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We present mode conversion between the higher order ${{\bf E}}_{21}^{\boldsymbol{x}}$ and ${{\bf E}}_{12}^{\boldsymbol{x}}$ optical modes in an out-of-plane silicon waveguide exhibiting Berry's phase. Superpositions of the ${{\bf E}}_{21}^{\boldsymbol{x}}$ and ${{\bf E}}_{12}^{\boldsymbol{x}}$ waveguide modes form quasi-Laguerre-Gaussian modes with total angular momentum of $1\hbar $ per photon for a 720 × 600 nm2 silicon waveguide core. When the waveguide is deflected out-of-plane by 22.5°, 50% mode conversion occurs from the ${{\bf E}}_{21}^{\boldsymbol{x}}$ mode to the ${{\bf E}}_{12}^{\boldsymbol{x}}$ mode. The concatenation of a quarter wavelength straight section results in an output with $0.89\hbar $ orbital and $0.15\hbar $ spin angular momentum per photon. Orbital angular momentum generation in a waveguide platform provides a route for on-chip applications that utilize the angular momentum of light for sensing, optical manipulation, non-linear optics, and communications.

We study analytically and numerically the possibility of vortex modes propagation over planar dielectric rectangular waveguides, and consider the problem of waveguide geometry optimization for the support of vortex modes. The results show, that theoretically rectangular waveguides can provide transmission of quasi-TE and quasi-TM modes with high purity states of orbital angular momentum (OAM) in the dominant field component. However, only for the quasi-generate mode of azimuthal order ±1 the constituent eigenmodes can propagate in a phase-matched regime, and the vortex modes of higher azimuthal orders can propagate only with a certain beat length. Moreover, as the target azimuthal order increases, the normalized power of the corresponding OAM state in the modal superposition decreases. The analytical predictions have been verified by numerical electromagnetic simulations of silicon nitride waveguides providing field distributions and OAM spectra of the corresponding modal superpositions.

Radially polarized orbital angular momentum (OAM) beams could be applied in optical manipulation and optical microscopy. An integrated OAM beam emitter with radially polarized radiation is proposed on shallow-ridge silicon microring with azimuthally distributed gratings etched on top of the ring waveguide. Two key structural parameters, the number of grating elements, and the dimension of each grating element are optimized by considering both the OAM order purity (Cp) and the total radiation efficiency (ηall). With elaborate design, Cp = ~98%, ηall = ~49% are achieved by simulations, and the calculated energy ratio between the far-field radially and azimuthally polarized component is more than 11 dB, which indicates that the radially polarized component is predominant in the radiated electromagnetic field.

A simple on-chip integrated structure is proposed to generate optical orbital angular momentum (OAM) beams, where only silicon waveguides and couplers are involved. The operating principle is based on mode converting and proper controlling the phase shift of second-order propagating mode so that OAM modes with charge numbers of 1 or -1 can be selectively generated with mode purity > 90%. The proposed device is very compact with footprint of