1. Introduction

The recent progress in quantum technologies has increased the demands for a robust scalable platform to realize an efficient quantum interface between light and matter. Building such interface is important for many applications ranging from optical sensing and metrology [1] to quantum information and quantum computation [2]. One of the most promising type of platforms involves an atom coupled to an optical resonator to allow a coherent energy exchange in a cavity QED system [3–5]. Towards this goal, several micro-cavities have been developed including Fabry-Perot cavities [6,7], silica microspheres [8], and microtoroids [9]. Despite the fact that the customary micro-cavities possess high quality factors, their relatively large volume makes the integration of many devices in one chip very challenging. In addition, the large mode volume leads to a small cooperativity that results in an inefficient atom-photon interaction. Photonic crystal (PhC) cavities have recently emerged as a scalable platform for efficient light-matter interactions due to their small mode volumes accompanied with high quality factors [10–14].

In this framework, Silicon nitride offers many advantages over other alternative materials, mostly due to its wide band gap and compatibility with standard CMOS processes. However, the moderately low index of refraction has limited the quality factor of PhC cavities on $\textrm{Si}_{3}\textrm{N}_{4}$ films to Q < $10^4$ in visible wavelengths [15–20]. In this report, we exceed that limit and demonstrate nanobeam PhC cavities with Q > $10^4$. Unlike the previous report [21], our devices are characterized by accurate measurements that are suitable for further QED experiments.

On the other hand, nanobeam PhC cavities are not inherently suited to the free-space optical coupling or fiber coupling due to the mismatch in the mode size and the effective refractive index. Previous work have used either notches [22] or inverse-designed vertical couplers [23] for the free-space interface, and end-fire technique for the fiber interface [24]. The most efficient technique is based on evanescent coupling from a biconical fiber to a suspended waveguide with a coupling efficiency of $90\%$ [25,26]. This technique was used recently to collect single-photon with a record efficiency of 10$\%$ [27]. Here, we employ the same principle using a single-sided optical fiber tip and demonstrate a coupling efficiency of 96$\%$, similar to detached devices [28].

2. Silicon nitride nanobeam photonic crystal cavities

For the demonstration detailed here, we employed two nanobeam designs which are based on tapering the nanobeam width smoothly while other parameters remain constant, as depicted in Fig. 1(a). We note that both devices are designed based on the quadratic tapering method which is meant to generate a Gaussian-like field profile inside the cavity [31,32]. We focused only on TE modes since the corresponding TM bandgap is almost vanished in both devices. Figure 1(b) and 1(c) show the band structure corresponding to device A and device B, respectively. The size of the band gap for silicon nitride devices is small compared to that for high refractive index materials considered in original designs. In addition, the resonant frequencies shift closer to the light line especially for device B, indicating extra radiation loss. Nevertheless, this can be mitigated by increasing the width of the cavity or reducing the holes radii. The parameters have been adjusted such that the simulated intrinsic quality factor for both devices reaches $\sim 10^6$. In this work, the spacing between holes for device A (device B) is set to $0.21 \mu$m ($0.22 \mu$m) to adjust the cavity resonant around 602 nm, the zero phonon line emission of the germanium-vacancy color center in diamond [33]. The cavity transmission and quality factor dependence is shown in Fig. 1(d). It can be seen that the quality factor in device B exceeds the other one to some extent, similar to the case for gallium phosphide substrate [30]. The trade-off, however, is that device B is more sensitive to the fabrication imperfections.

 

Fig. 1. (a) Sketch of $\textrm{Si}_{3}\textrm{N}_{4}$ nanobeam PhC cavity design adopted from [29] for device A, and from [30] for device B. for device A and device B, respectively. (b)&(c) The corresponding band structure for TE modes calculated by FDTD simulations. The dashed line marks the resonant frequency. (d) Transmission dependence on $Q/V$ value with the following parameters: the initial width $\textrm{W}_{0}/\textrm{a} = 1.5$, the final width $\textrm{W}_{\textrm{f}}/\textrm{a} = 2$, and the hole radius r/a = 0.3.

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We carried out the fabrication on 200 nm thick stoichiometric LPCVD $\textrm{Si}_{3}\textrm{N}_{4}$ membrane deposited on Si wafer (Rogue Valley Micro Devices). Polymethyl methacrylate (PMMA) is first spun directly on top of the silicon nitride membrane without a metallic layer or conductive polymer [34]. The resist is then patterned using an EBL system (TESCAN MIRA3) with an accelerating voltage of 30 kV, before developed in MIBK developer mixed with Isopropyl solution 1:3. Following the EBL process, the pattern is transferred to the $\textrm{Si}_{3}\textrm{N}_{4}$ using $\textrm{CHF}_{3}$-based dry etching (ICP-RIE, Oxford Instruments). After stripping the resist, $30\%$ KOH solution is used to etch the exposed silicon at $100 ^{\circ }\textrm{C}$ for 10 minutes. Figure 2 displays SEM images of the suspended devices fabricated in a silicon nitride membrane. Each nanophotonic device contains a nanobeam cavity coupled to a tapered waveguide and connected to a nearby surface at both ends. The dimensions of the waveguide taper and its final width are 12 $\mu$m and 150 nm, respectively. These parameters were optimized based on the fiber-waveguide adiabatic coupling method discussed in this letter.

 

Fig. 2. (a) SEM images of an array of $\textrm{Si}_{3}\textrm{N}_{4}$ nanophotonic structures that consist of integrated nanobeam PhC cavities cavities (b)&(c) and free-standing waveguides tapered at one end (d).

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In the first characterization, the optical fiber network shown in Fig. 3(a) is employed to collect reflection light spectra from the waveguide-coupled nanobeam cavities. An optical fiber tip is placed on top of a 3-axis stage controlled precisely by a piezo controller (MDT693B, Thorlabs) to bring it into physical contact with the waveguide taper. The supercontinuum laser (SuperK EVo, NKT Photonics) is coupled into the fiber network. The optical fiber at the end of the fiber network is coupled to the on-chip devices, and the reflected light is collected by the optical spectrometer. The spectra displayed in Fig. 3(b) and Fig. 3(c) show three resonant modes separated by $\sim$ 10 nm inside the photonic bandgap. The quality factor of the fundamental mode ranges from 10,000 to 24,000, measured by a fine spectrometer. The spectra of device A exhibit higher quality factors owing to the large bandgap size and better imperfection tolerance compared to device B. The above measurement was conducted on device A (device B) with 20 (14) holes in the tapered region holes with 4 additional mirror holes. Reducing the number of holes in the tapered region keeps the mode volume to a minimum and lessens the number of high order modes, and adding mirror holes enhances the quality factor. The mode volume of device A (device B) is 0.93 (0.85) in unit of ($\lambda$ / n)$^3$, and the quality factor of device A (device B) is 45,000 (40,000). The calculations were obtained from 3D-FDTD numerical simulations free software (MEEP).

 

Fig. 3. (a) Schematic optical characterization of $\textrm{Si}_{3}\textrm{N}_{4}$ nanobeam PhC cavities. (b)&(c) Normalized reflection spectra of the cavity TE modes obtained by launching a supercontinuum laser to device A and device B, respectively. (d) Normalized cavity reflection obtained by scanning a tunable laser around the cavity resonance of device A. The Lorentzian fit yields a quality factor of Q $\sim 24,000 \pm 250$.

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For a precise measurement of the quality factor, the tunable laser (Spectra-Physics Model 380 ring dye laser) is employed and scanned around the TE fundamental mode of device A. The reflected laser beam is collected by the avalanche photodiode (APD). The tunable laser sources is scanned around the cavity resonance of the pre-selected device. Finally, the reflected laser beam is collected by the avalanche photodiode (APD). The reflection signal shown in Fig. 3(d) reveals the cavity resonance with a quality factor of 24,000 $\pm$ 250 obtained by scanning the laser around 599.74 nm. We utilize two photodetectors (PD1) and (PD2) to optimized and stabilize the coupling between the optical fiber and the waveguide during the experiment. The details of the fiber-waveguide coupling are described next.

3. Efficient fiber-chip interface

The light couples to the device using a single mode optical fiber tip that is coupled to the waveguide taper, see Appendix. The fabrication of the optical fiber tip adopted here is based on wet-chemical etching. In this approach, a commercial single mode optical fiber (S405-XP, Thorlabs) is dunked in hydrofluoric acid (HF) covered by an organic solvent (e.g. xylene) to provide a oil-water interface, see Fig. 4(a). The non-stripped fiber is clamped on a motorized stage (MT1-Z8, Thorlabs) to control the pulling speed via a motor controller (KDC101, Thorlabs). The fiber diameter continues to shrink gradually as it is pulled out of the HF solution. The height of the oil-water interface mainly depends on the fiber diameter and the surface tension difference between the acid and the organic solvent [35]. The key parameter in the fabrication process is the pulling speed that governs the angle of the optical fiber tip. The desired angle is dictated by the criterion of adiabatic transition of the fiber mode over the tapering region, similar to the waveguide taper discussed above. Since the cladding is etched away across the fiber tip, optical fiber cladding modes do not play any role in the coupling mechanism. This eases some restrictions in angles of the fiber tip which is limited to $\theta < 5 ^{\circ }$ for an alternative technique that keeps the fiber cladding intact during the fabrication process [28]. SEM image of the optical fiber tip is shown in Fig. 4(b) with an angle of $\sim 3^{\circ }$. Fiber tips with angles $5^{\circ } > \theta > 3^{\circ }$ shows the optimal performance.

 

Fig. 4. (a) Schematic of etching process of an optical fiber. (b) SEM image of an optical fiber tip following the etching process. (c) Schematic optical characterization of the fiber-waveguide coupling. (d) Optical micrograph of a suspended waveguide coupled to an optical fiber tip obtained from CCD camera. (e) Normalized broadband reflection spectrum of the cavity TE modes (blue) and a fiber-coupled retroreflector (yellow) obtained by a coarse spectrometer.

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The fabricated optical fiber tips were characterized by several measurements. We first measure the power transmission of the optical fiber tip using a custom setup where an objective of 0.6 numerical aperture is used to collect the power from the end of the optical fiber tip. The collected power is then normalized to the power obtained from a similar optical fiber with a clean core/cladding cross section. We routinely obtain high power transmission ($99\%$) even for optical fiber tips even with relatively large angles ($10 ^{\circ }> \theta > 5 ^{\circ }$). This measurement is necessary to ensure the adiabatic transition of the fiber mode all over the optical fiber tip. However, we sometimes observe low power transmission due to the fabrication imperfections such as insufficient acid etching and inaccurate fiber adjustment of the clamp, and some remains of polymer coating. These remains can be removed in piranha cleaning prior to the acid etching.

In the next measurement, we measure the coupling efficiency ($\mu _{\textrm{c}}$) between optical fibers and suspended $\textrm{Si}_{3}\textrm{N}_{4}$ cavities. The experiment is carried out as illustrated in Fig. 4(c). The supercontinuum laser is launched into the dichroic mirror and polarizer before the beam is filtered by the bandpass filter (605nm CWL, 15nm Bandwidth). The laser beam is coupled into fiber network and then to the chip in the same way explained above. Figure 4(d) displays an optical micrograph of the $\textrm{Si}_{3}\textrm{N}_{4}$ nanophotonic structures coupled to the fiber tip. The light passes the tapered waveguide and all frequencies other than cavity modes get reflected by the cavity Bragg mirrors. The optical spectrometer is used to analyze the spectrum of the reflected beam. Figure 4(e) shows the spectra obtained from the cavity and retroreflector. The ratio between the two spectra provides a qualitative estimate of the coupling efficiency near the cavity resonance. To verify high coupling efficiency, we carried a precise measurement in which photodetectors (PD1 and PD2) are used to record the ratio between the incoming and reflected optical power ($\gamma$) while the fiber is coupled to the waveguide. Next, we connect a retroreflector device to the incoming beam in the fiber network instead of the optical fiber tip. The resulting ratio of obtained from both photodetectors ($\zeta$) is used to calculate the total coupling efficiency given by $\mu _{\textrm{c}}^2 = \gamma /{\zeta \mu _{\textrm{Bragg}}}$, where $\mu _{\textrm{Bragg}}$ is the reflection of the cavity Bragg mirror which is assumed to be unity. For optical fibers with high power transmission, we routinely achieve a coupling efficiency $\mu _{\textrm{c}} > 90\%$. The maximum coupling efficiency we have achieved is $\mu _{\textrm{c}} = 96\%\pm 2\%$. The error bar reflects the fluctuations in the signal collected from the photodetectors. It is worth noting that the coupling between an optical fiber and device B is always lower than device A. The underlying reason is attributed to the back reflection at the mirror-waveguide interface [36]. Though we have appended transition holes to reduce the impedance mismatch in both devices, semicircular holes add more complexity at the transition region, therefore, require advanced tools for more precise adjustment. Nevertheless, we were able to achieved a coupling efficiency of $\mu _{\textrm{c}} = 91\%\pm 2\%$ for device B.

4. Conclusion

In summary, we have presented the design, fabrication, and characterization of nanobeam PhC cavities based on silicon nitride at visible wavelengths. We were able to demonstrate devices with quality factors higher than $10^4$ by scanning laser around the cavity resonance. The device offers promising a platform for strong coupling in solid-state cavity QED experiments. Specifically, we aim to use diamond color centers embedded in nanodiamonds and couple them in cavity QED systems to realize an efficient light-matter interface. Nanodiamonds with small sizes could be precisely positioned on top of nanobeam cavities in various ways [37,38]. In addition to diamond color centers, our device can be used for other single photon emitters such as quantum dots [39,40] and layered 2D materials [41]. Moreover, we have developed a technique for coupling light from optical fibers to on-chip suspended $\textrm{Si}_{3}\textrm{N}_{4}$ nanobeam PhC cavities. Utilizing the coupling technique presented here, we were able to demonstrate coupling efficiencies higher than $90\%$. This work is useful for quantum optics applications, including long-distance quantum networking [42] and optical quantum computing [43].

5. Appendix

The technique used here for coupling the optical fiber to the waveguide is based on adiabatic transfer of an optical power between the optical fiber mode and the waveguide fundamental mode. The key idea is to change the effective refractive index of the target mode gently such that all the optical power are contained in the same mode profile. Therefore, the criterion of an adiabatic transfer is fulfilled if the change in the effective refractive index of the fundamental mode is less than the difference between effective refractive index of the fundamental mode and the nearest mode [25]. This requires the tapering length to be longer than the beat length, that is, the length over which the optical power could leak into another mode. The beat length is given by $Z_{\textrm{b}}=\lambda /(n_{\textrm{eff},1}- n_{\textrm{eff},2})$ [44], and it corresponds to $Z_{\textrm{b}}\backsim$ 2 $\mu$m for the geometry shown in Fig. 5(b). The waveguide is stretched over 10 $\mu$m to allow the mode transfer and ensure the stability of the optical fiber tip. In order to verify adiabatic mode transfer, numerical simulations were performed in which a fundamental mode was launched at the beginning of the waveguide and monitored across the contact region, see Fig. 5(c). Simulation results show that $\sim 98 \%$ of the optical power has coupled to $\textrm{TE}_{11}$ optical fiber mode, while the other $2 \%$ leaks over the rectangular mechanical support that is connected to the chip. This result is in agreement to the side coupling approach aimed for detached devices [28].

 

Fig. 5. (a) Schematic of fiber-waveguide taper adiabatic coupling. (b) effective refractive index of the waveguide mode (blue), fiber mode (orange), and super-mode of the combined structure (green). The opening angle of the fiber (waveguide) is of 3.5$^{\circ }$ (2.2$^{\circ }$). (c) Cross sections of $E^2$ obtained from the FDTD simulation at different normal planes of the combined structure. The locations of the $E^2$ cross sections in the axial position z plotted in (b) are 5um, 10um, and 13um, left-to-right. (d)&(e) Simulated coupling efficiencies for the power transmission from the TE-polarized waveguide mode to the optical-fiber HE11 mode as a function of waveguide final width dx and fiber-waveguide overlap dz, respectively. The waveguide minimum width in (e) is set to 140 nm.

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In order to characterize the influence of the rectangular mechanical support, we have calculated the coupling efficiency for various rectangle widths ranging from 1.4 $\mu$m to 0.5 $\mu$m. Figure 5(d) shows that the coupling efficiency drops exponentially as the rectangle width increases. This behavior is expected due to the swift change in the effective refractive index of the super-mode created in contact region. Mechanical support with dx < 150 nm is preferable for optimal performance. On the other hand, the length of the physical contact region in which the optical fiber tip overlaps with the waveguide taper is another crucial parameter. Figure 5(e) shows that the coupling efficiency saturates when the length of the overlap reaches only 7 $\mu$m. This is relatively short compared to the biconical fiber taper technique [25], and to the stepwise technique reported more recently [45]. High coupling efficiency can be realized with such short lengths mainly due to the small tapering length that is restricted by the beat length for both structures. In addition, the spatial mode profile plays an important role in the length of the fiber-waveguide overlap. Numerical simulations were used to determine the minimum distance in which a Gaussian beam centered at 602 nm can transfer between the two structures.

Funding

Texas A and M University (X-grant 497); National Science Foundation (PHY-1820930).

Acknowledgments

The authors would like to thank Denis Sukachev for valuable discussions. Device fabrication is performed in part at the AggieFab Nanofabrication Facility at Texas A&M University. The authors acknowledge the Texas A&M University Brazos HPC cluster that contributed to the research reported here.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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