Abstract

We present an erratum to our Letter [Opt. Lett. 46, 1486 (2021) [CrossRef]  ]. This erratum corrects an inadvertent error in defining the electric field and a typographical error in Eq. (5). The corrections have no influence on the results and conclusions of the original Letter.

© 2021 Optical Society of America

There was an inadvertent error in writing the electric field in our Letter [1] that we intend to correct in this erratum. In the numerical simulation, we had already taken the correct definition of the electric field, and the error occurred while writing the equations in our Letter. Therefore, the correction does not affect our results and conclusions.

The electric field at frequency ${\omega _l}$ in the Letter [1] should be defined as

$${E_l}(x,y,z,t) = \sqrt {2c{\mu _0}P_{{\omega _p}}^0/{n_l}} {A_l}(y){\psi _l}(x,z){e^{i({\omega _l}t - {\beta _l}y)}} + \text{c.c.},$$
where $P_{{\omega _p}}^0$ is the input power of fundamental frequency ${\omega _p}$ and the optical power ${P_{{\omega _l}}}$ carried out by the frequencies at ${\omega _l}$ is given by $P_{{\omega _p}}^0|{A_l}{|^2}$. This correction does not change the form of coupled Eqs. (1)–(4), except for a slight modification in defining ${\alpha _1}$, which should be read in the corrected form as ${\alpha _1} = (2/\pi){d_{\text{eff}}}\sqrt {2c{\mu _0}P_{{\omega _p}}^0/n_p^2{n_{2p}}}$.

There was also an error in writing the equation for the dark mode given by Eq. (5), where the square root should only be in the denominator. The corrected equation must be read as

$$A_p^0 = \frac{{{\kappa _2}}}{{\sqrt {8\kappa _1^2 + \kappa _2^2}}};A_{2p}^0 = 0;A_s^0 = - A_i^0 = \frac{{2{\kappa _1}}}{{\sqrt {8\kappa _1^2 + \kappa _2^2}}}.$$

This gives the dark mode at $y = L$ as $A_p^0 \approx 0,{A_{2p}} = 0,A_s^0 \approx 1/\sqrt 2 ,A_i^0 \approx - 1/\sqrt 2$.

REFERENCE

1. P. Aashna and K. Thyagarajan, Opt. Lett. 46, 1486 (2021). [CrossRef]  

References

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  1. P. Aashna and K. Thyagarajan, Opt. Lett. 46, 1486 (2021).
    [Crossref]

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Equations (2)

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E l ( x , y , z , t ) = 2 c μ 0 P ω p 0 / n l A l ( y ) ψ l ( x , z ) e i ( ω l t β l y ) + c.c. ,
A p 0 = κ 2 8 κ 1 2 + κ 2 2 ; A 2 p 0 = 0 ; A s 0 = A i 0 = 2 κ 1 8 κ 1 2 + κ 2 2 .

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