Nonreciprocal Localization of Photons

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Nonreciprocal Localization of Photons

Hamidreza Ramezani, Pankaj K. Jha, Yuan Wang, and Xiang Zhang

Phys. Rev. Lett. 120, 043901 – Published 24 January 2018

Abstract

We demonstrate that it is possible to localize photons nonreciprocally in a moving photonic lattice made by spatiotemporally modulating the atomic response, where the dispersion acquires a spectral Doppler shift with respect to the probe direction. A static defect placed in such a moving lattice produces a spatial localization of light in the band gap with a shifting frequency that depends on the direction of incident field with respect to the moving lattice. This phenomenon has an impact not only in photonics but also in broader areas such as condensed matter and acoustics, opening the doors for designing new devices such as compact isolators, circulators, nonreciprocal traps, sensors, unidirectional tunable filters, and possibly even a unidirectional laser.

Received 10 October 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.043901

Physics Subject Headings (PhySH)

Classical optics Defects Integrated optics Localization Magneto-optical effect Photonic crystals Photonics

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Hamidreza Ramezani^1,2, Pankaj K. Jha¹, Yuan Wang^1,3, and Xiang Zhang^1,3,*

¹Nanoscale Science and Engineering Center (NSEC), 3112 Etcheverry Hall, University of California, Berkeley, California 94720, USA
²Department of Physics and Astronomy, University of Texas Rio Grande Valley, Brownsville, Texas 78520, USA
³Materials Science Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road Berkeley, California 94720, USA

^*xiang@berkeley.edu

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Vol. 120, Iss. 4 — 26 January 2018

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Images

Figure 1
Schematic of a spatiotemporally modulated photonic crystal with a static defect membrane at the center of the crystal. The right inset schematically shows reflection ( $R$ ) and the place of localized mode for two different cases: (upper) no time modulation where the localized mode is reciprocal, (middle and lower) spatiotemporal modulation where the position of localized mode depends on the direction of the incident beam. The photonic crystal is formed (see the left inset) from a driven Rb atom-cell ( $Λ$ -type three-level system) with a standing wave field with detuning $δ$ between the two components.
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Figure 2
(a) Transmission (red) and reflection (blue) for the static and reciprocal photonic crystal ( $δ = 0$ ) with a defect in the middle of the lattice. The defect mode appears at the $Δ_{f} \approx - 0.13 MHz$ . (b),(c) Left and right transmission and reflection for the space and time-modulated photonic crystal ( $δ = 0.015 γ_{a b}$ ) with the defect in the middle of it. For the left (right) incident, (b),(c), the defect mode is appeared at the $Δ_{f} \approx - 0.38 (- 0.29) MHz$ (see the insets), highlighted with a dash green (orange) line. The position of the dash line, shows that the frequency for which we have the defect mode for left (right) incident beam, the right (left) incident beam observes the band gap (bandpass) and has zero (finite) transmission. The atomic parameters are $γ_{a b} = γ_{a c} = 6 \times 10^{6} s^{- 1}$ , $Ω_{1} = 30 \times 10^{6} s^{- 1}$ , $Ω_{2} = 25 \times 10^{6} s^{- 1}$ , $N = 1 0^{19} m^{- 3}$ .
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Figure 3
(a)–(c) Distribution of the field intensity for the zero detuning (a) at the defect mode, (b) in the passband window, and (c) in the gap. (d)–(f) Distribution of the field intensity for left incident beam when $δ = 0.015 γ_{a b}$ (d) at the defect mode $Δ_{f} \approx - 0.38 MHz$ , (e) in the passband window $Δ_{f} \approx - 0.29 MHz$ , and (f) at $Δ_{f} \approx - 0.155 MHz$ . (g)–(i) Distribution of the field intensity for the right incident beam when $δ = 0.015 γ_{a b}$ (g) at the gap $Δ_{f} \approx - 0.38 MHz$ , (h) at the defect mode $Δ_{f} \approx - 0.29 MHz$ , and (i) at passband with $Δ_{f} \approx - 0.155 MHz$ . Notice that the defect mode of the left incident beam is located at the gap for the right incident beam while the defect mode of the right incident beam is located at the passband and has a scattering feature.
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Figure 4
Position of the defect mode vs the detuning for the left (squares) and right incident (circles) beams. A linear fit is depicted by a continuous line on top of the symbols. The splitting of the position of the modes shows a linear behavior similar to the Zeeman effect, showing the similarities between time-dependent modulated lattice and a magnetic biasing.
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