Fig. 1. (a) Simulation results for uniform power distribution and Gaussian power distribution. (b) Simulated near field of uniform power distribution and Gaussian power distribution for φ direction, θ direction, and φ+θ direction.

Fig. 2. (a) Schematic of the through-type cascaded coupler with Gaussian power distribution. (b) Required power, residual power, and coupling efficiency for the largest Gaussian center-to-edge ratio. (c) The largest SLSR is only 20 dB for the through-type cascaded coupler. (d) Schematic of the Y-branch-assisted cascaded coupler with Gaussian power distribution. (e) Required power, residual power, and coupling efficiency for the largest Gaussian center-to-edge ratio. (f) The largest SLSR can achieve 66 dB for the Y-branch-assisted cascaded coupler.

Fig. 3. (a) Designed 12 dB Gaussian power distribution on 120-channel OPA. (b) Far-field figure with SLSR of 25 dB. (c) Required power, residual power, and coupling efficiency for each channel. (d) Coupling length for each channel.

Fig. 4. (a) Apodized grating emitter with Gaussian power distribution in the near field. (b) Zoomed-in figure in (a).

Fig. 5. (a) Designed 12-dB Gaussian power distribution along 2-mm-long apodized grating emitter. (b) Corresponding SLSR in the far-field figure. (c) Simulated emitting efficiency per pitch and SiO2 duty cycle along the apodized grating emitter. (d) The adjusted value of pitches guarantees the beam in the same direction.

Fig. 6. (a) Schematic of proposed dual-Gaussian power distribution OPA. (b) Microscopy of proposed OPA. (c) SEM image of the apodized grating emitter with the largest SiO2 duty cycle.

Fig. 7. (a) Schematic of the measurement setup. (b) The 2.1  cm×2.1  cm silicon OPA chip is wire-bonded on a PCB.

Fig. 8. (a) Far-field figure before and after calibration. (b) Far-field figure in φ direction; φ SLSR is 15.1 dB at φ=−2.4°. (c) Cross- section of the calibrated far-field figure; θ SLSR is 25 dB.

Fig. 9. (a) Peak-to-valley far-field intensity vibration when phase varies from 0 to 2π for each channel. (b) Simulated far-field figure with measured amplitude distribution of (a).

Fig. 10. (a) Far-field figure of the beam steered in φ direction. (b) Cross section in φ direction; the maximum far-field intensity on each φ value is obtained, and therefore, the largest sidelobe value is obtained. (c) Calculated SLSR and beam width when the beam is steered in φ direction.

Fig. 11. (a) Far-field figure of the beam steered in θ direction when the input wavelength is changed from 1496 to 1580 nm. (b) Cross section in θ direction. (c) Calculated SLSR and beam width when the beam is steered in θ direction. (d) The beam is steered in both φ and θ directions simultaneously.

Fig. 12. (a) Schematic of cascaded couplers. (b) Simulated relationship between coupling efficiency and coupling length. (c) Experimental measurement results for designed 15 dB Gaussian power distribution along 64 channels.

Fig. 13. Number of channel limitations for through-type cascaded couplers. (a) The maximum number of channels is 420 for uniform power distribution. (b) Corresponding coupling lengths. (c) Power distribution, residual power before the nth channel, and coupling efficiency of the nth channel curves. (d) Far-field figure of uniform power distribution in theory, whose SLSR is 13.26 dB.

Fig. 14. Number of channel limitations for Y-splitter-assisted cascaded couplers. (a) The maximum number of channels can reach 1024 with 12 dB Gaussian power distribution. (b) Corresponding far-field pattern with SLSR of 25 dB. (c) Power distribution, residual power before the nth channel, and coupling efficiency. (d) Coupling length distributions.

Fig. 15. (a) Periodic grating emitter with a fixed SiO2 duty cycle of 0.5. (b) Far-field figure of the grating with Λ=0.7  μm; the emitting angle is θ0=8.4°. (c) Emitting efficiency per pitch unit versus SiO2 duty cycle. (d) Grating neff versus SiO2 duty cycle. (e) Far-field emitting angle versus SiO2 duty cycle.

Fig. 16. Principle of PWM technique.

Fig. 17. Gradient algorithm optimization process.

Fig. 18. (a) The far-field intensity changes when electric power increases from 0 to 7 mW, indicating power consumption of 2.7  mW/π. (b) Electric power consumption on each channel when the beam is steered 14° in φ direction; the total power consumption is 332 mW for the proposed 120-channel OPA.

Fig. 19. (a) Measured PWM signal [30]. (b) Every three I/O ports share a common ground in the designed OPA. (c) Improved electric circuits of individual ground.