Cold atoms are central components of precision scientific tools^[1,2], which play an important role in atomic timing^[3], quantum computing^[4,5], and quantum sensing^[6–8]. The cooling and trapping of neutral atoms generally use the balanced scattering force created by the combination of six opposing laser beams and a magnetic field gradient to confine the atoms in up to three dimensions^[9]. The restoring force on the atoms confines them in space, reducing their velocity and thus their temperature^[9]. However, conventional atom trapping and cooling systems, i.e., magneto-optical traps (MOTs), require free-space lasers and various optics, which make it bulky, unstable, and costly with a high power cost^[10]. It also leads to limited application scenarios for cold atom systems.

Over the last few years, the MOTs have made progress in miniaturization and integration in order to make the cold atom system available for practical applications. These methods generally fall into the following categories: metasurface MOT^[11], photonic integrated circuit MOT^[12], mirror MOT^[13], pyramid MOT^[14], grating MOT^[15], and planar integration MOT^[16]. Among them, the photonic integrated circuit method attracted a lot of attention due to its ability to integrate lasers and various optical devices into a planar fabricated waveguide-based structure in the integrated platform. For photonic integrated circuit MOTs, it is important to design the photonic outcoupler properly to generate a pristine free-space beam. Firstly, the number of cold atoms can be increased by the larger beam overlap volume within the vacuum cell and higher optical power of beams^[17]. Then, the scattering forces on the atoms must be balanced and strong enough to trap and cool the atoms from the background vapor of the cell^[9]. The scattering force depends on the propagation directions of the cooling beams, usually six beams. Finally, the intersection of these beams must also coincide with the null point of the magnetic field gradient within the cell.

Grating coupling is the most common method to convert on-chip waveguide mode to free-space mode^[18]. The uniform grating couplers generally do not consider the phase or intensity distribution of the diffracted field, which is optimized mainly by changing the structural parameters in order to maximize the power transfer to the fiber. Due to the exponential decay of power in the guided wave mode, an exponentially decaying diffracted field profile is generated in the plane, which results in a mismatch between the diffraction field and the fiber mode and limits the coupling efficiency^[19]. However, apodized gratings can form Gaussian profiles in the diffraction field and have been used to improve the efficiency of fiber-to-chip coupling^[20].

In this paper, we proposed and experimentally demonstrated a large-mode-diameter grating outcoupler with a near-Gaussian-profile emission beam at 780 nm wavelength on a silicon nitride (Si3N4) platform using the principle of apodized gratings. By mirroring the coupling strength and limiting the minimum size, the process difficulty is reduced to make it easier to fabricate. The device emission angle is experimentally tested to be 24.38°. Finally, we design an on-chip emission system to demonstrate the MOT application by appropriately arranging the positions of the grating outcouplers on the chip.

The grating outcoupler consists of a large-area adiabatic single mode waveguide to a slab waveguide beam expander and a apodized grating as shown in Fig. 1(a). Gaussian beam shaping is achieved by spatially varying the coupling strength according to^[20]α(z)=G(z)2[1−∫−∞zG(t)dt],(1)where z is the propagation direction, α(z) is the spatially varying coupling strength, and G(z) is the Gaussian beam intensity profile, with unity total power. Figures 1(b) and 1(c) show a Gaussian beam intensity profile with a 1/e2 radius W=100μm, and its corresponding α(z), respectively. The reason for choosing 100 µm is that as the waist radius increases, the coupling strength decreases, which leads to an increase in the coupling loss^[20]. Therefore, there is a trade-off between the beam waist radius and the coupling loss.

The physical properties of the diffraction grating coupler unit cell, as shown in Fig. 2(a), can be described by the Bragg condition. By considering the first-order diffraction, the Bragg condition can be reformulated as ne·FF+no·(1−FF)−n1sinθ=λΛ,(2)where n0 and ne are the effective indicies of the unetched tooth and of the etched trench of the waveguide grating section, FF is the grating duty cycle, n1 is the refractive index of the top medium, θ is the diffraction angle, λ is the wavelength, and Λ is the period. When the etching depth and diffraction angle are determined, the pitch and duty cycle can be calculated from the Bragg condition. For uniform grating couplers, the output beam has an exponentially decaying power P(z)=P0exp(−2αz)^[19,20]. We can numerically simulate uniform gratings for each duty cycle and the corresponding pitch. The scattering strength can be extracted by fitting the remaining power in the guided mode along the propagation direction to an exponential decay. According to previous studies^[20,21], by fitting the extracted coupling strengths, we can obtain the fitting equation α=b·sin2(π·FF), where b is the fitted value and is related to the etching depth. It can be seen that we correlate the spatially varying coupling strength with the structural parameters of the grating outcoupler. We can then calculate the required spatially varying structural parameters using the Bragg condition of Eq. (2).

However, the grating outcoupler is more dependent on the minimum feature size. When FF is 0.5, α reaches its maximum value. If we allow αmax≥α(300) in Fig. 1(c), then the grating structure at the initial area will require a high level of process resolution and be more difficult to prepare due to its small feature size. Here, considering the symmetry of the Gaussian distribution and low coupling strength required for the grating, we can make a mirror image of the α(z) at 150 µm, i.e., α(z)=α(300−z)(z≥150), as shown in Fig. 2(a), where the intensity of the Gaussian profile will consist of the coupled light intensity of each grating unit. At this point, we can allow αmax≥α(150) by changing the etching depth to reduce the difficulty of preparation. Therefore, we choose the 20 nm etching depth, which satisfies our process capability and also keeps αmax as close as possible to α(150). Here, the Si3N4 film thickness in our design is 300 nm, and the etching depth is chosen to be 20 nm. For our work, the grating is designed to emit at an angle of 30° at the wavelength of 780 nm. Figure 2(b) shows the calculated pitch versus duty cycle for a diffraction angle of 30°. By fitting the extracted coupling strengths and connecting them with our target Gaussian profile, we can obtain a final equation: α(z)=G(z)2[1−∫−∞zG(t)dt]=0.024sin2(π·FF).(3)

Moreover, limited by the process resolution of our platform, the minimum feature size is limited to 30 nm, as shown in Fig. 2(c). Figure 2(d) shows the near-field power distribution of the beam through the numerical simulation. The result indicates the diffraction field power of the grating is near-Gaussian distributed.

In our work, the devices are fabricated on a Si3N4 substrate with a 300 nm Si3N4 layer on top of a 3 µm-thick silicon dioxide (SiO2) layer. The fabrication process is CMOS foundry-compatible. Figure 3(a) shows the process of the grating outcoupler. Firstly, the wafer is cut into small pieces to access facets for fiber edge-coupling. Then, the waveguide layer is made by CSAR 6200.13 resist, which is spin-coated onto the samples. The resist is exposed by electron beam lithography and subsequently developed. The patterns can be transferred to the Si3N4 device layer via reactive ion etching (RIE), where the etching depth of the waveguide layer is 300 nm. The sample is then thoroughly cleaned. Later, the grating layer is processed by CSAR 6200.09 resist and RIE. The grating layer etching depth is 20 nm. After a final clean, plasma-enhanced chemical vapor deposition (PECVD) is used to deposit 500 nm of SiO2 upper cladding.

For our grating outcoupler, the single-mode waveguide to slab waveguide beam expander and apodized grating are shown in Fig. 3(b). The length of the slab waveguide beam expander is designed to be 2 mm, which allows for better beam expansion. The size of the apodized grating area is 300μm×300μm. Moreover, the chip uses the edge coupler shown in Fig. 3(c) to couple light from the lens fiber to the single-mode waveguide. In order to facilitate coupling, we use a 1×2 multimode interference (MMI) coupler for beam splitting, as shown in Fig. 3(d). One beam of light is received by the lens fiber after passing through the single-mode waveguide and edge coupler, and one beam of light passes through the slab waveguide beam expander into the grating outcoupler. Figure 3(e) shows the confocal micrograph of the grating.

Afterwards, we measure the on-chip grating outcoupler. Our measurement setup uses a beam quality analyzer mounted on a 3D displacement stage to image the beam emitted by the grating and measure the beam profile at different heights above the chip surface. Figure 4(a) shows an optical image of the beam emitted from the grating outcoupler on the chip. Figures 4(b) and 4(c) show the beam profiles along the y and z directions along with Gaussian fits, respectively. The results indicate the fitted beam waist radius along y and z as 814 and 972 µm, respectively. As we can see, the beam waist radius is different from the theoretical design value, which indicates the existence of a divergence angle of the beam. By measuring the beam at different heights of the chip [Fig. 4(d)], we can obtain the emission and divergence angle. It can be seen from Fig. 4(e) that beam position varies with height, and the linear fit reveals a slope of −0.45, which corresponds to an emission angle of 24.38°. The measured emission angle is smaller than 30°, which is mainly attributed to the larger grating etching depth of 20 nm. Similarly, by a linear fit of beam spot size with height in Fig. 4(f), we obtain the slopes of 0.05 and 0.06 along the y and z directions, respectively, i.e., divergence angles of 2.98° and 3.32°. Furthermore, the measured loss from the lens fiber to beam emission is in total 17.3 dB, which includes edge coupling loss, single-mode waveguide propagation loss, 1×2 MMI coupler insert loss, and grating outcoupler loss.

To demonstrate the application of our designed device in MOTs, here we design an on-chip emission system as shown in Fig. 5(a). The three grating outcouplers are located at 120° positions centered on a circle of radius 2.9 mm. The light is coupled from the lens fiber into the single-mode waveguide by the edge coupler and expanded to a lateral Gaussian profile at the end of the slab waveguide beam expander. In addition, the incident light is divided into four beams using three 1×2 MMI couplers, where three beams are transmitted to the grating outcouplers and one beam is used for coupling alignment. Figure 5(b) exhibits an optical image of emitting beams at 6 mm height. The area inside the red circle is the intersection of the three grating emission beams, whose area size is about 2mm×2mm. The red dashed box area is a higher-order diffraction mode. This mode does not intersect in MOTs and hence neither contributes nor is detrimental to cooling. The blue dashed box area is the scattered light at the end of the grating outcoupler. The optical images of the beam at different heights of the chip for our system are shown in Fig. 5(c). The result shows that the beam gradually separates as the height increases.

In summary, we proposed and demonstrated a large-mode-diameter grating outcoupler with a near-Gaussian-profile emission beam at 780 nm wavelength on the Si3N4 platform using the principle of apodized gratings. By mirroring the coupling strength to reduce the process difficulty and optimizing the pitch and duty cycle of the grating, the grating outcoupler can theoretically allow a free-space beam waist radius of 100 µm. The experimental results show that the device achieves an emission angle of 24.38° and divergence angles of 2.98° and 3.32° along the y and z directions, respectively. Using the divergence angle, we can obtain a beam on the millimeter scale. Moreover, the measured loss from the lens fiber to the beam emission is in total 17.3 dB, which is mainly composed of 0.35 dB insertion loss of the 1×2 MMI coupler, 4.69 dB edge coupler coupling loss, 9.76 dB grating outcoupler coupling loss, and 2.5 dB waveguide transmission loss, and can be further reduced by optimization. We also designed an on-chip emission system with three grating couplers, which can achieve a 2mm×2mm beam intersection area at a height of 6 mm on the chip. However, the cooling and trapping of atoms also involve changing the polarization of the six beams. We can convert these beams to the required circularly polarized light by designing a metasurface on the surface of a chip or using an electro-optical modulator to shift the phase of light^[22]. As for the reflection of the beams, it can be achieved by a metasurface^[23]. Combining these optimizations and research is expected to achieve a large-scale application of on-chip MOTs in the future.