• Photonics Research
  • Vol. 10, Issue 2, 574 (2022)
Flore Hentinger1, Melissa Hedir1, Bruno Garbin1, Mathias Marconi2, Li Ge3、4, Fabrice Raineri1、5, Juan A. Levenson1, and Alejandro M. Yacomotti1、*
Author Affiliations
  • 1Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, 91120 Palaiseau, France
  • 2Université Côte d’Azur, Institut de Physique de Nice, CNRS-UMR 7010, Sophia Antipolis, France
  • 3Department of Physics and Astronomy, College of Staten Island, CUNY, Staten Island, New York 10314, USA
  • 4Graduate Center, CUNY, New York, New York 10016, USA
  • 5Université de Paris, 75205 Paris Cedex 13, France
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    DOI: 10.1364/PRJ.440050 Cite this Article Set citation alerts
    Flore Hentinger, Melissa Hedir, Bruno Garbin, Mathias Marconi, Li Ge, Fabrice Raineri, Juan A. Levenson, Alejandro M. Yacomotti. Direct observation of zero modes in a non-Hermitian optical nanocavity array[J]. Photonics Research, 2022, 10(2): 574 Copy Citation Text show less

    Abstract

    Zero modes are symmetry protected ones whose energy eigenvalues have zero real parts. In Hermitian arrays, they arise as a consequence of the sublattice symmetry, implying that they are dark modes. In non-Hermitian systems that naturally emerge in gain/loss optical cavities, particle-hole symmetry prevails instead; the resulting zero modes are no longer dark but feature π/2 phase jumps between adjacent cavities. Here, we report on the direct observation of zero modes in a non-Hermitian three coupled photonic crystal nanocavities array containing quantum wells. Unlike the Hermitian counterparts, the observation of non-Hermitian zero modes upon single pump spot illumination requires vanishing sublattice detuning, and they can be identified through far-field imaging and spectral filtering of the photoluminescence at selected pump locations. We explain the zero-mode coalescence as a parity-time phase transition for small coupling. These zero modes are robust against coupling disorder and can be used for laser mode engineering and photonic computing.
    I(ω;X)=|jfj(X){ωRe[εj(X)]}i+Im[εj(X)]|2,

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    I(ω;X)j|fj(X)|2{ωRe[εj(X)]}2+{Im[εj(X)]}2.

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    dadt=a[1τc+1τa(N)]+ia[ωc+ΔωQW(N)],(A1)

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    1τa(N)=vg0ωcΓ2cnrΔχQW(N),ΔωQW(N)=ωcΓ2nr2ΔχQW(N),(A2)

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    α(N)=ωcnrcln(N+AN0+A),(A3)

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    Re(ω±)=ω0+Δω(h)±g(h).(C1)

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    H=(ω0+Δω(h)g(h)0g(h)ω0+2×Δω(h)g(h)0g(h)ω0+Δω(h)).(C2)

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    H˜=(0TT0)+ω˜01,(E1)

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    H˜=(0TT0),(E2)

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    H˜=(00g00gggΔ).(E3)

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    Flore Hentinger, Melissa Hedir, Bruno Garbin, Mathias Marconi, Li Ge, Fabrice Raineri, Juan A. Levenson, Alejandro M. Yacomotti. Direct observation of zero modes in a non-Hermitian optical nanocavity array[J]. Photonics Research, 2022, 10(2): 574
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