High finesse microcavities in the optical telecom O-band

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 single-photon 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 $P=3ϒη/4π2$⁠, 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. 1(a).

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 $1×108$⁠. 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.⁴² 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.⁴³ Moreover, PhC cavities from 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.^44,45 The performance of spin centers can, furthermore, be adversely impacted in PhC structures by the unavoidable proximity to the surface.⁴⁶ The emitters can be placed outside the PhC cavity, albeit at the cost of a reduced coupling strength and additional optical losses.⁴⁷ 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 micro-toroid and micro-sphere cavities, which have larger mode volumes usually on the order of several tens of $λ3$ 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.⁴⁸ The open-access cavity allows one 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. 1(a)].

Here, we report on progress in creating a scalable architecture for open-access FP micro-cavities with high quality factors and small mode volumes, and the reported $Q/(V/λ3)≈1.33×105$ value exceeds the performance of all open-access optical microcavities to date.^34,37,49 Our microcavity mirrors are coated for the telecom O-band wavelength range (⁠$1.26−1.36 μm$⁠), where high-performance, open-access microcavities have not been demonstrated so far [Fig. 1(b)]. We have chosen this band since several promising emitters exist in this spectral region such as the vanadium (V) center in silicon carbide (SiC)^50,51 and the G and T centers in Si.^52–54 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 

An important figure of merit for FP cavities is the finesse $F$⁠, which is the ratio of the cavity free spectral range $ΔνFSR$ to the linewidth of the resonance modes $ΔνFWHM$⁠, 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 is 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, and 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 w₀ 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 $zr=πw02/λ$ of the cavity mode of the Gaussian beam, the radius of curvature (ROC) is then given by $R=z[1+(zr/z)2]$⁠, 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 Ref. 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 $3×3 mm2$⁠, 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 and 12 ppm results in a coating-limited finesse of $5.2×105≤Fmax≤6.3×105$⁠. 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 $∼0.3$° 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. 3(a)] and from the measured radius of the curvature. The ROC is related to the effective cavity length L by

where (p, q) is the Hermite–Gaussian beam order, $Δνp+q$ is the frequency difference between $TEM0,0$ and $TEMp,q$ Gaussian modes, and c is the speed of light. With Eq. (4), the calculated effective length of the shortest cavity that supported a $TEM0,0$ 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 $ΔνFSR=c/2L=(20.3±1.4) THz$ [see Fig. 3(a)]. Hence, the mode volume is $V=(30.8±5) λ3$⁠. 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 in the mode volume.³⁹ 

The cavity linewidth was measured by scanning the probe laser over the fundamental $TEM0,0$ 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. 3(b)]. The highest observed cavity finesse for the shortest possible cavities was $F≈3.5×105$⁠, which corresponds to a round trip loss of 18 ppm. The finesse is $∼45%$ lower than 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 one 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 us 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 $F≈4.9×105$⁠, which is close to $80%$ of the upper theoretical limit (see Table I, 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 $F≈1.33×105$⁠. 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 the cavity length, and Fig. 4 shows a similar degradation with increasing cavity length. For cavity lengths between $≈15 and 35 μm$⁠, 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 the ideal shape, which becomes non-negligible for the larger spot sizes resulting from larger mirror separations.

To investigate this hypothesis, we simulated the impact of a non-parabolic mirror shape on the cavity finesse using a transfer matrix method.⁵⁶ The mirror shape deviations from the ideal parabolic shape were extracted from white light interferometer measurements Fig. 4(a) and averaged over multiple mirrors, which showed that the ROC varies laterally on the mirror and is larger in the central area of the mirrors. In the case of an ideal parabolic mirror and a lateral mirror size significantly larger than the beam size (i.e., negligible clipping losses), the losses would remain independent of the cavity length up until the ROC (critical length). Assuming a parabolic shape, but with the diameter of the mirror limited to $50 μm$ in the simulation, clipping losses become dominant and the finesse starts to decrease around 70% of the critical length. Finally, if the measured non-parabolic mirror profile is included, the finesse decreases significantly for cavities longer than 35% of the ROC, in good agreement with the measured performance, as shown in Fig. 4(b).

In conclusion, we have built high finesse optical Fabry–Pérot 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-ideal 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 $ϒ=1.33×105$⁠, more than two times larger than other types of open-access microcavities. This improvement is highly desirable for spin-photon interfaces, cavity cooling of nanoparticles, and other applications requiring extreme enhancement of the interaction of light and matter.

J.F. acknowledges funding by the Czech Science Foundation GAČR (No. 19-14523S) and OeAD-GmbH (Aktion Österreich-Tschechien Program No. ICM-2019-13725); S.P. acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 801110 and the Austrian Federal Ministry of Education, Science, and Research (BMBWF). M.T. acknowledges funding from Austrian Science Fund (FWF): Nos. I 3167-N27 and P 27297-N27 and from the European Union's Horizon 2020 research and innovation program under Grant No 862721 (QuanTELCO).