• Photonics Research
  • Vol. 9, Issue 8, 1645 (2021)
Qi Geng1、2 and Ka-Di Zhu1、2、*
Author Affiliations
  • 1Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Shanghai 200240, China
  • 2School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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    DOI: 10.1364/PRJ.423996 Cite this Article Set citation alerts
    Qi Geng, Ka-Di Zhu. Discrepancy between transmission spectrum splitting and eigenvalue splitting: a reexamination on exceptional point-based sensors[J]. Photonics Research, 2021, 9(8): 1645 Copy Citation Text show less

    Abstract

    In the study of exceptional point (EP)-based sensors, the concrete form of the output spectrum is often dismissed, and it is assumed that there is a corresponding relation between the peaks/valleys in the transmission spectrum and the real parts of the eigenvalues of the system. We point out that this assumption does not always hold. An effect, which is mathematically similar to electromagnetically induced transparency (EIT), may result in a ‘pseudo spectrum splitting’ that does not correspond to the splitting between the eigenvalues. The effect shall be taken care of when designing an EP-based sensor since it may cause measurement error and misunderstanding such as recognization of the spectrum splitting as the eigenvalue splitting at the exceptional point. We also propose to intentionally utilize this ‘pseudo splitting’ to design a sensor, which does not work at an EP, that has an EP-like spectrum splitting.
    H=(w1iκ12μμw2iκ22).

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    ddt(a1a2)=i(w1iκ12μμw2iκ22)(a1a2)+(κexain0),

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    i(ww1+iκ12μμww2+iκ22)(a1(w)a2(w))=(κexain(w)0),

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    a1(w)=iκex(ww2+iκ22)|ww1+iκ12μμww2+iκ22|ain(w),

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    a1(w)=iκex(ww2+iκ22)(wλ1)(wλ2)ain(w),

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    aout=ainκexa1.

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    aout(w)=P(w)(wλ1)(wλ2)ain,

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    P(w)=(wλ1)(wλ2)iκex(ww2+iκ22).

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    T=|(wr1)(wr2)(wλ1)(wλ2)|2,

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    r=10±2Δμ+Δμ2.

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    Qi Geng, Ka-Di Zhu. Discrepancy between transmission spectrum splitting and eigenvalue splitting: a reexamination on exceptional point-based sensors[J]. Photonics Research, 2021, 9(8): 1645
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