Topologically Controlled Intracavity Laser Modes Based on Pancharatnam-Berry Phase Elhanan Maguid, †,§ Ronen Chriki, ‡,§ Michael Yannai, † Vladimir Kleiner, † Erez Hasman, † Asher A. Friesem, ‡ and Nir Davidson* ,‡ † Micro and Nanooptics Laboratory, Faculty of Mechanical Engineering and Russell Berrie Nanotechnology Institute, Technion - Israel Institute of Technology, Haifa 3200003, Israel ‡ Weizmann Institute of Science, Department of Physics of Complex Systems, Rehovot 7610001, Israel ABSTRACT: Incorporation of a metasurface that involves spin-orbit interaction phenomenon into a laser cavity provides a route to the generation of spin-controlled intracavity modes with different topologies. By utilizing the geometric phase, Pancharatnam-Berry phase, we found a spin-enabled self-consistent cavity solution of a Nd:YAG laser with a silicon-based metasurface. Using this solution we generated a laser mode possessing spin-controlled orbital-angular momentum. Moreover, an experimental demonstration of a vectorial vortex is achieved by the coherent superposition of modes with opposite spin and orbital angular momenta. We experimentally achieved a high mode purity of ∼95% due to laser mode competition and purification. The photonic spin-orbit interaction mechanism within a laser-cavity can be implemented with multifunctional shared- aperture nanoantenna arrays to achieve multiple intracavity top- ologies. KEYWORDS: meta-surface, optical resonator/cavity, topology, laser beam shaping, nanophotonics, Berry phase M anipulation of the lasing mode has been achieved in the past by inserting engineered optical elements inside a laser cavity to control the properties of the output beam. 1-6 Specific examples include (i) intracavity binary masks, amplitude, and phase masks, and diffractive elements for obtaining pure and high order laser modes, 4,7,8 (ii) intracavity polarization elements to obtain radial and azimuthal polar- izations, 9 and (iii) intracavity optical elements to achieve efficient phase locking and beam combining. 10,11 Moreover, intracavity elements in degenerate or near degenerate cavity lasers enable to form large arrays of lasers 12 with tunable spatial coherence 13,14 and to focus light through a rapidly changing scattering medium. 2 Incorporation of a metasurface element, which involves spin-orbit interaction phenomenon, into a laser-cavity may leverage the generation of exotic modes that can be controlled by coupling the spin and orbital angular momentum (OAM) of photons traveling inside the cavity. 15-18 A metasurface is an engineered array of subwavelength nanostructures which enhance light-matter interactions and modulate electromag- netic wave scattering properties. 19-29 By varying the local in- plane orientations θ(x, y) of these nanostructures, a geometric phase mechanism is obtained, 30,31 forming Pancharatnam-Berry phase optical elements (PBOEs). 15,19,20 Specifically, the local in-plane orientations θ(x, y) of the PBOE cause phase delays according to ϕ g (x, y)= -2σθ(x, y), where σ = σ ± = ±1 denotes the sign of spin angular momentum of light (ℏσ ± ). The polarization helicity of light is defined as right (left) circular polarization if the direction of its spin is the same as (opposite to) the direction of propagation. Recently, reflective PBOEs were exploited as output couplers in a solid state laser to obtain scalar vortex beams carrying OAM and optical vectorial vortex beams. 32 As output couplers, the PBOEs do not interact with the laser cavity and do not affect the lasing mode. Also, single mode operation of THz quantum cascade lasers was achieved by focusing light with metasurfaces, and active metasurface waveguide arrays were used to control and switch between the two polarizations of a THz quantum cascade laser. 33,34 Here, we report on the incorporation of a PBOE into a laser in order to achieve a topologically controlled intracavity mode, as shown schematically in Figure 1. This work is the first demonstration of intracavity mode control by the use of dielectric metasurface. Specifically, we designed an efficient dielectric PBOE based on silicon nanoantennas operating in transmission mode shown in Figure 2a. The nanoantennas were 100 nm wide and 400 nm deep, arranged 300 nm apart from each other (center to center) within a diameter of 200 μm. Finite difference time domain simulation predicted a theoretical metasurface efficiency of 82% at a wavelength of 1.064 μm, whereas the experimental efficiency was found to be 73%, due Received: December 12, 2017 Published: March 15, 2018 Letter Cite This: ACS Photonics 2018, 5, 1817-1821 © 2018 American Chemical Society 1817 DOI: 10.1021/acsphotonics.7b01525 ACS Photonics 2018, 5, 1817-1821