1. Introduction

Integrated photonics is a rapidly developing technology, not only offering compact, low-power devices for classical communication and sensing applications, but also promising realization of scalable photonics quantum computations and quantum nonlinear optics with integrated quantum emitters. In particular, by realizing strong light-emitter interaction in chip scale, integrated photonic circuits could form much sought-after scalable quantum platforms with improved component density, low optical loss, and phase stability [1–3]. Achieving large-scale, high-fidelity quantum operations with photonic circuits, however, would very much rely on highly efficient chip-to-chip or fiber-to-chip photon coupling for network communications, as well as low-loss connections to single-photon sources or detectors. Realizing nearly perfect nanophotonics interfaces with standard fiber optics would thus be a fundamental necessity. Various schemes have been proposed and implemented to minimize coupling losses, such as grating couplers, edge couplers, and adiabatic couplers [4,5]. However, efficiencies of these couplers are typically sensitive to wavelength, polarization, coupler geometry and misalignment, thus making it difficult to satisfy stringent requirements of many demanding quantum applications.

In silicon and silicon nitride photonics, conventional inverse-tapered waveguide edge-couplers are easy to fabricate, but they usually achieve low coupling efficiency with flat-cleaved optical fibers due to mode-mismatch [4,6]. In most common designs, an edge-coupler is buried inside a thick oxide cladding. The width of the coupling waveguide would taper down to a small size at the end facet (typically with $d<100\,$nm) to expand its mode field approaching that of an optical fiber. The height of the edge-coupler $h$, on the other hand, remains fixed as required in standard 2D lithography and is pre-determined by the thickness of the device layer. However, for optical circuits with device thickness $h>600\,$nm, fiber edge-coupling efficiency could still be limited by the minimal achievable width $d\gtrsim 50\,$nm at the facet, leading to significant mode-mismatch. Coupling efficiency is also polarization-sensitive due to highly asymmetric waveguide edge-coupler geometry.

To achieve higher coupling efficiency $\gtrsim 90\%$ ($\lesssim 0.5$dB loss) in fiber edge-coupling methods, existing solutions would use spot-size converters (SSCs) with either lensed or cleaved fibers [4,5,7]. However, lensed fibers have very low misalignment tolerance ($\geq 1$ dB loss for displacement less than $\pm 0.5\mu$m), thus necessitating precise fiber alignment that may be difficult to achieve in various integrated applications [8,9]. On the other hand, SSCs for cleaved fiber usually require additional complicated 2.5D/3D fabrication steps for a thick cladding layer [10–14] or a large-core waveguide [15,16].

In this letter, we present an alternative solution – a 3D tapered waveguide edge-coupler (TWC), which could overcome the device thickness limitation to achieve polarization-insensitivity and high fiber-coupling efficiency. We adopt a simple lithography technique to create smooth local ramps in the device layer thickness prior to patterning TWCs. This allows us to fabricate precise 3D taper profiles on a functional nanophotonic quantum circuit similar to those described in Refs. [17,18]. We discuss details of the design and fabrication technique of the 3D TWCs, and demonstrate efficient coupling efficiency with flat-cleaved optical fibers with $<0.8\,$dB loss – for both the fundamental transverse-electric (TE) and transverse-magnetic (TM) modes, and in a wide spectral range. Our experiment result shows more than 6 dB improvement from a previous work [19], thus demonstrating the practical functionality of 3D TWCs. Moreover, our fabrication technique may also be extended to create other thickness-tapering structures or novel 3D lithographic photonic devices.

2. Design of the tapered waveguide end facet

We begin our design by finding optimized mode-matching conditions between an optical fiber (780HP) and the end facet of a Si$_3$N$_4$ waveguide embedded in a SiO$_2$ cladding structure of various width and thickness, as shown in Fig. 1. Our calculation focuses on optical wavelengths near 852 nm [17], but the design can be easily rescaled to accommodate other wavelengths. In principle, a 3D TWC can achieve high coupling efficiency as long as the cladding is thick enough to cover the guided mode emitted from an optical fiber. However, the coupler can also be optimized for devices with smaller cladding or asymmetric stacks of cladding layers. Later in our simulations, we have also included a layer of silicon nitride ($500$ nm thickness) in the substrate as this is present in our actual fabricated devices [17]. For general photonic structures, this may be replaced by silicon as well as other materials or be removed.

 

Fig. 1. 3D tapered waveguide coupler. (a) Schematics of a tapered waveguide edge-coupled with a flat-cleaved optical fiber. Insets show mode intensity profiles along the coupler. A silicon nitride layer is present as a substrate in the device under test (DUT). (b) Cross-sectional view at the coupler facet. (c) Intensity profiles of the fundamental TM modes at the facets with different geometries $(W,H,d,h)=$ (i) $(8,8,0.12,0.12)\,\mu$m, (ii) $(7,7,0.05,0.05)\,\mu$m, (iii) $(8,8,0.05,0.8)\,\mu$m, and (iv) the DUT. Red (white) dashed line marks the mode field diameter of the optical fiber (edge-coupler). (d) Mode field overlap versus width $d$ at various facet geometries. Legend marks the size $(W=H,h)/\mu$m, and coupled modes (TE/TM) in the case of asymmetric couplers. The substrate is ignored in (c-d).

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We calculate the overlap between waveguide ($w$) and fiber ($f$) fundamental modes at the coupler facet using $\mathcal {T}=\operatorname {Re}\left [\frac {\left (\int \mathbf {E}_{w} \times \mathbf {H}_{f}^{*} \cdot d \mathbf {A}\right )\left (\int \mathbf {E}_{f} \times \mathbf {H}_{w}^{*} \cdot d \mathbf {A}\right )}{\int \mathbf {E}_{w} \times \mathbf {H}_{w}^{*} \cdot d \mathbf {A}}\right ]\bigg /\operatorname {Re}\left (\int \mathbf {E}_{f} \times \mathbf {H}_{f}^{*} \cdot d \mathbf {A}\right )$, where the mode electric fields $\mathbf {E}_{f,w}$ as well as magnetic fields $\mathbf {H}_{f,w}$ are extracted using a finite difference eigenmode (FDE) solver [20]. The overlap $\mathcal {T}$ quantifies the initial coupling efficiency between the fiber and the edge-coupler. The geometry is shown in Fig. 1(b).

We consider simple cases where the width and height of a coupler facet and its cladding are symmetric ($d=h$ and $W=H$), and the structure is aligned to the fiber core. We find that for 3D TWCs, the best achievable mode overlap and characteristics of coupled modes largely depend on the cladding size and geometry. In a reasonably large cladding thickness that we have considered ($W=H=8\,\mu$m), the mode overlap could reach an optimal value $\mathcal {T}\approx 97\%$ at $d = h \approx 120$ nm, as shown in Fig. 1(d). In this case with a clear optimal waveguide facet size, the mode is guided by the Si$_3$N$_4$ waveguide and is well-defined within the cladding, as shown in Fig. 1(c)(i). We note that $\mathcal {T}$ may be higher with even thicker cladding. For cases with $W=H \lesssim 7\,\mu$m, the optimal waveguide size ($d=h$) approaches zero, indicating that the best mode-matched profile is actually confined by the SiO$_2$ cladding. Nevertheless, mode overlap $\mathcal {T}$ is already $\gtrsim 90\%$ at finite $d = h \lesssim 100\,$nm.

In contrast, for 2D tapered waveguides with larger constant thickness $h$, sufficient mode overlap occurs only when the width $d \lesssim 50\,$nm, as shown in Fig. 1(c)(iii) and (d). It is however challenging to fabricate such a narrow waveguide especially for a thick device layer, which would require a thick photoresist or e-beam resist layer that may collapse during the lithography process.

We also show that a 3D TWC is more tolerant on asymmetry in the oxide cladding. For example, the device under test (DUT) in this work has a thinner layer of buried oxide (thickness $H_1=2.2\,\mu$m) and a thicker top cladding (thickness $H_2=3.5\,\mu$m). It has limited total height $H=H_1+H_2=5.8\,\mu$m and width $W=6.2\,\mu$m, and a small waveguide facet geometry $d=h=50$ nm. The mode profile at the facet fills the oxide cladding [Fig. 1(iv)], but could still reach $\mathcal {T}\gtrsim 85\%$ mode-matching efficiency even when the mode is slightly distorted by the waveguide facet.

3. Simulation results

Once the end facet geometry has been determined, the taper length will be optimized for maximizing coupling efficiency into a nominal Si$_3$N$_4$ waveguide. An optimal length exists for there is substrate leakage loss and possibly scattering loss (not included in the simulation), which demand a shorter taper length, and the mode mismatch loss, which prefers a more adiabatic taper profile.

We compare optimized taper lengths of three different silica cladding and facet geometries. We consider (i) a symmetric coupler with thick cladding $W=H=8\,\mu$m and an optimal facet size $d=h=0.12\,\mu$m, and (ii) a $7\,\mu$m-thick silica cladding with a small facet size $d=h=50\,$nm. Lastly, we discuss (iii) our DUT with asymmetric cladding and $W\approx H\approx 6\,\mu$m. These three geometries represent coupling an optical fiber to end-facet modes of three different characteristics: (i) a waveguide-guided mode, (ii) a cladding-guided mode, and (iii) an asymmetric cladding-guided mode, respectively.

We perform simple taper length optimization by linearly ramping the waveguide cross-section from its initial size to an intermediate size of $d=h=300\,$nm in a variable distance $L$. We then calculate the total transmission $T$ from an optical fiber to the end of the taper by using a bidirectional eigenmode expansion (EME) solver [20], as shown in Fig. 2. In these simple scans, we find that, for (i), the field of a waveguide-guided mode suffers lower substrate leakage, and could thus afford longer taper length at $L\approx 380\,\mu$m to achieve smaller mode-mismatch loss and a larger overall coupling efficiency $T\approx 95\%$. For (ii) [(iii)], we find that a taper length of $L\approx 200\,\mu$m (170 $\mu$m) is required to efficiently transfer a cladding-guided mode (asymmetric mode of DUT) into a nominal waveguide-guided mode. For both (ii) and (iii), coupling efficiencies drop as $L>200\,\mu$m due to finite leakage into the substrate.

 

Fig. 2. Taper length optimization and broadband transmission spectrum. (a) Simulated transmission at 852 nm versus taper length $L$ for DUT and other labeled coupler geometries $(W=H, d=h)/\mu$m. (b) Simulated and measured (symbols) transmission spectrum at the optimal taper length.

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In addition, we find that fiber coupling to a waveguide TM-mode is generally less efficient, up to $5$% smaller (at 852 nm) via either the cladding-guided or asymmetric modes. This is due to a TM mode’s stronger electric field near the substrate, which results in higher leakage loss. Direct coupling to the waveguide-guided case with thick cladding ($8\,\mu$m), on the other hand, is nearly symmetric for TE and TM modes and is thus polarization insensitive.

We show that a 3D TWC could also work in a wide spectral range. Shown in Fig. 2(b) are simulated transmission spectra of 3D TWCs initially optimized for $\lambda =852\,$nm. Here the coupling efficiencies in almost all cases remain nearly constant over a wide spectral range $\Delta \lambda \sim 250\,$nm, with less than $\pm 0.1\,$dB or $\pm 2.5$% variation. The bandwidth is limited by the substrate leakage loss at longer wavelengths ($\lambda \gtrsim 950\,$nm) and mode mismatch at shorter wavelengths ($\lambda \lesssim 750\,$nm).

4. Experiment results

To compare with simulation results, we have fabricated 3D TWCs on photonic circuits designed for cold atom cavity quantum electrodynamics (cavity QED) experiments similar to those described in Refs. [17,18,21]; see also Fig. 5. In our previous works, deep U-shaped grooves in a photonic chip are patterned to allow fiber placement and edge-coupling with top-cladded 2D taper couplers. In this work, the original edge-coupler design is replaced with 3D TWCs. Due to our application requirements [17,21,22], thickness of the buried oxide layer is limited to $\sim 2\,\mu$m, and thus we have fabricated 3D TWCs with asymmetric cladding under the geometric parameters shown as DUT in Figs. 1 and 2(b). The fabricated 3D TWCs are connected in pairs, each through a 4 mm-long Si$_3$N$_4$ bus waveguide of 1 $\mu$m nominal width, and an additional $200\,\mu$m-long 2D taper region on either end of the bus waveguide. The end facet of each 3D TWC is facing a U-groove [Fig. 4(e)], where it edge-couples to a flat-cleaved 780HP optical fiber placed within the groove. Detailed fabrication procedures of the 3D TWC region will be described in the next section.

To perform optical fiber-to-bus waveguide transmission measurements, we align two cleaved optical fibers to a pair of 3D TWCs to maximize the total transmission $T_\mathrm {tot}$ at 852 nm through the connecting bus waveguide. To extract the transmission coefficients of individual 3D TWCs, we select an isolated surface scatterer residing roughly mid-point along the bus waveguide and measure its brightness through an optical microscope. We launch probe light of fixed intensity and polarization through either coupler, and record the resulting brightness ratio $\eta$ ($\gtrsim 1$), which approximately gives the ratio of the transmission coefficients of two couplers. We extract $T = \sqrt {\eta T_\mathrm {tot}}$ for the coupler with optimized fiber alignment. Note that, for simple demonstration purposes, we do not separate propagation loss in the bus waveguide (estimated to be $\sim -0.06$ dB/mm) from the measured transmission coefficients. This tends to give us a slightly lower $T$ value than the actual transmission coefficient of a 3D TWC.

We report measurement results in Fig. 2(b), which shows high transmission coefficients $T>80$% for the TE-polarization at three different wavelengths $\lambda =852$ nm (D2 line of atomic cesium), 894 nm (D1 line of atomic cesium), and 935 nm. Transmission coefficients of the TM-polarization are generally around 3% lower than that of TE-polarization but are still close to the $\sim 80\%$ value. The measurement results and wavelength dependence are consistent with simulation but are generally 3% to 5% lower than expected, likely due to unaccounted propagation loss in the bus waveguide. At a shorter wavelength, $\lambda =780$ nm (D2 line of atomic rubidium), our results drop significantly below the simulated values, which may be additionally due to higher scattering loss ($\propto \lambda ^{-3}$) from the surface and side wall roughness in the 3D TWC region that was not included in our EME simulation.

Lastly, we have tested the misalignment tolerance of our fabricated 3D TWC. As shown in Fig. 3, our coupler shows $\approx -0.8$ dB$/\mu$m misalignment tolerance, much better compared to $-3.3$ dB$/\mu$m of a top-cladded ($H_2\approx 1\,\mu m$) 2D TWC coupled to a lensed fiber (2 $\mu$m beam waist) in our previous work [17]. These measurements also show excellent agreement with our simulation results.

 

Fig. 3. Measured (circles) and simulated (triangles) transmission (normalized to peak value $T_0$) of TM-polarization versus horizontal (H) and vertical (V) fiber displacements $\Delta$. One dB misalignment loss occurs at $\Delta \sim 1.2 \mu$m.

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5. Fabrication

In this section, we focus on describing the fabrication processes of 3D TWCs, which are fully compatible with general fabrication processes of integrated photonic circuits. Our fabrication procedures are summarized in Fig. 4, where 3D patterning can be split into two major steps: (a) slope fabrication and (b) waveguide pattern transfer. In the first step, slope structures in the device layer are generated, which create the necessary vertical ramp profiles for making the 3D TWCs. In the second step, the horizontal profiles of the TWCs and other photonic components that only require 2D patterning are defined in a single lithography step.

 

Fig. 4. Fabrication process. (a) 3D lithography using PMMA e-beam resist. Ramp profile: $h_1\approx 100\,$nm, $h_2\approx 500$ nm, and $L_R\approx 230\,\mu$m. (b) 3D pattern transfer onto the Si$_3$N$_4$ layer via plasma etching. Desired height ($h\approx 50$ nm) and taper length $L\approx 170$ nm is controlled by the etching time and selectivity $S$. (c) 3D TWC fabricated following e-beam lithography and plasma etching. The tilted SEM image shows the entire 3D TWC after pattern transfer. (d) Top SiO$_2$ cladding deposited using a HDPCVD process. (e) Coupler facet defined using photolithography and plasma etching. The optical and SEM images show a fabricated 3D TWC (scale bar: $25\,\mu$m).

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As shown in Fig. 4, the slope fabrication process starts with grayscale lithography [23–25]. Firstly, a new chip is spin-coated with a thick PMMA (MicroChem 950PMMA A6) layer. The resist layer is then exposed with spatially varying e-beam doses using a 3D proximity effect correction function in a pattern data processing software (BEAMER, GenISys GmbH). After development, staircase structures would form in the resist layer because different exposures result in different development rates. The resist is then thermally re-flowed by a hot-plate thermal treatment at around $110^{\circ }$C for 2 hours, turning the staircase structures into smooth and continuous slopes. The slope patterns are then transferred to the underlying Si$_3$N$_4$ device layer using inductively coupled plasma reactive-ion etching (ICP-RIE) with CHF$_3$/O$_2$ gas chemistry.

To achieve a desired slope/taper pattern without damaging the surface of the device layer, it is crucial to create a proper PMMA slope pattern and control the time and selectivity in the dry etching process. As shown in Fig. 4(a,b), we carefully select the parameters in a PMMA slope, $h_1, h_2,$ and $L_R$, to produce a desired Si$_3$N$_4$ slope that ramps from an initial thickness $h$ to the nominal thickness $h_{w}$ in a taper length $L$. There are some design rules to ensure high fabrication yield and performance of 3D TWCs. Firstly, we avoid high contrast in e-beam doses and large variation of resist height after development, by keeping the thinnest part of the PMMA layer, i.e., $h_1$ to be $\sim 20\%$ of the nominal PMMA thickness $h_2$. Given the etch selectivity $S\approx 1.2$ between PMMA and Si$_3$N$_4$ (adjustable by the CHF$_3$/O$_2$ gas ratio), the taper length $L$ can then be determined from the following ideal relation,

After slope fabrication, 3D TWCs and other structures in the device layer are fabricated using standard e-beam lithography and etch process. Next, the SiO$_2$ top cladding is deposited with high-density plasma chemical vapor deposition (HDPCVD) at low temperatures (as low as 50 to 70 °C) for lift-off additive processing while obtaining good film properties [26–28]. Here, the top cladding materials are deposited only in regions not protected by a resist mask. This process is ideal for non-cladded applications such as atom-light interaction or sensing. Following HDPCVD and lift-off, the fiber U-grooves, the cladding structures, and the facets of the 3D TWCs are defined with photolithography, followed by the ICP-RIE dielectric material etching and silicon deep-reactive-ion-etching (DRIE). Figure 5 shows a sample nanophotonic circuit integrated with 3D TWCs and fabricated using the prescribed recipe. For full functionality of the circuit design, see Refs. [17,21].

 

Fig. 5. A nanophotonic circuit integrated with 3D TWCs. (a) Optical image of the device layer following e-beam lithography. (b) Fabricated circuit with (i) nanophotonic devices as shown in (a), (ii) 3D TWCs, and (iii) fiber grooves (separation between the grooves is 450 $\mu$m).

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Lastly, we discuss the fabrication yield. Although all procedures involved in the 3D TWC fabrication are relatively straightforward, patterning a narrowly tapered waveguide on a slope may be challenging. In particular, during resist development for 2D waveguide pattern transfer (Fig. 6), a tall step-coverage of spin-coated e-beam resist can be found near the bottom of a slope [Fig. 6(a)], which may collapse after development. For a slope that ramps from $h=50\,$nm to $h_\mathrm {w}=300\,$nm, the step-coverage would reach $650\,$nm following spin-coating of a $400\,$nm-thick e-beam resist. In making narrowly tapered waveguides, such a tall resist pattern can collapse during the subsequent developing processes, as shown in the SEM image in Fig. 6(a). A simple slope design in Fig. 6(a) thus leads to a yield rate of $\sim 60\%$.

 

Fig. 6. Improvement of fabrication yield. (a) Tall step-coverage of e-beam resist (ma-N2400) at the bottom of the ramp (top schematic) may cause collapsed pattern during development, as shown in the optical and SEM images. (b) Improved ramp design (top) with uniformly coated e-beam resist (bottom schematic). (c) Optical images of an improved ramp after PMMA lithography (top), and a 3D TWC structure after e-beam lithography (middle) and waveguide pattern transfer (bottom).

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To avoid tall step-coverage and improve fabrication yield, we replace all vertical steps in the PMMA structure with ramps. This gives a slope structure with wide opening in all directions, and allows e-beam resist to spin-coat the device layer with more uniform thickness; see Fig. 6(b) for schematics and the top image of (c) for a fabricated ramp with wide opening. This uniform resist coating avoids collapse during resist development and pattern transfer, as shown in the middle and bottom images of Fig. 6(c), respectively. Using ramp structures in PMMA, we have achieved a nearly $100\%$ yield rate of 3D TWCs.

6. Conclusion

In this letter, we incorporate a grayscale fabrication technique with conventional 2D lithography [29–32] to create 3D TWCs for efficient coupling to cleaved optical fibers. The enabling technique and 3D TWC design would ideally permit high and polarization-insensitive fiber-coupling efficiency $>95\,\%$ ($<0.2\,$dB loss), wide bandwidth ($\Delta \lambda \approx 250\,$nm), and large misalignment tolerance $-0.8\,\mathrm {dB}/\mu$m. Our experiment with a non-ideal, asymmetric design demonstrates the robustness of 3D TWC coupling, showing $\approx 85\%$ transmission efficiency ($\approx 0.8\,$dB loss) and the expected misalignment tolerance. Overall, we have focused mainly on optimizing symmetric waveguide couplers ($d=h$). Further improvements on mode overlap may be considered with non-symmetric couplers (facet height $h<$ width $d$), where the minimum achievable height $h\approx 5\,$nm could be controlled by the dry etching process during slope fabrication. Such design may be particularly useful for 2D lithography techniques such as deep UV lithography, which has a limited single-line resolution $d\gtrsim 150$ nm. Lastly, the 3D lithography technique presented in this study offers a new tuning knob for mode field shaping and effective refractive index engineering. It also shows the potential for applications in waveguide crossing [33–35], interplanar coupling [36–38], and chip-to-chip coupling [39–41].