Aliasing-free optical phased array beam- steering with a plateau envelope

We investigate the feasibility of generating a plateau envelope for beam-steering with optical phased arrays (OPAs). The design guidelines are summarized from numerical simulations and verified with a fabricated chip, which incorporates both a couplingsuppressed curved waveguide array with a pitch of 0.8 μm for light emission and a 1-μm-long silica cavity for envelope tailoring. This silicon-on-insulator (SOI) based device demonstrates aliasing-free beam-steering over the entire field-of-view available (−32°~32°) with a far-field addressability of 6.71°. The steered beam exhibits a plateau envelope, with a peak intensity fluctuation of less than 0.45 dB, from −30° to 30°. These results represent a significant step towards realizing integrated OPA for optical beam-forming with a large aliasing-free steering range and a uniform beam intensity. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

main advantag (72% in [14]) That being far-field diffra the peak inten OPAs exhibit the diffraction efficient wide smaller emitti numerically d in the field o required.
Here, we a array of a uni the plateau en through the im both the refle emitting struc verified nume The paper phased arrays will be review We will then envelope via will be presen concluding se

Operating
Phased array active emitter common inpu multiple cohe individually. When the bea pattern will e approximation element diffra while the con beam-steering ges of such dis provided by th g said, the bea action pattern nsity of the m t similar steerin n pattern of th e range operatio ing structure w demonstrated it f optical phase address the abo form 0.8 μm p nvelope. The f mplementation ection in the s cture, to prune erically and dem r is organized a s, especially th wed. Basic con elaborate on simulation in s nted in section ection.
g principle a is an array of rs or with pas ut. Generally, erent channels Figure 1 depic ams processed merge, enablin n, the far-field action pattern. ntinuous spatia g. 1. Schematic of mon laser input, a b corresponding ante spersion-engin he uniform arra am-steering en of the single e main lobe at la ng behavior du e element. To on, Fourier opt with enhanced ts feasibility [ ed arrays due ove issues by c pitch, together w former introdu n of curved wa silica cavity, a e the diffractio monstrated wit as follows. In s he half-wavelen ncepts concern the investigati section 3 where ( ) I θ represents the far-field angular intensity distribution of a phase-aligned (an identical phase difference of ϕ is applied between adjacent channels) array with N antennas of size a placed at a pitch of d , 0 I stands for the unitary peak intensity in the far-field if only one channel is excited, the second term 2 (sin ) α α is a squared sinc function, representing the far-field diffraction pattern of a uniformly-lit square slit, the last term, a function of ( ) , corresponds to the multi-slit interference pattern, and k represents the free space wavenumber of current light frequency. For unmodulated grating lobes, each lobe possesses a peak intensity of 2 0 N I . Equation (1) indicates that the far-field intensity distribution of a uniform array is comprised of a multi-slit interference pattern modulated by the far-field diffraction pattern of the elementary emitter.
Additionally, from the Fourier Optics perspective, the source field could be expressed as an a-size square slit being spatially convolved to a d-pitch comb, while in the far-field, convolution is transformed into multiplication, applying the modulation effect to the multi-slit interference pattern. Therefore, it could be concluded that, for uniform arrays, the overall envelope is solely dependent on the emission properties of the elementary emitter. Besides, the number of interference grating lobes are exclusively dependent on the comb pitch. This insight permits the universal application of the following conclusions as long as the array is uniform, allowing both their extension into two-dimensional arrays as well as the tailoring of the envelope by designing the elementary emitter.
The first conclusion is derived through locating the grating lobes, i.e., the maximums of the last term: , implying that the far-field addressability is largely dependent on the total array span Nd .

Dispersion engineering and coupling suppression
The major obstacle to implement a uniform array with a small pitch originates from the intrinsic drawback of dielectric waveguides, where a significant portion of the guided mode resides outside of the geometry boundaries of the high-index core [15,16]. Under the circumstances that such wave-guiding structures are narrowly spaced for a long propagation length [12], which is common in phased arrays with grating structures as passive phased antennas responsible for steering the beam via wavelength tuning [1,7,9], strong coupling will emerge and subsequently compromise the far-field pattern as demonstrated in [13].
To alleviate the undesirable coupling, dispersion engineering relies on the introduction of phase mismatch between the modes inside abreast waveguides, so adjacent channels guide light-wave modes of different propagation constants. This technique has been demonstrated both in the field of mode-division multiplexing (MDM) [16][17][18] as well as in the efforts to achieve a higher waveguide density from a platform perspective [19,20]. As mentioned in section 1, superlattice comprising waveguides of different widths [20] have been adopted for coupling suppression of an OPA with a half-wavelength pitch in [14], demonstrating the feasibility of the aforementioned principle.
Based on the same scheme, we propose to introduce the phase mismatch by implementing an array of curved waveguides with different radii, imposing a unique propagation constant to each phased channel [21]. A similar structure has been simulated and demonstrated as an MDM MUX/DEMUX in [22], exhibiting an averaged crosstalk suppression of 20 dB. Therefore, the related design details are omitted here. The main advantages for adopting a curved waveguide array for coupling suppression include a simplified yet robust design where the coupling is not only suppressed in adjacent channels but throughout the array, an improved luminous uniformity across the array, as well as comparable scalability if the prior transition stages are carefully designed.

Generation of the plateau envelope
To the best of our knowledge, this is the first time that a plateau envelope has been investigated and characterized in the field of OPAs. As previously discussed, the beamsteering envelope is the far-field diffraction pattern of the emitting element. More precisely, the envelope is the averaged diffraction pattern of all emitting elements should they differ from each other. Before providing the related evidence, we first claim that the silica cavity renders different tailoring to the diffraction pattern of the emitter w.r.t. its relative position inside the array. Nonetheless, the varying diffraction patterns converge sharply from the flank to the center, allowing the characterization of the overall tailoring effect via the characterization of the far-field diffraction pattern of the central emitter. Additionally, it should be noted that the silica cavity exists between the emission facet of the uniform array and the free space. Therefore, it is relatively insensitive to the optical circuit design of the array. That is why in this section, most simulations will be based on uniform arrays comprising straight waveguides with coupling strengths tuned by coupling length. By default, the simulation wavelength is 1.55 μm, the array pitch is 0.8 μm, the coupling length is 7 μm, which introduces a limited coupling close to that of the curved waveguide array. Besides, the cross-section of the standard waveguide is 220 nm high, 500 nm wide, surrounded by thick silica layers as cladding and perfectly matched layers (PMLs) to eliminate reflection on all sides. The central waveguide indicates the 8th waveguide in an array of 16 channels.

Observation and characterization
The initial observation of this effect emerged from the device design stage, the goal of which is to establish a finite-difference time-domain (FDTD) model to simulate the beam-steering process of a g of the silicon air, where mu of the central array, i.e., the in the out-of- Figure 3 show far-field diffra the silica cavi  Regardless of the configurations, the intensity distributions generally rise from −90° to the peak/plateau and decline from the peak/plateau to 90°. The strength of the tailoring is characterized by calculating the angular range between the points where its optical intensity drops to 90% of the peak value, namely the angular plateau size. It has been confirmed in all parametric sweeps that the in-band intensity variation is correlated with the angular plateau size, implying that the larger the plateau is, the smaller the in-band variation is. Therefore, only the angular plateau size illustrated in Figs. 3(e) and 3(f) are adopted for the characterization of the tailoring strength. A comparison between the parallel-axis intensity distribution with or without the silica cavity is provided in Fig. 3(g) to highlight the tailoring.

Analyses and design guidelines
Though 3D-FDTD simulation provides accurate modeling for general purposes, it would be computationally intense to perform parameter sweeps with the desired accuracy. Besides, albeit our conclusions could be extended to two-dimensional arrays regardless of their architecture, our current design is a one-dimensional array involving no variation in the axis perpendicular to the circuit (namely the Z axis). Therefore, two-dimensional FDTD simulation incorporating circuit level propagation feature, i.e., the variational FDTD solver, is employed for the following simulations. In such a scenario, it should be noted that the simulated far-fields are the Fourier transform from one-dimensional source fields with no information concerning the expansion of the mode in the Z axis. In other words, the far-field is projected with the assumption that the mode field is uniform in the Z axis, implying that the cavity effect is more explicitly revealed for a well-defined one-dimensional source field, rather than being averaged over the Z axis with Gaussian distribution characteristics.
Based on the characteristic metric, i.e., the angular plateau size, we provide the guidelines as well as the analyses on how to obtain a plateau envelope. To begin with, the cavity effect on a single waveguide is verified by varying the cavity length, exhibiting no tailoring effect as commonly reported in other applications. By calculating the output-transmitted intensity as a function of cavity length, the typical Fabry-Pérot (F-P) resonant effect emerges, implying that the cavity could potentially facilitate the out-coupling of the beam from the waveguide to the free-space. Therefore, we introduce another metric, namely transmittance, which calculates the average output intensity in the far-field over the largest angular plateau range ever documented in the parameter sweep, for the characterization of the out-coupling. Note that the transmittance here is a redefined relative metric which is proportional to its commonlyknown physical definition. The simulated field pattern, as well as the extracted performances, are presented in Fig. 4, revealing the aforementioned phenomenon.
Since the cavity has no tailoring effect on one single waveguide, we then vary the total number of waveguides inside the array from 1 to 55, while the cavity length is fixed to 1 μm, to verify the contribution from the size of the array. The results are shown in Fig. 5. It is confirmed that with this arrangement, the corresponding far-field diffraction patterns converge to the plateau envelope rapidly both in terms of their shape as well as the shaping factor, i.e., the angular plateau size. Meanwhile, the out-coupling transmittance is generally stabilized.
Additionally, the default configuration is revisited to investigate the contribution of the cavity length. Light is launched from the 8th channel in a fixed array comprising 16 waveguides. The cavity length varies from 0 to 2 μm with a step-size of 0.05 μm. As shown in Fig. 6, the length of silica cavity largely modifies the far-field pattern, which is quantized by the fluctuation of the angular plateau size. The out-coupling measured by the mean value of transmittance follows the pseudo-periodic trend as previously presented in Fig. 4(b) with a similar period. It is revealed that a 1-μm-long silica cavity provides a significant tailoring effect, together with a moderate improvement in transmittance compared to no cavity.  Finally, to as well as to excited with l the array. By exhibiting a p is close to the in Section 2. fluctuates wit   To conclude, the demonstrated uniformity among the peak intensities of the main lobes not only extends the effective steering range for LiDAR application operating in a noisy environment, but also, it provides a hardware efficient solution for OPA-based free-space optical communications, where the angular plateau implies a stable quality of service (QoS) throughout the typical indoor scenario. Additionally, the dynamic range of the sensors in the aforementioned applications could now be traded for refined resolution, providing either a more precise distance measurement, or more symbols for signal representation.

Conclusions
We have reported an SOI-based OPA with a curved waveguide array for inter-channel coupling suppression. The far-field diffraction pattern presents a plateau envelope, caused by the F-P effect from a silica cavity at the emitting end of the waveguide array. Numerical simulations were conducted to investigate the influence of various geometric parameters on the far-field pattern. It was revealed that a 1-μm-long silica cavity can effectively increase the plateau size in the envelope of the diffraction pattern and the optical transmittance of the OPA. The measurement of the OPA demonstrates aliasing-free beam-steering with a plateau envelop with intensity fluctuation of less than 0.45 dB from −30° to 30°, consistent with the numerical simulations. For the current design, it is estimated that the total insertion loss is around 12.4 dB with a major portion originated from the regular uniform grating coupler with an etched depth of 70 nm. By adopting more complicated designs, e.g. adiabatic grating with an underlying metal layer [24], the coupling loss can be reduced to 0.58 dB/facet. Additionally, by substituting strip waveguides with shallowly-etched rib waveguides [25] for long straight sections, and by fabricating the strip waveguides with ArF immersion lithography [26], the average waveguide propagation loss can be reduced to 0.2 dB/cm. The MMI loss can be controlled within 0.06 dB/stage with an improved design [27]. By striking a compromise between the plateau size and the emitting efficiency, the emitter reflection loss can be suppressed to below 2 dB. Therefore, we estimate that the device insertion loss can be less than 3 dB with an optimized design. Moreover, low loss waveguides and MMIs also increase the scalability of the design. To conclude, it is demonstrated that the silica cavity can tailor the far-field diffraction pattern of the OPA, which opens a new degree of design freedom to achieve the desired beamforming and steering with high energy concentration and uniformity of luminescence.