Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides: erratum

Dileep V. Reddy; M. G. Raymer; C. J. Mckinstrie; L. Mejling; K. Rottwitt

doi:10.1364/OE.25.007998

Abstract

We correct typographical errors in four equations showing the integral forms of the equations of motion and the corresponding perturbative approximation. Subsequently presented derivations, results, and conclusions remain unchanged.

In Section 3 of article [1], we presented the integral forms of the coupled-mode equations governing pulsed, quantum frequency conversion in single-mode χ⁽²⁾-nonlinear waveguides in Eqs. 9a and 9b. The time-argument t in the function κ(z′, t) is missing a prime and a subscript in both equations. The correct equations should read:

A_{r} (L, t) = A_{r} (0, t - β_{r} L) + i \int_{0}^{L} d z^{'} κ (z^{'}, t_{r}^{'}) A_{s} (z^{'}, t_{r}^{'}),

A_{s} (L, t) = A_{s} (0, t - β_{s} L) + i \int_{0}^{L} d z^{'} κ * (z^{'}, t_{s}^{'}) A_{r} (z^{'}, t_{s}^{'}) .

Additionally, Eqs. 10a and 10b show the same equations in the perturbative limit. The time arguments of the functions in the intergrand need to be modified thusly:

A_{r} (L, t) \approx A_{r} (0, t_{r}) + i \int_{0}^{L} d z^{'} κ (z^{'}, t_{r}^{'}) A_{s} (0, t_{r} + β_{r s} z^{'}),

A_{s} (L, t) \approx A_{s} (0, t_{s}) + i \int_{0}^{L} d z^{'} κ * (z^{'}, t_{s}^{'}) A_{r} (0, t_{s} + β_{r s} z^{'}) .

All the other text, equations, figures, results, and conclusions of the article remain unaffected. We thank Nicolás Quesada for spotting the typographical errors in these four equations.

References and links

1. D. V. Reddy, M. G. Raymer, C. J. McKinstrie, L. Mejling, and K. Rottwitt, “Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides,” Opt. Express 21, 13840–13863 (2013). [CrossRef] [PubMed]

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Equations (4)

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A_{r} (L, t) = A_{r} (0, t - β_{r} L) + i \int_{0}^{L} d z^{'} κ (z^{'}, t_{r}^{'}) A_{s} (z^{'}, t_{r}^{'}),

A_{s} (L, t) = A_{s} (0, t - β_{s} L) + i \int_{0}^{L} d z^{'} κ * (z^{'}, t_{s}^{'}) A_{r} (z^{'}, t_{s}^{'}) .

A_{r} (L, t) \approx A_{r} (0, t_{r}) + i \int_{0}^{L} d z^{'} κ (z^{'}, t_{r}^{'}) A_{s} (0, t_{r} + β_{r s} z^{'}),

A_{s} (L, t) \approx A_{s} (0, t_{s}) + i \int_{0}^{L} d z^{'} κ * (z^{'}, t_{s}^{'}) A_{r} (0, t_{s} + β_{r s} z^{'}) .

Abstract

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Equations (4)

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