Fig. 1. Working principle of emitting OAM beams with different topological charges using an on-chip OPA. (a) Schematic of the proposed OAM OPA chip, detailing the essential components and interconnection structures. (b) Method of generating the proposed multiple-OAM OPA. The etching pattern of the forked grating is achieved using a spiral phase distribution ($l=1$) and a $1\times 3$ Dammann grating array. The layout of the multiple-OAM OPA is the intersection of the forked grating and the waveguide array.

Fig. 2. (a) Schematic of the designed $1\times 3$ Dammann grating. The grating pitch ($\mathrm{\Lambda }$) is $2.6\mu \mathrm{m}$, and the lengths of the various segments within the grating are $L_1=0.838\mu \mathrm{m}$, $L_2=0.160\mu \mathrm{m}$, $L_3=0.666\mu \mathrm{m}$, $L_4=0.349\mu \mathrm{m}$, $L_5=0.282\mu \mathrm{m}$, and $L_6=0.305\mu \mathrm{m}$. (b) Emitted diffraction orders $+3$, $+4$, and $+5$ of far-field patterns with the left input as a function of wavelength. The red regions indicate the blind zone. (c) Far-field patterns with left and right inputs as a function of wavelength. The dashed box indicates that six diffractions (orders $\pm 3$ through $\pm 5$) with bidirectional inputs cover a 180-deg FOV in the wavelength range of 1510 to 1630 nm. (d) Spacing between the waveguide and grating as a function of distance before and after PSO. (e) Schematic of the WG-DC structure. (f) Optical power distributions within the proposed WG-DC structure at 1510, 1570, and 1630 nm. The power distributions at these wavelengths resemble Gaussian distributions.

Fig. 3. Simulated and measured far-field intensities for vertical emission ($\phi =0\mathrm{deg}$). (a) Simulated far-field patterns, amplitudes, and phase profiles of three orders ($+3$, $+4$, and $+5$) at 1565 nm with left input. (b) Measured far-field intensities and interference patterns of the emitted OAM lights. (c) Measured far-field intensity profiles of the $y$-polarized ${\mathrm{OAM}}_{+4}$ at 1565 nm following a rotation of the polarizer (0, 45, and 90 deg). The arrows indicate the angles of the polarizer. (d) Zoomed-in and microscopic images of the packaged device, consisting of the $3.5\mathrm{mm}\times 4.5\mathrm{mm}$ multiple OAM OPA chip wire bonded to a silicon interposer, along with left and right optical fiber inputs. (e) Experimental setup used to characterize the far-field profiles of the multibeam OPA (laser: Keysight 81960A). PC, polarization controller; VOA, variable optical attenuator; HWP, half-wave plate; P1 and P2, polarizers; BS, beam splitter; $\text{L}1$, $\text{L}2$, and $\text{L}3$, lenses; IR-CCD, infrared charge-coupled device. Inset: FoM versus iteration and far-field profiles before and after phase alignment.

Fig. 4. Simulated and measured far-field intensities of emitted multiple vortices with different wavelength inputs. (a) and (b) Simulated and measured far-field emission patterns in a wavelength range from 1480 to 1640 nm with left input (up) and left and right inputs (down), respectively. (c) Angle sweeping of emitted diffraction orders $\pm 3$, $\pm 4$, and $\pm 5$ with bidirectional inputs. (d) Measured far fields of multiple vortices at different emission angles with respect to the $\phi$ axis.