Nonlinearity-induced PT-symmetry without material gain

Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously sat...

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Bibliographic Details
Published in:New journal of physics 2016-05, Vol.18 (6), p.65001
Main Authors: Miri, Mohammad-Ali, Alù, Andrea
Format: Article
Language:English
Subjects:
Beams (radiation)
Hamiltonian functions
Lattice vibration
Lattices
nonlinear optics
Nonlinearity
Parameter modification
parametric processes
Parity
parity-time symmetry
Physics
Symmetry
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Summary:Parity-time symmetry has raised a great deal of attention in optics in recent years, yet its application has been so far hindered by the stringent requirements on coherent gain balanced with loss. In this paper, we show that the conditions to enable parity and time symmetry can be simultaneously satisfied for a pair of modes with mixed frequencies interacting in a nonlinear medium, without requiring the presence of material gain. First, we consider a guided wave structure with second order nonlinearity and we derive the PT-symmetric Hamiltonian that governs the interaction of two waves of mixed frequencies when accompanied by a high intensity pump beam at the sum frequency. We also extend the results to an array of coupled nonlinear waveguide channels. It is shown that the evolution dynamics of the low-frequency waves is associated with a periodic PT-symmetric lattice while the phase of the pump beams can be utilized as a control parameter to modify the gain and loss distribution, thus realizing different PT lattices by design. Our results suggest that nonlinear wave mixing processes can form a rich platform to realize PT-symmetric Hamiltonians of arbitrary dimensions in optical systems, without requiring material gain.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/18/6/065001