Metallic finite fibers have proven to be unique obscurants of electromagnetic radiation. An analytical theory [1] and numerical solution [2] have been developed to solve the problem of electromagnetic scattering and absorption by finite conducting fibers. The theory has been comprehensively confirmed in the long wavelength region in experiment [3]; the measurements were performed at 35 GHz using single fiber measurement systems. Moving to the short wavelength (i.e., visible and infrared), a sample of randomly oriented silver fibers was measured using FTIR to test the theory in the infrared wavelength spectral region [4]. At the time of this experiment, it was common among researchers that the orientational average extinction efficiency for a randomly oriented conducting fiber was 1/3 of the maximum value achieved when the electric field was aligned along the fiber, regardless of the dimensions and material content of the fibers. More recently, we showed that this 1/3 factor is not quite correct and does not apply to all fiber lengths [5]. In [5], it was shown that an extra resonance between every two aligned resonances is induced due to the variation of this factor. More details of that study can be found in [5]. In [4], we compared the experimental values against the computed values using the criteria that the extinction efficiency is 1/3 of the aligned value. In this correction article, we recalculate the spectra using the accurate orientational average factors published in [5]. For example, Figs. 1(a), 1(b), and 1(c) show the orientational average extinction cross section for a randomly oriented silver fiber of diameter 42 μm at wavelengths 2.5, 5, and 8.2 μm. Figure 1 shows the orientational average extinction cross section that was used to generate the spectra in [2] and the corrected orientational average extinction cross section using [5]. As we see in Fig. 1, the average factor of 1/3 is quite correct for most fiber lengths, but an extra resonance is induced between every two resonances of the aligned case. These extra resonances will change the efficiency by a rate depending on the length distribution of the sample of the silver fibers.

 

Fig. 1. Mass normalized orientational average extinction cross section versus fiber length for a solid fiber of diameter 42 nm at wavelengths (a) 2.5 μm, (b) 5 μm, and (c) 8.2 μm.

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The length distribution of the measured sample was reported in [4]. The extinction spectra of [4] was recalculated according to [5] and is shown in Fig. 2. As seen in Fig. 2, the correction is larger for the lowest wavelengths and almost negligible for the longer wavelengths. This is because most of the silver fibers in the sample have lengths in the range between 0.5 to 2 μm. For the smaller wavelength, the first extra resonance due to random orientation catches some of the fibers and, as the wavelength increases, the extra resonance catches fewer fibers. Also, as shown in Fig. 2, the computed corrected values are now closer to the experimental curve, which improves the fit between theory and experiment.

 

Fig. 2. Measured and computed spectral extinction efficiencies of straight thin randomly oriented silver fibers. Experimental and computed spectra (squares) were taken from [4].

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A previously computed extinction infrared spectrum of a sample of silver fibers was corrected and reported. The correction was based on a recently published article that accurately computes the orientational average extinction efficiencies for finite conducting fibers. Even though the correction reported here is small and does not change the fit and conclusions of [4], we feel that reporting this correction is necessary for future studies of randomly oriented fibers of different length distribution. The difference could be drastically large if most of the fiber lengths were in the region of the extra resonances.