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‘Trapped rainbow’ storage of light in metamaterials


Light usually propagates inside transparent materials in well known ways1. However, recent research2,3,4,5,6 has examined the possibility of modifying the way the light travels by taking a normal transparent dielectric and inserting tiny metallic inclusions of various shapes and arrangements. As light passes through these structures, oscillating electric currents are set up that generate electromagnetic field moments; these can lead to dramatic effects on the light propagation, such as negative refraction. Possible applications include lenses that break traditional diffraction limits3,4 and ‘invisibility cloaks’ (refs 5, 6). Significantly less research has focused on the potential of such structures for slowing, trapping and releasing light signals. Here we demonstrate theoretically that an axially varying heterostructure with a metamaterial core of negative refractive index can be used to efficiently and coherently bring light to a complete standstill. In contrast to previous approaches for decelerating and storing light7,8,9,10,11,12,13, the present scheme simultaneously allows for high in-coupling efficiencies and broadband, room-temperature operation. Surprisingly, our analysis reveals a critical point at which the effective thickness of the waveguide is reduced to zero, preventing the light wave from propagating further. At this point, the light ray is permanently trapped, its trajectory forming a double light-cone that we call an ‘optical clepsydra’. Each frequency component of the wave packet is stopped at a different guide thickness, leading to the spatial separation of its spectrum and the formation of a ‘trapped rainbow’. Our results bridge the gap between two important contemporary realms of science—metamaterials and slow light. Combined investigations may lead to applications in optical data processing and storage or the realization of quantum optical memories.

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Figure 1: Trapped rainbow.
Figure 2: Wave propagation in an axially varying LHH.
Figure 3: Ray analysis reveals that the effective left-handed guide thickness is smaller than the physical thickness and can become zero or even negative.
Figure 4: Honed conditions for waveguide coupling, showing simultaneous impedance, thickness and mode matching in adjoining RHH and LHHs.


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We thank A. Klaedtke and D. P. Aryal for discussions and technical assistance. This work was supported by the Engineering and Physical Sciences Research Council (UK).

Author Contributions K.L.T. and O.H. conceived the presented idea. K.L.T. developed the theory, performed the computations and wrote a draft of the paper. A.D.B. contributed to the discussions. O.H. encouraged K.L.T. to investigate metamaterials and slow light and supervised the findings of the work.

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Correspondence to Kosmas L. Tsakmakidis or Ortwin Hess.

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Supplementary Information

This file contains Supplementary Equations. Sections 1 and 3 of the document include the derivation of Eqs. (1)-(4) used in the main body of the Letter. Section 2 discusses the derivation of closed-form expressions for the distances xp12 and xp13 between the ray cross points and the 1-2 and 1-3 media interfaces, respectively. The fourth section contains analytic expressions for the calculation of the characteristic impedance in right- and left-handed waveguides. (PDF 400 kb)

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Tsakmakidis, K., Boardman, A. & Hess, O. ‘Trapped rainbow’ storage of light in metamaterials. Nature 450, 397–401 (2007).

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