# STRUCTURED LIGHT Informe resumido

Project ID:
629114

Financiado con arreglo a:
FP7-PEOPLE

País:
Israel

## Final Report Summary - STRUCTURED LIGHT (Structured Light in Photonics Media)

Dynamics of light has fascinated mankind for centuries. Over the last decade the ability to control the propagation of light has become extremely important from the fundamental and technological point of view. By controlling the structure of the light, a wavepacket of light can be endow with unique propagation characteristics. For example, beams with optical vortices carry angular momentum; nondiffracting beams can propagate without diffraction in a finite region of free space; accelerating beams self-bend as they travel, and topological edge modes are robust to defects.

The objective of this project was to discover new structured electromagnetic waves and beams with unique propagation characteristics in novel photonic media. We studied three topics in parallel. We investigated how to control the propagation of light in new fundamental ways by controlling its topological properties, the curvature of the space and by the introducing artificial gauge fields. Our emphasis was on fundamental issues, exploring universal features that also exist in other systems beyond optics.

Now, we will briefly describe the objectives and the work carried out in each one.

Topological insulators are a phase of matter with an insulating bulk and conducting edges. A topological insulator is characterized by a bulk bandgap where topological gapless unidirectional edge states reside. These edge states are robust to any perturbation that does not close the bandgap. In this way, deformations of the system like disorder, strain, or imperfections have little effect on the transport of such topological edge modes. The discovery of topological insulators has motivated the study of several topological systems in optics and photonics with the aim to engineer robust optical devices. Photonic systems are excellent platforms to study topological physics that would be extremely difficult in solid state (e.g., exquisitely tuned disorder) or entirely impossible (e.g., 2D quasicrystals, non-Hermiticity). During this project, we studied fundamentally new topological effects that have never been observed in any system. We show that a photonic quasicrystal lattice can have topological protected photonic transport, and hence we open the study of topological transport to the vast field of quasicrystals. We show that it is possible to store & release and scatter topological edge states into flat bands, allowing new way to control topological light. We study Bloch oscillation of edge state wavepackets in topological photonic lattices and introduce in this way a novel mechanism for controlling the flow of light via band topology. Finally, in contrast to the current mindset, we show that it is possible to have topological protected transport in non-Hermitian photonic lattices with PT-symmetry. We find that in this “merging of non-Hermiticity and topological insulators” gives rise to many new interesting physical phenomena: for example, the existence of “sources and sinks” for the unidirectional protected edge states. Finally, all this let us to propose the first topological lasing system, which is major step in integrating topological properties to optical devices.

Wave propagation in non-Eucledian geometry have very rich dynamics, since the curvature of the space introduces an effective potential which is impossible to obtain in any flat-space homogeneous medium. In this framework, optics represent an ideal platform to study curved-space phenomena, mainly due to the ability to confine light in a curved surface layer covering a 3D body. For example, the pioneering work of Peschel's group that includes theoretical and experimental results on the propagation of light in several curved geometries using curved surface waveguides. We present non-diffracting accelerating beams propagating on spherical surfaces theoretically and experimentally. We demonstrate that these wavepackets have accelerating lobes that propagate on trajectories different from a shortest line between two points due to the interference and curvature of space. We also present a new class of nanophotonic structures with intricate design in full three dimensions inspired by General Relativity (GR) concepts. These photonic structures facilitate control over the dynamics of light, through the space curvature, allowing control over the trajectories, the rate of diffraction and the phase and the group velocities by manipulating the spatial curvature. Finally, we present for the first time topological photonics in curved space. We show that the curvature of the space can induce topological novel physical phenomena that is not possible in flat space.

Gauge fields are a fundamental concept in physics, describing the fundamental interactions between particles. Perhaps the most prominent example is the electro-magnetic field, which is the gauge field describing electromagnetic interaction between electrically charged particles. The concept of an "artificial gauge field": it arises in systems of uncharged particles that behave as if under the influence of a gauge field. An artificial gauge field is not a fundamental property of the physical system – it arises through the geometrical design of the system or through some specific external modulation. We propose and demonstrate an effective Rashba effect –the coupling between the spatial and spin degrees of freedom– in photonic lattices through photonic gauge field engineering. Also, we experimentally demonstrate for the first time wave guiding by purely using artificial gauge fields. That is, we show waveguiding in a composite structure, made of the same material subject to different gauge fields. This new type of optical waveguiding opens new possibilities to confined and manipulated light on chip.

In conclusion, we investigated how to control the propagation of light in new fundamental ways by controlling its topological properties, the curvature of the space and by the introducing artificial gauge fields. The impact of our research is that by changing current mindsets it set the ground for new research areas in optics. Moreover, although we used a photonic platform, we investigate universal features of waves that can also exist in other physical systems beyond optics.

The objective of this project was to discover new structured electromagnetic waves and beams with unique propagation characteristics in novel photonic media. We studied three topics in parallel. We investigated how to control the propagation of light in new fundamental ways by controlling its topological properties, the curvature of the space and by the introducing artificial gauge fields. Our emphasis was on fundamental issues, exploring universal features that also exist in other systems beyond optics.

Now, we will briefly describe the objectives and the work carried out in each one.

Topological insulators are a phase of matter with an insulating bulk and conducting edges. A topological insulator is characterized by a bulk bandgap where topological gapless unidirectional edge states reside. These edge states are robust to any perturbation that does not close the bandgap. In this way, deformations of the system like disorder, strain, or imperfections have little effect on the transport of such topological edge modes. The discovery of topological insulators has motivated the study of several topological systems in optics and photonics with the aim to engineer robust optical devices. Photonic systems are excellent platforms to study topological physics that would be extremely difficult in solid state (e.g., exquisitely tuned disorder) or entirely impossible (e.g., 2D quasicrystals, non-Hermiticity). During this project, we studied fundamentally new topological effects that have never been observed in any system. We show that a photonic quasicrystal lattice can have topological protected photonic transport, and hence we open the study of topological transport to the vast field of quasicrystals. We show that it is possible to store & release and scatter topological edge states into flat bands, allowing new way to control topological light. We study Bloch oscillation of edge state wavepackets in topological photonic lattices and introduce in this way a novel mechanism for controlling the flow of light via band topology. Finally, in contrast to the current mindset, we show that it is possible to have topological protected transport in non-Hermitian photonic lattices with PT-symmetry. We find that in this “merging of non-Hermiticity and topological insulators” gives rise to many new interesting physical phenomena: for example, the existence of “sources and sinks” for the unidirectional protected edge states. Finally, all this let us to propose the first topological lasing system, which is major step in integrating topological properties to optical devices.

Wave propagation in non-Eucledian geometry have very rich dynamics, since the curvature of the space introduces an effective potential which is impossible to obtain in any flat-space homogeneous medium. In this framework, optics represent an ideal platform to study curved-space phenomena, mainly due to the ability to confine light in a curved surface layer covering a 3D body. For example, the pioneering work of Peschel's group that includes theoretical and experimental results on the propagation of light in several curved geometries using curved surface waveguides. We present non-diffracting accelerating beams propagating on spherical surfaces theoretically and experimentally. We demonstrate that these wavepackets have accelerating lobes that propagate on trajectories different from a shortest line between two points due to the interference and curvature of space. We also present a new class of nanophotonic structures with intricate design in full three dimensions inspired by General Relativity (GR) concepts. These photonic structures facilitate control over the dynamics of light, through the space curvature, allowing control over the trajectories, the rate of diffraction and the phase and the group velocities by manipulating the spatial curvature. Finally, we present for the first time topological photonics in curved space. We show that the curvature of the space can induce topological novel physical phenomena that is not possible in flat space.

Gauge fields are a fundamental concept in physics, describing the fundamental interactions between particles. Perhaps the most prominent example is the electro-magnetic field, which is the gauge field describing electromagnetic interaction between electrically charged particles. The concept of an "artificial gauge field": it arises in systems of uncharged particles that behave as if under the influence of a gauge field. An artificial gauge field is not a fundamental property of the physical system – it arises through the geometrical design of the system or through some specific external modulation. We propose and demonstrate an effective Rashba effect –the coupling between the spatial and spin degrees of freedom– in photonic lattices through photonic gauge field engineering. Also, we experimentally demonstrate for the first time wave guiding by purely using artificial gauge fields. That is, we show waveguiding in a composite structure, made of the same material subject to different gauge fields. This new type of optical waveguiding opens new possibilities to confined and manipulated light on chip.

In conclusion, we investigated how to control the propagation of light in new fundamental ways by controlling its topological properties, the curvature of the space and by the introducing artificial gauge fields. The impact of our research is that by changing current mindsets it set the ground for new research areas in optics. Moreover, although we used a photonic platform, we investigate universal features of waves that can also exist in other physical systems beyond optics.