Analysis and design of supercontinuum pulse generation in a single-mode optical fiber: erratum

Kunihiko Mori; Hidehiko Takara; Satoki Kawanishi

doi:10.1364/JOSAB.32.001174

Abstract

We have corrected an erroneous definition of a normalized parameter that was introduced in our earlier paper [J. Opt. Soc. Am. B 18, 1780 (2001) [CrossRef] ] and resulting figures and parameters.

We have found the normalized pulse duration $τ_{0}$ defined as Eq. (9) in our earlier paper [1], that is,

τ_{0} = {(- \frac{Δ_{0}}{Δ_{2}})}^{1 / 2} = \frac{2 π c}{λ_{0}^{2}} {(- \frac{D_{0}}{D_{2}})}^{1 / 2} T_{0},

to be erroneous; that is, it does not provide the condition for conserving the spectral shape of a supercontinuum (SC) lightwave [1].

We derived the corrected definition as follows: from the definitions of the normalized parameters in Eq. (8) in Ref. [1], we have an identity

ζ_{0} = \frac{λ_{0}^{2}}{2 π c} \frac{D_{0} L_{0}}{T_{0}^{2}} \frac{1}{Δ_{0}},

which connects the normalized effective length

ζ_{0}

and the normalized chromatic dispersion

Δ_{0}

, where all the parameters in this paper are the same as those in Ref. [1]. By modifying Eq. (1), we obtain another dimensionless identity:

\sqrt{\frac{2 π c}{λ_{0}^{2}} \frac{1}{D_{0} L_{0}}} T_{0} = \frac{1}{\sqrt{Δ_{0} ζ_{0}}} \equiv τ_{0},

which is the corrected definition of

τ_{0}

. Since the normalized parameter set of

ζ_{0}

and

Δ_{0}

is equivalent to that of

ρ_{0} = ζ_{0}

[1], and

τ_{0} = {(Δ_{0} ζ_{0})}^{- 1 / 2}

, it is obvious that the corrected definition of

τ_{0}

works.

Figure 1 shows a corrected graph that represents the map of the SC bandwidth in nanometers based on the corrected definition of $τ_{0}$ to be substituted for Fig. 9 in Ref. [1], where the effect of stimulated Raman scattering is not included. The dashed curve corresponds to the condition for producing flat spectra where the minimum $ρ_{0}$ is obtained at $τ_{0} = 0.990$ , which was 285 before correction.

Fig. 1. Corrected graph that represents the map of the SC bandwidth in nanometers based on the corrected definition of $τ_{0}$ to be substituted for Fig. 9 in Ref. [1], where the effect of stimulated Raman scattering is not included. The dashed curve corresponds to the condition for producing flat spectra, where the minimum $ρ_{0}$ is obtained at $τ_{0} = 0.990$ which was 285 before correction.

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Figure 2 shows another corrected graph to be substituted for Fig. 14 in Ref. [1], where the effect of stimulated Raman scattering is included. The minimum $ρ_{0}$ is obtained at $τ_{0} = 0.989$ which was 287 before correction.

Fig. 2. Corrected graph that represents the map of the SC bandwidth in nanometers based on the corrected definition of $τ_{0}$ to be substituted for Fig. 14 in Ref. [1], where the effect of stimulated Raman scattering is included. The dashed curve corresponds to the condition for producing flat spectra, where the minimum $ρ_{0}$ is obtained at $τ_{0} = 0.989$ which was 287 before correction.

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Reference [1] also includes some errors in the units of the parameters; namely, ps/(ns/km) for chromatic dispersion $D$ or $D_{0}$ and $ps / ({ns}^{3} / km)$ for $D_{2}$ in Ref. [1] have to be corrected to $ps / (ns \cdot km)$ and $ps / ({ns}^{3} \cdot km)$ , respectively.

Reference

1. K. Mori, H. Takara, and S. Kawanishi, “Analysis and design of supercontinuum pulse generation in a single-mode optical fiber,” J. Opt. Soc. Am. B 18, 1780–1792 (2001). [CrossRef]

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Fig. 1. Corrected graph that represents the map of the SC bandwidth in nanometers based on the corrected definition of

τ_{0}

to be substituted for Fig. 9 in Ref. [1], where the effect of stimulated Raman scattering is not included. The dashed curve corresponds to the condition for producing flat spectra, where the minimum

ρ_{0}

is obtained at

τ_{0} = 0.990

which was 285 before correction.

View in Article | Download Full Size | PDF

Fig. 2. Corrected graph that represents the map of the SC bandwidth in nanometers based on the corrected definition of

τ_{0}

to be substituted for Fig. 14 in Ref. [1], where the effect of stimulated Raman scattering is included. The dashed curve corresponds to the condition for producing flat spectra, where the minimum

ρ_{0}

is obtained at

τ_{0} = 0.989

which was 287 before correction.

View in Article | Download Full Size | PDF

Equations (3)

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τ_{0} = {(- \frac{Δ_{0}}{Δ_{2}})}^{1 / 2} = \frac{2 π c}{λ_{0}^{2}} {(- \frac{D_{0}}{D_{2}})}^{1 / 2} T_{0},

ζ_{0} = \frac{λ_{0}^{2}}{2 π c} \frac{D_{0} L_{0}}{T_{0}^{2}} \frac{1}{Δ_{0}},

\sqrt{\frac{2 π c}{λ_{0}^{2}} \frac{1}{D_{0} L_{0}}} T_{0} = \frac{1}{\sqrt{Δ_{0} ζ_{0}}} \equiv τ_{0},

Abstract

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Equations (3)

Journal of the Optical Society of America B