Direct phase mapping of broadband Laguerre-Gaussian metasurfaces

We report on the fabrication of metasurface phase plates consisting of gold nanoantenna arrays that generate Laguerre-Gaussian modes from a circularly polarized Gaussian input beam. The corresponding helical phase profiles with radial discontinuities are encoded in the metasurfaces by the orientation of the nanoantennas. A common-path interferometer is used to determine the orbital angular momentum of the generated beams. Additionally, we employ digital holography to record detailed phase profiles of the Laguerre-Gaussian modes. Experiments with different laser sources demonstrate the broadband operation of the metasurfaces.

Optical vortex beams have been the subject of intense research activities in recent years 1,2 and have found numerous applications in optical micromanipulation 3 , quantum optics 4 , imaging 3 , and communications 5 . Their characteristic feature is a helical phase distribution with a phase singularity on the optical axis. As a consequence of this, optical vortex beams possess annular intensity cross sections with strictly zero on-axis intensity. Moreover, they carry an orbital angular momentum (OAM) ofhl per photon, which is independent of the polarization state of the beam. Here, l is the so-called topological charge that determines the Optical vortex beams can be generated by a number of different methods, e.g., astigmatic mode converters 1 , spiral phase plates 6 , spatial light modulators 7,8 , and diffraction gratings 9 .
These so-called meta-atoms serve as light scattering elements with properties that can be engineered by their geometry and material composition. A light beam impinging on the metasurface interacts with the meta-atoms and gives rise to a scattered wave. The resulting wave front is thereby determined by the spatial variation of the scattering properties of the metasurface. By encoding an azimuthal phase factor exp (ıϕl) into the metasurface, one can generate an optical vortex beam with topological charge l from a Gaussian input beam. In particular, geometric metasurfaces based on the Pancharatnam-Berry phase concept 12,13,15 are suited for this purpose, as they combine a simple design principle with broadband operation and ease of fabrication. This type of metasurface employs simple dipole antennas, e.g., plasmonic nanorods, as scattering elements to partially convert a circularly polarized input beam into light with the opposite circular polarization. The phase shift φ introduced by one of the dipoles is given by φ = 2σθ, where θ is the angle enclosed between the dipole axis and a reference axis (in our case the x-axis) and σ characterizes the circular polarization state of the incident light (right circular polarization (RCP): σ = 1, left circular polarization (LCP): σ = −1). Based on this simple rule, the desired phase distribution φ(x, y) can be directly translated into the required orientation θ(x, y) of the meta-atom at the position (x, y) in the metasurface.
In this article, we report on the generation of Laguerre-Gaussian beams using geometric metasurfaces consisting of gold nanorod antennas. A circularly polarized Gaussian input beam is transmitted through a metasurface to imprint the phase distribution φ l,p (r, ϕ) of the desired LG l,p beam onto the scattered wave with the opposite circular polarization: Here, u(x) is the unit step function, L l p (x) is a generalized Laguerre polynomial, and w 0 is the waist radius of the incident Gaussian beam. The first addend ϕl in equation (1) is responsible for the helical phase profile, while the second addend accounts for the phase jumps of the LG l,p beam in radial direction.
The geometric metasurface phase plates are fabricated on top of an indium tin oxide covered glass substrate by standard electron beam lithography in combination with thermal evaporation of gold. Each metasurface has a circular shape with a diameter of 100 µm and consists of a square array of gold nanorods with a period of 500 nm. The dimensions of a nanorod are 220 nm × 60 nm × 40 nm (length × width × height). For these parameters, the nanorods support a localized plasmon mode with a resonance wavelength of 1080 nm. The orientation of the nanorods in a given metasurface encodes the desired phase distribution.
LG 0,0 LG 0, 1 LG 0,2 LG 1,2 LG 1,1 LG 1,0 For the generation of a Laguerre-Gaussian beam with indices l and p, the angle θ(r, ϕ) between the long axis of the nanorod at the position (r, ϕ) and the x-axis is chosen to be θ = φ l,p (r, ϕ)/2. To record detailed phase profiles of the generated Laguerre-Gaussian beams directly behind the metasurface phase plates, we employ a coherence-controlled holographic microscope (CCHM). This microscope allows the use of spatial and temporal incoherent light source for illumination 17,18 . While typical off-axis systems cannot operate with incoherent light, the CCHM can handle the introduced incoherence. Therefore, it holds the advantage of an in-line system utilizing incoherent light for the suppression of coherent noise and combines LG 1,0 LG -1,0 LG -2,0 LG 2,0 LG 3,0 LG LG 2,0 LG 1,0 LG 0,0 LG 0,1 LG 1,1 LG 2,1 LG 2,2 LG 1,2 LG transmitted through the sample arm still contains a contribution of the driving field. To retrieve solely the field scattered by the metasurface, we measured and reconstructed the field transmitted through a non-active part of the sample (i.e., without nanorods), which represents the portion of the driving field transmitted due to imperfect setup. This field was subsequently numerically subtracted from the total field transmitted through the active part of the sample. Figure 4b shows the phase reconstructed from CCHM measurements for metasurfaces generating various Laguerre-Gaussian modes. Clearly, there is very good agreement with designed phase distribution. The experiment can also be conducted at different wavelengths. We additionally chose wavelengths of λ 2 = 633 nm and λ 3 = 980 nm to illustrate the broadband working regime of the metasurface. None of these sources drives the rods in resonance. Figure