, an adaption to quantum dots has been reported by Huang et al.,³⁸ yielding a collection efficiency of around 19% with an air objective with NA = 0.85. Although there exist theoretical^39,40 and first experimental studies⁴¹ to adapt this design also to color centers in diamond, a thorough demonstration is now missing.

Thus, we start in Sec. II with a detailed model of a dipole emitting in a planar metallo-dielectric stack based on a diamond membrane, identifying the design most generally as a monolithic Fabry–Pérot cavity. In contrast to the studies mentioned above, we optimize the design toward a high absolute photon rate from a single SnV⁻ center in the diamond membrane, collectible with an air objective. We show that for certain thicknesses of the involved layers, the cavity enhances the collectible photon rate from single emitters inside the diamond membrane and the coupling of an excitation laser to these emitters, satisfying the definition of an optical antenna. The theoretical description is followed by an optimization of the free parameters, revealing the main fabrication challenge: Whereas single molecules and quantum dots can be deposited by a bottom-up-approach, thin diamond membranes are typically fabricated by a top-down-approach involving plasma etching of high quality bulk diamond^42,43 and subsequent doping with color centers. Thus, we continue with briefly describing the fabrication of the diamond membrane and metallo-dielectric layers (Sec. III). To verify the functionality of the fabricated antenna, we perform a spectroscopic investigation of single SnV⁻ centers prior to and after applying the coatings in Sec. IV. Yielding a nearly six-fold enhancement of the single photon emission rates in accordance with theory, together with a severe reduction of the required excitation power, we demonstrate the operation of the fabricated cavity in terms of an optical antenna as defined above. Specifically, for the implementation of single photon sources or spin–photon interfaces, a monolithic and thus inherently stable optical antenna together with an intrinsically high scalability and low technical overhead paves the way toward the usage of color centers in diamond as versatile building blocks for present and future quantum technologies.

In the following, we focus entirely on the SnV⁻ center with its comparably high photon rate already out of bulk diamond, typically reaching the order of 10⁴ to 10⁵ counts per second (cps) at the detectors (compare saturation statistics in Fig. 6 and earlier work¹⁰). Working with the SnV⁻ center is further motivated by its favorable spin coherence: Whereas, e.g., the SiV⁻ center needs to be operated at mK temperatures to suppress the phonon-induced decoherence of the spin states,^13,14 the much larger ground state splitting of the SnV⁻ center enables operation above 1 K.^7,44 Recently, the all-optical control of the spin states of the SnV⁻ center with close to ms spin coherence time has been demonstrated,¹⁵ allowing for the implementation of spin–photon interfaces operating at liquid helium temperatures. The atomic structure of the SnV⁻ center is depicted in Fig. 1(a). Made up of a substitutional tin atom and an adjacent vacancy, the tin atom moves to an interstitial position between the two lattice positions, forming a split-vacancy configuration.^1,45 In contrast to the NV center, this gives rise to an inversion symmetry, yielding a strongly reduced sensitivity of the electronic levels to external perturbations, in particular to electric fields. The photoluminescence (PL) spectrum of the SnV⁻ center consists of the ZPL at 620 nm, followed by a phononic side band (PSB) extending to over 700 nm. In previous work, we have thoroughly studied the temperature-dependent Debye–Waller factor, quantifying the branching ratio between the ZPL and PSB as 30:70 at room temperature.¹⁰ This exceeds the corresponding value of the NV center by one order of magnitude, rendering the SnV⁻ center a promising candidate for the implementation of efficient room temperature single photon sources. An exemplary spectrum of an SnV⁻ center in bulk diamond at room temperature is shown in Fig. 1(b).

First experiments on coupling of individual SnV⁻ centers to resonant nanostructures have been conducted recently,^46,47 yielding high Purcell factors due to their implementation as photonic crystal cavities with small mode volumes. The major difference of our approach is that a large fraction of the emission is channeled into spatial modes that can be collected with a standard air objective with no need for further photonic elements, e.g., grating couplers or tapered fiber couplers as in the case of nanobeam cavities. Second, the design is entirely planar and thus does not require more sophisticated nanofabrication techniques than reactive ion etching with macroscopic shadow masks.

In Sec. II A, we thus discuss the emission characteristics of a single SnV⁻ center situated inside a planar metallo-dielectric stack. From a photonic point of view, the SnV⁻ center can be modeled as an electric point dipole with a dominant dipole axis along one of the high symmetry ⟨111⟩ axes of the diamond lattice,^3,10 depicted as a red solid line in Fig. 1(a). An electric dipole radiating inside a planar metallo-dielectric stack is sketched in Fig. 1(c): We assume the dipole to be embedded in a diamond layer of thickness t₀ and refractive index n₀, enclosed by two arbitrary layer systems. The whole stack is embedded within semi-infinite layers on both sides. We further assume the collection optics to be placed in the half-space above the dipole with real refractive index n₊, allowing us to collect all emission from the dipole leaving the stack in the positive z-direction up to a detection angle θ_NA defined by the NA of the collection optics via NA = n₊ · sin(θ_NA). We call this half-space the collection half-space.

The dipole emission in such a stack can be treated completely by classical electrodynamics, which has been shown multiple times in the literature:^48–51 Starting with a plane wave expansion of the emitted electric field, the corresponding plane waves and evanescent fields are propagated through the layers using generalized Fresnel coefficients for the layer system above and below the diamond layer obtained via a transfer matrix method.⁵² In the semi-infinite half-spaces, we perform a far field transformation using the method of stationary phase.⁵³ With this formalism, we can derive expressions for the radiated far fields that can be evaluated numerically.

The optical antenna design is based on a thin (t₀ < 1 μm) diamond membrane with refractive index n₀ = 2.414 at 620 nm,¹⁶ which itself can be modeled as a slab waveguide when surrounded by air (n₊ = n₋ = 1.0). Consequently, most of the emission from color centers is trapped inside the membrane due to total internal reflection at the diamond–air interfaces. The corresponding guided modes can be calculated by solving the transcendental eigenvalue equations.⁵⁴ Another possibility to reveal the guided modes is to virtually place an electric point dipole inside the slab and look at its emitted power, which is dependent upon the local density of states (LDOS): In a homogeneous medium with refractive index n₀, the emitted power is given as P_hom = n₀ · P₀, with P₀ the emitted power in vacuum. An arbitrarily shaped inhomogeneous environment, such as a slab waveguide, gives rise to a modified LDOS and thus a change in the emitted power.⁵⁵ This change can be modeled by splitting the total power P_tot emitted by the dipole in a sum of the homogeneous power P_hom and an additional contribution P_inhom. Furthermore, P_inhom can be expressed in terms of a plane wave expansion as shown in the following equation:

The integrals in Eq. (1) break down the electric field of the dipole into a series of plane waves and evanescent fields. Each component of the series propagates in a different direction, which is determined by the parallel component k_∥ = kn₀  sin(θ) of the wave vector with k = 2π/λ and λ the vacuum wave number and wavelength, respectively. Thus, k_∥ is directly related to the polar emission angle θ, and we call the function p(k_∥) the angular power emission spectrum. Defining n_eff = n₀  sin(θ), we find the term n_eff, which is well known from guided wave optics and is called the effective index of the guided modes. As k_∥ is a rather unhandy value, we evaluate p(n_eff) instead of p(k_∥), enabling us to directly extract the effective index of the guided modes. As an example, Fig. 2(a) shows p(n_eff) for a diamond slab (t₀ = 350 nm and n₀ = 2.414 at λ = 620 nm¹⁶) surrounded by air and a dipole placed exactly in the middle of the slab (d = 175 nm), oriented parallel to the interfaces (ϑ = 90°). At certain n_eff, the LDOS and thus the emission of the dipole are enhanced due to the presence of a guided mode, yielding peaks in p(n_eff). For a loss-less waveguide, these peaks correspond to the poles of p(n_eff). To avoid this numerically, we introduce a small absorption of κ = 5 · 10⁻⁴ to the refractive index of the diamond layer.

If the layer above and below the diamond slab is chosen to be air with refractive index n₊ = n₋ = 1, the range 1 < n_eff < n₀ corresponds to the plane waves of the expansion, which are trapped in the slab. In this regime, we see peaks corresponding to the guided modes, delivering the same effective indices as the direct approach of solving the transcendent equations for a slab waveguide. By evaluating p(n_eff), however, we can extract to which modes the dipole actually couples, as due to the chosen dipole orientation and position, it does not couple to all existing guided modes.

These considerations also hold when we introduce silver coatings (n₁ = n_1^′ = 0.05 + 4.21i at 620 nm⁵⁶) on both sides of the diamond slab. Instead of having total internal reflection, the diamond–silver interfaces possess a high reflectance independently of the angle of incidence, leading again to modes in the diamond slab, which can also be calculated using suitable eigenvalue equations.⁵⁷ In the absence of a critical angle, all peaks with n_eff < n₀ in p(n_eff) correspond to the guided modes of the stack. Reducing the thickness of the top silver layer to values well below 100 nm, the layer becomes transparent enough to let the formerly guided modes leak out of the diamond slab trough the thin silver layer into the collection half-space with n₊ = 1.0. This effectively implies that modes with n_eff < n₊ = 1.0 will be converted to free-propagating radiation at well-defined polar angles in the collection half-space beyond the thin silver layer. Consequently, these modes are often named leaky modes. The resulting angular power emission spectrum for an upper silver mirror with t₁ = 50 nm thickness is shown in Fig. 2(b). The lower silver mirror is kept thick and thus opaque with t₁′ = 300 nm. The two peaks in p(n_eff) at n_eff = 0.475 (s-pol.) and n_eff = 0.542 (p-pol.) correspond to leaky modes. Using Snell’s law, we can calculate the polar angles θ_up at which these modes propagate as plane waves in the collection half-space. Additionally, we can probe the reflectance of the stack by evaluating Fresnel’s equations for plane waves incident on the stack from the collection half-space. This is shown in Fig. 2(c), where we see sharp drops in reflectance at angles of incidences coinciding with the propagation angles of the plane waves corresponding to the leaky modes. Consequently, we can identify the stack with a plane-parallel Fabry–Pérot cavity because we can probe it independently of the dipole emission via reflectance calculations. For a matching cavity length, the cavity alters the dielectric environment and thereby the LDOS and enables a dipole inside it to couple to the leaky modes, which are efficiently transferred to free-propagating radiation in the collection half-space. Vice versa, light sent onto the cavity at matching angles is efficiently coupled to the cavity and thus to the dipole. This matches well the definition of an optical antenna.³³ In Sec. II B, we will determine the ideal cavity length for an efficient antenna operation as part of a general optimization of all free parameters.

The planar design considered here has already been discussed as a cavity in the literature and is thus conceptually well understood, especially in the context of enhancing light extraction from LEDs.^51,58,59 We, however, point out that some of the underlying theoretical concepts are much more sophisticated than the presented model. As the transmission through the thin silver layer is the major loss source of the cavity, the leaky modes can no longer be taken as confined between the mirrors, which is a major assumption in resonator theory. Instead, they span through the semi-transparent mirror toward infinity, defining the system as a so-called open cavity. Such open cavities have already been discussed at a fundamental level,⁶⁰ identifying Fox–Li quasimodes as the exact solutions. However, as will be shown in Sec. IV B, the model presented above describes the experimental results successfully without the need for specific assumptions on the cavity modes.

After discussing the basic concept of the design, it becomes obvious that the thickness of the diamond and thin silver layer can be optimized to enhance the coupling of an SnV⁻ center to the cavity, enabling the functionality as an optical antenna. To quantify the brightness of a single photon emitter driven by an off-resonant continuous-wave laser, a well-suited figure of merit is given by the collection factor ξ in the following equation:

where Γ_NA is the far field photon rate into a solid angle defined by the NA of the collection optics and Γ_hom is the radiative decay rate of an electric dipole transition inside a homogeneous medium. Thus, we have Γ_hom = n₀Γ₀, with Γ₀ the vacuum emission rate. The collection factor ξ hence defines a handy and comparable value for the absolute collectible photon rate Γ_NA under continuous-wave excitation. Due to an enhanced LDOS, we may also find ξ > 1, which can be attributed to a lifetime reduction of the emitter (Purcell effect²⁶).

As we calculate classical electromagnetic fields and optical powers but aim at investigating the quantum mechanical emission rates of single quantum emitters, we use the following relation:

Equation (3) links both classical optical powers P and quantum mechanical rates Γ, allowing us to restrict the investigations to purely classical calculations. It can be derived by comparing classical Green’s function of an electric point dipole and the quantum mechanical decay rate of an electric dipole transition.⁵⁵ 

Next, we probe the theoretical limits of the design in terms of the above-defined figure of merit ξ. The open parameters are the thickness of the diamond membrane t₀, the depth of the dipole below the thin silver layer d, and the thickness of the thin silver layer t₁ on top of the diamond membrane. As we place the collection optics in the half-space above the thin silver layer, we leave the thickness of the lower silver layer fixed at t_1^′ = 300 nm to avoid any radiation from leaking to the lower half-space. The collection optics is assumed to be an air objective with a collection angle of around 53° defined by NA = 0.8. Additionally, we introduce a silica layer of thickness t₂ on top of the thin silver layer to prevent the latter from corroding over time.

We carry out the calculations with a self-developed implementation of the plane wave expansion using Python. For the optimization, we employ a particle swarm optimization algorithm (pyswarm) in combination with a classical optimization algorithm (scipy, L-BFGS-B). For the refractive indices, we use literature values for λ = 620 nm, yielding n₁ = n_1^′ = 0.05 + 4.21i for silver,⁵⁶ n₂ = 1.464 for silica,⁶¹ and n₀ = 2.414 for diamond.¹⁶ A dipole orientation parallel to the interfaces (ϑ = 90°) is the most efficient configuration by symmetry argumentation. We name this optimal case as case (I). In addition, we also perform the optimization with a dipole polar angle of ϑ = 54.7°, corresponding to the actual orientation of the SnV⁻ center symmetry axis and thus the dipole axis in commonly available (001)-oriented diamond [case (II)]. The results of both optimizations are summarized in Table I.

The values in case (I) lead to the highest ξ value that is theoretically achievable, given the optical properties from the literature. With ξ = 2.01, we get an 87-fold enhancement of the collectible photon rate compared to the bulk case with ξ = 0.023. For the realistic case (II) of a non-parallel dipole orientation, ξ = 1.34 still corresponds to a 58-fold increase. Having identified the design as a cavity in Sec. II A, it is intuitive that the optimization tends to a very thin diamond membrane. More precisely, the stack forms a λ/2 cavity in cases (I) and (II), considering the effective index of the leaky modes and the correct penetration depth d_pen into the mirrors⁶² according to the following equation:

As an example, for case (I), we find n_eff = 0.33 for the s-polarized mode and d_pen = 52.1 nm (50.8 nm) for its penetration depth into the upper (lower) stack, summing up to 309.8 nm. This matches λ/2 = 310 nm very well. The thickness t₂ of the silica layer tends to λ/(4 · n₂), working as an anti-reflective coating.

To gain a deeper insight, Fig. 3(a) provides ξ in dependence of t₀ and h for case (I). As expected, high values of ξ, corresponding to the dipole being in resonance with the cavity, occur only for t₀ fulfilling Eq. (4), and the number of field nodes increases with t₀. We emphasize that in Fig. 3(a), we do neither plot the cavity resonances directly in terms of Purcell factor nor show an actual field distribution. ξ is shown as a measure of the collectible photon rate. It becomes obvious that an enhanced emission is given only for a good coupling to the cavity; thus, ξ maps the field distribution inside the cavity. For thicker diamond layers, additional modes with n_eff > 1.0 start to appear. As mentioned above, modes with n_eff > 1.0 are confined in the slab and do not contribute to ξ. Additionally, the coupling to the leaky modes reduces because of a reduced field enhancement for thicker cavities, comparable to an increasing mode volume, leading to a reduction of ξ.

Figure 3(b) shows p(n_eff) for case (I), indicating its physical limitations: The metallic mirrors introduce absorption losses and coupling to plasmonic resonances, i.e., surface plasmon polaritons (SPPs). SPPs can occur either at the silver–silica interface or at one of the diamond–silver interfaces. The former are excited by plane waves; compare the peak at n_eff = 1.5 in Fig. 3(b). The latter can only be excited by the near field of the dipole and are thus visible in the evanescent part of the angular power emission spectrum. Circumventing these plasmonic resonances is possible by increasing the optical distance of the dipole to the silver layers, yet the color center creation method limits us in this work: We utilize ion implantation, yielding a mean implantation depth for the tin ions of only d = 27.5 nm as we will discuss in Sec. III. In future implementations, this limitation can be overcome by either implanting at higher energies or by introducing buffer layers with a low refractive index, such as silica between the diamond and silver layers.^38,39 This, however, requires a more precise control over the layer deposition and, more challenging, a thinner diamond membrane.

A more severe limitation becomes evident when looking at the width of the cavity resonance for case (I) shown in Fig. 3(c). As designed, ξ peaks around the ZPL at 620 nm. Although the resonance is comparably broad (FWHM, 23 nm), it implies that we have to choose an excitation wavelength inside it because the cavity will reflect most of the incident light outside. A common experimental situation for the off-resonant excitation of many color centers in diamond is using a green laser; in this work, we employ a laser emitting at 516 nm. Consequently, for such a situation, we have to find a cavity length at which both the green excitation light and the ZPL of the SnV⁻ center are resonant. Sweeping t₀ while keeping the other parameters fixed as in case (I), we find t₀ = 609 nm as the smallest thickness at which the cavity is resonant for both wavelengths, defining this thickness as the working point of the cavity as an optical antenna for the off-resonant excitation. We redo the optimization to check whether for this thicker membrane and the limited implantation depth, other thicknesses of the thin silver and silica layer yield a better enhancement. Indeed, as can be seen from case (III) in Table I, the optimal silver layer thickness decreases here to t₁ = 24.9 nm, whereas the silica thickness stays nearly the same. With ξ = 0.28, the enhancement is still 12-fold, yet we lose a factor of 5 compared to case (II) with resonant excitation. To demonstrate the functionality, the off-resonant excitation should, however, provide a measurable change in the collectible photon rate. In future experiments, we may explore resonant excitation to benefit from the full potential of the design. The last row [case (IV)] of Table I lists the parameters of the fabricated antenna device presented below, deviating only slightly from case (III) and resulting in ξ = 0.214. Finally, it is worth mentioning that in all four cases, the cavity is only resonant for excitation light incident at the correct angle. This can be seen from the reflectance curves in Fig. 3(c), which show a dip in reflectance overlapping with the peak in ξ. Here, the reflectance is calculated assuming an angle of incidence covering the broad emission angle distribution that is inferable from the far field plot in the inset. The white ring in the far field plot indicates the collection angle covered with our experimentally used air objective with NA = 0.8. As the white ring includes most of the emitted light and the excitation is performed via the same objective, we can vice versa be sure to cover the required angles of incidence in excitation.

As the starting material, we use commercially available single crystal diamond grown by chemical vapor deposition (Element Six, electronic grade). The bulk (001)-oriented diamond plates are subsequently polished (Delaware Diamond Knives) to a final thickness of 30 μm and cut to a lateral dimension of 2 × 4 mm². After cutting and polishing, we perform a solvent cleaning procedure (2 × 5 min acetone + 2 × 5 min isopropyl alcohol with ultrasonic support) to remove residual contaminants from polishing. The solvent clean is followed by an annealing step (4 h at 1200 °C and <10⁻⁶ mbar) to reduce potential damage in the diamond. Prior to annealing, we purge the furnace with pure nitrogen. The annealing starts with a temperature ramp over 36 h to maintain pressures well below 10⁻⁶ mbar at any time. During annealing, the beforehand colorless and transparent diamond turns grayish because of non-diamond carbon forming at the surface. To remove this non-diamond carbon, we perform a tri-acid cleaning procedure [1 part nitric acid (65%):1 part sulfuric acid (95%):1 part perchloric acid (70%), heated to the boiling point] and a subsequent oxidation step (2 h at 450 °C in air at ambient pressure), ending up again with a transparent diamond. After this initial processing, the diamond plates are ready for the first dry etching step, which is performed on a reactive ion etching machine (RIE, Roth & Rau MicroSys 350) according to the recipe described by Jung et al.⁶³ Prior to etching, we glue the diamond plates to a clean silicon substrate and cover them with a quartz mask. Windows in the masks define the places where the diamond plates will be thinned down by the RIE process. To avoid local overetching and thus the formation of trenches, the windows in the masks possess angled sidewalls as described by Challier et al.⁴² We remove around 19 μm in the non-masked regions of the diamond plates. After etching, the diamond plates possess well-defined windows and the mask can be removed. The etched diamond plates are subsequently taken to an ion accelerator to perform the implantation of tin ions.

Limited by the analyzing magnet of the accelerator, we implant the tin ions at 80 keV, yielding a depth of 27.5 nm with an axial straggle of 5 nm according to the Monte Carlo simulation stopping ranges of ions in matter (SRIM⁶⁴). For the simulation, we assumed the density of diamond to be 3.52 g cm⁻³. We implant at a fluence of 10⁹ ions/cm², which is equal to 10 ions/μm². After the implantation, we remove the diamond plates from the silicon substrate and repeat the cleaning and annealing steps as outlined above to finally generate the SnV⁻ centers.

To yield diamond membranes with thicknesses below 1 μm in the windows, we perform a series of short etching steps from the not yet etched backside of the diamond plates without the need for masks. These etching steps are done with an inductively coupled plasma (ICP, Oxford Plasmalab 600) supported RIE process using an oxygen plasma.⁴² Every etching step is followed by a white light microspectrometry measurement (A.S. & Co. PDA Vis) to determine the thickness of the membranes.

Finally, we apply the coatings via electron beam evaporation (Pfeiffer Classic 500 L). For silver and silica evaporation, we use a deposition rate of 1 Å/s. Together with the diamond, we always add silicon substrates as control samples to the evaporation chamber to check the resulting thickness via a lift-off process and a subsequent measurement via atomic force microscopy (Park AFM XE-70). Additionally, the optical properties of the evaporated layers are determined via spectroscopic ellipsometry (HORIBA Jobin Yvon UVISEL-NIR) of these control samples. This thorough characterization enables us to feed the model with precisely measured thicknesses and the dispersion and absorption data of the actually fabricated device. Only for the diamond itself, we take the dispersion values provided by Element Six.¹⁶ 

To characterize the diamond membrane and the SnV⁻ centers inside prior to and after coating, we perform spectroscopy using a home-build confocal laser-scanning PL microscope. For excitation, a continuous-wave diode laser emitting at 516 nm (Toptica iBeam Smart) is used, which is coupled to a single mode fiber for the spatial cleaning of the beam. For spectral cleaning, a narrow bandpass filter is placed behind the fiber outcoupler. The collimated laser beam is guided via a dichroic mirror (cut-on wavelength: 567 nm) to an air objective (Olympus LMPlan FL 100x, NA = 0.8), which is also used to collect the PL from the sample. The sample itself is mounted on linear tables under ambient conditions. The PL is separated from the reflected laser light by the dichroic mirror, and an additional 610 nm long-pass filter suppresses the laser light. A 650 nm short-pass filter may be added to further narrow the detection bandwidth. The filtered PL is coupled into a single mode fiber, working as a confocal pinhole, and can be sent to a Hanbury Brown–Twiss (HBT) setup for photon statistics and generation of PL maps or to a grating spectrometer. The HBT setup involves a 50:50 beam splitter and two avalanche photon diode detectors (PerkinElmer SPCM-AQR-13),yielding a measured total detection time jitter of around 700 ps, which we take into account when fitting measured coincidence rates.

After several etching cycles, we end up with a diamond membrane possessing an average thickness well below 1 μm. In the white light microscopy image in Fig. 5(a), thin-film interference can be observed. The orientation of the fringes indicates a thickness gradient in the membrane, which we estimate to be around 1.8 nm change in thickness per μm change in the lateral position in the direction of the steepest slope. Although this gradient can be seen as a fabrication imperfection, it effectively provides us a varying cavity length.

Using microspectrometry, we can measure the average thickness in small areas of the membrane. This together with a model to calculate the color-dependent reflectance of the membrane enables us to match the interference fringes with certain thicknesses of the membrane. Prior to applying the coatings, we look for individual SnV⁻ centers in the thinnest part of the diamond membrane to measure their saturation properties. We find many bright spots, yet not all of them show a clear signature of single photon emission, i.e., a measured g⁽²⁾(0) value below 0.5, where the deviation to a perfect dip is fully explained by the detection time jitter and uncorrelated background emission from the diamond surface. Emitters with 0.5 ≤ g⁽²⁾(0) < 1.0 are not taken into account. Figures 4(a)–4(c) show a set of measurements performed on the same single SnV⁻ center in the bare membrane, representative for the emitters we include in the statistics. In the spectrum in Fig. 4(a), a clear signature of SnV⁻ center emission is given by the ZPL at 620 nm, which has a linewidth of around 6 nm at room temperature. Recording the detected photon rate I(P) for increasing excitation power P, we find a saturation behavior as shown in Fig. 4(b). We fit I(P) with a sum of three contributions,⁶⁵ namely, constant contribution D accounting for the detector dark counts (500 cps in total), a linear contribution c · P accounting for uncorrelated background fluorescence, and a non-linear saturation term modeling the actual PL of the SnV⁻ center, yielding the following equation:

For most of the investigated SnV⁻ centers, however, we are not able to satisfactorily fit the data with a positive linear background contribution constant c although we observe background fluorescence. The fits tend to the nonphysical regime of c < 0, which cannot be explained by the corresponding model. We attribute this behavior to two different observations. First, we see a locally varying blinking background fluorescence that randomly adds up to the measured photon rates. However, even for emitters where this blinking is not pronounced, we can hardly fit a positive c value to the measured data. We thus assume that the observed effects originate from a complex charge state dynamics at high excitation powers, yet the underlying mechanism is still unclear and beyond the scope of this paper. As a workaround, we show raw, uncorrected data and set a lower bound of c = 0 in the fits. The resulting values for I_sat, thus, may include background fluorescence, but they are reliable and suitable for the relative comparison of emitters in the bare membrane and in the antenna, as can be seen from the fit (red line) in Figs. 4(b) and 4(e), modeling the measured data well in both cases. For moderate excitation powers, we measure a photon autocorrelation with the HBT setup as shown in Fig. 4(c), yielding in this example g⁽²⁾(0) = 0.3. The detection time jitter is taken into account in the form of a convoluted fitting function. Because of the missing possibility to estimate the background contribution directly from the saturation measurement, we independently estimate the background by integrating a PL spectrum at a position nearby the emitter. For the exemplarily shown g⁽²⁾(τ) value in Fig. 4(c), the residual coincidences from the fit yield a ratio of the emitter PL to the total PL (emitter and background) of 0.87(4), in perfect agreement with a value of 0.88 calculated from an integration of the corresponding spectra.

In addition to the thickness of the diamond membrane, the final performance of the antenna strongly depends on the quality and thus the reflectance of the silver layers. Most probably, due to an insufficient calibration of the evaporator, we do not reach the target thicknesses of the layers. We end up with t₁ = 30 nm of silver, followed by t₂ = 128 nm of silica for the upper layers. The thick silver layer on the backside has a thickness of t₁′ = 160 nm.

The optical constants chosen for the optimization in Sec. II B are taken from the study by McPeak et al.⁵⁶ The optical properties of the thick silver layer we actually fabricate is close to their values; we measure n + ik = 0.07 + 4.10i at 620 nm. For the thin silver layer, however, we measure deviating optical properties, n + ik = 0.15 + 3.95i, resulting in a reduced performance of the antenna. The measured n = 1.45 value for silica at 620 nm is close to the literature value. Based on these measured optical properties and coating thicknesses of the evaporated layers, we can calculate ξ for the actually fabricated device for different membrane thicknesses t₀ and dipole emission wavelengths λ with d = 27.5 nm and ϑ = 54.7° fixed. This calculation is summarized in the plot in Fig. 5(d). Before investigating single emitters, we verify this plot and thus the model, in general, with the measurements of the cavity resonances at different positions and thus thicknesses of the membrane.

Exchanging the fluorescence filters in the detection path of the confocal microscope with a neutral density filter enables us to spatially map the reflectance and thus the cavity resonances for the excitation laser emitting at 516 nm. Figure 5(b) shows a scan over the whole membrane with applied coatings. It can clearly be seen that the detected photon rate, in this case corresponding to the reflected laser power, drops at sharply defined positions on the membrane, forming fringes of low reflectance. When we perform the same scan again with a 610 nm long-pass filter instead of a neutral density filter, we observe the inverted situation in fluorescence [see Fig. 5(c)]: Whenever the laser hits a resonance, the PL increases. The PL originates from the background fluorescence of the diamond membrane that couples to the cavity modes. As we know that the cavity has to be resonant to the laser at these positions, we can directly deduce the membrane thickness at these positions from the plot in Fig. 5(d). From the derived thickness, we can look up the other resonance wavelengths of the cavity for this thickness and compare those against the measured spectra of the enhanced background fluorescence. As can be seen from Fig. 5(e), the exemplarily shown measured spectra match the theoretical prediction of the cavity resonances, confirming the theoretical model based on the measured properties of the layers. At the position marked with the plus sign (+), both the excitation wavelength and SnV⁻ center emission are in resonance with the cavity. As we see in the following, this is the working point of the antenna.

Setting the detection bandwidth to 610–650 nm, we measure a PL map as shown in Fig. 6(a). In contrast to the map in Fig. 5(c), we now see pairs of resonances approaching each other spatially as the membrane thickness and thus the cavity length increase until they finally merge in a resonance, marking the optical antenna working point at a membrane thickness of around 609 nm. Each pair of resonances consists of one resonance for the excitation laser wavelength and one overlapping with the detection bandwidth. In the former case, the visible PL originates from the background fluorescence of the diamond membrane, which feeds the cavity resonance. The cavity resonance, on the other hand, overlaps to a certain degree with the narrow detection filter window, generating a detectable signal. These are the resonances we also see in Fig. 5(c). In the latter case, the cavity resonances are centered within the narrow detection bandwidth and the weak coupling of the laser is enough to induce a significant PL.

The brightest line in the PL map in Fig. 6(b) at a diamond thickness of around 609 nm indicates the spatial overlap of a cavity resonance for the excitation laser and detection bandwidth, yielding a strong PL signal. This is the working point of the optical antenna where we finally look for single emitters and their emission enhancement. From Fig. 5(d), we can extract a maximum ξ = 0.214 value at t₀ = 608.6 nm. For the emitters we measured in the bare membrane at an approximate thickness of around 190 nm, we calculate a collection factor of ξ = 0.022. Thus, we expect a nearly tenfold theoretical enhancement of ξ due to the optical antenna, compared to the bare membrane.

We search for single SnV⁻ centers at the working point, i.e., close to the bright fringe in Fig. 6(a). A finer scan, as can be seen in Fig. 6(b), reveals the existence of several individual spots that can be investigated for single photon emission. When photon autocorrelation shows a dip below 0.5 and can be fully explained with the uncorrelated background and detection time jitter, we measure the saturation behavior and add it to the statistics. Figures 4(d)–4(f) show an exemplary spectrum, saturation measurement, and photon autocorrelation measurement for a single SnV⁻ center at the working point. From the spectrum in Fig. 4(d), it is inferable that for this emitter, the spectral overlap of the cavity resonance and ZPL is very good, yielding a high saturation photon rate I_sat. Additionally, the laser power P_sat needed to saturate the emitter drops to very small values.

Figure 6(c) finally summarizes the main results of this work. Shown in red are the measured saturation parameters for the emitters in the bare membrane, with photon rates well below 100 kcps and a saturation power of 6 mW on average. Shown in green are all reliably identified single emitters in the antenna around the working point of d = 609 nm, yielding single photon emission rates up to 500 kcps. As mentioned above, we would expect an around tenfold enhancement of the photon rate at the antenna working point. There is, however, some other influence on the photon rate to consider when interpreting the data: First, it is evident that even for the emitters in the bare membrane, we find varying saturation properties. We attribute this mainly to varying quantum efficiencies. For the emitters in the antenna, these variations are even larger: as the emitters are not always spatially located exactly at the proper membrane thickness but may be slightly offset, we expect to see strong variations of the saturation parameters depending on the exact position of the emitter, yielding a reduced enhancement below ten-fold on average. Nevertheless, from Fig. 6(c), it is directly visible that P_sat is tremendously reduced for all emitters found. To quantify the effect on I_sat, we have to look at the underlying numbers in more detail. The lowest (highest) I_sat value of an emitter in the bare membrane is 20 kcps (95 kcps), whereas it is 93 kcps (495 kcps) for an emitter in the antenna, yielding an enhancement of 4.7 (5.2). The measured average saturation count rate on all seven emitters in the bare membrane (antenna) is 46 ± 27 kcps (271 ± 183 kcps), yielding an average enhancement of 5.9, matching the expectations well. Due to the small number of emitters investigated, the error bars on this statistics are fairly large. The reason for this low number of emitters that were suitable to be taken into account is not only the fact that not all the actually measured emitters were satisfying the restrictions on the g⁽²⁾(0) value. Moreover, during the measurement of the antenna, we found the coatings to severely degenerate. All the emitters in the statistics of the optical antenna have been measured before a break in order to examine the first data. After this two month break, the silver layers showed severe color changes, indicating degradation, although we applied a silica protection coating. As a consequence, no more reliable measurements could be carried out. Additionally, we tried to recycle the membrane by removing the silica and silver coatings via wet chemical processes, which unfortunately led to a destruction of the thin diamond membrane.

Thin free-standing single crystal diamond membranes are a key requirement for the creation of many advanced nanophotonic structures to enhance single photon emission or spin–photon interaction for color centers. We demonstrated the successful fabrication of such a membrane starting with a commercially available high-purity diamond material. Creation of single color centers inside the membrane was shown to be straightforward using ion implantation techniques and subsequent annealing. Transforming the thin diamond membrane into a cavity-based optical antenna requires, in principle, only established thin-film deposition and analysis technologies. Finally, the investigation of the color centers in the bare membrane and subsequently in the antenna has been carried out thoroughly in both cases taking great care to unambiguously identify single emitters. As a main result, we found a significant enhancement of single photon emission and reduction of saturation powers of the color centers coupled to the optical antenna compared to the uncoupled case in the bare diamond membrane, yielding count rates up to around half a million photons per second from a single SnV⁻ center. The theoretical framework predicts these enhancements to be in good agreement with the measured data. Additionally, the occurrence of resonances in PL and reflectance is well explained by the model.

We consider this work as a proof of concept with many options for improvement: Although the emitters proved to be photostable even at high excitation powers, we observe randomly switching background fluorescence from the membrane, severely reducing the signal-to-background ratio of the actual emitter PL. This blinking background is currently the main limitation for the comparably low single photon purity. We observe it independently of the color center PL on all samples that have been plasma etched and subsequently annealed and cleaned as described in this work. We do not further observe it when focusing deep into the diamond, indicating that it originates from the surface. It has been shown that a hydrogen termination⁶⁶ or a disordered oxygen termination⁶⁷ of the diamond surface may act as a source of charge traps, leading to random charge fluctuations upon laser excitation. Promising options to remove this potential source of the blinking background fluorescence are more sophisticated post-processing techniques, e.g., oxygen annealing⁶⁷ or a treatment with a purely inductively coupled oxygen plasma.^68,69 Both methods have been shown to introduce a highly ordered oxygen termination, severely enhancing the charge state stability and spin coherence of shallow color centers. Moreover, the vanishing linear background contribution in the measured saturation curves gives rise to a different emission dynamics compared to the SiV⁻ center. For more sophisticated applications using SnV⁻ centers, a thorough investigation of this potentially novel photophysics will be mandatory.

As already indicated in the main text, the coating of the diamond membranes appeared to be sufficient for our purposes in the beginning, yet the degradation of the silver layers proved us wrong. A possible explanation for this degradation is the weak chemical bonding between the silver and silica layers: It is well known that the adhesion between noble metals and oxides, such as silica, is comparably weak already directly after deposition and degrades over time.⁷⁰ Specifically, thin silver layers are known to be susceptible to dewetting even at room temperature.⁵⁶ A commonly used adhesion promotion can be established via a thin titanium or chromium layer between the oxide and the noble metal. In future work, we may thus need to include such an additional layer in our antenna design. As the comparably low reflectance of chromium or titanium may reduce the final performance,³⁸ one could also think of protecting the upper silver layer with an additional gold layer. The same consideration holds for the adhesion of silver to diamond, which is also predicted to be comparably weak.⁷¹ In addition, for this interface, we may consider adding a thin layer of a carbide-forming and thus adhesion-promoting metal, such as titanium. Finally, the thickness gradient in the membrane provides us a varying cavity length but limits the areas in which the cavity operates as an optical antenna. This raises the question which gradient can be tolerated at most. Our model covers only completely planar stacks, and it is obvious that a wedged membrane will, at some point, severely change the properties of the cavity. Under the assumption that the gradient in the first order only shifts the resonance wavelength, we can extract this shift from our model to be 14 nm for a change in the thickness of the membrane of 10 nm. With the confocal microscope, we collect only the PL from a spot with a diameter of around 800 nm. If we accept a change in the resonance wavelength of 6 nm within this spot diameter, equal to the linewidth of the SnV center, we find an upper bound for the gradient of 4.4 nm change in thickness per μm change in the lateral position. With the estimated 1.8 nm per μm gradient we achieve here, we were thus able to show the successful antenna operation. Anyway, the long-term goal is surely to produce membranes with a well-defined thickness and with well-defined gradients in areas spanning hundreds of micrometers to fully harness the potential of this planar design. A first step toward dry etching processes that actively planarize diamond membranes has already been shown,⁷² demonstrating the feasibility of such approaches.

In addition to the technical imperfections summarized above, we have successfully demonstrated a design for an optical antenna based on a planar Fabry–Pérot cavity, which is able to boost the emission rate of a single SnV⁻ center even in the worst scenario (case III in Table I) to around half a million photons per seconds at the detectors in saturation. In future work, we focus on near-resonant and resonant excitation (case II in Table I), which would allow for photon rates on the order of several million counts per second. Additionally, a reduction of the background fluorescence and thus an improvement of the single photon purity should be feasible by employing surface treatments as described above. Already at room temperature, such high photon rates together with a reasonable single photon purity would pave the way toward applications in quantum metrology or quantum sensing. For the implementation of an efficient spin–photon interface, however, cryogenic temperatures are unavoidable. Even for the SnV⁻ center with favorably large ground state splitting, the need for cryogenic operation to enable long spin coherence times is unquestioned. Because of the monolithic design and thus the absence of moving parts, the design presented here may also perform well at low temperatures. Operation of the antenna under cryogenic conditions and resonant excitation will consequently fully harness the potential of this comparably simple nanophotonic design.

We thank B. Lägel and S. Wolff (Nano Structuring Center, NSC, University of Kaiserslautern) for helpful discussions on evaporation and use of their facilities. We also thank R. Hensel (Leibniz Institute for New Materials, INM, Saarbrücken) for access to the Oxford ICP RIE and E. Neu, M. Challier, O. Opaluch, and J. Görlitz for helpful discussions on etching and spectroscopy. This research received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 820394 (ASTERIQS), The EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme (Project No. 17FUN06 SIQUST), and the German Federal Ministry of Education and Research (Bundesministerium für Bildung und Forschung, BMBF) within the project Q.Link.X (Contract No. 16KIS0864).

The data that support the findings of this study are openly available in Zenodo at http://doi.org/10.5281/zenodo.5055763.⁷³