Abstract

Some errors and particular conclusions drawn in our Letter [Opt. Lett. 42, 5206 (2017) [CrossRef]  ] are corrected.

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First, there is a typo in formula (4) of [1], the first part of which must read ϕL=MϕR.

Second, the symmetry of the transfer matrix for the potential (12) is M*=σ2Mσ2, which results in modified formula (13):

M11(k)=M22*(k),M12(k)=M21*(k)forallk>0.
Consequently, the conclusion on the absence of spectral singularities drawn in the respective paragraph of [1] and following Eq. (13) is invalid for potentials given by Eq. (12). In other words, the existence of self-dual spectral singularities a priori is not forbidden for complex potentials of this type.

Third, for potentials (14) of [1], the relation M*=σ1Mσ1 holds, but the conclusion on the absence of spectral singularities applies only if c=0, provided that the localized function g(x) is chosen, such that potential V(x) in Eq. (14) is bounded, localized, and tends to constant limits at x±.

REFERENCE

1. V. V. Konotop and D. A. Zezyulin, Opt. Lett. 42, 5206 (2017). [CrossRef]  

References

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  1. V. V. Konotop and D. A. Zezyulin, Opt. Lett. 42, 5206 (2017).
    [Crossref]

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Equations (1)

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M 11 ( k ) = M 22 * ( k ) , M 12 ( k ) = M 21 * ( k ) for all k > 0 .

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