High finesse microcavities in the optical telecom O-band

Optical microcavities allow to strongly confine light in small mode volumes and with long photon lifetimes. This confinement significantly enhances the interaction between light and matter inside the cavity, with applications such as optical trapping and cooling of nanoparticles, single-photon emission enhancement, quantum information processing, and sensing. For many applications, open resonators with direct access to the mode volume are necessary. Here we report on a scalable, open-access optical microcavity platform with mode volumes<30 $\lambda^3$ and finesse approaching $5x10^5$. This result significantly exceeds the highest optical enhancement factors achieved to date for Fabry-P\'erot cavities. The platform provides a building block for high-performance quantum devices relying on strong light-matter interaction.


I. INTRODUCTION
The confinement of the electromagnetic field inside a small volume is key in building devices with high quantum efficiency, by enhancing the interaction strength between photons and matter. For instance, cavities can increase the singlephoton count rate from an emitter due to the Purcell effect 1 . More generally, the strong confinement enables coherent interactions of light and atoms in cavity quantum electrodynamics (CQED) 2,3 , or with dielectric particles in cavity quantum optomechanics 4 .
In many applications, the performance of the device depends on the spatial confinement of the electromagnetic field given by the volume of the cavity mode V and the temporal confinement of the field given by the quality factor Q. Thus the figure of merit is the optical enhancement given by the relation with the refractive index of the cavity medium n and the wavelength λ . This term is a key quantity in the coherent interaction of nanoparticles, atoms, or molecules with photons. An important example is the well known Purcell factor, which can be expressed in terms of the optical enhancement factor as P = 3ϒη/4π 2 , where η is the branching ratio of the relevant two-level transition. Many types of optical resonators exist, such as Fabry-Pérot (FP), micro-sphere, micro-disc or photonic crystal (PhC) cavities, that can be used to enhance light-matter interactions 5,6 . The comparison of Q and V values for several types of microcavities found in the literature is shown in Fig. 1a. a) These authors contributed equally to this work b) Correspondence should be sent to: michael.trupke@univie.ac.at PhC cavities confine light in a high index material and typically feature a mode volume on the order of (λ /n) 3 . There are numerous realizations of PhC cavities, ranging from 2D PhCs with missing holes, PhC waveguides with local modification of the holes' position or diameter, or 1D PhC nanobeam cavities. The smallest optical mode volumes, far smaller than a cubic wavelength, can be achieved in bowtie photonic crystal structures 7 , which enable a maximal optical enhancement on the order of 10 8 . The monolithic structure of PhC cavities reduces the mechanical noise and the presence of an optical bandgap may reduce undesired radiative transitions.
The optical performance in photonic crystal cavities is outstanding for many applications, but they also present several practical limitations. Spectral tuning of the PhC cavity modes is cumbersome and requires technically challenging procedures, e.g. post-fabrication etching 41 . This prevents fast response to changes in the surrounding environment required for frequency locking and stabilization. Approaches to achieve in-situ tunable operation have been implemented. However, these methods mostly enable only slow tuning or a moderate tuning range 42 . Moreover, PhC cavities form closed systems and emitters must be placed directly inside the PhC cavity material to achieve maximal coupling. Precise placement of emitters in PhC cavities is extremely challenging, and the emitters' properties may be negatively affected by material defects and stress originating from the fabrication process 43,44 . The performance of spin centers can furthermore be adversely impacted in PhC structures by the unavoidable proximity to the surface 45 . The emitters can be placed outside the PhC cavity, albeit at the cost of a reduced coupling strength and additional optical losses 46 . Finally, coupling of light into and out of the PhC cavity requires careful mode matching and poses significant challenges for achieving a high collection efficiency of light at the output. Similar issues affect microtoroid and micro-sphere cavities which have larger mode volumes, usually on the order of several tens of λ 3 , compensated by correspondingly higher Q-factors 32 . In contrast, FP cavities offer high versatility, enabling an open-access system that can be tuned both broadly and precisely by changing the mirror spacing, which can be done in a scalable manner 47 . The open-access cavity allows to place atoms, molecules, nanoparticles, or thin solid membranes inside the cavity. However, this comes at the expense of larger cavity mode volumes when compared to PhC cavities, which cannot be compensated fully by the generally higher quality factors of FP cavities (See Fig. 1a). We increase the calculated cavity mode volume of FP cavities by assuming that the mode penetrates to a depth of 0.8λ into each mirror 48 and the cavity is effectively longer than what follows from the free spectral range.
Here, we report on progress in creating a scalable architecture for open-access FP micro-cavities with high quality factors and small mode volumes. To the best of our knowledge, the reported Q/(V /λ 3 ) ≈ 1. 33 (Fig. 1b). We have chosen this band since several promising emitters exist in this spectral region, such as vanadium (V) center in silicon carbide (SiC) 50,51 and the G and T centers in Si [52][53][54] . SiC and Si are stable host environments and offer superb optical properties in wafer-scale substrates. They are therefore prime candidates for implementation in long range quantum communication networks 55 .

II. RESULTS
An important figure of merit for FP cavities is the finesse F , which is the ratio of the cavity free spectral range ∆ν FSR to the linewidth of the resonance modes ∆ν FW HM , and is directly related to the quality factor Q and to the total round-trip optical losses l rt : where λ is the cavity mode wavelength and L the effective optical length of the cavity (approximately equal to the mirror spacing). The total round-trip losses comprise: scattering losses that depend on the surface roughness of the cavity mirrors, clipping losses caused by the lateral size and shape of the mirrors, absorption losses inside the cavity and by the transmission of the input/output mirrors. The finesse F is proportional to the number of round trips before a photon leaves the cavity or is lost via dissipation, while the Q-factor is proportional to the average number of optical cycles before a photon is lost from the cavity, and for the shortest possible cavity where L = λ /2, the finesse becomes equal to the Q-factor. In the paraxial approximation, the effective cavity length L and the radius of curvature R of the mirrors determine the mode properties of the resonator. The beam waist w 0 defines the mode volume V given by with the wavelength λ and α = {1, 2} for plano-concave (PC) and concave-concave (CC) cavities, respectively. With the Rayleigh range z r = πw 2 0 /λ of the cavity mode of the Gaussian beam, the radius of curvature (ROC) is then given by , where z is the distance measured longitudinally from the beam waist.
Short cavities with a small beam waist naturally require a small ROC, which is challenging to fabricate with high precision. Our micromirrors were fabricated from four-inch silicon wafer substrates by a two-step dry etching process, followed by oxidation smoothing (see Wachter et al. 37 for details). The mirror shape was determined using a white light interferometer (Filmetrics Profilm 3D) to extract R. The structured substrate is diced into chips of 3 × 3 mm 2 which host hundreds of mirrors with a square pitch of 125 µm (see Fig. 2). The Si chips are coated with a dielectric high-reflectivity (HR) Bragg multi-layer coating with a specified transmission of 5 ppm transmissivity at 1280 nm and an excess coating loss of up to 1 ppm per mirror. The total coating loss between 10 ppm and 12 ppm results in a coating-limited finesse of 5.2 × 10 5 ≤ F max ≤ 6.3 × 10 5 . The backside of the Si chips is coated with a broadband anti-reflection (AR) layer. To characterize the cavities, we used a continuously tunable, narrow linewidth laser source (EXFO T100S-HP). The laser light is coupled into the cavities in free space and the reflected laser light is routed through a fiber circulator and detected by a high-bandwidth photodiode.
The shortest cavities are assembled in a PC configuration by gluing two mirror chips together. The length of each cavity is fixed, but in order to vary the resonance frequency of the cavities across the array, a spacer with ∼ 16 µm thickness was inserted between the Si chips on one side, forming a narrow wedge with ∼ 0.3 degrees tilt. The curved mirrors have R = (69.3 ± 8.3) µm and the depth of the mirrors is ≈ 4.5 µm. The cavities are characterized by scanning the laser wavelength over a broad range and recording the position and spectral distance between fundamental and higher order modes. The FSR for such short cavities could not be observed directly as it exceeds the wavelength tuning range of the laser. Instead, we determined the effective cavity length from the spectral position of fundamental and higher order modes (see Fig. 3a), and from the measured radius of curvature. The ROC  Table I is related to the effective cavity length L by: where (p, q) is the Hermite-Gaussian beam order, ∆ν p+q is the frequency difference between TEM 0,0 and TEM p,q Gaussian modes, and c is the speed of light. With Eq. (4) the calculated effective length of the shortest cavity that supported a TEM 0,0 mode at 1275.7 nm and a mode with p + q = 1 at 1263.5 nm was L = (6.7 ± 0.5) µm, which corresponds to ∆ν FSR = c/2L = (20.3 ± 1.4) THz (see Fig. 3a). Hence the mode volume is V = (30.8 ± 5) λ 3 . We conservatively reduce the optical enhancement factor for all FP cavities by assuming that the mode penetrates to a depth of 0.8λ ≈ 1 µm into each mirror leading to an increase of the mode volume 48 . The cavity linewidth was measured by scanning the probe laser over the fundamental TEM 0,0 cavity resonance while a 200 MHz sideband modulation was applied to the carrier, and the observed linewidth is compared to the known splitting of the sidebands (see Fig. 3b). The highest observed cavity finesse for the shortest possible cavities was F ≈ 3.5 × 10 5 which corresponds to a round-trip loss of 18 ppm. The finesse is ∼ 45% lower then the theoretical upper limit and the excess dissipation of ≈ 8 ppm is attributed to the combination of slight distortions of the curved mirror shape, the tilt between mirrors, and scattering losses on the mirrors. An overview of all measured cavity configurations can be found in Table I.
We also assembled cavities with variable mirror spacing by mounting one of the mirrors on a piezoelectric actuator, enabling rapid tuning of the resonance frequency. Moreover, the chips can be shifted and tilted relative to each other, which allows to assemble CC cavities and also to better compensate for the losses originating from the non-ideal mirror tilt. For this setup we measured PC and CC cavity configurations with L ≥ 15 µm. These longer cavities allowed to directly measure the free spectral range and determine the cavity length. We found good agreement between the effective cavity length L obtained via the FSR and the value computed using Eq. (4). For the actuated cavities we used mirrors with larger R = 105.6 µm with a mirror depth of 8.5 µm, giving the minimum spacing between the mirror chips of ∼ 6 µm. This configuration reaches F ≈ 4.9 × 10 5 which is close to 80% of the upper theoretical limit (see Table 1: PC-a). The corresponding losses 13 ± 3 ppm are dominated by the mirror transmissivity. For the CC cavity configuration we observed slightly lower finesse values of F ≈ 1.33 × 10 5 . We presume that this reduction is due to transverse misalignment of the cavity chips with respect to each other. The finesse of all measured cavity configurations degrades with increasing cavity length (Table I). To measure this systematically we used piezo actuated cavities and measured the optical finesse as a function of cavity the length, Fig. 4 shows a similar degradation with increasing cavity length. For cavity lengths between ≈ 15 − 35 µm, the finesse decreases slowly with increasing cavity length. This behavior can be explained by an increasing beam waist on the curved mirror for longer cavities, which increases the scattering, absorption and clipping losses. This moderate downward trend is followed by a sharp drop of the finesse for cavity lengths longer than ≈ 35 µm and no resonance could be observed for cavities longer than ≈ 40 µm. The losses at L ≈ 39 µm amount to 50 ppm and exceed the other types of losses, even considering the imperfections listed above (blue data set in Fig. 4.) The finesse could not be measured for cavities longer than ≈ 40 µm as the contrast of modes measured in reflection was too small. It is likely that the extra losses are induced by the deviation of the cavity mirrors from an ideal parabolic shape, which becomes non-negligible for the larger spot sizes resulting from larger mirror separations.

III. CONCLUSION
In conclusion, we have built high finesse optical Fabry-Perot microcavities in the telecom wavelength O-band at 1280 nm. We showed that the finesse remains high for a cavity length of up to ≈ 35 µm or L/R ≈ 0.35, where losses due to a non the parabolic mirror shape become dominant. The cavities are suitable for enhancement of photon count rates from vanadium in silicon carbide (SiC) or G centers in silicon. The extracted optical enhancement value reaches ϒ = 1.33 ×  4. (a) White light interferometer measurement used to determine the mirror radius of curvature of mirror PC-a. The fit is a two dimensional parabolic fit with a higher order correction term. The dependence of the finesse on the cavity length for PC-a (red) and PC-a2 (blue, mirror with additional excess losses).
microcavities. This improvement is highly desirable for spinphoton interfaces, cavity cooling of nanoparticles, and other applications requiring extreme enhancement of the interaction of light and matter.