Annealing of UV Ar<sup>+</sup> and ArF excimer laser fabricated Bragg gratings: SMF-28e fiber

Georgios Violakis; Hans G. Limberger

doi:10.1364/OME.4.000499

1. Introduction

The kinetic study of systems using annealing dates back to the middle of the last century where Vand introduced the concept of the superposition of processes distributed in activation energy [1] in order to model the kinetics of irreversible resistance changes due to heating, assuming first order reaction kinetics. Primak generalized the theory to n^th-order kinetics [1–5]. Both authors used isothermal annealing or tempering which is the continuous heating with a ramp rate.

The decay of UV-written fiber gratings was first presented by Erdogan et al. introducing the concepts of integrated coupling constant, decay frequency, and demarcation energy [6]. Assuming a distribution of energy states where excited electrons are trapped, the decay of refractive index changes in Er-doped fibers was obtained from several isothermal (T = const.) annealing measurements. Rathje et al. introduced the annealing method based on linear temperature change for the annealing of fiber gratings assuming first order reaction kinetics [7]. Both groups measured single activation energy distributions for pristine fibers. Shen et al. extended Erdogan’s theoretical approach to a superposition of several distributions assuming Gaussian functions for the single activation energy distribution [8] and Vasiliev et al. decomposed a master curve into two Gaussian curves for gratings in highly doped GeO₂-silica fibers prepared by cw-Ar⁺ laser [9].

Recently we demonstrated the fabrication of fiber Bragg gratings in SMF-28e optical fibers using both ArF and cw Ar⁺ laser [10, 11]. The stability of these gratings was investigated using the “continuous isochronal annealing” method proposed by Ref [7]. Following Primak and Vand we call this method “tempering” [1–5].

From the thermal annealing data, refractive index master curves that depend on irradiation condition and decay frequency were obtained. A decomposition of the fibers’ energy distributions into a sum of Gaussian shaped distributions allowed for a determination of the peak positions and widths of the underlying distributions. In addition to the analysis reported in [12] we determined one single data set for the two differently irradiated fibers consisting of common peak positions and respective widths. Using this data a very good fit of the master curves was obtained using analytical erf-functions. The procedure allows for determining the relative contributions of the processes that decay at different demarcation energies. Moreover, stability maps can easily be calculated.

2. Thermal annealing by tempering

In the range of refractive index changes and annealing temperatures studied here the laser-induced refractive index change $Δ n (T, t)$ as a function of temperature T and time t normalized to the initial refractive index $Δ n_{0}$ at initial temperature T₀ can be approximated by the normalized integrated coupling constant, which is directly obtained from the measured reflectivity R:

I C C_{n} = \frac{I C C (T, t)}{I C C (T_{0})} = \frac{arctanh (\sqrt{R (T, t)})}{arctanh (\sqrt{R (T_{0}, 0)})}

Assuming that the confinement factor of the fiber mode remains constant, the normalized refractive index change that decays with time t and temperature T during annealing is given by

P (T, t) = \frac{Δ n (T, t)}{Δ n_{0}} \approx I C C_{n}

with P(T₀, t = 0) = 1. The decay might be described using the typical annealing function

θ (E, T, t)

and by assuming that there is a distribution of activation energies around the energy E_c. Therefore the decay is described as an integral over the activation energy spectrum

g (E)

:

P (T, t) = \int_{0}^{\infty} g (E) θ (E, T, t) d E

The annealing function is given by [2–7]:

θ (E, T, t) = \exp [- ν_{0} t \exp (- \frac{E}{k_{B} T})] ≅ {\begin{matrix} 0 & E < E_{d} \\ 1 & E > E_{d} \end{matrix}

The function

θ (E, T, t)

is very close to a step function which goes from 0 to 1 around the demarcation energy E_d [2, 13]:

E_{d} = k_{B} T \ln (ν_{0} t)

where k_B is the Boltzmann constant, and ν₀ is the decay frequency in Hz. Approximating the annealing function

θ (E, T, t)

by a step function at the demarcation energy E_d, Eq. (3) becomes the so called “master curve”:

P (E_{d}) = \int_{E_{d}}^{\infty} g (E) d E,

and the total energy distribution spectrum is obtained by differentiation with respect to E_d:

g (E_{d}) = - \partial P (E_{d}) / \partial E_{d}

In the following we assume that the total refractive index (RI) change Δn₀ is a sum of RI changes, Δn₀_,i, which are due to different not otherwise specified effects i. Possibilities are color center changes [14, 15], glass compaction [5, 16], dopant diffusion and chemical reactions [17, 18], regeneration [19], glass annealing [20, 21]. Their relative contributions are expressed as

c_{i} = \frac{Δ n_{0, i}}{Δ n_{0}}

where

\sum_{i}^{} c_{i} = 1

. We further assume that the different contributions are independent and decay at different absolute temperatures T and at different time t, i.e. they have their own individual activation energy distribution. Therefore we write the total activation energy spectrum

g (E_{d})

as a sum of m different Gaussian contributions similar to Shen et al. [8]:

g (E_{d}) = \sum_{i = 1}^{m} c_{i} g_{i} (E_{d})

Every single activation energy spectrum i, is centered around the energy E_c,i with a width (standard deviation)

σ_{i}

and is described by the following normalized Gaussian function:

g_{i} (E_{d}) = \frac{1}{σ_{i} \sqrt{2 π}} \exp (- \frac{1}{2} {(\frac{E_{d} - E_{c, i}}{σ_{i}})}^{2})

where the FWHM is connected to the standard deviation

σ

through:

F W H M = w = σ \cdot 2 \sqrt{2 \cdot \ln 2} \approx 2.3548 \cdot σ

. In this case the amplitude of the Gaussian is c_i multiplied by the factor

{(σ_{i} \sqrt{2 π})}^{- 1}

. Since the integrated coupling constant (ICC_n) is normalized to 1, the sum over all weighted activation energy distributions should also be equal to 1:

\int_{- \infty}^{\infty} \sum_{i = 1}^{m} c_{i} g_{i} (E_{d}) d E_{d} = \sum_{i = 1}^{m} c_{i} \int_{- \infty}^{\infty} g_{i} (E_{d}) d E_{d} = 1

The decaying refractive index change is given by the cumulative distribution function (CDF), i.e. integral over the sum of the individual activation energy spectra with their individual weights c_i:

P (E_{d}) = c_{i} \int_{E_{d}}^{\infty} \sum_{i = 1}^{m} g_{i} (E_{d}) d E_{d} = 1 - \sum_{i = 1}^{m} D_{i} (E_{d})

where D_i are the weighted integrals of the Gaussian functions (see Eq. (10)):

D_{i} (E_{d}) = \frac{c_{i}}{2} \cdot (1 + e r f (\frac{E_{d} - E_{c, i}}{σ_{i}^{} \sqrt{2}}))

This function can be used to determine the probability of a process with its activation energy

E_{c, i}

to have decayed in the interval [0, E_d]. The sum of the individual weighted distribution functions will actually provide the decay characteristics of all observed distributions and can be used to analytically reconstruct the master curve to get the stability map

P (T, t)

which describes the evolution of normalized refractive index with time and temperature.

2. Experiment

FBGs were fabricated in SMF-28e using the cw Ar⁺ laser (244 nm) with a laser intensity of ~500 W/cm² [22] and the ArF excimer laser (193 nm) with an energy density per pulse of 150 to 176 mJ/cm². The repetition rate of the pulsed laser was 10 Hz and the pulse duration 15 ns. The length of the fiber gratings was 0.7 mm (1/e²) and 10 mm for the cw and the pulsed laser, respectively. Thermal annealing was realized using a computer controlled split tube furnace (Fig. 1). The optical fiber under investigation was connected to a broadband light source (BLS) through a 50/50 coupler, so that both transmission and reflection spectra could be measured using an optical spectrum analyzer (OSA). The fabricated fiber Bragg gratings were placed in the middle of the furnace cavity that has a homogeneous heating zone of ~10 cm. A thermocouple was placed in close proximity to the FBG to acquire accurate temperature readings. The furnace was programmed for linear ramping and all devices were interfaced to a personal computer for automatic data acquisition.

Fig. 1 Set-up for thermal annealing (tempering) experiments (ramp rates 0.25 K/s, 0.025 K/s, 0.004 K/s).

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Annealing data were acquired using 3 different ramp rates (0.25, 0.025, and 0.0038 K/s) which differ by two orders of magnitude. The three different decay curves obtained by tempering for the two different laser irradiations are shown in Fig. 2.By adjusting the frequency factor, all three annealing curves overlap as a function of demarcation energy E_d [7, 22]. The frequency factor that leads to the minimum standard deviation between the three curves is chosen and a high order polynomial is fitted to the master curve to get the energy distribution by differentiation. The energy distribution is a superposition of individual activation energy distributions $g_{i}$ (see Eq. (10)), each described by a Gaussian function similar to Shen et al. [8] and Vasiliev et al. [9]. The minimum number of $g_{i}$ distributions can be determined by examining the local maxima of the energy distribution curve. The sum of these Gaussian functions is used to fit the energy distribution obtained from the derivative of the master curve (Eq. (7)). The quality of the fit was determined by minimizing the sum of the squared difference between the measured and the calculated fit data (χ²−value). The equation used for the Gaussian distributions is given by Eq. (10), where c_i are constants describing the relative importance of the effect i, E_c,i is the central energy and $σ_{i}$ the width, i.e. the standard deviation of the spectrum i.

Fig. 2 Average (dc) and amplitude (ac) refractive index changes of the SMF-28e fiber as a function of exposure time for the cw Ar⁺ (a) and pulsed ArF laser irradiations (b).

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From the two independent measurements obtained with two different lasers average E_c,i and σ_i values were calculated and used to determine the relative contributions c_i to the total index change by fitting P(E_d) to the master curves (Eq. (12)). This procedure is more reliable as the derivative of the master curve contains at the beginning of the annealing the reversible index change which is obtained using high total dose [23].

3. Results and discussion

The modulated index changes for the gratings fabricated in SMF-28e fibers using the cw and the ArF laser were 8.4 × 10⁻⁴ and 2.7 × 10⁻⁴, respectively for a total irradiation dose of 1730 kJ/cm² and 5.4 kJ/cm². Typical refractive index evolution curves for the Ar⁺ and the ArF laser irradiations are presented in Figs. 2 (a) and 2(b), respectively. The much lower dose required for the ArF laser is due to the fact that this laser is more efficient and the FBGs were 15 times longer. A summary of the inscription results is presented in Table 1.

Table 1. SMF-28e refractive index changes and reflectivity

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The annealing results are presented in Figs. 3(a) and 3(b) for the cw-Ar⁺ and ArF fabricated FBGs. The annealing data were processed using custom code in order to determine the decay frequency for each case. The master curve, ICC_n, of the fiber was obtained for decay frequencies ν₀ of 10^{13.0 ± 1.0} Hz and 10^{14.5 ± 1.0} Hz for the cw-Ar⁺ and ArF irradiated fibers, respectively.

Fig. 3 Thermal annealing of cw-244-nm Ar⁺ (a) and ArF (b)-fabricated FBG in SMF-28e: Normalized integrated coupling constant versus temperature.

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The resulting master curve was approximated by a 9^th order polynomial to calculate the energy distribution spectrum by differentiation for the two sets of data (Figs. 4 (a) and 4(b)). By inspection of the two curves it is evident that both spectra contain 4 different underlying distributions. Both energy spectra were decomposed into 4 Gaussian-shaped individual activation energy distributions.

Fig. 4 Gaussian decomposition of the total activation energy spectra of (a) cw and (b) ArF fabricated gratings in SMF-28e. Gaussian distributions D1-D4, sum of distributions D_i, and energy distribution obtained by differentiation of the master curve.

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The peak positions (E_c,i) and FWHM-widths w_i of the individual distributions i are the same for the two lasers (Table 2). The experimental error is estimated to 10% due to the dispersion in the frequency factor. The differences between the two very different irradiation conditions are the frequency factors and the relative importance of the different individual activation energy distributions. We refined our data analysis assuming a common activation energy spectrum data set (mean) that depends on the fiber only, based on the average peak positions, widths of the distributions $({\bar{E}}_{c, i}, w_{i}; i = 1, ...4)$ , and individual frequency factors. The two master curves were fitted using Eq. (12), i.e. the sum of normalized erf-functions. As a result, the four weighted parameters c_i were obtained for both laser irradiation conditions. A summary of the parameters together with the average values is presented in Table 3.

Table 2. Individual Gaussian band parameters

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Table 3. Activation energy distribution parameters of SMF-28e

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The sum of the c_i is slightly different from 1 due to the cumulative error. For the Ar⁺-cw data 4 distributions were observed, but mainly two at 3.15 and 4.25 eV contribute to the total energy spectrum. In contrary, for the ArF data the distribution at 1.75 eV contributes with 15%, followed by the 3.15-eV-distribution with 28%, and the 4.25-eV-distribution with 57%. The presence of low energy distribution results in a faster decay at lower demarcation energy and the strong contribution of the high energy spectrum results in a slower decay at high demarcation energies. The presence of the strong peak above 4 eV leads to quite stable gratings.

Figure 5 shows the master curves (experimental data) together with fitted sum of erf-functions Eq. (13). It is obvious that the fit underestimates the experimental data in the case of the cw-Ar⁺ data at low demarcation energies (up to ~2.5 eV). This might be explained with the reversible index change that increases with temperature and hence with E_d and is expected for irradiations of high total dose [23]. For the ArF data the total fluence is sufficiently low to avoid this effect.

Fig. 5 Thermal annealing of cw-244-nm Ar⁺ (a) and ArF (b)-fabricated FBG in SMF-28e. Experimentally obtained master curves and cumulative distribution functions.

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The normalized integrated coupling constant (ICC_n) as a function of temperature and time is represented as a contour plot in Fig. 6 for the fabricated fiber gratings, covering a time scale from less than 0.1 h to ~23 years and a temperature range from 0 to 1100 °C. The lines for $E_{d} = c o n s t .$ have the same color. The tempering measurements covered the range from 20 to 1100 °C and up to 1, 10, and 100 h.

Fig. 6 Stability maps (ICC_n(T,t)) for the SMF-28e fiber using the average frequency factor and Gaussian functions. Differences between the two irradiation conditions are contained in weighted contribution of different RI changing processes.

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4. Discussion

Two different laser systems were used to fabricate FBGs in SMF-28e fiber to study its annealing behavior. Each set of FBG fabricated by a laser was described with an individual frequency factor v₀. Primak investigated the question of a dispersion in the frequency factor and concluded that two distributions can be represented by a single one using as a frequency factor the logarithmic mean value [3, 5]. It is therefore obvious that similar to the work of Primak an average frequency factor was obtained in our work that fits the whole energy spectrum. However, this may lead to an error in the absolute position of the maxima. The energy distribution turned out to be a sum of different individual activation energy distributions, each possibly corresponding to another physical mechanism of refractive index change and having each its own frequency factor. This frequency factor is weighted by the relative contribution of each mechanism to the total index change and depends therefore on irradiation conditions. This may explain why two different frequency factors, i.e. 10^13.0 Hz and 10^14.5 Hz were observed for Ar⁺ and ArF irradiatied FBG, respectively. Frequency factors of this order of magnitude have been observed in the past for annealing of compaction induced density changes in silica and annealing of laser induced irradiation changes in optical fibers: A decay frequency of ~10¹⁴ Hz was reported by Primak for neutron induced densification of silica [5], by Rathje et al. for laser induced RI changes in a 15 mol% germanium doped photosensitive fiber (10^{13.5 ± 1.0}), by Erdogan et al. for FBGs fabricated in a 15 mol% germanium doped fiber (1.9 × 10^{15.0 ± 1.0}). In demarcation energy mapping, frequency factors up to 10¹⁸ Hz might be expected without specifying the physical or chemical process involved [24].

The energy distribution is described as a cumulative distribution function that consists of a sum of activation energy distributions each described by a Gaussian function. The analysis of two different irradiation conditions (cw and ns-pulsed laser) reveals that the distributions have identical peak energies (E_c,i) and bandwidths (standard deviation, σ_i). The difference between the two very different irradiation conditions (low intensity with high irradiation dose for the cw-Ar⁺ on one side and the high intensity with low dose for the ArF laser on the other side) is the relative contribution of the different Gaussian shaped activation energy (AE) spectra [9]. It is not a priori given that the individual AE spectra are symmetric and of Gaussian shape. However, without the measurement of a single effect it is not possible to obtain any other shape or asymmetry.

The origin of the observed bands in the UV-irradiated SMF28e is different for each distribution. The lower energy distributions are most probably due to color centers, while the high energy distribution due to structural changes, i.e. compaction. The D1 (1.15 eV) and D2 bands (1.75 eV) might be related to paramagnetic SiE’ or GeE’ centers ( $\equiv {Si}^{•}$ , $\equiv {Ge}^{•}$ where the symbol “ $\equiv$ ” indicates three bonds with oxygen atoms, and “ $^{•}$ ” stays for an unpaired electron). Nuccio et al. reported for the annealing of silica E’ centers, which were created by γ-irradiation, an asymmetric activation energy distribution with a maximum at 1.23 eV [25]. The annealing process involved H₂O and was reaction limited, i.e. limited by the annealing temperature. Tsai et al. observed a correlation of refractive index change and of GeE’ centers in annealing up to about 650°C [26]. A number of authors observed a distribution at 2.3 eV with a width of 0.9 eV in fibers with higher GeO₂ concentrations [9, 27–29]. Vasiliev et al. observed that the distribution at 2.3 eV appears as an intermediate step to the formation of the 2.9 eV band. They assigned the 2.3 band to the annealing of GeE’.

The distribution D3 (3.15 eV) is compatible in position and width with the distributions observed by other authors, i.e. Erdogan (2.9 eV, FWHM = 1.57eV) [6] and Pal et al. (3.1 eV, FWHM = 1.4 eV) [30]. Distribution D4 (4.25 eV) observed at very high energies might be due to UV-induced glass compaction. Annealing of drawing induced stress appears above 3 eV [20, 21]. Such changes are not expected to occur in reflectivity, as it influences the average refractive index and hence the position of the FGB.

The decomposition of the activation energy spectrum into underlying bands allowed the reconstruction of the master curve with an analytical expression. The amplitude of each erf-function provides quantitative information on the contribution of the corresponding physical mechanism to the total index change. The analytical expression of the master curve allows the creation of decay maps as a function of temperature and time, providing a tool to assess lifetime under any set of operational temperature and time as well as the determination of stabilization conditions of FBGs by accelerated aging [6, 7, 24].

The refractive index stability map can be used to visualize the isochronal (t = const.), the isothermal (T = const.), or the isoenergetic (E_d = const.) behavior. One could choose operating temperature and time and follow the isocolor line (ICC_n = const.) to get an estimation of the pre-annealing conditions or estimate the decay for a given preannealing. For a more precise calculation one could use Eq. (5) to get the relation between an initial (T₁,t₁) pre-annealing and an operation point (T₂,t₂):

t_{2} = \frac{1}{ν_{0}} \exp [\frac{T_{1}}{T_{2}} \ln (ν_{0} t_{1})]

In particular, if e.g. one of the Ar⁺-fabricated gratings was pre-annealed at typically 120 °C for 20 h the decay over respectively 68 days at 80° C, or 10 years at 50° C operation temperature could be anticipated. In the same way ArF-fabricated gratings would be stabilized for 130 days at 80° C, or 35 years at 50° C, respectively.

5. Conclusion

Fiber gratings were prepared by cw-low intensity Ar⁺ laser and a pulsed high intensity ArF laser irradiation in SMF-28e fibers. Thermal annealing by tempering revealed the master curves that depend on irradiation conditions. The master curve is the integral of a superposition of several activation energy spectra, each presenting a physical process responsible for refractive index changes. Most probable are color center changes and densification in the present case.

Using two lasers with different photon energy and beam intensity (4 orders of magnitude), common activation energy spectra were observed. This shows that the decay of a system could be described using a common physical parameter set, despite the different means used to induce the RI changes: the material composition and manufacturing process of the optical fiber dominates over excitation path ways at high total dose.

The decomposition of the SMF-28e fibers defect distribution curves into individual activation energy spectra revealed 4 different Gaussian spectra with peak positions and widths that are within the error equal for the two different lasers used. Each spectrum represents a different physical mechanism and its contribution to the total index change varied with the inscription laser, as observed in the amplitude differences of each spectrum between the two lasers. Although each mechanism might have its own frequency factor a weighted factor for each fiber proved being sufficient to reconstruct the defect distribution curve from the activation energy spectra and the master curve from the cumulative distribution functions.

The method which is based on activation energy mapping is independent of the origin of the refractive index change, as long as we assume a first order reaction kinetics for the decay. Refractive index changes due to diffusion, stress changes, temperature induced glass density changes might be investigated in a similar way assuming the common frequency factor in the annealing spectrum.

Acknowledgement

The authors thank V. Mashinsky and S.A Vasiliev (FORC of the Russian Academy of Sciences) for critical remarks and useful discussions. Financial support from Swiss National Science Foundation (SNSF) projects 200020-126900 and 200020-138012 is acknowledged.

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		Laser intensity	Total fluence	R	Grating length	Max. RI changes (10⁻⁴)
Fiber	Laser	[kW/cm²]	[kJ/cm²]	(%)	(mm)	Mean	Amplitude
SMF-28e	Pulsed ArF	10000	5.4 ± 0.2	96	10.0	7.1 ± 0.3	2.7 ± 0.2
SMF-28e	cw Ar⁺	0.55	1730 ± 50	43	0.7	13.6 ± 0.7	8.4 ± 0.8

		E_i, w_i = FWHM_i in [eV]
Laser	$\log (ν_{0})$ [log(Hz)]	E₁	w₁	E₂	w₂	E₃	w₃	E₄	w₄
ArF	14.5 ± 1.0	1.2	0.24	1.7	0.94	3.2	1.18	4.3	0.59
Ar⁺	13.0 ± 1.0	1.1	0.24	1.8	0.94	3.1	1.41	4.2	0.52
	Mean	1.15	0.24	1.75	0.94	3.15	1.29	4.25	0.57

		E_i, w_i in [eV] and relative contribution c_i in [%]
Laser	$\log (ν_{0})$ [log(Hz)]	E₁	w₁	c₁	E₂	w₂	c₂	E₃	w₃	c₃	E₄	w₄	c₄	$\sum_{i}^{} c_{i}$
ArF	14.5 ± 1.0	1.15	0.24	2	1.75	0.94	15	3.15	1.29	28	4.25	0.57	57	102 ± 5
Ar⁺	13.0 ± 1.0	1.15	0.24	1	1.75	0.94	1	3.15	1.29	60	4.25	0.57	43	105 ± 5

		Laser intensity	Total fluence	R	Grating length	Max. RI changes (10⁻⁴)
Fiber	Laser	[kW/cm²]	[kJ/cm²]	(%)	(mm)	Mean	Amplitude
SMF-28e	Pulsed ArF	10000	5.4 ± 0.2	96	10.0	7.1 ± 0.3	2.7 ± 0.2
SMF-28e	cw Ar⁺	0.55	1730 ± 50	43	0.7	13.6 ± 0.7	8.4 ± 0.8

		E_i, w_i = FWHM_i in [eV]
Laser	$\log (ν_{0})$ [log(Hz)]	E₁	w₁	E₂	w₂	E₃	w₃	E₄	w₄
ArF	14.5 ± 1.0	1.2	0.24	1.7	0.94	3.2	1.18	4.3	0.59
Ar⁺	13.0 ± 1.0	1.1	0.24	1.8	0.94	3.1	1.41	4.2	0.52
	Mean	1.15	0.24	1.75	0.94	3.15	1.29	4.25	0.57

Annealing of UV Ar⁺ and ArF excimer laser fabricated Bragg gratings: SMF-28e fiber

Abstract

1. Introduction

2. Thermal annealing by tempering

2. Experiment

3. Results and discussion

4. Discussion

5. Conclusion

Acknowledgement

References and links

Cited By

Figures (6)

Tables (3)

Equations (14)

Optical Materials Express