High-Q nanobeam cavities on a silicon nitride platform enabled by slow light

Optical cavities with a high quality factor (Q factor) are of great importance in various applications, such as narrow-band filtering, ultra-low energy switching and modulation, sensing, and cavity quantum electrodynamics.^1–5 In particular, nanobeam cavities (one-dimensional photonic crystal cavities) have attracted much attention because they can achieve large Q factors in addition to offering design flexibility and relatively simple fabrication.^6,7 Recently, silicon nitride (SiN) nanobeam cavities have been proposed, bringing advantages over their silicon counterparts such as a broader operation range covering the visible and the near-infrared spectra and the absence of two-photon absorption in the telecommunication band.^8–10 Nonetheless, the low refractive index of this material poses challenges to achieving high Q factors because of the lower index-contrast attainable compared to silicon.^11–14 To improve their Q factor, most SiN nanobeam cavity designs to date have resorted to using suspended (air-cladded) architectures, reporting measured Q factors in the range of 10⁴–10⁵.^15–17 However, the increased Q factors come at the cost of a more complex fabrication process and structural fragility. A recent effort to tackle this problem has reported an encapsulated SiN nanobeam cavity design with theoretical and measured Q factors of ∼10⁵ and 7000, respectively.¹² While this represents important progress, more work is still required to achieve Q factors comparable to those of suspended SiN or silicon nanobeam cavities while maintaining the device’s ease of fabrication and structural robustness.

In this work, we use the concept of slow light to show, both theoretically and experimentally, significant enhancements in the Q factor of SiN cavities. Slow light refers to optical modes with a small group velocity. There are two standard mechanisms to generate slow light, both of which require spectral regions of high dispersion. One of them uses material dispersion such as that created near an atomic resonance, while the other uses structural dispersion such as that created in photonic crystals.¹⁸ Slow-light waveguides of both types have been used in the past to increase the photon lifetime in various cavities,^19–24 showing that the Q factor increases with the group index, n_g. However, despite its potential, this approach has not been thoroughly investigated, thus far overseeing aspects such as the effect of the cavity length on the cavity performance. Here, we show experimentally that nanobeam cavities incorporating a slow-light photonic crystal waveguide exhibit a Q factor that increases with the cube of the cavity length (as opposed to the characteristic linear dependence of standard cavities²⁵), enabling the design of high-Q SiN nanobeam cavities with modest footprints despite a low refractive index contrast. Using this approach, we report experimental measurements of Q factors as large as 4.42 × 10⁵ and theoretical estimations of several millions for glass-cladded SiN nanobeam cavities. These values are the largest Q factors reported to date for non-suspended SiN nanobeam cavities, and are comparable to those reported in suspended nanobeam cavities.^15–17 Furthermore, our numerical simulations indicate that the Purcell factor of these slow-light cavities increases quadratically with the cavity length despite the increased mode volume, which could be useful for applications involving molecule sensing and strong interaction with quantum emitters.

The remainder of the paper is organized as follows. In Sec. II, the principles of operation, cavity design, and simulation results are discussed. In Secs. III and IV, the experimental results are presented and discussed, respectively. In Sec. V, the major conclusions are summarized.

Although the analysis leading to Eq. (2) considers a small sinusoidal index variation, a similar result is expected for more complicated periodic patterns. To verify the validity of Eq. (2) for other cavities, we perform 2.5D finite-difference time domain (FDTD) simulations (Lumerical) on three slow-light waveguides with different group indices (n_g = 24, n_g = 14, and n_g = 7) and examine the effects of n_g and L on the Q factor. The designed slow-light waveguides are made of SiN strip waveguides periodically patterned with elliptical holes spaced by a distance of Λ = 515 nm. SiN is modeled by the Sellmeier equation given in Ref. 27 to take into account the material dispersion. Since the material absorption of our low-pressure chemical vapor deposition (LPCVD) SiN is vanishingly small, it is neglected in the simulation. The elliptical shape of the holes results in a wider stopband and a larger mirror reflectivity compared to the circular one.²⁸ The cross section of the waveguides is 1200 × 300 nm², which is chosen to support only the fundamental transverse modes (TE and TM) maintaining at the same time a good mode confinement. The entire structure is encapsulated in SiO₂, having substrate and upper-cladding thicknesses of 10 μm and 4 μm, respectively.

The band structures of the three slow-light waveguide designs are plotted in Fig. 1(a). Only the first two bands corresponding to the dielectric mode (solid line) and the air mode (dashed line) are shown. For the dielectric mode, most of the mode power is confined in the high index material. Thus, larger Q factors could be obtained for this mode in comparison to the air mode for which most of the power is in the low index material. To define a cavity, we simply truncate the number of holes in the slow-light waveguides, N_W, as shown in the inset of Fig. 1(b). This acts as a uniform-reflectivity mirror because the effective indices of the waveguide mode do not vary much over the wavelength range of interest. As can be inferred from Fig. 1(a), the first band (solid line) of the three waveguides is far away from the light cone (gray region), meaning that the radiation loss to the light cone is negligible for all the cavities. Thus, the contribution of the radiation loss and mirror reflection to the Q factor is decoupled from that of n_g. Figure 1(b) illustrates how the Q factor of the fundamental TE mode in each of these three cavities is enhanced as N_W is increased. As expected from our previous analysis leading to Eq. (2), the simulation results fit the form $Q=aNW3+bNW$ very well (note that L scales linearly with N_W as L = ΛN_W; here we have replaced L with N_W). It is also worth noting that the larger the n_g is, the larger the Q factor is for a constant L.

For further analysis, we use the slow-light waveguide with the largest group index (n_g = 24 obtained for the hole radii of 500 nm and 110 nm) in the remaining of this paper. To achieve high Q factors, the slow-light waveguide (with N_W holes) is bounded by Bragg mirrors on both sides (with N_M holes each) to form a nanobeam cavity, as depicted in Fig. 2(a). Two tapers (with N_T holes each) are used between the slow-light waveguide and the mirrors to adiabatically match their mode profiles and minimize scattering losses.⁶ The minor and major radii of the holes in the mirror sections are 60 nm and 200 nm, respectively. The hole parameters in the taper sections are adjusted to create a quadratic tapering of the filling factor and an exponential decay of the fields along the tapers.⁶ The magnetic field distributions of the fundamental TE resonant mode in the proposed cavity for three different N_W values of 40, 120, and 160 are plotted in Fig. 2(b). These field profiles are given for a constant number of holes in the taper and mirror sections (N_T = 80 and N_M = 60). The Q factor vs N_W for the same number of holes in the taper and mirror sections is also depicted in Fig. 2(c). The Q factor varies, again, with the cube of L and a high Q factor of ∼1.7 × 10⁷ is achieved at a wavelength of ∼1627 nm for N_W = 200. It should be noted that even larger Q factors are predicted by adding more holes to the mirror sections (For instance, a Q factor of ∼2.8 × 10⁷ is obtained for N_M = 70).

We fabricated a set of devices of different parameters (N_W, N_T, and N_M) using the structural specification detailed in Sec. II. Details of the fabrication procedure are given in Sec. VI. Since the nanobeam cavities are designed for TE polarization, when characterizing their performances, excess TM polarization is not desired. To eliminate unwanted TM light caused by our laser source and polarization optics, an on-chip TM filter was also implemented in addition to the nanobeam cavities. This allowed us to obtain a large TE/TM ratio of at least 50 dB required to observe the spectra of the TE resonant modes under study (see the supplementary material for how the residual polarization can affect the transmission spectrum). For the TM polarization filter, we chose periodical circular holes as a grating, and by adjusting its period, we can align its stopband around the edge of the TE bandgap of the nanobeam cavity, where resonant peaks are located. Scanning-electron micrographs of a section of a TM filter and a section of a nanobeam cavity are shown in Figs. 3(a) and 3(b), respectively.

The measurement of fabricated devices was performed using the experimental setup as schematically drawn in Fig. 3(c). We use a tunable laser source operating in the 1450–1640 nm wavelength range and a power meter. The fiber rotator in Fig. 3(c) controls the input polarization. A butt-coupling technique is applied to couple light into the chip from a polarization-maintaining fiber, and the input waveguide width is optimized for the maximum coupling efficiency.³⁰ An index-matching liquid is also applied to minimize reflection losses. The offset between the input and output waveguides is to avoid stray light coupling into the output fiber.

Figure 4 plots the measured transmission spectra of a nanobeam cavity with N_W = 200, N_T = 80, and N_M = 60 for both polarizations, respectively. The blue and red curves correspond to the measurement results obtained from the coarse and fine sweeping of the tunable laser, respectively. The two shaded regions mark the locations of the stopband of the designed TM polarization filter. Clearly, TE resonant peaks are revealed with a large contrast of at least 50 dB, due to the proper alignment of the TM filter stopband with those TE resonant peaks.

It is worth mentioning that although the nanobeam cavities are originally designed for TE polarization, they do have some TM resonances as well, as indicated by the peaks appearing in the 1540–1560 nm wavelength range. However, we note that the Q factors are lower for TM polarization because the effective index of the TM-polarized mode of the cavity is smaller than that for the TE polarization.

For TE polarization, the resonant peak at 1604.7 nm has a 3-dB linewidth of 3.63 pm, corresponding to a Q factor of 4.42 × 10⁵, with a transmission of −48.7 dB. The highest measured Q factor for TM polarization of the same cavity is 1.88 × 10⁵ (with a 3-dB linewidth of 8.18 pm at 1542.8 nm). The measured Q factors for all fabricated devices are listed in Table I.

To experimentally verify the cubic relation between the Q factor and cavity length, we fabricated two sets of nanobeam cavities with (I) N_M = N_T = 15 and (II) N_M = N_T = 25 and N_W increasing from 40 to 220 for both sets. Then, we measured the highest Q factor of the TE resonant modes in the first set, and the highest Q factor of the TM resonant modes in the second set [note that the derivation of Eq. (2) does not require a specific polarization]. The two sets have different N_M and N_T values in order to keep the Q factors in a similar regime (<∼2.5 × 10⁴) for both polarizations. From Figs. 5(a) and 5(b), we observe a nonlinear dependence of Q on N_W.

We find that for both polarizations, the experimental data follow a cubic dependence for a limited range of cavity lengths, as indicated by the shaded areas in Figs. 5(a) and 5(b). The blue curves in the two figures are fits of the cubic expression $Q=aNW3+bNW$ to the data points in the shaded areas. Figures 5(c) and 5(d) are zoom-ins of the shaded areas to show the associated data points and fits. Note that in this regime of relatively low Q, the data fit (SSE of 1 and 0.469 and R-squared of 0.9972 and 0.9979) the cubic relation very well. However, we note a clear deviation from the cubic fit for the data out of the shaded areas, corresponding to cavities with N_W > 160 and Q > ∼2.5 × 10⁴. We attribute this deviation to the effect of power dissipation by light scattering, which would inevitably be present in our devices due to the material roughness and fabrication imperfections. As mentioned earlier, power dissipation, P, plays an important role in defining the Q factor, as seen by the 1/P dependence in Eq. (2). Thus, since power dissipation in our devices is always an increasing function of the cavity length, it is expected that the dependence of Q on the cavity length deviates from the cubic relationship for long cavities.

The highest measured Q factor in the proposed cavity is 4.42 × 10⁵, which was obtained for N_W = 200, N_T = 80, and N_M = 60, and the total cavity length of 247.2 μm. A Q factor as high as 1.29 × 10⁵ was also measured for a smaller number of holes in the mirror and taper sections (N_W = 200, N_T = 15, and N_M = 15 and the total length of 133.9 μm), as shown in Fig. 5(a). To the best our knowledge, these are the highest reported Q factors obtained experimentally for non-suspended SiN nanobeam cavities.^11–13 The slow-light waveguide inside the proposed cavities affects the Q factor in two ways: (I) its group index defines the minimum achievable Q factor for a zero-length cavity with a fixed number of holes in the mirror and taper sections, and (II) its increased length can enhance the Q factor significantly, considering that the Q factor has a cubic dependence on L, as opposed to the linear dependence in conventional cavities.²⁵ It is also in contrast to the nanobeam cavities with a conventional strip waveguide in between the mirrors in which the maximum attainable Q factor is obtained for a zero-length cavity.^6,31 Furthermore, our analysis indicates that the Purcell factor varies quadratically with L, suggesting the possibility of enhancing this figure by increasing the cavity length. The maximum useful waveguide length is limited due to the pronounced scattering loss in slow-light waveguides^32,33 which consequently reduces the maximum Q factor in practice. The effect of the loss on the Q factor and the Purcell factor will be further studied and reported elsewhere. It is also worth mentioning that the Q factors reported in this work are comparable to those previously measured for suspended SiN nanobeam cavities with larger index contrasts.^15–17 A comparison of several reported SiN nanobeam cavities is summarized in Table II.

In this paper, we report the design and experimental characterization of high-Q non-suspended nanobeam cavities fabricated on a 300-nm-thick SiN platform. The structures consist of 1D slow-light photonic crystal waveguides (n_g ∼ 24) of various lengths bounded by Bragg mirrors. We show that the Q factor of these slow-light cavities exhibits a cubic dependence on the cavity length, which enables them to achieve large Q factors with modest cavity lengths. We report measured Q factors as large as 4.42 × 10⁵ and numerically predicted values of up to 2.8 × 10⁷, which are comparable to those of suspended SiN nanobeam cavities previously reported. In addition, a TM polarization filter is designed and included to enable the high-contrast detection (>50 dB) of the TE resonant modes, which would otherwise be buried under the transmission of excess TM polarization. The proposed cavities are mechanically robust and have a great potential to be integrated with new photonic materials such as 2D materials. Thus, these high-Q cavities are promising for a wide variety of applications such as narrowband filtering, ultra-low energy switching and modulation, sensing, and cavity quantum electrodynamics.

The devices are fabricated in the following procedure. First, 300-nm-thick stoichiometric SiN is deposited via low-pressure chemical vapor deposition (LPCVD) on silicon wafers with 10-μm thermal SiO₂ on top. Device patterning is performed by e-beam lithography with a ZEP-520A resist, followed by a developing process. Next, a thin chromium layer is deposited as the hard mask and nanobeam cavity patterns are then transferred into SiN by a CHF₃–SF₆ based plasma etching process. The hard mask is removed with an acid and 4-μm-thick SiO₂ cladding is deposited via plasma-enhanced chemical vapor deposition (PECVD).

See the supplementary material for further details regarding the TM polarization filter.

J.Z. and Z.J. contributed equally to this work. I.D.L and M.D. supervised all aspects of the project.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We thank the University of Maryland Fablab staff member Mark Lecates for assistance with the fabrication procedure. J. Zhan, M. Dagenais, and S. Veilleux acknowledge the support from the National Aeronautics and Space Administration (NASA) through Grant No. 16-APRA16-0064. J. Zhan, Z. Jafari, M. Dagenais, and I. De Leon were supported by the UMD-TEC Seed Award, Grant No. 2-957016 (0020240I10). I. De Leon and Z. Jafari acknowledge the financial support from CONACyT Grant No. CN-17-109 and from the Federico Baur Endowed Chair in Nanotechnology.