March 2018
Spotlight Summary by Riccardo Borghi
Fully controllable adiabatic geometric phase in nonlinear optics
The wave nature of light is revealed whenever interference and diffraction phenomena take place. Such phenomena are related to the phases of the wavefields which, in the underlying superposition process, are combined in such a way that — following Max Born — "interference may be described by the paradoxical words: light added to light does not necessarily give intensified light, but may become extinguished." A fundamental aspect of light is its vectorial nature, which is manifested through polarization properties. Like the phase, also the polarization degree of freedom can be used to control interference effects. The superposition of two coherent waves having orthogonal polarization states does not produce interference fringes, contrary to the superposition of waves of identical polarizations. About 60 years ago, Pancharatnam proved that, by suitably mixing phase and polarization, an additional degree of freedom can be produced. This new degree of freedom is now called Pancharatnam–Berry phase and its nature is purely topological. The geometrical character of this phase was explored about 35 years ago by Berry within the context of the so-called geometric phase. In particular, Berry found that an optical wavefield can accumulate the Pancharatnam phase when its polarization state moves along a closed path on the sphere that represents polarization states (the so-called PoincarĂ© sphere).
In this case, the extra phase coincides with one-half of the solid angle associated to the closed path. Karnieli and Arie propose a new theoretical scheme to produce geometric phases that uses nonlinear optical processes to combine different frequencies and to mimic, in this way, the role played by polarization within the Pancharatnam framework. The authors call such a scheme "spectral polarization." Through an interesting mathematical analogy with the well-known evolution of a spin-1/2 particle in a magnetic field, they devise conceptual schemes to generate geometric phases (via closed as well as open trajectories of the state on the corresponding Poincaré sphere analog), which could be of potential interest in photonics and optoelectronics.
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In this case, the extra phase coincides with one-half of the solid angle associated to the closed path. Karnieli and Arie propose a new theoretical scheme to produce geometric phases that uses nonlinear optical processes to combine different frequencies and to mimic, in this way, the role played by polarization within the Pancharatnam framework. The authors call such a scheme "spectral polarization." Through an interesting mathematical analogy with the well-known evolution of a spin-1/2 particle in a magnetic field, they devise conceptual schemes to generate geometric phases (via closed as well as open trajectories of the state on the corresponding Poincaré sphere analog), which could be of potential interest in photonics and optoelectronics.
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Article Information
Fully controllable adiabatic geometric phase in nonlinear optics
Aviv Karnieli and Ady Arie
Opt. Express 26(4) 4920-4932 (2018) View: HTML | PDF