Re-evaluation of literature values of silver optical constants

Yajie Jiang; Supriya Pillai; Martin A. Green

doi:10.1364/OE.23.002133

1. Introduction

The optical constants of silver have been studied by many groups since the key features of the electronic behaviour were first identified by Drude [1]. The response of a non-magnetic medium to electromagnetic radiation of frequency ω can be represented by complex dielectric function ε as

ε (ω) = ε_{r} (ω) + i ε_{i} (ω)

From Maxwell’s equation the relation between dielectric constant and the complex refractive index $n^{'}$ is given as

ε (ω) = n^{'} {(ω)}^{2} = {(n (ω) + i k (ω))}^{2}

While ε is more relevant for electronic properties, $n^{'}$ is more relevant for optical properties. The real and imaginary parts of ε and $n^{'}$ can be related in a fundamental way by means of the Kramers-Kronig dispersion relations. Drude applied electromagnetic theory to analyse metallic optical constants by treating metals as a gas of free electrons [2]. The real and imaginary parts of the dielectric constants described by the Drude free-electron theory are

ε_{r} (ω) = 1 - \frac{ω_{p}^{2} τ {(ω)}^{2}}{1 + ω^{2} τ {(ω)}^{2}}

ε_{i} (ω) = \frac{ω_{p}^{2} τ (ω)}{ω (1 + ω^{2} τ {(ω)}^{2})}

respectively. Here

τ (ω)

is the relaxation time and

ω_{p}

is the plasma frequency. The theory has been confirmed by detailed comparison with experiments [3].

The expression for frequency-dependent relaxation time $τ (ω)$ can be determined by the ratio of Eq. (3) and (4),

τ (ω) = \frac{1 - ε_{r} (ω)}{ε_{i} (ω) ω}

A related relaxation time can also be estimated from observed direct current (DC) conductivity $σ_{0}$ as [4]

τ_{0} = σ_{0} \frac{m}{N e^{2}}

where m is the effective optical mass, N is the density of conduction electrons and e is the elementary charge.

Since the frequency-dependent (or AC) optical conductivity σ(ω) is given by

σ (ω) = \frac{σ_{0}}{1 - i ω τ (ω)}

the AC relaxation time

τ (ω)

can also be obtained from the real part of inverse σ(ω) [5],

\frac{1}{τ (ω)} = \frac{ω_{p} {(ω)}^{2}}{4 π} R e (\frac{1}{σ (ω)})

where

ω_{p}

, known as plasma frequency, is given by

ω_{p} = \sqrt{\frac{4 π N e^{2}}{m}}

Equation (8) provides another method to estimate the DC relaxation time when the frequency is approaching zero. However, this value $τ_{0}^{'}$ could be different from $τ_{0}$ determined by Eq. (6) as will be discussed in Section 4.4. Relaxation time is an important parameter for plasmonic research, as it will directly affect the calculated performance. By comparing the relaxation time obtained by different methods, the self-consistency of the assumed dielectric constants can be estimated.

It is the real, positive values of the optical constants n and k that are usually directly measured in most optical experiments. A commonly used technique is by measuring reflectance over a wide range of optical frequencies with the dielectric constants obtained by Kramers- Kronig analysis of the reflectance data [6–11]. Surface plasmon resonance excitation is another method for obtaining the dispersion relations of both bulk and thin-film samples from the visible to the near-infrared wavelength and can be measured in the Otto [12, 13] or Kretschmann configuration [14]. Measurements of reflection/transmittance at different angles of incidence or with different polarizations are also used [15]. Use of polarimetric methods like ellipsometry is another approach which involves finding the ratio of reflectivities perpendicular and parallel to the plane of incidence at an angular incidence together with the difference of phase shifts upon reflection [16–19]. Detailed computer modelling and fitting of reflection, transmission and/or ellipsometric measurements over a large spectral range is also used [20, 21].

2. Background

One difficulty with optical constants measurements is that surface tarnish layers form rapidly when silver is exposed to air. Silver sulphide (Ag₂S) and silver oxide are the two main surface contaminants reported for silver [22]. Different Ag₂S growth rates have been reported in the literature [23–25]. This fast growing tarnish layer can have a large effect on any measurement that uses reflectance to obtain the optical constants, since silver sulphide is strongly absorbing especially in the visible spectrum. While silver sulphide is believed to be the dominant contaminant for air exposed silver, recent research regarding the surface tarnishing on silver nanoparticles shows silver oxide as the tarnishing layer in standard atmospheres [26].

There are numerous publications discussing the optical constants of silver. However, the discrepancy between the commonly used values of the silver optical constants has been pointed out by many researchers [16, 21, 27, 28]. Nash and Sambles (henceforth referred to as N&S) comprehensively reviewed the published silver optical constant data in 1996 [27]. N&S questioned all data sets derived from air exposed samples. An obvious difference in the optical constants derived from measurements in ultra-high vacuum and in air is attributed to the film properties being altered by air [29]. The thickness of the film can also affect the crystallographic properties [11, 30]. Bulk silver samples have been used in some studies, however most groups choose to use thin films [8, 15, 27] with these expected to have the same properties as bulk silver when optically opaque [31]. In addition, thin film samples normally present better surface qualities, because bulk samples often require electrolytic or chemical polishing to obtain optically flat surfaces. This is likely to damage the surface and introduce surface irregularities [7, 17, 32]. The optical constants can also be very sensitive to the grain structure of the film. For this reason single crystalline silver can show different reflectance values to that of a deposited film [9].

The accuracy of the published values has been brought to attention more recently with the widespread adoption of silver in plasmonic research. Small variation in the optical constants can be magnified several fold in plasmonic work leading to inaccuracies in the modelling and interpretation of results. Despite the dependencies noted above, the main obstacle in deriving an accurate set of silver data is the formation of surface tarnish layer discussed above.

3. Published data sets

While there are many published data sets for the optical constants for silver, the two most cited in the literature - Palik [33] and Johnson and Christy (henceforth referred to as J&C) [15], will be more closely examined in this work. One reason for their widespread use is that the two data sets give tabulated optical constants in a relatively wide wavelength range compared to other data in the literature that are either not tabulated [7, 17, 31, 34, 35] or limited to a narrow region involving only a few data points [27, 36–39].

3.1 Revisiting Palik, J&C and N&S data

Palik’s handbook of optical constants is one of the most cited references for metals including silver. However, the handbook entry for silver combines the work of four research groups that utilise different sample preparation methods and includes data from samples exposed to air. This causes inconsistencies in the tabulated values. The optical dielectric function models that are derived merely by fitting this data set are also questionable [20]. Another very heavily cited source for the optical constants of evaporated silver films is J&C [15], probably because their data yields the lowest parasitic losses when used in modelling. However, on closer scrutiny, we observed several issues with their data as discussed below. N&S claim the credit for the best data set for silver as their measurements avoid silver surface exposure to air. However, their results are limited to the 450-900 nm wavelength range, not sufficient to cover the spectral range of interest for most applications. The n and k values for the 3 data sets are compared in Fig. 1(a) and Fig. 1(b) respectively. Whilst Palik and J&C’s values are the most cited, N&S’s values are believed to be the most reliable. Disparity can be noticed both in the visible region and near IR regions among the three data sets.

Fig. 1 Comparison of the optical constants of silver published by Palik [33] (restricted to region of interest), J&C with originally published uncertainty estimates [15] and N&S [27].

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3.2 The effect of silver optical constants on plasmonic efficiency

The last decade has seen a surge in plasmonic research investigating the unique optical properties of both localised surface plasmons (LSP) seen in nanostructured metal films and particles, as well as propagating surface plasmon polaritons (SPP) seen in smooth metal films. The technological advancements in nanostructure fabrication and high speed computation have allowed the engineering of optimal geometries of metal or metamaterial structures. The functionality of the nanostructures relies on the fundamental properties of the metal and the engineered geometries. The accuracy of the optical properties of the metal is a critical factor for the design and optimization of such plasmonic nanostructures.

Realistic predictions require accurate optical data, considering that even small variations can influence calculation of plasmonic effectiveness [40]. Quality factors or figures–of–merit can be adopted as a criterion for materials’ plasmonic performance that depend on both the real ( $ε_{r}$ ) as well as imaginary part of permittivity ( $ε_{i}$ ). Considering that both LSP and SPP resonances are characterised by enhanced electric fields, the quality factor can be defined as the ratio of enhanced local-field to incident field. For the LSP and SPP resonances, appropriate quality factors are $Q_{L S P} (ω) = \frac{- ε_{r} (ω)}{ε_{i} (ω)}$ and $Q_{S P P} (ω) = {\frac{ε_{r} (ω)}{ε_{i} (ω)}}^{2}$ , as discussed elsewhere [41].

It may seem that there is little difference in the optical constants of Fig. 1, however significant difference can be seen in the corresponding quality factors as shown in Fig. 2. J&C’s data produces up to 6 fold higher quality factor than the other two data sets, which could explain its popularity in modelling work. The accuracy of their data is therefore critical to the reliance that can be placed on modelling in most plasmonic research.

Fig. 2 Difference in quality factors for the three published silver optical constants from Palik, J&C and N&S for (a) localized surface plasmon resonances, and (b) surface plasmon polaritons.

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Discrepancies due to different optical constants have been noted earlier. For example, Dionne and associates conducted a numerical analysis on surface plasmon properties using both J&C and Palik’s data [42]. Notably, the discrepancy observed for the propagation distance in their calculation was different by an order of magnitude. Similarly, silver nanoparticle plasmon relaxation time calculated by Maier et al. [43] based on J&C’s data exhibits a marked difference between values calculated with Palik’s data and using the optical constants published for silver clusters [44].

4. Reinterpretation of silver optical constants

In this section we revisit the data for both Palik and J&C and reinterpret their results based on theoretical considerations, simulations and experimental findings. Reflectance and ellipsometry data were used for experimental verification. WVASE^® software [45] was used to fit experiments to simulations and thereby extract optical constants. WVASE^® software is a powerful and comprehensive ellipsometric analysis program from J. A. Woollam Co. that allows building a model based on the sample structure and describing the property of target materials using different oscillators.

4.1 Palik’s data

Lynch and Hunter authored the section “Comments on the optical constants of metals and an introduction to the data for several metals” in Palik’s handbook reviewing the optical constants of metals. These sets of data are therefore also known as Lynch and Hunter’s data. Four different data sources were chosen for different wavelength ranges and arbitrarily combined to produce the final optical data set for silver. The wavelength regions and their sources are 0.15nm - 46nm wavelength range (Hagemann et al [8]), 46nm - 360nm (Leveque et al. [9]), 360nm - 2070nm (Winsemius et al. [32]) and 1265nm −10000nm (Dold and Mecke [46]). Note the overlapping of data from the two groups in the wavelength region from 1265nm −2070nm, with inconsistency in the tabulated values as can be seen in Fig. 1.

These four sources used different sample preparation and measurement methods. Moreover, Hagemann and Dold’s data is from samples exposed to air. Similarly, Winsemius’s measurements were conducted in vacuum. However, the samples were exposed to air during the process of transferring to the vacuum chamber, also is expected to affect the accuracy of the data. Hagemann and Leveque’s n spectra show good agreement at 46nm (not shown here), but diverge at long wavelengths. Conversely the k spectra show a two fold difference at 46nm, but converge at 100nm. Another common point at 360nm shows fair agreement.

Among these four sources, Winsemius’s data set falls in the region of interest for most plasmonic applications from 360nm-2070nm. In addition to their samples being exposed to air, the electrolytic and chemical polishing used in sample preparation may distort surface structure. The post annealing process at 700K may also cause surface roughness that can alter optical properties.

4.2 J&C’s data

To generate their widely reported data, J&C used 30.4 nm and 37.5 nm thick silver films, with the silver rapidly evaporated onto fused quartz substrates. Since silver of this thickness is semi-transparent, its properties may differ from those of a bulk film [11]. However J&C confirmed that, above the critical thickness of 25nm, the extracted dielectric constants were independent of film thickness. They utilised three measurements - reflection and transmission at normal incidence, together with p - polarised transmission at an incident angle of 60°. The measurement approach is appropriate, but it can cause ambiguity in deriving the optical constants of silver at some wavelengths [47]. Reflection measurements can be affected by strains and crystal defects particularly for evaporated films [17]. The significant difference seen in n as opposed to k in Fig. 1(a) and Fig. 1(b) could be because n depends on the conductivity of the sample which is affected by strains and defects while k depends on the density of free electrons in the metal [37].

Importantly, their samples were exposed to air before and whilst conducting the measurements. Even more importantly, if we take a careful look at their tabulated optical constants, the estimated errors in some specific spectral regions are too large to neglect. From 0.64eV - 3.37eV (~370nm - 1950nm or so), the error estimates are at least half or even larger than their tabulated silver n values. This region is where the electron behaviour approximates the Drude model. The J&C paper explicitly states the error in the value of n to be ± 40% in the infrared.

4.3 Optical characterisation

To check the accuracy of the optical constants in literature, we repeat the original experiments. We used reflectance and ellipsometry measurements to characterise our samples which were measured immediately after evaporation to minimise chances of contamination. We then compare our measured results to those obtained by reversing the data extraction process used by Palik and J&C, by finding the required reflectance and ellipsometry data to comply with the published optical constants data. Since our samples were exposed to air, we would expect our experimental measurements to agree well with the results of J&C and Palik.

Reflectance at close to normal incidence was measured using a VARIAN Cary spectrophotometer with calibrated specular reference standard STAN-SSH-NIST (Ocean Optics), and compared with the values deduced from the tabulated data with results. The reflectance and, where appropriate, transmission data were extracted from the optical constants data published by Palik and J&C after applying the Fresnel equations for an absorbing medium [48]. Ellipsometry data for three incident angles of 45°, 50° and 55° were also collected from these specimens by using a J.A. Woollam Co. M-2000 spectroscopic ellipsometer. The ellipsometry data for Palik and J&C were generated automatically using WVASE^® which is also the default analysis software for the ellipsometer.

4.3.1 Thick silver film - 1μm

Since all the samples used to extract optical data were either evaporated opaque or bulk polycrystalline silver films, we rapidly evaporated1µm thick optically opaque silver films on quartz substrate (20Ǻ/s) to avoid any surface distortions or roughness. Based on the measured reflectance, transmission and ellipsometry data, we were able to extract the optical constants of the silver films. These optical constants were then used to generate the various data which is plotted as ‘this work refitted’ in Fig. 3. Drude-Lorenz oscillators in WVASE^® were used for the purpose. The measured reflectance and ellipsometry data from this sample was then compared to the generated reflection and ellipsometry data for Palik, J&C and our data as shown in Fig. 3. Our results show that Palik’s data underestimated experimental results while J&C’s data overestimated the values, especially at long wavelengths. The extracted ellipsometry data for both cases show some variations compared to our experimental measurements. The inconsistency in Palik’s data at long wavelength is evident as some unphysical peaks in the generated data in reflectance R, amplitude component ψ and phase difference Δ. J&C’s data generates an unphysical trend for ψ at long wavelengths (Fig. 3(d)). These inconsistencies confirm the need for improvement of these data sets and also suggest that ellipsometry measurements can provide additional information about film properties that can improve the accuracy in extracting optical constants.

Fig. 3 Comparison of generated data (Palik - black solid and J&C - red dash dot) based on published data sets, experimental (green solid) and refitted (purple dash) data. The refitted curves are our results by fitting to the experimental data. (a) (b) Reflectance, (c) (d) Amplitude component Ψ and (e) (f) the Phase difference Δ. The insets (b) (d) (f) show data in higher resolution for regions of (a) (c) and (e) respectively. The refitted results are only shown in insets (b) (d) (f).

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A 0.5nm Ag₂S surface tarnishing layer [49] was included in the model for all the above cases and provided the best fit with minimum mean squared error between generated results and experimental data. This is further evidence to the presence of tarnish layers on silver data. Since the published optical constants of Ag₂S are limited to the 350 nm - 600 nm range [49], linear extrapolation was used to deduce values at longer wavelengths.

4.3.2 Thin silver film - 30.4nm

Since J&C’s data is the most favoured for plasmonic research, we took up the data analysis in more detail. We repeated the process of J&C by rapidly evaporating a 30.4nm thick silver film on quartz substrate similar to what is described in their paper. Similar to the previous section, the experimental results from the thin layer was compared to the plots generated using the optical constants by J&C.

The good agreement of our experimental reflectance and transmittance results with that of J&C was the starting point for this study as shown in Fig. 4(a) and Fig. 4(c). However the optical constants finally extracted from this film are very different to those published by J&C as discussed in Section 4.33. Similar to applying J&C’s data to 1µm thick film, it generates an unphysical trend for ψ at long wavelengths. In addition, J&C’s data exhibit up to 10% error around 300nm for Δ.

Fig. 4 Comparison of generated (red dash dot), experimental (green solid) and refitted (purple dash) data based on a film with similar characteristics to that reported by J&C. The ellipsometry data are collected from three incident angles 45°, 50° and 55°. (a) (b) show reflectance R, (c) (d) show transmission T, (e) (f) show the amplitude component Ψ and (g) (h) the phase difference Δ. The insets (b) (d) (f) (h) are the zoomed in sections of figs. (a) (c) (e) and (g) respectively. The refitted results are only shown in insets (b) (d) (f) (h).

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The refitted and experimental reflectance, transmission and ellipsometry data in Fig. 4 for the 30.4nm silver film showed good agreement with minor differences. A 0.5nm thick Ag₂S tarnishing layer was also included in the model to achieve the best fit with minimum mean squared error between generated results and experimental data.

4.3.3 Comparison of optical constants from different films

In addition to the different silver films discussed earlier, we also measured a single crystalline silver [(100) orientation] sample that has been polished to give good surface quality with roughness of < 4nm as measured using Atomic Force Microscopy. The newly extracted optical constants from the silver film of thickness 1μm, 30.4nm, and single crystalline bulk silver are compared with J&C’s data in Fig. 5. The extracted optical constants from our 30.4nm film do not agree with J&C values even though the films had very similar properties and our results agreed well to the R and T in Figs. 4(a) and 4(c). The k value variations are small, however, n values show a significant difference with n known to be highly sensitive to grain strain and crystal defects [37]. J&C’s paper claim that films thicker than 25nm could be treated as bulk films. Our results also corroborate J&C’s conclusion that thinner semi-transparent films above 25nm thickness can give optical constants similar to those of optically opaque films. The effect of grain size on optical constants has not been investigated in this study and will form part of another detailed study.

Fig. 5 Comparison of the optical constants of silver: (a) real part n (b) imaginary part k. (i) refitted optical constants by reproducing J&C’s experiment; (ii) extracted optical constants of opaque silver film; (iii) J&C’s data with error bars and (iv) extracted optical constants of single crystalline bulk silver.

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The discrepancy between experimental results and generated values based on Palik and J&C’s data highlights drawbacks in their original data set. J&C used only normal incident R and T measurements which does not give a unique set (p-polarized transmission at 60° was also measured, but not at all energies). Since instrument errors for optical measurements are inevitable and different optical constants combination can lead to same measured values, the best-fit optical constant set might not be physically consistent. While many optical analysis software (e.g. WVASE^®, CODE) allows users to build their own models using different oscillators for each material, the oscillators or dispersion equations can be selected based on physical models. The oscillator method allow a more consistent and physical set of data to be extracted with the coherent error averaging producing more accurate data than by deriving point by point.

4.4 Relaxation time analysis

The relaxation time τ (or scattering time) is the characteristic time for a distribution of electrons in a solid to relax to equilibrium after a disturbance is removed. Relaxation time calculations were used as another check to validate the consistency of the optical constants. The related equations have been discussed in Section 1. The AC relaxation time can be accurately determined by the Drude model as Eq. (5) and the Extended Drude model (EDM) as Eq. (8). The AC conductivity in EDM can be extracted from dielectric constants as described elsewhere [5]. The relaxation times for the three most popular silver data sets were calculated, as well as a single crystalline silver sample. It is expected that the values from single crystalline silver is slightly lower than the intrinsic value due to reduction by surface roughness due to polishing and tarnishing.

Using the Drude model, the relaxation times for the four data sets are plotted as shown in Fig. 6(a). Palik, N&S and the single crystalline silver cases give constant relaxation times in the free electron region, whereas J&C’s data shows an unphysical fluctuating trend. Using the EDM as shown in Fig. 6(b), the scattering rate 1/τ (inverse of relaxation time) determined by AC conductivity is plotted as a function of ω². DC relaxation time can also be extracted from this plot by taking the y-intercept (ω = 0).

Fig. 6 Silver relaxation time calculated by different methods comparing different optical constant data sets: (a) Relaxation time τ plotted by Drude model expression τ = $(1 - ε_{r}) / ε_{i} ω$ .(b) Scattering rate (1/τ) vs. ω² of silver by EDM.

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To check the consistency of each data set, the AC relaxation time at 2000nm (0.62 eV) $τ (2000 n m)$ was calculated by both methods and the DC relaxation time $τ_{0}^{'}$ was determined by EDM as shown in Table 1. Comparing the relaxation times deduced by different methods, the AC relaxation times show fairly good agreement as deduced by the Drude and EDM methods for all data sets except for J&C. It is found that the AC and DC relaxation time values of J&C’s data deviate significantly from the other calculated values.

Table 1. Calculated values for AC relaxation times at 2000nm by Drude model and EDM, together with the DC relaxation times determined by EDM for Palik, J&C and N&S’ work. Also shown are corresponding values for single crystalline silver. All values are in femtoseconds.

View Table

Anomalies in Palik’s data are very likely due to stitching of multiple data sets with different deposition and measurement conditions, especially in the lower energy region. Youn et al. pointed out that the relaxation time obtained for silver using their method differs from the one reported in the J&C’ paper by a factor of 2.4, with the large deviation unexplained [5]. While N&S data appears to be the most accurate, their tabulated data for a very small spectral region makes them unsuitable for most applications.

The DC resistivity for single crystalline silver has been measured as 1.58 × 10⁻⁸ Ωm using a four point probe. The DC relaxation time $τ_{0}$ has been calculated as 38.3 fs using Eq. (6). All constants’ values were obtained from reference [50]. As is noted, this relaxation time value differs substantially from the one determined from EDM. This variation may rise from the spectral range limitation of our optical measurements up to 2000nm in wavelength (0.51eV). The band structure of silver exhibits a feature in mid-infrared, which lead to a contribution to the silver dielectric function in the 0.2-0.3eV range. The influence on optical constants in this range could also be confirmed from the longer wavelength values published in Palik’s handbook [33]. Hence, the relaxation time obtained by fitting the optical data above 0.5eV yields different values from the one determined from DC conductivity measurements [51].

The accuracy of the optical constants can also be affected by the crystallinity of the silver deposited. This may vary due to deposition conditions, rate of deposition as well as deposition temperature effects. The effect of grain structures on the optical constants will be investigated in our future studies.

5. Conclusions

In this article we examine the reliability of the most widely-used optical constant data sets for silver published by Palik [33] and Johnson and Christy [15]. The strategy followed was to prepare samples similar to those used in the original measurements giving similar reflectance and, in some cases, transmission properties to those originally reported. By conducting more detailed measurements on these samples, particularly using ellipsometry at multiple incidence angles, and by accounting for tarnish layers, we show the reflection and transmission data alone is insufficient for extracting the parameters of air exposed samples. After comparing optical and ellipsometry experimental characterisation results with generated results based on these two data sets, together with relaxation time calculations, we come to the conclusion that these data sets have deficiencies that could affect the accuracy of the many theoretical analyses based on them. Extracting the most accurate set of data for silver is important since most of the literature in plasmonic research cite questionable data. Accurate and reliable data will help optimise calculations for plasmonic applications. We anticipate coming up with a more stringent tarnish-free data set for the optical constants of silver for further research.

Acknowledgments

The authors acknowledge the support of the Australian Government through the funding provided by the Australian Renewable Energy Agency (ARENA). Responsibility for the views, information or advice expressed herein is not accepted by the Australian Government. The ellipsometry measurements were performed in part at the UNSW node of the Australian National Fabrication Facility (ANFF), a company established under the National Collaborative Research Infrastructure Strategy to provide nano and micro-fabrication facilities for Australia’s researchers. The authors acknowledge the useful discussion and technical support from J.A. Woollam Co.

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	Palik (fs)	J&C (fs)	N&S (fs)	single crystal (fs)
$τ (2000 n m)$ -Drude	10	30	*14.5*	*14.2*
$τ (2000 n m)$ -EDM	*10.2*	*30.4*	*14.7*	*14.4*
$τ_{0}^{'}$ -EDM	*12.3*	*89.5*	*14.9*	*14.9*

Re-evaluation of literature values of silver optical constants

Abstract

1. Introduction

2. Background

3. Published data sets

3.1 Revisiting Palik, J&C and N&S data

3.2 The effect of silver optical constants on plasmonic efficiency

4. Reinterpretation of silver optical constants

4.1 Palik’s data

4.2 J&C’s data

4.3 Optical characterisation

4.3.1 Thick silver film - 1μm

4.3.2 Thin silver film - 30.4nm

4.3.3 Comparison of optical constants from different films

4.4 Relaxation time analysis

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (6)

Tables (1)

Equations (9)

Optics Express