Spontaneous parametric down-conversion of photons at 660 nm to the terahertz and sub-terahertz frequency range: erratum

Björn Haase; Björn Haase; Mirco Kutas; Mirco Kutas; Felix Riexinger; Felix Riexinger; Patricia Bickert; Andreas Keil; Daniel Molter; Michael Bortz; Georg von Freymann; Georg von Freymann

doi:10.1364/OE.451527

Abstract

In this erratum, we correct two typing errors from our previously published manuscript [Opt. Express 27, 7458 (2019) [CrossRef] ]. In the original manuscript, the two errors were limited to the theoretical derivation and did not touch the numerical calculations such that the results and conclusions remain unchanged.

In our previously published manuscript [1] we presented the signal count rate density in dependence of the opening angle $\theta _{\mathrm {s}}$ and wavelength $\lambda _{\mathrm {s}}$. The variable transformation from $|\mathbf {k}_\mathrm {s}|$ to $\lambda _{\mathrm {s}}$ gives a factor of $|\mathbf {k}_\mathrm {s}|^{2}$ which is missing in Eqs. (13) and (14). The correct equations should be as follows:

(13)$$\Gamma(\theta_\mathrm{s},\lambda_\mathrm{s}) =\frac{1}{T_\mathrm{I}} \int \mathrm{d}\varphi_\mathrm{s} \langle{\psi}| a_\mathrm{s}^{{\dagger}} a_\mathrm{s}|{\psi}\rangle |\mathbf{k}_\mathrm{s}|^{4} \sin(\theta_\mathrm{s})$$

(14)$$= Z \sum_{m\ \text{odd}} \int_{\Omega(\theta_\mathrm{s})} \mathrm{d}\varphi_\mathrm{s} \mathrm{d}^{3}k_\mathrm{THz} | A(\mathbf{k}_\mathrm{p},\mathbf{k}_\mathrm{s},\mathbf{k}_\mathrm{THz}) |^{2} |\mathbf{k}_\mathrm{s}|^{4} \sin(\theta_\mathrm{s}).$$

Further, the constant factor within the signal count rate density which is defined in Eq. (16) was given erroneously. Using $\chi ^{(2)}_{\mathrm {eff}}$ instead of $d_{\mathrm {eff}}$ we are missing a factor of $4$. Combined with two typing errors we gave an incorrect definition of the factor. The correct version is:

(16)$$Z = \frac{\left(\chi^{(2)}_{\text{eff}}\right)^{2} P_{\mathrm{p}} w_{\mathrm{0}}^{2} L^{3}}{(2\pi)^{6} c \epsilon_0 n_{\mathrm{p}} u_{\mathrm{p}} }.$$

The presented mistakes are limited to the theoretical derivation of the signal count rate density. In our code which produced the numerical results for Fig. 7 the definitions were used correctly. The scientific discussion and conclusion of our work are based on the numerical and experimental results. These remain unchanged by the correction, and therefore the conclusions remain unaffected by these mistakes.

Funding

Fraunhofer-Gesellschaft (Lighthouse project QUILT).

Disclosures

The authors declare no conflicts of interest.

References

1. B. Haase, M. Kutas, F. Riexinger, P. Bickert, A. Keil, D. Molter, M. Bortz, and G. von Freymann, “Spontaneous parametric down-conversion of photons at 660 nm to the terahertz and sub-terahertz frequency range,” Opt. Express 27(5), 7458–7468 (2019). [CrossRef]

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Equations (3)

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Γ (θ_{s}, λ_{s}) = \frac{1}{T_{I}} \int d φ_{s} ⟨ ψ | a_{s}^{†} a_{s} | ψ ⟩ | k_{s} |^{4} \sin (θ_{s})

= Z \sum_{m odd} \int_{Ω (θ_{s})} d φ_{s} d^{3} k_{T H z} | A (k_{p}, k_{s}, k_{T H z}) |^{2} | k_{s} |^{4} \sin (θ_{s}) .

Z = \frac{{(χ_{eff}^{(2)})}^{2} P_{p} w_{0}^{2} L^{3}}{(2 π)^{6} c ϵ_{0} n_{p} u_{p}} .