Daniel Gaertner
email: daniel.gaertner@ird.fr

Loreleï Guéry
email: lorelei.guery@ird.fr

N Goñi

Justin Monin Amandé
email: m.amande@africanmarineexpertises.com

P Pascual Alayon

F N'gom

J Pereira
email: pereira@uac.pt

E Addi

L Ailloud
email: lisa.ailloud@noaa.gov

D Beare
email: doug.beare@gmail.com

Alayon P Pascual

Gom F N'

Tag-shedding rates for tropical tuna species in the Atlantic Ocean estimated from double-tagging data

Keywords: Tropical tunas, Atlantic Ocean, tag-shedding estimates, Bayesian analysis Highlights

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The 5-year Atlantic Ocean tropical Tuna Tagging Programme (AOTTP) was designed to improve estimates of key parameters commonly used as inputs in the stock assessments of the three main species of tropical tunas: bigeye (Thunnus obesus), skipjack (Katsuwonus pelamis) and yellowfin (T. albacares). To date, 119 427 tropical tunas have been marked and released in different places in the Eastern Atlantic (Azores, Madeira, Canary Islands, Senegal, Gulf of Guinea, St Helena, South Africa) and in the Western Atlantic (Brazil, Caribbean, U.S.A.) with approximately 15.6% of the released fish recovered 11 .

Tag-return data are commonly used for estimating mortality rates, either in stand-alone models (e.g., [START_REF] Brownie | Statistical inference from band-recovery data: a handbook[END_REF][START_REF] Kleiber | Assessment of Pacific skipjack tuna (Katsuwonus pelamis) resources by estimating standing stock and components of population turnover from tagging data[END_REF][START_REF] Hoenig | Multiyear tagging studies that incorporate fishing effort data[END_REF][START_REF] Polacheck | Classifying tagging experiments for commercial fisheries into three fundamental types based on design, data requirements and estimable population parameters[END_REF] or by incorporating the tagging data into an integrated stock assessment package (e.g., [START_REF] Hampton | A spatially disaggregated, length-based, age-structured population model of yellowfin tuna (Thunnus albacares) in the western and central Pacific Ocean[END_REF]. The results of tagging studies can, however, be compromised if tags or data are lost (i.e., through tag-shedding and non-reporting). Both occurrences can lead to underestimations in tag-return rates, which create a negative bias in fishing mortality estimates, rates of fishery interactions, and tuna movements [START_REF] Gaertner | Tag shedding by tropical tunas in the Indian Ocean and other factors affecting the shedding rate[END_REF]. Ultimately, this leads to biased estimates of stock status. The objective of this paper is to use AOTTP double-tagging experiments to estimate the tag-shedding rates for the three species of tropical tunas in the Eastern Atlantic Ocean.

There are two types of tag losses [START_REF] Wetherall | Analysis of double tagging experiments[END_REF]Hampton and Kirkwood, 1990): Type-I losses, which reduce the number of tags initially put out (immediate tag-shedding), and Type-II losses which occur steadily over time (long-term tag-shedding). In this paper, we estimate the Type I and II tag-shedding components of total tag losses for Atlantic Ocean tropical tunas, combining prior knowledge on these parameters from other regions with AOTTP release-recapture data from double-tagging experiments within a Bayesian framework.

Material and Methods

Data

Double-tagging experiments, "i.e., experiments in which a fish is tagged with two conventional "spaghetti" tags simultaneously, were conducted in the Atlantic Ocean from 2016 to 2020. The dataset was analysed by AOTTP staff and after the quality control process a total of 20 009 double-tagged release records remained from which 3 095 were recovered (15.5%), which includes 256 fishes (0.13%) that have lost one of their tags (Table 1).

Methods

Calculations to estimate tag-shedding rates from double-tagging experiments rely on the assumption that the first and second tags are shed at the same rate, independently of one another (e.g., [START_REF] Kirkwood | Generalised models for the estimation of rates of tag shedding by southern bluefin tuna. Thunnus maccoyii[END_REF][START_REF] Wetherall | Analysis of double tagging experiments[END_REF][START_REF] Kirkwood | A new method for estimating tag shedding rates, with application to data for Australian salmon, Arripis trutta esper Whitley[END_REF].

The most appropriate approach to model the tag-shedding process is to use individual exact times-at-liberty that account for differences in the reporting rates of double and single tags (including differences in detection rates). This approach also accounts for differences in tag loss driven by the choice of insertion point (i.e., left side or right side) of each double tag (e.g., [START_REF] Barrowman | Estimating tag-shedding rates for experiments with multiple tag types[END_REF][START_REF] Xiao | A general model for estimating tag-specific shedding rates and tag interactions from exact or pooled times at liberty for a double tagging experiment[END_REF]Lenarz and Shaw, 1997;[START_REF] Cadigan | Reporting and shedding rate estimates from tag-recovery experiments on Atlantic cod (Gadus morhua) in coastal Newfoundland[END_REF][START_REF] Smith | Fishing mortality in North Carolina's Southern flounder fishery: Direct estimates of instantaneous fishing mortality from a tag return experiment[END_REF]. Based on previous tag-shedding studies [START_REF] Gaertner | Tag shedding by tropical tunas in the Indian Ocean and other factors affecting the shedding rate[END_REF], exact time-at-liberty tag-shedding models are formulated by constant-rate model as follows. The probability QA(t) of a tag-type A being retained at time t after release can be expressed as: [START_REF] Bayliff | Estimates of the rates of shedding of dart tags from yellowfin tuna[END_REF], where is the retention probability of the immediate Type-I shedding rate and is the continuous Type-II shedding rate of this tag-type A.

= (Bayliff
Given this assumption, the probability of observing a fish released with a single A-tag at time t after release is a combination of the reporting rate , and the probability of tag A being retained, which can be expressed as:

=

A similar expression can be used to determine differences in the proportion of tags returned over time for fish that were tagged with a different type of tag or at a different insertion position. For non-permanent doubletagging experiments, the reporting rate did not factor into the above equation because the only recapture information available to estimate shedding rates is whether a fish has retained one or both its tags. If we assume that when a fish is recovered with two tags, both tags are always reported, i.e., there is no loss of one of the tags due to non-reporting, which would then be incorrectly attributed to shedding, the possible tag combinations at recapture are two tags (RL), right-tag only (R), and left-tag only (L), which can be expressed as the following outcomes:

1 = 2 = 1 3 = 1 , respectively
The probability of observing the outcome i (i.e., one of the recovered tag combination with ni occurences), for a fish captured at time t, for each of these three possible outcomes is given by: Estimates of the model parameters are obtained by minimizing the negative log-likelihood of the data conditional on recapture times [START_REF] Barrowman | Estimating tag-shedding rates for experiments with multiple tag types[END_REF]:

= ! " # $ " " %
The Bayesian information criterion (BIC) was used to objectively select a model from the set of candidate models considered [START_REF] Schwarz | Estimating the dimension of a model[END_REF].

&'( = 2 # ) * , , -. . / 0 # #
where n is the number of observations, K is the number of model parameters, and

) * , , -. . is the value of the maximized log-likelihood over the unknown parameters, conditional on the data. The lowest BIC value identifies a posteriori which is the most probable model.

However, it is problematic to choose the most probable model among R candidate models when the BIC values are nearly equal. To account for any uncertainty associated with model selection, a Bayesian posterior model probability (Pri) was calculated for each candidate model i as:

1 = xp 4 5 &'( 2 6
$exp 8 9 :;< ! = > % ?

where, 5&'( = &'( min &'(, [START_REF] Burnham | Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach[END_REF].

It is noteworthy that the inferential model weights from the BIC selection have the same formula as the Akaike weights [START_REF] Akaike | A Bayesian analysis of the minimum AIC procedure[END_REF], but may be interpreted as probabilities of the model, given the data, model set, and prior model probabilities of each model [START_REF] Raftery | Bayesian Model Selection in Social Research (With Discussion)[END_REF][START_REF] Burnham | Multimodel Inference: Understanding AIC and BIC in Model Selection[END_REF]. The above posterior model probabilities are based on assuming that prior model probabilities are all 1/R. Therefore, the model with the largest Pri is the one with the highest probability of being the best model for the data set.

Notice that in the absence of any effect of the insertion point on the tag loss, i.e., = , the negative loglikelihood of the data can be simplified as follows:

= # C = D1 E F G # C D1 E F G
with the probabilities of 2 , 1 and no tags being retained at time t after release, respectively as:

= = = = ; = / = 2 1 ; E = 1 = where = =
Numerous tropical tuna tagging programs have been carried out for several decades in different oceans, and thus results of previous analyses with a similar setting are available in the literature. Such historical data may provide information that is relevant to the research questions of the current Atlantic tagging program. For instance, including this historical information in the analysis of the shedding rate could improve the precision of the current estimates. However, historical studies should only be considered relevant if there are no reasons to believe that the shedding rate parameters in the historical and actual double tagging experiments differ systematically. This means that the same shedding rate model must have been used in the historical studies and that there are no deviations due to time or local phenomena, even if this does not imply identical parameter values. Unlike tag-reporting rates which commonly depict large variability between fishing gears, landing ports and over time, it can be assumed that tuna species tagged and released in similar conditions have comparable shedding rates. This assumption is supported by the very close estimates of type-I and type-II shedding rates from previous double tagging experiments on tunas conducted in different oceans (Table 2). Based on these estimates, we can reasonably express our prior knowledge on tag loss by eliciting a prior distribution for each parameter of tag-shedding before analyzing the AOTTP data.

To derive a prior from historical information we assumed that the Beta distribution was a suitable model for describing the distributions of the immediate and long-term shedding rates obtained in the literature (Fig. 1).

Note that because Lambda is measured in yr^{-1} and has no upper limit, a gamma distribution would be a logical choice. However considering that the observed values for Lambda are lower than 1, for the sake of simplicity we also used a Beta distribution as the prior distribution for this parameter. Instead of using the method of moments, with the sample mean and sample variance, to estimate the hyperparameters of the Beta distribution, it is easier to evaluate them indirectly through statements about the two distinct quantiles of the distribution [START_REF] Van Dorp | Solving For the parameters of a beta a distribution under two quantile constraints[END_REF][START_REF] Albert | Bayesian Computation with R (2nd Edition[END_REF]. To find the shape parameters that matches best-guess estimates of two quantiles of each of the shedding rate distributions, we used the beta.select() function found in the R library(LearnBayes) 12,13 .

Assuming both independence in tag-shedding (as showed in the Result section) and that double-tag recoveries and single-tag recoveries are reported with the same probability, we followed the approach described by [START_REF] Chambers | Southern Bluefin tuna (Thunnus maccoyii) shed tags at a higher rate in tuna farms than in the open ocean -two-stage tag retention models[END_REF][START_REF] Chambers | Frailty models for the estimation of tag shedding rates with tagger effects[END_REF] in which the observed double-tag recoveries were modelled as realizations of a Bernoulli random variable (1 for both tags recovered, 0 for a single tag recovery) with a success probability π (t) as follows:

I t = K L = K L = / 2 1 ⁄ = 2 ⁄
The Bayesian analysis was conducted in R using the R2jags 14 package, with informative Beta priors elicited from previous tag-shedding studies as mentioned previously. However, to test the sensitivity of the posterior distributions to their priors, we generated Markov chain Monte Carlo (MCMC) samples with alternative noninformative Beta (1,1) priors. Final inference was based on posterior distributions obtained by generating 50000 MCMC samples and discarding the first 1000 as burn-in. The convergence of MCMC chains was evaluated visually by plotting the generated values of the parameter against the iteration number after running 3 chains that have different starting values and by checking convergence diagnostics: e.g., the potential scale factor (Rhat), known as the Gelman-Rubin convergence statistic, and a measure of effective sample size (n.eff) which is an estimate of the number of independent draws from the posterior distribution of the estimate of interest [START_REF] Gelman | Inference from Iterative Simulation Using Multiple Sequences[END_REF].

To assess potential differences in terms of types I and II tag-shedding according to the size (FL) at release, the tag-shedding Bayesian model was applied to three size-at-release categories for bigeye and yellowfin (i) <= 45 cm FL, (ii) between 45 and 65 cm FL and (iii) > 65 cm FL, and only two categories for skipjack: <= 45 cm, > 45 cm.

Results

To investigate the effect of tag position on the tag-shedding rate for tropical tuna, we assumed that the potential effect of the insertion position on the tag loss was related to the skill of the tagger, the at-sea conditions during the tagging experiment, the tagging place onboard the tagging vessel, etc. These effects were not explicitly modelled for two reasons: 1) a large number of different vessels and taggers were used with little overlap of taggers across vessel types, making it difficult, if not impossible, to tease out effects; and 2) tagging events lacked detailed information on the tagging conditions onboard. To test this effect, we assessed four different models in which tag-retention parameters were varied according to the position of the tag.

-Model 1 (A1) assumed that tag position had no effect on tag loss; -Model 2 (A2; three model parameters) allowed both λ R and λ L to vary as a descriptor of position effect on the instantaneous rate of long-term tag loss (α is assumed unique); -Model 3 (A3; three model parameters) assumed a position effect in the probability that a fish retained its tag immediately after tagging (αR and αL can differ, but λ is assumed to be independent of the insertion point(s)); -Model 4 (A4) assumed a specific position estimate for all four parameters (αR, αL, λ R, and λ L).

To reflect the uncertainty associated with ranking and selecting the most plausible model to depict the probability of observing the various combinations of right-and left-tagged releases possible, we used both the Akaike information criterion corrected for small sample sizes (AICc) and BIC.

Although AIC and BIC are both penalized-likelihood criteria, they reflect subtle theoretical differences: AIC focuses on the best variance-bias trade-off in a set of candidate models (i.e., the parsimonious model in terms of a frequentist approach), while BIC identifies the "quasi-true" model. Consequently, the type of criteria used can drive some differences in which model is selected. In this analysis, the BIC-selected model (A1) suggests that tag position did not affect tag-shedding. For the AICc, except for the full model, which has the less evidence, neither model dominated the others (Table 3). It should be noted that the study conducted in the Indian Ocean showed that the tag position did affect Type-1 shedding for bigeye and yellowfin [START_REF] Gaertner | Tag shedding by tropical tunas in the Indian Ocean and other factors affecting the shedding rate[END_REF]. Accounting for this aspect can be relevant in single-tagging experiments, and considering that about 90% of the human population are right hand dominant 15 , tags are likely most-commonly inserted into the right side of the fish. However, this effect was not confirmed with AOTTP data and the simplest model (A1) assuming no tag location effect was retained in this study.

The recovery over time of double-tagged individuals with two tags or one tag remaining is presented in Figure 2. The estimates of the shedding parameters according to different approaches or assumptions are presented in Table 4. The trace plot and the density plot for each parameter are provided by species in the supplementary material for the Bayesian model using an informative Beta (Figures S1 to S3). On average, from the frequentist model to the Bayesian model using informative Beta priors, there is an increase of the immediate tag-shedding estimates (i.e., 1-α) and a decrease in the long-term tag-shedding. Retaining the Bayesian model with informative Beta prior, Type-I and Type-II tag-shedding rates were estimated at 0.007, 0.084/yr for bigeye tuna, 0.021, 0.051/yr for skipjack and 0.021, 0.088/yr for yellowfin tuna, and are close to the values obtained in previous tagging studies. Based on these results and using draws from the MCMC posterior distributions, we estimated that the shedding rate reaches 50% of the tags after seven and a half years at sea for yellowfin and after eight years at sea for bigeye tuna. Surprisingly, the loss rate for skipjack was lower than for the two other tropical tuna species (Table 5 and Fig. 3), despite the fact that skipjack are reported to be extremely hardy during the tagging operation [START_REF] Hallier | Indian Ocean Tuna Commission. Tuna tagging manual in tropical tuna fisheries[END_REF].

To assess potential differences in tag-shedding with size (FL) at release, the AOTTP double-tagging dataset was divided into 3 size categories for bigeye and yellowfin and only two categories for skipjack. Estimates of tagshedding were obtained using the Bayesian model with informative Beta prior. Due to the low number of recaptures with one tag lost for some combinations of species -size category results must be interpreted with caution. Although there is not a clear change in Type-I shedding by size category (Table 6, Fig. 4), the results suggest that the continuous Type-II shedding rate increases for larger bigeye and larger yellowfin at-release; e.g., between FL<= 45cm and FL > 65 cm: from 0.040 to 0.128 per year and from 0.051 to 0.163 per year, respectively (Table 6, Fig. 5). This corresponds to a three-fold increase.

Discussion

In double-tagging studies, where two temporary tags are lost, it is assumed that both tags were shed independently of one another (and thus an adjustment is made to the remaining number of fish assumed to be alive). In situations where individuals are prone to losing (or retaining) both their tags in the same event, the assumption of tag independence may lead to underestimation in tag losses, which has broader implications for the estimation of vital life-history traits. Given the lack of evidence suggesting otherwise, we followed the assumption that losing the first tag did not affect the probability of losing the second tag (i.e., independent tag shedding) but assessed the assumption that both tags have an equal probability of retention. Our results did not show evidence of an effect of the insertion of the tag on the right, or left side of the body on the loss rate. The same conclusion was drawn by [START_REF] Vincent | Background analyses for the 2019 stock assessment of skipjack tuna[END_REF] in the Western Pacific. Differences in shedding rate due to the location of the tag has also been reported for some species of marine mammals [START_REF] Diefenbach | Modeling and evaluation of ear tag loss in blackbears[END_REF][START_REF] Bradshaw | Modelling tag loss in New Zealand fur seal pups[END_REF][START_REF] Mcmahon | Tag loss probabilities are not independent: assessing and quantifying the assumption of independent tag transition probabilities from direct observations[END_REF][START_REF] Oosthuizen | Cohort and tag-site-specific tag loss rates in mark-recapture studies: a southern elephant seal cautionary case[END_REF][START_REF] Schwarz | The implications of assuming independent tag loss in southern elephant seals[END_REF] and marine turtles [START_REF] Rivalan | Maximum likelihood estimates of tag loss in leatherback turtles[END_REF]. This aspect is linked to the behaviour of the tagged individuals but as far we know that was not observed for tunas.

Another important point discussed in many double tagging studies is the presence of a tagger effect. The underlying idea is that less-experimented taggers may increase Type-I and Type-II shedding rates, as noted by [START_REF] Hearn | An examination of a tag-shedding assumption, with application to southern bluefin tuna[END_REF], and [START_REF] Chambers | Frailty models for the estimation of tag shedding rates with tagger effects[END_REF] in tagging programs targeting southern Bluefin tuna. However, after comparing the parameter estimates with and without less-experienced taggers, [START_REF] Gaertner | Tag shedding by tropical tunas in the Indian Ocean and other factors affecting the shedding rate[END_REF] concluded that shedding-rate models applied to tropical tunas in the Indian Ocean did not require adding estimates of individual shedding rates associated with each tagger. This is further supported by the findings of [START_REF] Hampton | Estimation of tag reporting and tag-shedding rates in a large-scale tuna tagging experiment in the western tropical Pacific Ocean[END_REF] who reported that, despite identifying an apparent tagger effect, the subsequent consideration of this effect in the shedding-rate model did not significantly improve model performance. Although estimating a tagger effect on a variable of interest (e.g., shedding rate, tagging induced mortality) makes sense from a theoretical point of view, uncertainty in the way the tag release data were recorded and the lack of contrast and balance in the data (i.e., some taggers operating only in a few strata), is likely to be problematic. In addition, as mentioned by [START_REF] Hoyle | Covariates of release mortality and tag loss in large-scale tuna tagging experiments[END_REF], the efficiency of the tagging assistants who supply fish to the taggers as well the decision of whether or not to release a fish given its condition, may be additional sources of variation among taggers, which make it difficult to isolate the effect of skill when manipulating fish during tagging operations.

This study reinforces the needs to account for tag shedding rate with other sources of uncertainty, such as the reporting rate, in order to estimate exploitation and mortality rates derived from tagging data. For instance, large variations in return rates by unloading locations, flags and years have been highlighted (Hampton, 1997, Akia et al. (a) submitted in this issue). [START_REF] Carruthers | Estimating tag reporting rates for tropical tuna fleets of the Indian Ocean[END_REF] showed that although reporting rates in the Indian Ocean can be high for the European purse seiners (94%), they were estimated at 26% for baitboats and only between 2 and 16% for different fleets of longliners.

In this paper we focused only on estimating the Type I and II tag-shedding components of total loss. The tagging-induced mortality is not estimable by double tagging experiments as the entire statistical procedure is based on selecting individuals that have survived the tagging operation. In analyzing the recapture rates of largescale tuna tagging programs in the Western Pacific and Indian Oceans, [START_REF] Hoyle | Covariates of release mortality and tag loss in large-scale tuna tagging experiments[END_REF] proposed to account for "tagging failure" by estimating the difference in return rates between the "base levels" of mortality and tag shedding (i.e., fish tagged and release in good condition by an expert tagger) and all other situations in which additional effects were due to factors being less than ideal (i.e. suboptimal release condition, lower levels of tagging experience). Based on low shedding rate estimates, they assumed that the majority of the high tagging failure estimates (20.5% in the Indian Ocean, and up to 28.4% (skipjack) and 44.9% (bigeye and yellowfin) in the western Central Pacific) may be due to post-release mortality. It should be noted that based on this study, stock assessments conducted in the Indian Ocean used larger initial tag loss (i.e., "For the bigeye tuna, the recent assessments applied an initial tag loss of 30.5%, based on the initial tag mortality estimate of 20.5% [START_REF] Hoyle | Covariates of release mortality and tag loss in large-scale tuna tagging experiments[END_REF], with a further 10% increase to account for an assumed level of tag mortality associated with the best (base) tagger" (IOTC, 2020)).

It is unclear however if these estimates reflect only tag-induced mortality, as previous studies suggested that the combination of type 1 tagging mortality and tag shedding should be low [START_REF] Kleiber | Assessment of Pacific skipjack tuna (Katsuwonus pelamis) resources by estimating standing stock and components of population turnover from tagging data[END_REF]. They based their conclusion on the high return rate (> 50%) observed in the eastern Pacific and on the absence of difference in mortality on about 16 tagged and 14 untagged control skipjacks maintained in captivity for 7 weeks at Kewalo Basin, Honolulu. In the absence of further quantitative information, they assumed a figure of 10% for the total Type-1 losses. However, correcting the tagging database to account for these different uncertainties before introducing the tagging information in stock assessments models is fundamental and correcting procedures have been proposed [START_REF] Berger | Analysis of tagging data for the 2014 tropical tuna assessments: data quality rules, tagger effects, and reporting rates[END_REF].

Fig. 1 .

 1 Fig. 1. Hyper-parameters of the Beta prior distribution (dashed line in red) for type I and II tag-shedding rates obtained from previous double-tagging experiments (histogram) conducted on different species of tunas in different parts of the world (see table 2).

Fig. 2 .

 2 Fig. 2. Recaptures by time at liberty of tunas with 1 or 2 tags. From top to bottom: Bigeye (BET), Skipjack (SKJ), Yellowfin (YFT). Each bin represents one month at sea.

Fig. 3 .

 3 Fig. 3. Simulated proportion of tags lost (1 -Q(t)) from date at release for the Bayesian tag-shedding model with Beta priors estimated from previous double tags experiments conducted in different parts of the world. From top to bottom: Bigeye (BET), Skipjack (SKJ), Yellowfin (YFT).

Fig. 4 .

 4 Fig. 4. MCMC posterior mean and 95% credible interval estimates of the Type-I shedding parameter α using the Bayesian model with informative Beta prior for the constant shedding rate model by tuna species and size category at release.

Fig. 5 .

 5 Fig. 5. MCMC posterior mean and 95% credible interval estimates of the Type-II shedding parameter λ using the Bayesian model with informative Beta prior for the constant shedding rate model by tuna species and size category at release.

Table 1 .

 1 Number of tropical tunas double-tagged by the AOTTP and percentage of recaptures made with two tags (Both) and one tag (Tag 1, assumed to be Left or Tag 2 assumed to be Right).

	_______________________________________________
	Species Releases Recovered %Both %Right %Left
	_______________________________________________
	BET	4872	1172	93.69	3.92	2.39
	SKJ	8786	486	90.74	4.94	4.32
	YFT	6351	1437	90.47	4.66	4.87
	Total	20009	3095
	_______________________________________________

Table 2 .

 2 Parameter estimates for the constant-rate shedding model for different tuna species; bigeye (BET), skipjack (SKJ), yellowfin (YFT), albacore (ALB), bluefin (BFT), southern bluefin (SBY) from previous doubletagging studies in the world's oceans.

	_______________________________________________________________________________
	Species α	95% C.I.	λ (per year)	95% C.I.	Study
	_______________________________________________________________________________
	BET	0.993	(0.985 -1.000) 0.017	(0.008 -0.025)	Gaertner and Hallier 2015
		0.953		<0.001		Hampton 1997
	SKJ	0.993	(0.987 -1.000) 0.028	(0.018 -0.040)	Gaertner and Hallier 2015
		0.970	(0.940 -1.000) 0.220	(0.090 -0.350)	Adam and Kirkwood 2001
		0.965		0.086		Hampton 1997
		?		0.088		Kleiber et al. 1987
	YFT	0.977	(0.968 -0.986) 0.038	(0.027 -0.050)	Gaertner and Hallier 2015
		0.934		0.018		Hampton 1997
		0.913	(0.852 -0.974) 0.278	(0.271 -0.285)	Bayliff and Mobrand 1972
	ALB	0.880		0.092	(0.086 -0.098)	Laurs et al. 1976
	BFT	0.973		0.310		Lenarz et al. 1973
	BFT	0.960		0.205		Baglin et al. 1980
	SBT	0.979	(0.960 -0.998) 0.066	(0.060 -0.072)	Hearn et al. 2002
	SBT	0.960	(0.900 -0.976) 0.170	(0.049 -0.290)	Hampton and Kirkwood 1989
	________________________________________________________________________________

Table 3 .

 3 The different parameterizations of the constant-rate shedding model (A1, A2, A3, and A4) considered to determine how tag position (subscripts L and R, insertion in the left or right side of the fish, respectively) differentially affects shedding rates. K is the number of model parameters, nll is the negative log-likelihood, BIC is the Bayesian information criterion, Pri is the Bayesian posterior model probability, AICc is the small-samplesize corrected version of the Akaike information criterion, and Wi is the AICc weight.

	_______________________________________________________________________________________
	Model	α	α R	α L	λ	λ R	λ L	K nll	BIC	Prj	AICc Wj
	_______________________________________________________________________________________
	A1	0.992 NA NA 0.102 NA NA 2 424.923 864.549 0.950 853.854 0.529
	A2	0.992 NA NA NA	0.098 0.106 3 424.880 871.800 0.025 855.755 0.202
	A3	NA 0.992 0.992 0.102 NA NA 3 424.923 871.886 0.024 855.861 0.194
	A4	NA 0.992 0.993 NA	0.098 0.107 4 424.872 879.136 0.001 857.769 0.075
	_______________________________________________________________________________________

Table 4 .

 4 Parameter estimates with 95% C.I. (bootstrapped confidence intervals for the frequentist model and MCMC credible intervals for the Bayesian model) for the constant shedding rate model for the 3 main tropical tuna species in the Atlantic Ocean. N.2 and N.1 represent the number of recaptures with 2 or 1 tag(s), respectively. Note that Type-I shedding is 1 -α

	_________________________________________________________________________________________
	Species α	95% C.I.	λ (per year) 95% C.I.	N. 2 N. 1	Model
	_________________________________________________________________________________________
	BET	0.999 (0.995 -1.000)	0.096 (0.080 -0.108)	568 35	Frequentist approach
	BET	0.997 (0.991 -1.000)	0.095 (0.063 -0.134)	568 35	Bayesian prior non informative
	BET	0.993 (0.986 -0.998)	0.087 (0.056 -0.122)	568 35	Bayesian prior calculated
	SKJ	0.988 (0.972 -1.000)	0.062 (0.000 -0.120)	228 13	Frequentist approach
	SKJ	0.985 (0.965 -0.998)	0.068 (0.010 -0.143)	228 13	Bayesian prior non informative
	SKJ	0.980 (0.964 -0.992)	0.059 (0.016 -0.116)	228 13	Bayesian prior calculated
	YFT	0.985 (0.972 -0.996)	0.108 (0.048 -0.166)	706 56	Frequentist approach
	YFT	0.984 (0.970 -0.994)	0.110 (0.052 -0.176)	706 56	Bayesian prior non informative
	YFT	0.980 (0.968 -0.990)	0.094 (0.047 -0.146)	706 56	Bayesian prior calculated
	_________________________________________________________________________________________

Table 5 .

 5 MCMC simulated yearly breakdown of proportions of tags lost, beginning immediately posttagging and up to ten years post-release, estimated using the Bayesian constant-rate shedding model incorporating informative Beta priors.

	_________________________________________________________________________________
	Year(s) post-release 0	1	2	3	4	5	6	7	8	9	10
	_________________________________________________________________________________
	BET	0.007 0.089 0.164 0.233 0.296 0.354 0.406 0.455 0.499 0.539 0.576
	SKJ	0.020 0.075 0.127 0.175 0.221 0.263 0.302 0.339 0.374 0.407 0.437
	YFT	0.020 0.107 0.185 0.256 0.321 0.379 0.432 0.481 0.525 0.564 0.601
	_________________________________________________________________________________

Table 6 .

 6 MCMC parameter estimates (with informative Beta priors) and credible intervals (95% C.I.) for the constant shedding rate model by size category for the 3 main tuna species in the Atlantic Ocean. N.2 and N.1 represent the number of recaptures with 2 or 1 tag(s), respectively. Note that Type-I shedding is (1 -α).

	__________________________________________________________________________
	Species/size	α	95% C.I.	λ (per year)	95% C.I.	N. 2 N. 1
	__________________________________________________________________________
	BET <= 45 cm 0.984 (0.964 -0.996)	0.039	(0.007 -0.101) 72	0
	BET 45 -65 cm 0.989 (0.978 -0.996)	0.071	(0.037 -0.113) 336 20
	BET > 65 cm	0.987 (0.971 -0.997)	0.128	(0.066 -0.202) 158 15
	SKJ <= 45 cm 0.979 (0.958 -0.993)	0.064	(0.014 -0.139) 99	4
	SKJ > 45 cm	0.976 (0.954 -0.991)	0.057	(0.014 -0.122) 129	8
	YFT <= 45 cm 0.974 (0.949 -0.992)	0.052	(0.010 -0.124) 65	3
	YFT 45 -65 cm 0.976 (0.962 -0.989)	0.065	(0.020 -0.126) 377 27
	YFT > 65 cm	0.981 (0.962 -0.994)	0.163	(0.077 -0.255) 262 26
	__________________________________________________________________________

Table 7 .

 7 MCMC simulated yearly estimated breakdown of proportions of Atlantic yellowfin tags lost for 3 size categories at release, beginning immediately post-tagging until ten years-at-liberty, by the Bayesian constant-rate shedding model incorporating informative Beta priors.

	____________________________________________________________________________________
	Year after release	0	1	2	3	4	5	6	7	8	9	10
	____________________________________________________________________________________
	BET <= 45 cm	0.016 0.054 0.090 0.125 0.157 0.188 0.217 0.245 0.272 0.297 0.321
	BET 45 -65 cm	0.011 0.079 0.142 0.200 0.254 0.304 0.350 0.393 0.433 0.470 0.505
	BET > 65 cm	0.013 0.131 0.235 0.325 0.403 0.472 0.533 0.586 0.633 0.674 0.710
	SKJ <= 45 cm	0.020 0.081 0.137 0.189 0.236 0.281 0.322 0.360 0.395 0.428 0.459
	SKJ > 45 cm	0.024 0.078 0.129 0.175 0.219 0.260 0.298 0.334 0.367 0.399 0.428
	YFT <= 45 cm	0.026 0.074 0.120 0.162 0.202 0.239 0.274 0.307 0.338 0.367 0.394
	YFT 45 -65 cm	0.024 0.085 0.142 0.195 0.244 0.289 0.332 0.371 0.408 0.442 0.474
	YFT > 65 cm	0.020 0.166 0.289 0.392 0.479 0.553 0.615 0.668 0.714 0.752 0.785
	____________________________________________________________________________________

https://cran.r-project.org/web/packages/LearnBayes/index.html

https://www.r-bloggers.com/2013/09/the-beta-prior-likelihood-and-posterior/

Acknowledgements

The AOTTP was funded by the Directorate-General for Development and Cooperation (DG DEVCO) of the European Commission and other ICCAT Contracting Parties and Cooperating non-Contracting Parties (CPCs) and partners. This study was part of a service contract between ICCAT and the CISEF consortium (ICCAT/AOTTP 22/2018) for the analysis of tagging data within the AOTTP.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT authorship contribution statement


Vincenzo De Michele
email: vincenzo.demichele@univ-st-etienne.fr

Emmanuel Marin
email: emmanuel.marin@univ-st-etienne.fr

Aziz Boukenter
email: aziz.boukenter@univ-st-etienne.fr

Marco Cannas
email: marco.cannas@unipa.it

Sylvain Girard
email: sylvain.girard@univ-st-etienne.fr

Youcef Ouerdane
email: ouerdane@univ-st-etienne.fr

Multiphoton process investigation in silica by UV femtosecond laser

Keywords: Silica, Point defects, Strong-field ionization, Femtosecond laser, Photoluminescence Highlights

Introduction

The extremely short pulse temporal width of sub-picosecond lasers has pushed forward the technology of integrated photonics in wide band-gap materials, allowing to achieve new optical properties [START_REF] Strickland | Compression of amplified chirped optical pulses[END_REF][START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Mao | Dynamics of femtosecond laser interactions with dielectrics[END_REF][START_REF] Itina | Interaction of femtosecond laser pulses with dielectric materials: insights from numerical modelling[END_REF]. A relevant example consists in the inscription of waveguides or Bragg gratings of controlled period by focused femtosecond (fs) laser pulses, able to induce permanent refractive-index change (RIC) in the material [5][START_REF] Malinauskas | Ultrafast laser processing of materials: from science to industry[END_REF][START_REF] Ali | Review of laser nanomachining[END_REF][START_REF] Gross | Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications[END_REF]. Indeed, focusing ultrashort high-intensity laser pulses into bulk dielectrics, it is possible to excite electrons in the conduction band [START_REF]Nonlinear Optics[END_REF][START_REF] Nathan | Review of multiphoton absorption in crystalline solids[END_REF][START_REF] Keldysh | Ionization in the field of a strong electromagnetic wave[END_REF] by laser-induced strong-field ionization (SFI), according to the multiphoton ionization (MPI) and/or strong ionization field (tunneling ionization) regimes of interaction. MPI consists in the simultaneous absorption of several photons, induced at the typical intensity reached by femtosecond pulsed lasers. For this phenomenon, the rate of photons' absorption WMPI is driven by the following relation:

W MPI ∝ I N . ( 1
)
Where I is the laser intensity and N the number of photons necessary to realize the band-toband transition [START_REF] Nathan | Review of multiphoton absorption in crystalline solids[END_REF][START_REF] Itina | Electronic excitation in femtosecond laser interactions with wide-band-gap materials[END_REF][START_REF] Grojo | Exciton-seeded multiphoton ionization in bulk SiO2[END_REF].

The tunneling photoionization regime is dominant when the electric field induced by the laser pulses is high enough to distort the potential wall that maintains the electrons bounded to the nuclei, allowing a transition from the valence to the conduction band [START_REF] Keldysh | Behavior of non-metallic crystals in strong electric fields[END_REF]. With such nonlinear ionization processes, the induced damage, driven by the density and the temperature distribution of the generated plasma in the focal region, could be controlled with a ~μm to ~nm precision scale [START_REF] Ali | Review of laser nanomachining[END_REF]. The development of highly localized structural modifications on transparent material leads to potential applications in telecommunications, optical sensing and optical signal processing domains [START_REF] Malinauskas | Ultrafast laser processing of materials: from science to industry[END_REF][START_REF] Gross | Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications[END_REF].

Despite the importance of the nonlinear light absorption on high-intensity laser-based technology, it also plays a crucial role in solid-state physics from several points of view.

Nonlinear absorption limits the transmission properties of transparent materials, leading to color centers' generation as well as important permanent structural modifications, such as densification and/or hollow voids and shock waves in the focal region [START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Mao | Dynamics of femtosecond laser interactions with dielectrics[END_REF][START_REF] Itina | Interaction of femtosecond laser pulses with dielectric materials: insights from numerical modelling[END_REF]. SFI is particularly efficient in generating a uniform concentration of careers along the illuminated volume, unlike linear absorption, which is generally attenuated at the sample surface [START_REF] Nathan | Review of multiphoton absorption in crystalline solids[END_REF].

Moreover, SFI could be used to investigate the intrinsic processes leading to the non-linear absorption of the light, providing unique information on the laser-material interactions.

In this framework amorphous silica (a-SiO2) is a reference among transparent materials, particularly suitable for applications deriving from the interaction with ultrashort laser pulses.

Its electronic structure is mainly determined by the fundamental unit SiO4 tetrahedron and is, therefore, quite similar to that of crystalline α-quartz; experimentally, this results in a comparable bandgap energy of ~9 eV [START_REF]Defects in SiO2 and Related Dielectrics: Science and Technology[END_REF]. Previous studies have demonstrated that the nonlinear deposition of laser energy into silica follows two types of interaction regimes, depending on the experimental conditions [START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Poumellec | Modification thresholds in femtosecond laser processing of pure silica: review of dependencies on laser parameters[END_REF][START_REF] Alessi | Confocal-micro-luminescence characterization of femtosecond laser irradiated silica and borosilicate glasses[END_REF]: Type I, characterized by positive and isotropic RIC, and Type II, which corresponds to a negative RIC, coupled with the appearance of birefringent phenomena. The spectroscopic fingerprint of Type I [START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Alessi | Confocal-micro-luminescence characterization of femtosecond laser irradiated silica and borosilicate glasses[END_REF][START_REF] Royon | X-ray preconditioning for enhancing refractive index contrast in femtosecond laser photoinscription of embedded waveguides in pure silica[END_REF][START_REF] De Michele | Near-IR-and UV-femtosecond laser waveguide inscription in silica glasses[END_REF] is the typical Non-Bridging-Oxygen-Hole-Center (NBOHC) PL band peaking at 1.9 eV (650 nm), while the Type II [START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Alessi | Confocal-micro-luminescence characterization of femtosecond laser irradiated silica and borosilicate glasses[END_REF] is characterized by a PL band at ~2.3 eV (540 nm), whose origin is still debated.

In the present work we investigate the PL acquired under 3.6 eV (343 nm) fs laser irradiation (online PL) of the induced defects in silica. The experiment is carried out as a function of the laser pulse power on two silica samples differing by their hydroxyls groups (OH) contents, highlighting the regime governing the strong field response of the samples. Indeed through fs irradiation we compare the SFI, in the multiphoton limit, influence on the matrix (intrinsic process) with the one involving the OH groups (extrinsic process) [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF], monitoring the optical signature of the induced PL-active point defects. Furthermore, the post mortem characterization of the laser damaged area clarifies how online measurements provides more in-depth information on the light-matter interaction.

Experimental description

The tested specimens are two different highly-transparent polished silica glasses (dimensions~20×10×4 mm 3 ) with different OH contents: a synthetic dry silica, with

[OH]<10 ppm (Suprasil 300), and a synthetic wet silica with [OH]~1000 ppm (Corning 7980).

The online PL experiment is performed with a homemade setup, reported in Figure 1, probing the induced photoluminescence as a function of the pulse peak power (between 0.15 MW and 0.40 MW). The ~3.6 eV (343 nm) irradiation beam is provided by the harmonic generator HIRO (Light Conversion), producing the third harmonic from the ~1.2 eV (1030 nm) fundamental signal, generated by a PHAROS (Light Conversion) femtosecond laser. The temporal pulse width is about ~200 fs and the whole experiment is performed with a repetition rate of 1 kHz. The beam power is controlled by a half-wave plate (HWP) followed by a polarizer (P) at the output of the HIRO module. Moreover, to ensure that the irradiated sample's surface is perpendicular to the beam direction, a LED source (collinear with the laser direction) is paired with a CMOS camera (from Thorlabs) in back reflection configuration, to align and focalized the probe signal onto the sample's surface (not present in Figure 1). The experiment is performed in transversal geometry. The femtosecond pulses are focalized into the specimen bulk through a UV objective with a numerical aperture NA=0.5 and the induced isotropic PL is collected by a telescope used to focalize the signal directly into the spectrometer (Hamamatsu), working in the [3.88 eV (320 nm) -1.16 eV (1070 nm)] spectral range. During the exposure, the detector integration time is set to 100 ms, measuring every spectra as an average of 100 pulses, irradiating for a total ~10 4 pulses at each fixed power.

Since the collected light mainly arises from the plasma emission in the focal spot, during the experiment the detection is focused above the focal point. For each power, the sample is shifted of 50 µm using a motorized translation stage (from Thorlabs), to avoid the induced damage overlap on the sample. To characterize the induced damage, we also performed a post mortem analysis, probing the induced RIC distribution and studying the permanent structural modification such as the presence of induced PL-active stable defects or possible network modifications. The former was probed in the damaged region by phase contrast microscopy (ZEISS AXIO microscopy) in transmission configuration. The latter through steady state PL and Raman measurements employing an integrated confocal micro-spectrometer ARAMIS (Horiba Jobin-Yvon) in backscattering configuration, equipped with a He-Cd CW probe laser line at ~3.8 eV (325 nm). The micro-spectrometer parameters are set in order to obtain a ~5 μm spatial resolution in the XY plane thanks to a confocal pinhole of 70 μm diameter. A spectral resolution of ~5 cm -1 was achieved with 2400 lines/mm grating for the Raman measurements.

Results and Discussion

Synthetic dry silica

Figure 2 shows the PL spectrum acquired after ~10 4 pulses, irradiated at a pulse peak power of ~0.40 MW, while the inset reports the zoom between 2.0 eV and 3.1 eV. Two spectral features are clearly distinguishable: an asymmetric band peaked at ~1.9 eV, associated with the well-known photoluminescence of the NBOHC [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF][START_REF] Skuja | Visible to vacuum-UV range optical absorption of oxygen dangling bonds in amorphous SiO2[END_REF]; a Gaussian shaped band centered at ~2.65 eV with a FWHM~0.4 eV. Regarding the last band, at least two PL-active defects are known to emit in this spectra region: the self-trapped excitons (STX), that are observed both in amorphous and crystalline SiO2 [START_REF] Trukhin | Temperature dependence of luminescence decay kinetics of self-trapped excitons, germanium and aluminium centres in crystalline quartz[END_REF][START_REF] Tanimura | Transient optical absorption and luminescence induced by band-to-band excitation in amorphous SiO2[END_REF][START_REF] Joosen | Femtosecond multiphoton generation of the self-trapped exciton in α-SiO2[END_REF], and the oxygen deficiency centers (ODC (II)) [START_REF] Uchino | Model of oxygen-deficiency-related defects in SiO2 glass[END_REF][START_REF] Trukhin | Peculiarities of photoluminescence excited by 157 nm wavelength F2 excimer laser in fused and unfused silicon dioxide[END_REF][START_REF] Skuja | Optically active oxygen-deficiency-related centers in amorphous silicon dioxide[END_REF]. To deeply study the dependence of the 1.9 eV and 2.65 eV bands as a function of the pulse number (equivalent to the irradiation dose), Figure 3 reports the spectra acquired after different numbers of accumulated laser pulses (Np). The inset shows the evolution of the normalized PL intensity (IPL) recorded at 1.9 eV and 2.65 eV, on increasing Np. These results suggest the same precursor site for the two bands that scale equally as a function of Np. In particular, it is possible to distinguish two different generation regimes: i) transient linear regime IPL proportional to Np, up to ~800 pulses; ii) sublinear dependence, after ~800 pulses, revealing an intrinsic generation process, that is described by equation 2 [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF]:

I PL ∝ (N p ) n (2)
where the n parameter range is 0 < n < 1. The best fit value is found to be n=0.33. The same trend is observed in the other measurements done varying the laser power. (red), 10 3 (blue), 5×10 3 (magenta) and in green after 10 4 pulses. The inset reports the evolution of the peak intensity as a function of the number of the pulses at pulse peak power of ~0.40MW, normalized with respect to the PL value at 10 4 pulses, at 1.9 eV and 2.65 eV, in black and blue circles respectively. The red line represents the best fit curve according to equation 2.

The observed kinetics indicate that the generation mechanism of the NBOHCs is a consequence of Si -O -Si breaking bond [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF][START_REF] Fukata | In situ spectroscopic measurement of transmitted light related to defect formation in SiO2 during femtosecond laser irradiation[END_REF][START_REF] Guizard | Time-resolved study of laser-induced colour centres in SiO2[END_REF][START_REF] Zoubir | Laserinduced defects in fused silica by femtosecond IR irradiation[END_REF]:

≡ Si -O -Si ≡ ħ ≡ Si -O • + • Si ≡ (3)
with simultaneous generation of E´ center, that is a very well characterized paramagnetic defect in silica, which absorbs in UV at 5.8 eV without any emitting PL band [START_REF] Skuja | Optically active oxygen-deficiency-related centers in amorphous silicon dioxide[END_REF][START_REF] Weeks | Review of some experiments in the 50 year saga of the E′ center and suggestions for future research[END_REF].

It is important to stress that the Suprasil 300 sample, in linear absorption conditions, is transparent to the incoming photons, then, only nonlinear processes are expected exciting at 3.6 eV (343 nm). By monitoring the dependence of the PL-active induced defects, it is possible to identify the nonlinear absorption regime of the deposited laser energy. In fact, considering the PL-active induced defects generated by MPI, as a consequence of the equation ( 1), the PL intensity is also proportional to the Nth power of the incident light intensity I [START_REF] Nathan | Review of multiphoton absorption in crystalline solids[END_REF][START_REF] Itina | Electronic excitation in femtosecond laser interactions with wide-band-gap materials[END_REF][START_REF] Grojo | Exciton-seeded multiphoton ionization in bulk SiO2[END_REF][START_REF] Mangini | Multiphotonabsorption-excited up-conversion luminescence in optical fibers[END_REF]:

I PL ∝ I N , ( 4
)
where N is the number of photons necessary to realize the band-to-band transition. Therefore, it is possible to determine the order of nonlinear light absorption process studying the PL intensity as a function of the pulse peak power. Figure 4 reports the PL dependence at both 1.9 eV and 2.65 eV as a function of the laser power acquired after 10 4 pulses (sub-linear regime) and after 500 pulses (linear regime) respectively. In the figure, the two data sets are scaled for a direct and easy trend comparison. In both cases, a super linear dependence with N=3±0.2 (red straight lines in the figure) is evident, supporting a pure-multiphoton absorption regime. Particularly, the absorption of three 3.6 eV photons agrees with a band-to-band transition around ~10.8 eV, which is close to the first excitonic absorption peak at 10.4 eV [START_REF] Messina | Generation and excitation of point defects in silica by synchrotron radiation above the absorption edge[END_REF][START_REF] Messina | Evidence of Delocalized Excitons in Amorphous Solids[END_REF], suggesting the generation and the self-trapping of an exciton. This exciton leads to the deformation and then the breaking of the Si -O -Si bond that is characterized by the emission of photons at 2.65 eV coupled with the NBOHC and E´ centers generation [START_REF] De Michele | Photoluminescence of Point Defects in Silicon Dioxide by Femtosecond Laser Exposure[END_REF],

explaining the origin of such PL band, according to equation 3. The inset in figure 4(a) shows the normalized spectra after 10 4 pulses, acquired at the highest and lowest investigated laser powers respectively: the comparison provides evidence that the induced PL maintains the same shape, regardless of the laser power. It is important to remark that at laser powers lower than 0.15 MW no PL is observed within the detection limits.

Synthetic wet silica

An analogous investigation was performed on the Synthetic wet silica sample (Corning 7980), characterized by a higher OH content (~1000 ppm) compared to the Suprasil 300. The online PL spectra at ~0.40 MW and different pulse numbers is reported in Figure 5 (a), while Figure 5 (b) presents the normalized kinetics of the peaks intensities at 1.9 eV and 2.65 eV. The observed spectral features are similar to those already encountered in the Suprasil 300, but with different relative amplitudes: the NBOHC related PL band centered at 1.9 eV, and the 2.65 eV peaked band, already attributed to the STX. In Figure 5 (b), the 2.65 eV kinetic could be described by an intrinsic process from the beginning of the irradiation, finding n=0.33 according to equation 2, while the 1.9 eV PL shows a totally different behavior. In the present sample, this kinetic reaches a maximum value around 500 pulses, to decrease down after to the value measured after 10 4 pulses. Analogous trends are observed at lower laser powers.

The explanation of this behavior is attributed to the high OH content, which introduces an extrinsic process described by [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF]:

≡ Si -OH ħ ≡ Si -O • +H, (5)
leading to the NBOHC generation through the breaking of OH bonds. It is possible to argue that the fast growth is due to the OH conversion into NBOHC, and once these precursor sites are exhausted, notwithstanding the intrinsic process, the number of bleached NBOHC is dominant [START_REF] De Michele | Photoluminescence of Point Defects in Silicon Dioxide by Femtosecond Laser Exposure[END_REF]. The nature of the observed bleaching could be linked to unstable defects induced at RT or directly by the incident laser pulses. Therefore, at fixed laser fluence, we observed two different pathways for the NBOHC's generation: an extrinsic dominant process, described by equation 5 and driven by the high OH content in the sample, and an intrinsic one, consequent to the STX relaxation, as described by equation 3. to the PL value at 10 4 pulses, for at the 1.9 eV (black) and 2.65 eV (blue) bands respectively. The red line represents the best curve fit according to equation 2.

Figure 6 shows the PL intensities, measured at both 1.9 eV and 2.65 eV as a function of the laser pulse peak power, after 10 4 pulses (Figure 6 (a)), at the end of the irradiation, and at 500 pulses (Figure 6 (b)), associated to the maximum PL intensity at 1.9 eV in Figure 5 (within the extrinsic process generation). In the figure, the two data sets are scaled for a direct and easy trend comparison. In Figure 6 (a) the two contributions follow the same power law, suggesting newly the SFI process in the multiphoton regime requiring ~3 photons for the same band-to-band transition already reported for the Suprasil 300 glass.

A different behavior is observed in Figure 6 (b) after 500 pulses: the intrinsic process represented by the normalized PL at 2.65 eV is still characterized by N=3±0.2, according to equation 4, while the 1.9 eV PL band shows a slightly different kinetic with N=2.6±0.2.

Albeit in the present case the PL dependence on the laser pulse peak power suggests a multiphoton absorption, it is near to the energy value required for the OH breaking bond [START_REF] Vaccaro | Radiation induced generation of non-bridging oxygen hole center in silica: Intrinsic and extrinsic processes[END_REF][START_REF] Zoubir | Laserinduced defects in fused silica by femtosecond IR irradiation[END_REF], which drives the extrinsic process. excitation (trace inside the blue delimited zone in Figure 7). At higher laser powers, the damaged area presents a more complex panorama: the intense energy concentration was able to drive the matrix into strong matter reaction, resulting in non-uniform damaged area in the focal spot (trace inside the red delimited zone in Figure 7). In particular, for pulse peak powers higher than 0.25 MW, the laser traces are reported in brighter and darker colors, with respect to the background (surrounding glass matrix), suggesting a transition from the Type I to Type II interaction regimes [START_REF] Mishchik | Ultrafast laser induced electronic and structural modifications in bulk fused silica[END_REF][START_REF] Alessi | Confocal-micro-luminescence characterization of femtosecond laser irradiated silica and borosilicate glasses[END_REF].

Post mortem Characterization

Conclusions

In the present work we have studied the nonlinear absorption of high intensity femtosecond ultraviolet pulses in amorphous silica monitoring the induced PL as a function of the laser power in samples having different OH contents. The observed spectral features have very close similarities in the two investigated samples: the NBOHC related PL band peaked at 1.9 eV and the STX emission band at 2.65 eV. The samples' chemical composition plays an important role in the NBOHC response, manifesting two different scenario: i) intrinsic generation process, observed in the sample with low OH content, caused by the STX relaxation as consequence of a band-to-band SFI process in the multiphoton ionization regime; ii) extrinsic process, observed in samples with relevant OH concentration, in which the NBOHC generation is driven by the breaking of OH bonds followed by a transition to an intrinsic behavior at higher fluencies. In particular we observed a non-monotonous evolution of the NBOHC band, highlighting a transition from an extrinsic generation process to an intrinsic one.

The MPI regime is revealed by the super-linear dependence of the PL intensity as a function of the laser power, suggesting that the NBOHC generation is basically due to the STX relaxation, coupled with the 3-photons absorption, which is in accordance with the first excitonic absorption peak. Different behaviors between the two samples are observed at low total accumulated doses: if the total PL intensity is still a third multiphoton order absorption process in the Suprasil 300, for the Corning 7980, at low doses the NBOHC's multiphoton absorption order is characterized by N~2.6, which is near to the OH broken bond energy, strongly supporting the presence of the extrinsic process.

The post mortem analysis of the exposed regions reveals the Type I/Type II transition in the investigated power range, confirmed both from the PCM and PL measurements, while no glass densification is observed. No difference between samples was individuated by the postmortem analysis, highlighting the importance of the online investigation to better understand the 'fs laser -amorphous silica' interaction processes.

Figure 1 .

 1 Figure 1. Experimental setup for online PL measurements upon UV fs laser exposure.

Figure 2 .

 2 Figure 2. Suprasil 300 PL spectrum acquired with 3.6 eV femtosecond laser pulses, after ~10 4 pulses at pulse peak power of ~0.40MW. The inset shows the zoom of the spectral region between 2.0 eV and 3.1 eV.

Figure 3 .

 3 Figure 3. Suprasil 300 PL spectra at different accumulated numbers of laser pulses: 10 2 pulses (black), 5×10 2

Figure 4 .

 4 Figure 4. Suprasil 300 PL intensity evolution at both 1.9 eV (green) and 2.65 eV (blue) as function of the pulse peak power after 10 4 and 500 pulses respectively (a) and (b). The red lines represent the best fit curves according to equation 4. The two data sets referred to the 1.9 eV and 2.65 eV PL bands are scaled for a direct and easy trend comparison. The inset represents the normalized PL spectra at the highest and lowest investigated laser powers.

Figure 5 .

 5 Figure 5. (a) Corning 7980 sample PL spectra at different accumulated pulses: 10 2 pulses (black), 5×10 2 (red), 10 3 (blue), 5×10 3 (magenta) and in green after 10 4 pulses, with a pulse power of ~0.40 MW. The inset zooms the spectral region between 2.0 eV and 3.1 eV. (b) Kinetics of the peak intensity measured at ~0.40MW, normalized

Figure 6 .

 6 Figure 6. PL Corning 7980 intensity evolution at 1.9 eV (green) and 2.65 eV (blue) as function of the pulse peak power after 10 4 and 500 pulses respectively (a) and (b). The red and violet lines represent the best fit curves according to equation 4. In both figures, the two data sets are arbitrarily scaled for viewing purposes.

Figure 7

 7 Figure 7 depicts the PCM image, as a function of the laser power, over the entire UV fs laser exposed area in the Suprasil 300 sample. In the figure, darker and brighter zones originate from the increase and decrease of the refractive index, respectively, compared to the surrounding medium. The elongated damage along the laser direction and its width depend on the pulse peak power. Being the darker color a fingerprint of positive ∆n, uniform smooth isotropic positive refractive index changes are observed at low pulse powers (0.15 MW ÷ 0.25 MW), indicating a gentle material response as a consequence of a soft laser-induced

Figure 7 .

 7 Figure 7. PCM image of the induced damages under 3.6 eV femtosecond pulses at different pulse peak powers for the Suprasil 300 sample. The red arrow indicates the laser direction propagation. The blue and red zones focus the reader on the morphological properties of the uniform smooth isotropic positive refractive index change trace and the uneven area damaged at high power, respectively.

Figure 8 .

 8 Figure 8. (a) Suprasil 300 Post mortem PL spectra, scaled for the area, of the laser induced traces at different powers: 0.20 MW (black), 0.30 MW (red) and 0.40 MW (blue). (b) Comparison between the Raman spectra, measured in the Suprasil 300 sample, acquired in the pristine sample (black line), 0.40 MW (blue line) and at 0.20 MW (red line).