Fabrication of hybrid Fabry-Pérot microcavity using two-photon lithography for single-photon sources.

: For an efficient single-photon source a high-count rate into a well-defined spectral and spatial mode is desirable. Here we have developed a hybrid planar Fabry-Pérot microcavity by using a two-photon polymerization process (2PP) where coupling between single-photon sources (diamond colour centres) and resonance modes is observed. The first step consists of using the 2PP process to build a polymer table structure around previously characterized nitrogen-vacancy (NV) centres on top of a distributed Bragg reflector (DBR) with a high reflectivity at the NV zero-phonon line (ZPL). Afterwards, the polymer structure is covered with a silver layer to create a weak (low Q) cavity where resonance fluorescence measurements from the NVs are shown to be in good agreement with analytical and Finite Difference Time Domain (FDTD) results.


Introduction
Solid-state single-photon sources are considered one of the most promising candidates for single-photon emission [1]. Quantum dots (QDs) and colour centres in crystals are among the most studied, although colour centres in diamond such as NV and Silicon-Vacancy (SiV) centers have the main advantage of emitting single-photons at room-temperature, convenient for quantum photonic integration and applications. An ideal single-photon source should emit photons at a high-rate into a single mode, however, the rate of emission is limited by the spontaneous decay of the source and the light is emitted into the dipole emission pattern covering almost a full solid angle of 4π [2]. Different ways have been developed through the years to increase the emission rate and reduce the angle of emission of the sources [3]. Geometrical approaches exist, such as solid immersion lenses (SILs) [4,5] along with cavity quantum electrodynamics (CQED) approaches that rely on the Purcell enhancement by using resonant structures to selectively enhance emission into relevant modes [6,7]. Tunable Fabry-Pérot cavities with Bragg reflectors as mirrors [8][9][10][11] and photonic crystals [12][13][14] have also proved to be a viable option since small mode volumes can be achieved [15]. Using polymer to make structures for both approaches (geometrical and CQED) creates a new alternative for the realization of photonic and resonant devices of nearly arbitrary shape. By a process called two-photon polymerization (2PP), in which only the liquid polymer exposed to a specific wavelength gets solidified, solid immersion lenses [16] and resonant disks [17] have been fabricated with quantum dots and nanodiamonds inside the structures, respectively. These polymer structures hold the potential for the realization of a fully integrated quantum optical chip incorporating single photon-emitters, SILs, resonant cavities, polymer waveguides [18] and polymer photonic crystals [19,20].
Here we present a new approach to build rapid and low-cost Fabry-Pérot cavities (with colour centres inside) combining the advantages of polymers, such as the ability to fabricate any geometrical shape desired, with the high-reflectivity of DBRs and metals to form a "hybrid" microcavity. The advantages and limitations of the newly developed hybrid Fabry-Pérot microcavities will also be mentioned.

Experimental setup
To find and characterize NV centres, we worked with a homebuilt confocal microscope  We then expect similar enhancement or inhibition of the fluorescence from each dipole due to this intracavity field [24,25].

Fabrication and measurements
The printing of 3D micro-structures with a commercially available direct laser writing system (Photonic Professional, Nanoscribe GmbH) uses the 2PP process [ Fig. 3(a)]. This method consists of illuminating a liquid photopolymer photoresist with light at 780 nm. When the photopolymer absorbs two photons simultaneously it triggers a chemical reaction that starts the solidification of the material.
As our next step, through a 2PP process, we built a polymer 'roof' of 15 Fig. 4(a)] to hold it at a determined height on top of the pre-selected ND [ Fig. 1(b)]. Reference marks were previously made on top of the DBR [ Fig. 3(b)] (also with the 2PP process) to localize and mark the position of the pre-selected ND. Afterwards we added a silver layer of 20 nm (thermal evaporative deposition) on top of our polymer to end up with a fully-developed hybrid Fabry-Pérot cavity with a ND inside [ Fig. 4]. White light reflectivity spectral measurements [ Fig. 5] for the hybrid planar cavity and substrate DBR was made with a home-built Fourier imaging spectroscopy system, which uses a high NA lens (0.75) to focus on samples and performs angular spectrum measurements as per angle [19]. Reflection at normal incidence was measured with a white light source and a spot size of 2.    Fig. 4. A free spectral range (frequency separation between successive longitudinal modes) of 25 FSR THz = was measured from Fig. 5(a) and a total cavity length of 6 total L m μ = is calculated from / 2 total FSR c L = [26], where c is the lightspeed in vacuum. Finally, in contrast with the preliminary results [ Fig. 2(a)], we measured the fluorescence of the pre-selected quantum emitter, showing now a resonant behavior [ Fig. 6(a)] due to the hybrid planar cavity where the peaks shown are the actual resonant modes of the cavity. Figure 6(a) also shows FDTD simulations in order to compare the experimental performance of the structures to an idealized performance. For these FDTD simulations performed, the polymer was treated as a lossless and non-dispersive dielectric so they don't take into account losses due to absorption or scattering due to surface roughness of the dielectric. We use a thickness of 2  Here there is broadening of the fluorescence enhancement due to the wide angle of emission and the slight curvature of the upper mirror. The FDTD simulation was restricted to a dipole parallel to the DBR in a 5 5 x m μ planar cavity for a reasonable computation time. Moreover, a ( ) 2 g measurement was also made on the pre-selected emitter [ Fig. 6(b)]. A similar excitation power was used to obtain this measurement, however, the cavity is not resonant at the excitation wavelength, and therefore much of the incident light is reflected at the silver mirror. Hence, count rate from the NV centre is reduced while extra background is seen from the polymer and silver layers. Thus the ( ) 2 g measurement is highly noisy and difficult to correct from background but a reduced visibility antibunching signal can still be seen.

Analytical model
We also compared our experimental results with an analytical model [ Table 1], where its main advantage relies on its simplicity to find the resonant modes of our cavity. For the analytical model, we use the resonant condition for a stable cavity [28], considering the extra phase shift ( ) 2 2 k L introduced by the polymer and using the effective mirror model [ Fig. 7 for the DBR [29] we found the total phase shift in our cavity for a one-way trip to be: where b a n n n Δ = − is the difference of index of refraction for the DBR alternating layers.

Conclusions
In summary, we have shown the fabrication steps for a hybrid planar microcavity deterministically placed around a pre-selected ND where FDTD and analytical results are in good agreement with the measured resonant modes, giving confidence on the resonant nature of our cavities. This simple analytical model could also be used, by fine-tuning the height of the cavity ( ) 1, analytical L and polymer thickness ( ) 2 L , to find the desired resonant modes prior to the fabrication process of the cavity. However, polymer, known for its malleability, still presents challenges for the fabrication of photonic integrated optical structures, where scattering and absorption challenges must be overcome in order to increase the optical quality of our hybrid microcavities. Post-processing of the cavities (e.g. focused ion beam nano-polishing) could be applied to minimize these issues. A direct comparison of the pre-selected ND fluorescence before and after the fabrication process of the cavity reassures the resonance behaviour predicted by the white light spectral measurements of Fig. 5. To the best of our knowledge, this is the first example of the use of 2PP lithography to fabricate a hybrid planar Fabry-Pérot microcavity showing evidence of resonance fluorescence even with a weak (low-Q) resonant cavity. This fabrication process opens new possibilities for more exotic structures for the emission enhancement of single-photon sources.