Tuesday 16th August 2022

Ultra-compact broadband polarization diversity orbital angular momentum generator with

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INTRODUCTION

The spin angular momentum (SAM) of light is one component of angular momentum that is associated with quantum spin and light having circular polarization states. When a light beam is circularly polarized, each of its photons carries an SAM of ±ħ, where ħ is the reduced Plank’s constant and ± sign is positive for left and negative for right circular polarizations. There is another component of angular momentum, known as orbital angular momentum (OAM) of light, that is dependent on the field spatial distribution but not on the polarization. When a light beam has a helical phase structure exp(iℓθ), as recognized by Allen and co-workers in 1992 (1), each of its photons carries an OAM of ℓħ, where ℓ is the topological charge and θ is the azimuthal angle. The magnitude and sign of ℓ represent the twist rate and twist direction of the helical phase structure. Unlike SAM having only two possible values, OAM, in principle, can take theoretically unbounded values of ℓ. OAM-carrying light has a basic property of “dislocations in wave trains,” characterized by phase singularity at the beam center and resultant donut-shaped intensity profile, also called optical vortex, a family of “singular optics.” The distinct features of OAM have promoted a variety of applications, including manipulation, trapping, tweezer, imaging, microscopy, sensing, metrology, astronomy, nonlinear interaction, and quantum information processing (28). Very recently, OAM has also seen its potential applications in free-space, fiber-based, and underwater optical communications (917). Traditionally, wavelength and polarization physical dimensions of light have been widely used to increase the transmission capacity by multiplexing multichannel data information. However, these conventional techniques have seen their capacity limit after being fully developed. The space-division multiplexing (SDM) exploiting the spatial structure (the only known physical dimension of light left) provides a promising solution to address the emerging capacity crunch and promises the sustainable increase of aggregate transmission capacity of optical communications (18). OAM-carrying spatial modes, forming another mode basis, offer an alternative approach to SDM-enabled optical communications (911).

To enable OAM communications, generating OAM-carrying light beams is of great importance. So far, many techniques have been demonstrated for generating OAM modes, such as laser cavities, mode converters, spatial light modulators (SLMs), spiral phase plates, q-plates, fibers, photonic integrated devices, metamaterials, and metasurfaces (2, 1935). The most convenient way to generate OAM modes is to use the commercially available SLMs (24), which, however, are expensive and relatively bulky. In recent years, photonic integrated OAM-carrying optical vortex emitters have been reported (2532). Silicon photonics is considered to be an attractive photonic integration platform because of its small footprint for high-density integration, low power consumption, and complementary metal-oxide semiconductor compatibility (36). These OAM generation techniques show impressive performance (1935). However, most of them have either narrow bandwidth or single-polarization operation or complicated structure with a relatively large footprint. OAM, in physics, is fully compatible with other physical dimensions of light such as wavelength and polarization. The fully combined use of OAM multiplexing technique with already existing well-established multiplexing techniques (wavelength and polarization) is essential to OAM-assisted multidimensional optical communications, that is, the wavelength and polarization properties should be also considered in the design of an OAM generator. In this scenario, a laudable goal would be to develop an ultra-compact broadband polarization diversity OAM generator on a silicon platform.

Here, we propose and demonstrate an ultra-compact broadband polarization diversity photonic integrated OAM generator on a silicon platform. A simple two-dimensional (2D) subwavelength surface structure (superposed holographic fork gratings) is formed on top of the silicon waveguide to couple the in-plane guided mode in the waveguide to the out-plane polarization diversity OAM mode in free space with superior performance (x-pol. OAM+1, x-pol. OAM−1, y-pol. OAM+1, y-pol. OAM−1). The distinct features of broadband and polarization diversity imply the full compatibility of the ultra-compact footprint OAM generator with existing physical dimensions of light such as wavelength and polarization.

RESULTS

Concept, principle, and theory

The concept and principle of the designed chip-scale broadband polarization diversity OAM generator on a silicon platform are illustrated in Fig. 1, in which the incident fundamental mode (TE0) from four ports (in-plane guided mode) is coupled into the polarization diversity free-space OAM mode (out-plane vertically emitted mode) by the 2D subwavelength surface structure (superposed holographic fork gratings). The zoom-in superposed holographic fork grating region is shown in Fig. 1A. The formation, principle, and theory of the surface grating on top of the silicon waveguide rely on the holographic method (37, 38), which could be briefly explained as follows.

<a rel="nofollow" href="https://advances.sciencemag.org/content/advances/5/5/eaau9593/F1.large.jpg?width=800&height=600&carousel=1" title="Concept and principle of chip-scale broadband polarization diversity OAM generator on a silicon platform. (A) Zoom-in 2D subwavelength surface structure (superposed holographic fork gratings) region. (B and C) Illustration of holographic method producing fork gratings. The coupled interference between the vertically incident x-pol. (B) or y-pol. (C) OAM mode and the x-pol. (B) or y-pol. (C) TE0 in-plane guided mode forms a fork grating on top of the silicon waveguide with the fork opening direction along x (B) or y (C). (D to F) Superposed holographic fork gratings G(x, y) (D) formed by the superposition of two fork gratings of G1(x, y) with the fork opening direction along x (E) and G2(x, y) with the fork opening direction along y (F). (D) to (F) correspond to (A) to (C), respectively. (G to J) Superposed holographic fork gratings for generating broadband polarization diversity x-pol. OAM+1 (G), x-pol. OAM−1 (H), y-pol. OAM+1 (I), and y-pol. OAM−1 (J) under different incident conditions of −y-input x-pol. (G), y-input x-pol. (H), −x-input y-pol. (I), and x-input y-pol. (J) TE0 in-plane waveguide mode. x-Pol., x-polarization; y-Pol., y-polarization." class="fragment-images colorbox-load" rel="gallery-fragment-images-786395598" data-figure-caption="

Fig. 1 Concept and principle of chip-scale broadband polarization diversity OAM generator on a silicon platform.

(A) Zoom-in 2D subwavelength surface structure (superposed holographic fork gratings) region. (B and C) Illustration of holographic method producing fork gratings. The coupled interference between the vertically incident x-pol. (B) or y-pol. (C) OAM mode and the x-pol. (B) or y-pol. (C) TE0 in-plane guided mode forms a fork grating on top of the silicon waveguide with the fork opening direction along x (B) or y (C). (D to F) Superposed holographic fork gratings G(x, y) (D) formed by the superposition of two fork gratings of G1(x, y) with the fork opening direction along x (E) and G2(x, y) with the fork opening direction along y (F). (D) to (F) correspond to (A) to (C), respectively. (G to J) Superposed holographic fork gratings for generating broadband polarization diversity x-pol. OAM+1 (G), x-pol. OAM−1 (H), y-pol. OAM+1 (I), and y-pol. OAM−1 (J) under different incident conditions of −y-input x-pol. (G), y-input x-pol. (H), −x-input y-pol. (I), and x-input y-pol. (J) TE0 in-plane waveguide mode. x-Pol., x-polarization; y-Pol., y-polarization.

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Fig. 1 Concept and principle of chip-scale broadband polarization diversity OAM generator on a silicon platform.

(A) Zoom-in 2D subwavelength surface structure (superposed holographic fork gratings) region. (B and C) Illustration of holographic method producing fork gratings. The coupled interference between the vertically incident x-pol. (B) or y-pol. (C) OAM mode and the x-pol. (B) or y-pol. (C) TE0 in-plane guided mode forms a fork grating on top of the silicon waveguide with the fork opening direction along x (B) or y (C). (D to F) Superposed holographic fork gratings G(x, y) (D) formed by the superposition of two fork gratings of G1(x, y) with the fork opening direction along x (E) and G2(x, y) with the fork opening direction along y (F). (D) to (F) correspond to (A) to (C), respectively. (G to J) Superposed holographic fork gratings for generating broadband polarization diversity x-pol. OAM+1 (G), x-pol. OAM−1 (H), y-pol. OAM+1 (I), and y-pol. OAM−1 (J) under different incident conditions of −y-input x-pol. (G), y-input x-pol. (H), −x-input y-pol. (I), and x-input y-pol. (J) TE0 in-plane waveguide mode. x-Pol., x-polarization; y-Pol., y-polarization.

The target OAM mode, having a 3D spiral phase structure (e.g., y-pol. OAM+1 in Fig. 1C), is vertically incident to the waveguide surface. Meanwhile, there is also an in-plane guided mode (e.g., y-pol. TE0 along x direction) propagating from left to right in the waveguide (Fig. 1C). The target OAM mode and the in-plane guided mode are expressed asEOAM=Aexp(iℓθ)(1)Ewaveguide=Bexp(ikx)(2)where A and B are amplitudes of the target OAM mode and the in-plane guided mode, respectively. ℓ is the topological charge or order of OAM mode (ℓ = +1 in Fig. 1C), and θ is the azimuthal angle. k is the propagation constant of the silicon waveguide mode. The azimuthal angle θ in polar…

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