Ali Ak

Estimating Metric Thresholds for Acceptability and Annoyance of User Generated Video Content

User expectation is one of the main factors that drives the user satisfaction for video streaming service providers and online social media platforms. Depending on the context, users may have different expectations of the video quality. Measuring the Quality of Experience (QoE) by taking user expectations into account provide online social media platforms with increased efficiency and users with higher satisfaction. In this work, we explore the relation between video quality and acceptability&annoyance of video quality in online social media platforms context. Moreover we present the methodology to determine the metric thresholds for acceptability&annoyance of video quality. We compare the estimated thresholds with previous studies.

Introduction

Quality of Experience (QoE) in video streaming context defines the user satisfaction and the level of fulfilment of user expectations when viewing a video content. There are many factors that affect the QoE as discussed in detail in Qualinet white paper [START_REF] Callet | European network on quality of experience in multimedia systems and services[END_REF]. Along with the traditional video quality, other factors that affect the QoE include fidelity, display specifications, delivery, storage and processing costs.

Many subjective quality assessment datasets and objective quality metrics were developed and proposed in the last decades to determine and predict the visual quality of professional and user generated video content. However, from the point of view of the video streaming service providers, visual quality of the video content is not the ideal metric to maximize since alone it is not enough to understand whether the delivered content fulfills the user expectations. It is rather important to optimize the imaging pipeline around the users' satisfaction which are driven by their expectations and the quality of the provided service (e.g., video quality). Therefore, it is desirable to understand the relation between visual quality and user satisfaction and filling the gap between the video quality and QoE. To this end, acceptability&annoyance paradigm has been introduced and further improved in recent years [START_REF] Angela | Quality in context-an ecological approach to assessing qos for mobile tv[END_REF][START_REF] Oeldorf-Hirsch | How bad is good enough? exploring mobile video quality trade-offs for bandwidth-constrained consumers[END_REF][START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF][START_REF] Ak | Video consumption in context: Influence of data plan consumption on qoe[END_REF]. Acceptability&annoyance scale contains three categories as "not acceptable (1)", "acceptable but annoying (2)", and "not annoying (3)". Acceptability&annoyance methodology was initially proposed as a multi-step evaluation scenario and later evolved into a single-step evaluation that would sufficiently capture the same effect [START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF], as shown in Figure 1 Previous studies in QoE domain demonstrates that the video quality does not necessarily indicate the acceptability&annoyance of the video content since the thresholds where the video quality drops to annoying and unacceptable levels are heavily influenced by user expectations [START_REF] Jumisko-Pyykkö | Does context matter in quality evaluation of mobile television?[END_REF]. However a relation between the video quality and acceptability&annoyance can be drawn for a given context [START_REF] Oeldorf-Hirsch | How bad is good enough? exploring mobile video quality trade-offs for bandwidth-constrained consumers[END_REF][START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF][START_REF] Pessemier | Quantifying subjective quality evaluations for mobile video watching in a semi-living lab context[END_REF]. We define the context here as the context in which the video content is consumed. For example, the context can vary from online social platforms (e.g., Instagram Reels, Tiktok, etc.) to online video streaming services (e.g., Netflix, Amazon Prime Video, etc.) based one where it is consumed. In addition it can define other aspects such as remaining battery or remaining data plan of the users [START_REF] Ak | Video consumption in context: Influence of data plan consumption on qoe[END_REF].

In this work, we utilize publicly available IPI-VUGC Dataset1 and estimate the VMAF [START_REF] Li | Toward a practical perceptual video quality metric[END_REF] metric thresholds for different video quality ranges. We then compare the estimated thresholds to previous studies with various contexts. Moreover, we provide a brief introduction of the IPI-VUGC dataset and the algorithm used to determine the metric thresholds.

IPI-VUGC Dataset

IPI-VUGC is a publicly available dataset of video quality and acceptability&annoyance for 336 videos. The subjective opinion scores are collected in laboratory conditions with an

Content

The content used in the dataset aims to reflect the properties of user generated video content typically found in online social media platforms. To this end 30% of the videos contain sticker or text overlays. The videos are 5 seconds long (typical short term video length) and has vertical orientation. An example stimuli with text overlay is presented in Figure 2-a. 6 Processed video stimuli (PVS) are generated for each SRC by compressing with h264 [START_REF] Itu-T | Reference software for itu-t h.264 advanced video coding[END_REF] at various resolutions and constant rate factors(CRF). Thus results in 336 videos, including the SRC videos. The videos are rendered in the native size and resolution of the display and the upscaling is handled by the device. The gaps due to aspect ratio differences between the display and the video content are filled with black color. The device is kept at a fixed brightness during the experiment. Participants could held the device freely during the experiment. Rest of the experiment details follows the ITU recommendations [START_REF] Itu-R | Methods for the subjective assessment of video quality, audio quality and audiovisual quality of internet video and distribution quality television in any environment[END_REF].

Experiment Design

Two separate experiments were conducted with the same content to collect subjective opinions on video quality and accept-ability&annoyance of the video content.

An Absolute Category Rating with Hidden Reference (ACR-HR) experiment is conducted to collect the video quality scores. Figure 2-c presents the voting screen shown after each video stimuli in this experiment. Classical video quality scale ("Bad", "Poor", "Fair", "Good", "Excellent") is used and numerically represented in [START_REF] Callet | European network on quality of experience in multimedia systems and services[END_REF][START_REF] Ak | Video consumption in context: Influence of data plan consumption on qoe[END_REF] range where higher values indicate higher video quality. They are represented as Mean Opinion Scores and referred as ACR-MOS in the dataset. ACR-MOS values are calculated with the ZREC [START_REF] Zhu | Zrec: Robust recovery of mean and percentile opinion scores[END_REF] MOS recovery algorithm.

To collect acceptability&annoyance labels, the dataset relies on the single step acceptability&annoyance procedure. Instruc- tions are used to simulate the user expectations similar to previous works [START_REF] Ak | Video consumption in context: Influence of data plan consumption on qoe[END_REF][START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF]. Precisely, the IPI-VUGC dataset uses the following instructions to set user expectations in the online social media platform context: "You are going to participate in an experiment determining the acceptability and annoyance of videos. You will need to imagine yourself scrolling through your preferred social media platform (e.g., Facebook, Instagram, TikTok, etc.) and encountering these videos. Based on your expectations of the video quality in these encounters, you will need to rate the quality of the video in terms of Acceptability and Annoyance.

• The video is not annoying when its quality satisfies or exceeds your expectations. • The video is annoying but acceptable when its quality is acceptable but not completely satisfies your expectations. • The video is not acceptable when its quality does not meet your expectations. Such video quality makes you think about skipping to the next video."

The acceptability&annoyance labels are referred as AccAnn-MOS in the dataset and are numerically in the range [START_REF] Callet | European network on quality of experience in multimedia systems and services[END_REF][START_REF] Oeldorf-Hirsch | How bad is good enough? exploring mobile video quality trade-offs for bandwidth-constrained consumers[END_REF]. 1, 2 and 3 corresponds to "Not Annoying" (NAnn), "annoying but acceptable" (AA), and "not acceptable" (NAcc), respectively. Similar to ACR-MOS, AccAnn-MOS values are calculated with the ZREC [START_REF] Zhu | Zrec: Robust recovery of mean and percentile opinion scores[END_REF] MOS recovery algorithm.

Determining Acceptability&Annoyance Categories and Thresholds

In IPI-VUGC Dataset, each stimuli is rated by 25 unique observers to collect the acceptability&annoyance labels. Simply averaging the numerical representations of these labels provides us with AccAnn-MOS. For certain applications, a simple accept-ability&annoyance category might be more desirable. To this end, we can estimate the acceptability&annoyance categories by using Barnard's test [START_REF] Barnard | A new test for 2× 2 tables[END_REF]. It is an exact test developed for 2 × 2 contingency tables. Without loss of generality, Barnard's test determines the statistically significant difference between the two sets of observations. We follow the algorithm summarized in Figure 3 similar to those in [START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF][START_REF] Ak | Video consumption in context: Influence of data plan consumption on qoe[END_REF]. In addition to the 3 acceptability&annoyance categories collected in the experiment, we utilize 2 threshold categories as "unsure about annoyance but acceptable" (UAnn) and Acceptability Annoyance Online Social Media 34 67 Basic Subscription [START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF] 58 80 Premium Subscription [START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF] 71 87

VMAF [START_REF] Li | Toward a practical perceptual video quality metric[END_REF] thresholds for acceptability and annoyance of video quality in the contexts of online social media platforms, basic and premium subscription to video streaming services.

"unsure about acceptability but annoying" (UAcc). If the mean acceptability&annoyance score is greater than or equal to 2, we assign the stimuli to one of the NAnn, UAnn, and AA categories based on the Barnard's test result. If the Barnard's test results show that there is not a statistically significant agreement among the participants on one of the neighboring main categories (NAnn or AA), they are assigned to the threshold category (UAnn). Similarly, if the mean acceptability&annoyance score is smaller than 2, we assign the stimuli to one of the AA, UAcc, NAccc categories based on the Barnard's test result.

To estimate the acceptability and annoyance thresholds in terms of objective metric scores, we simply take the average of objective quality metric scores of the stimuli in the threshold categories UAcc and UAnn for acceptability and annoyance thresholds, respectively. In this work, we rely on VMAF [START_REF] Li | Toward a practical perceptual video quality metric[END_REF] for threshold estimation. VMAF is an efficient and reliable full-reference video quality metric that is widely adopted in the industry. It is not a good predictor for video quality when the reference content is heavily distorted as it might be observed in the UGC domain. Despite the drawback, we relied on VMAF to be able to compare the estimated thresholds with the thresholds reported in previous studies exploring different contexts.

Comparison of VMAF Thresholds for Accept-ability&Annoyance in different contexts

Table 1 presents the estimated thresholds in terms of VMAF [START_REF] Li | Toward a practical perceptual video quality metric[END_REF] score for acceptability and annoyance of video quality. All thresholds are determined based on the algorithm described above. The thresholds for the online social media platform context is calculated over IPI-VUGC dataset while the thresholds for contexts of basic and premium subscription to video streaming services are calculated in [START_REF] Li | Accann: A new subjective assessment methodology for measuring acceptability and annoyance of quality of experience[END_REF].

As table 1 presents, we see that the threshold for annoyance of the video quality in terms of VMAF score is at the highest value of 87 for the premium subscription to a video streaming service context. When a basic subscription is taken into account we see that subjects are more forgiving in terms of video quality required for not annoying content. Even as low as 67 VMAF score is found to be enough for a not annoying video quality in online social media platforms. We also see a similar trend in the acceptability thresholds where subjects in the premium subscription context are more demanding in terms of video quality. Surprisingly, a satisfying video quality in the contexts of the online social media platforms can be seen not acceptable in the context of premium subscription to video streaming services.

Conclusion and Discussion

We showed that the acceptability&annoyance defines the QoE as a combination of user expectation and video quality. We provided a brief introduction to the publicly available IPI-VUGC dataset, that contains video quality ratings and accept-ability&annoyance labels in the online social media platforms context. We provided a detailed guideline to the methodology used for determining the acceptability and annoyance thresholds in terms of objective quality metric predictions. Moreover, we used VMAF predictions of video quality to estimate these thresholds and compared them with other datasets developed on video streaming service context.

VMAF score thresholds for acceptability and annoyance reveal that people are more forgiving of the lower video quality content in online social media platform context compared to the context of paid subscription to video streaming services. The VMAF range of 67 to 71 can be seen as not annoying for the context of online social media platforms while can be categorized as not acceptable in the context of using video streaming platforms on television with a premium subscription. This striking difference in thresholds reveal the impact of context on QoE.

The choice of VMAF for user generated videos is not ideal due to variance in source content quality. Despite this, we utilized VMAF to be able to compare with the results of previous studies. Therefore, the study could be further improved with other more appropriate video quality metrics such as UVQ [START_REF] Wang | Uvq: Measuring youtube's perceptual video quality[END_REF]. As future work, the study can be extended with more modern coding algorithms and high dynamic range content. The results of this work may help online social media platforms and streaming service providers to optimize their video delivery services without sacrificing from users' satisfaction.

Figure 1 .

 1 Figure 1. a) multi-step b) single-step acceptability&annoyance experiment design.

Figure 2 .

 2 Figure 2. Sample screens captured during a) stimuli presentation, b) voting screen in acceptability&annoyance experiment, and c) voting screen in video quality experiment. The screen captures are taken from IPI-VUGC dataset under a CC-BY-SA 4.0 license.

Figure 3 .

 3 Figure 3.Overview of the algorithm to determine the Acceptabil-ity&Annoyance categories.

https://zenodo.org/doi/10.5281/zenodo.10475209

https://www.apple.com/go/2022/iphone-14-pro/


domain: phys chim

text:
Yinwei Yang

Oumar Ba

Shixun Dai

Feifei Chen
email: chenfeifei1@nbu.edu.cn

Georges Boudebs

Large third-order optical nonlinearity of nonstoichiometric chalcogenide glasses within Ge-In-S ternary system

Keywords: Third-order optical nonlinearity, Ge-In-S chalcogenide glass, Z-scan

Large third-order optical nonlinearity of non-stoichiometric chalcogenide glasses within Ge-In-S ternary system

Introduction

Ultra-fast third order optical nonlinearity (TONL) process is the ideal mechanism for all-optical (AO) devices [START_REF] Christodoulides | Nonlinear refraction and absorption: mechanisms and magnitudes[END_REF][START_REF] Vogel | Glasses as nonlinear photonic materials[END_REF] , such as AO switching (AOS), wavelength converters and optical limiting. The must-go path to minimize size and energy-consumption of the NL optical devices is finding optical materials with high TONL susceptibility (χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] ). Chalcogenide amorphous semiconductors (i.e. chalcogenide glasses, ChGs) possess ultra-fast TONL and the highest χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] among all the optical glasses, as well as wide infrared (IR) transparent range [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] . These unique optical properties of ChGs make chalcogenide photonic [START_REF] Eggleton | Chalcogenide photonics[END_REF] compatible with both silica photonics and silicon photonics, thus the chalcogenide devices are considered as a critical component in the advanced AO and IR photonic systems [START_REF] Qiu | Ga 2 S 3 -Sb 2 S 3 -CsI chalcohalide glasses for mid-infrared applications[END_REF][START_REF] Grassani | Mid infrared gas spectroscopy using efficient fiber laser driven photonic chip-based supercontinuum[END_REF][START_REF] Ycas | Highcoherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 μm[END_REF][START_REF] Zhou | Large nonlinearity and low loss Ge-Sb-Se glass photonic devices in near-infrared[END_REF] .

On the other hand, In 2 S 3 known as a type of III-VI semiconductor with natural defects lately attracts considerable attentions for its unique photoelectric properties [START_REF] Horani | Unraveling the growth mechanism forming stable γ-In 2 S 3 and β-In 2 S 3 colloidal nanoplatelets[END_REF][START_REF] Huang | Controlled synthesis of ultrathin 2D β-In 2 S 3 with broadband photoresponse by chemical vapor deposition[END_REF][START_REF] Warrier | Plasmon-assisted enhancement and tuning of optical properties in β-In 2 S 3 quantum dots[END_REF] , such as distinctive photoconductivity and broadband spectral response. Our very recent work [START_REF] Yang | Performance modification of third-order optical nonlinearity of chalcogenide glasses by nanocrystallization[END_REF] has shown that the formation of β-In 2 S 3 nanocrystals in germanium-sulphur (Ge-S) based ChGs could significantly promote the χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] value of the glasses. However, details about the effect of In 2 S 3 compound to TONL properties of ChGs remain few and obscure, which is also confused by the previous studies that showed some controversial experimental results. For examples, Mao et al [START_REF] Mao | Structure dependence of ultrafast third-order optical nonlinearity for GeS 2 -In 2 S 3 -CsI chalcohalide glasses[END_REF] reported that the 15 mol% increase of In 2 S 3 content in the GeS 2 -In 2 S 3 -CsI ChGs could enlarge the χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] value by 2.7 times. Dong et al [START_REF] Dong | Study on the structure dependent ultrafast third-order optical nonlinearity of GeS 2 -In 2 S 3 chalcogenide glasses[END_REF] reported that incorporation of 20 mol% In 2 S 3 to GeS 2 ChG which promoted the linear refractive index (n 0 ) and reduced the optical band gap (E g ) could surprisingly smaller the χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] value by 1.7 times, and very similar experimental results were reported by Guo et al [START_REF] Guo | The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses[END_REF] in In 2 S 3 incorporated GeS 2 -Ga 2 S 3 ChGs. Since larger n 0 accompanied by smaller E g is the signature [START_REF] Tanaka | Nonlinear optics in glasses: How can we analyze?[END_REF][START_REF] Fedus | Nonlinear characterization of GeS 2 -Sb 2 S 3 -CsI glass system[END_REF] for materials possessing larger χ [START_REF] Adam | Chalcogenide glasses: preparation, properties and applications[END_REF] , the anomalous behavior observed in ChGs after In 2 S 3 incorporation is the motivation for us to carry out the more specific studies.

In this paper, we investigate the TONL properties of the In 2 S 3 incorporated Ge-S (namely Ge-In-S ternary system, GIS) ChGs including both chemical stoichiometric (CS) and non-stoichiometric (NS) compositions. Their NL refraction (n 2 ) and NL absorption (β) behaviors are characterized by using conventional based Z-scan techniques at two near-IR wavelengths (0.8 μm and 1.064 μm), and the evolution of the TONL parameters are explained in terms of glass network structure modifications and wavelength-dispersion dependence of the TONL properties.

Experimental

Composition design of the GIS ChGs are based on two CS compositions, i.e. 85GeS 2 -15In 2 S 3 (Ge 26 In 10 S 64 , labeled as Ge26) and 90GeS 2 -10In 2 S 3 (Ge 28 In 6 S 66 , labeled as Ge28), and selection of the other four NS compositions in S-rich and S-lack states are presented in Table 1. Each glass sample was prepared by melting analytical grade reagents of Ge, In and S elements in an evacuated silica tube at 850 o C for 10 hours, and then annealed at 20 o C below glass transition temperature for 12 hours in order to release inner stress. For the subsequent optical testing, each glass ingot was cut into plate and carefully polished to optical smooth on both surfaces and thickness of 1 ± 0.01 mm.

Absorption and transmission spectra of samples ranging within 0.4~2.5 μm were recorded using an UV-VIS-NIR spectrophotometer (Lamda950, PerkinElmer, USA).

IR transmission spectra ranging within 2.5~12 μm were obtained using a Fourier transform IR spectrometer (Nicolet381, Nicolet, USA). Raman spectra of the samples were measured by a micro-confocal Raman spectrometer (Invia, Renishaw, UK), with excitation wavelength of 785 nm. TONL properties of the samples were studied by conventional Z-scan and D4σ-Z-scan techniques performed at 0.8 μm and 1.064 μm, respectively. The D4σ-Z-scan method belongs to the family of techniques affiliated to the Z-scan. It involves scanning the sample in the focal plane region of a 4f setup and measuring the variation of the output beam size as a function of z (the position of the sample) using a CCD camera in the image plane of the system. One of the advantages is to be insensitive to pointing instability of pulsed lasers because no hard (physical) aperture is employed as in the usual Z-scan. Another advantage is to measure the nonlinear refractive signal independently of the nonlinear absorption one. More technical details can be found in [18], [19] and [20]. The laser source at wavelength of 0.8 μm is a Ti:sapphire laser (Mira 900-D, Coherent, USA) with a pulse width of 130 fs (FWHM) and repetition frequency of 76 MHz, and the central laser peak-intensity at focus is I 0 = 0.52 ± 0.04 GW/cm 2 . The other wavelength at 1.064 μm is delivered by a pulsed Nd:YAG laser (17 ps FWHM duration, 10 Hz repetition rate) using I 0 = 32 ± 2.7 GW/cm 2 . All these measurements were performed at room temperature with linearly polarized light incident perpendicularly to the sample surface.

Results

The visible and IR transmission spectra of the six GIS ChGs are shown in Fig. 1(a). It can be seen that the glasses have flat optical transmission window (transmittance > 60%) from about 0.6 μm to 11 μm, in spite of the OH group and Ge-O impurity at ~4 μm and ~9 μm respectively, which can be eliminated by further purification process. The photo of the samples in inset of Fig. 1(a) shows the evolution of their color from red to tan and then suddenly silver black with increase of Ge content, as a result of the shifting of the fundamental absorption edge (FAE). energy with absorption coefficient α = 100 cm -1 ) [START_REF] Bindra | Nonlinear optical properties of chalcogenide glasses: Observation of multiphoton absorption[END_REF] . It is clear from both the FAE location and the E g value (given in Table 1) that the dependency on Ge content is not straightforward but some insights can be given. The NS sample with most S-lack (Ge35) has the smallest E g of 1.90 eV, while the largest E g of 2.48 eV is present in a CS sample (Ge28). The other CS sample (Ge26) having E g of 0.12 eV smaller than Ge28 due to the 5 mol% substitution of GeS 2 by In 2 S 3 , is consistent with the experimental results in Ref. 14. Also given in Table 1, as compared to the Ge 20 S 80 binary glass [START_REF] Sun | Correlating structure with third-order optical nonlinearity of chalcogenide glasses within a germanium-sulfur binary system[END_REF] , addition of 10 mol% indium, namely being sample Ge20 (molar composition of Ge 20 In 10 S 70 ) could give rise to 0.52 eV of E g reduction, implicating a significant structural modification of the Ge-S network after indium incorporation.

2.

It should be noted that the BWRV technique gives a sign-signature opposite to that of the classical Z-scan one. So, the reversed evolution for the two curves (relative to the valley/peak) unambiguously shows that the NL refractive index (n 2 ) has the same positive sign at both wavelengths: 0.8 μm and 1.064 μm. The n 2 value of each sample was extracted from theoretical fitting [START_REF] Boudebs | Nonlinear characterization of materials using the D4σ method inside a Z-scan 4f-system[END_REF][START_REF] Yin | Determination of nonlinear absorption and refraction by single Z-scan method[END_REF] of the experimental curves and then normalized to that of fused silica (n 2 = 2.6×10 -20 m 2 /W) [START_REF] Milam | Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica[END_REF] . As tabulated in Table 1, it is clear that the majority n 2 s at 0.8 μm (especially Ge30 and Ge35) are larger than those at 1.064 μm, showing a normal wavelength-dispersion that had been observed in many other ChG systems [START_REF] Harbold | Highly nonlinear As-S-Se glasses for all-optical switching[END_REF][START_REF] Wang | Systematic z-scan measurements of the third order nonlinearity of chalcogenide glasses[END_REF] . More importantly, the maximum n 2 at 0.8 μm is yielded from Ge35, and the value is near 3000 times higher than that of the fused silica. We are aware that the NL measurements performed in different labs are sometimes difficult to compare but one may note that, this value might be one of the largest n 2 value ever reported in sulfide glasses, some of which are listed in Table 1 according to references [START_REF] Fedus | Nonlinear characterization of GeS 2 -Sb 2 S 3 -CsI glass system[END_REF][START_REF] Sun | Correlating structure with third-order optical nonlinearity of chalcogenide glasses within a germanium-sulfur binary system[END_REF][START_REF] Troles | Chalcogenide glasses as solid state optical limiters at 1.064 μm[END_REF] .

NL absorption behavior of the GIS ChGs at both wavelengths were investigated using open aperture (OA) Z-scan. Fig. 3 shows the traces obtained from Ge35 where a reverse saturable absorption signified by an evident transmittance dip in each curve center is observed, and it is the same for all other samples which also have normalized photon energy (NPE, hv/E g ) at 0.8 μm (hv = 1.55 eV) and 1.064 μm (hv = 1.17 eV) contained between 0.5 and 1. So, it seems logical to deduce that the two-photon absorption (TPA) is the dominate contribution to the NL absorption. By fitting the OA Z-scan traces with a TPA model [START_REF] Sheik-Bahae | Sensitive measurement of optical nonlinearities using a single beam[END_REF] , the NL coefficient (β) corresponding to the GIS ChGs were measured and tabulated in Table 1. Again, all the βs at 0.8 μm are much larger than those at 1.064 μm some of which are even absent, proving normal dispersion of the TONL properties of the GIS ChGs.

Discussion

Structural dependency

As mentioned above, E g value of the GIS ChGs is related to the state of sulfur in the glass network, compositions deviated from CS tend to have smaller E g . On the basis of the crystalline semiconductor models proposed by Sheik-Bahae et al [START_REF] Sheik-Bahae | Dispersion of bound electron nonlinear refraction in solids[END_REF] and Dinu [START_REF] Dinu | Dispersion of phonon-assisted nonresonant third-order nonlinearities[END_REF] , both n The enhancement of both n 2 and β in the GIS ChGs with NS compositions is surely related to their specific network structure. To find its structural origin, we performed Raman spectral analysis on the present GIS ChGs, as illustrated in Fig. 5.

According to the prior studies [START_REF] Dong | Study on the structure dependent ultrafast third-order optical nonlinearity of GeS 2 -In 2 S 3 chalcogenide glasses[END_REF][START_REF] Sun | Correlating structure with third-order optical nonlinearity of chalcogenide glasses within a germanium-sulfur binary system[END_REF][START_REF] Yang | Ga-Sb-S chalcogenide glasses for mid-infrared applications[END_REF] , each Raman spectrum can be perfectly decomposed into six Gaussian peaks, and the belonging of each peak to vibration mode of the specific structural unit is given in Table 2. For the S-lack samples (Ge35 and Ge30), they have a unique and strong Raman vibration mode of [GeS 2 Ge 2 ] and [GeSGe 3 ] sub-metallic tetrahedrons at ~230 cm -1 , which indicates the existence of considerable number of Ge-Ge homopolar (metallic) bonds in the glass network.

Thus, optical properties of the local glass matrix would behave more close to crystalline Ge which is known to have very large TONL properties [START_REF] Hon | The third-order nonlinear optical coefficients of Si, Ge, and Si 1-x Ge x in the midwave and longwave infrared[END_REF][START_REF] Ensley | Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared[END_REF] . The glass network of CS samples (Ge28 and Ge26) have both [S 3 Ge-GeS 3 ] (~250 cm -1 ) and [S 3 Ge-S-GeS 3 ] (~435 cm -1 ) link-like units which reinforce connectedness of the glass network and consequently stabilize the glass structures. Thus distortions of the electronic clouds of constructing elements in high-intensity illumination will be weakened in such glass network, i.e. lower the TONL property. As compared to the former two, the S-rich samples (Ge25 and Ge20) don't have Ge-Ge bond related vibration, but they have an unique vibration mode of [S 8 ] ring molecules (~475 cm -1 ) and strong [InS 4 ] tetrahedrons vibration at ~330 cm -1 , especially Ge20. So, the glass network consists of isolated [GeS 4 ] and [InS 4 ] tetrahedrons which are linked by bridging-sulfur and [S 8 ] rings. Since each S atom in [S 8 ] ring molecules have a couple of non-occupied lone pair electrons, they would certainly promote the TONL property [START_REF] Yang | Ga-Sb-S chalcogenide glasses for mid-infrared applications[END_REF] , but the efficiency is lower than that of the [GeS 2 Ge 2 ] and [GeSGe 3 ] submetallic tetrahedrons, according to the present experimental data.

In addition to the above vertical comparison of the Raman spectra, lateral comparison would give more details about the structural dependent TONL properties of the GIS ChGs, especially the specific role of [InS 4 ] tetrahedrons that was controversial as mentioned in the introduction section. In the couple of S-rich samples, Ge25 and Ge20 have the same [S 8 ] vibration (~475 cm -1 ) intensity for their equal S content, but the [InS 4 ] vibration (~325 cm -1 ) becomes remarkably dominant against the [GeS 4 ]-related vibrations (~350 cm -1 , ~370 cm -1 , ~410 cm -1 ) in sample Ge20 which has In content of 5 mol% higher than its counterpart. According to the data showing that Ge20 have both larger n 2 and β than Ge25, the impact of [InS 4 ] to TONL properties should be positive for the S-rich GIS ChGs. For the two CS compositions, substitution of [GeS 4 ] tetrahedrons by [InS 4 ] tetrahedrons as well as slight enhancement of vibration of [S 3 Ge-GeS 3 ] link units can be observed when 5 mol% GeS 2 was replaced by In 2 S 3 , namely converting from Ge28 to Ge26. As mentioned above, the [S 3 Ge-GeS 3 ] link units that stabilized the glass network would lead to reduction in the TONL properties, proving that the effect of [InS 4 ] tetrahedrons to TONL properties could also be positive for CS compositions based on the fact of Ge26 having larger n 2 and β than Ge28.

Contrary to the S-rich and CS ChGs, larger n 2 and β in the two S-lack ChGs are yielded from Ge35 which has lower In content than Ge30. According to their Raman spectra, vibration intensity of the [InS 4 ] and [GeS 4 ] tetrahedrons is also consistent with the In and Ge content, but one can note from Ge35 that the vibrations of [GeS 2 Ge 2 ] and [GeSGe 3 ] sub-metallic tetrahedrons had split from their envelope with [S 3 Ge-GeS 3 ] link units (as noted by the arrow in Fig. 5). In fact, the central wavenumber of the sub-metallic tetrahedrons in spectrum of Ge35 is 229 cm -1 , while the central is 239 cm -1 for Ge30. Shifting of this band towards smaller wavenumber (i.e. lower vibrating frequency) indicates that more Ge-Ge metallic bonds have formed in the sub-metallic tetrahedrons, namely the conversion of [GeS 2 Ge 2 ] to [GeSGe 3 ] or even [GeGe 4 ] [START_REF] Lucovsky | Structural interpretation of the infrared and Raman spectra of glasses in the alloy system Ge 1-x S x[END_REF] , which made the tetrahedrons naturally more metallic and consequently enhanced the TONL properties. Accordingly, the metallization process in local glass matrix of Ge35 makes the glass to have larger TONL properties than Ge30, in despite of Ge35 has weaker [InS 4 ] vibration. That could be the reason which caused the issue of the contradictory role relative to [InS 4 ] tetrahedrons in previous studies [START_REF] Mao | Structure dependence of ultrafast third-order optical nonlinearity for GeS 2 -In 2 S 3 -CsI chalcohalide glasses[END_REF][START_REF] Dong | Study on the structure dependent ultrafast third-order optical nonlinearity of GeS 2 -In 2 S 3 chalcogenide glasses[END_REF][START_REF] Guo | The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses[END_REF] .

NPE dependency

According to the experimental results of the two testing wavelengths given in Table 1, it can be found that the maximum and the minimum TONL parameters (n 2 and β) are from Ge35 and Ge28 which have the E g minimum and maximum, respectively. Obviously, it confirms the inverse dependency of the TONL properties on E g value. Meanwhile, normal wavelength-dispersion of the n 2 and β values means that the TONL properties also have a positive dependency on incident photon energy (hv). Therefore, by plotting the n 2 and β values of the GIS ChGs against their NPE (hv/E g ) as given in Fig. 6, two exponential-like growth curves can be obtained. As one can observe, both n 2 and β at two different wavelengths could generally match each other at the common NPE of 0.62, but the disparity between the n 2 value of Ge28 (at 0.8 μm) and Ge35 (at 1.064 μm) at the NPE is also remarkable because n 2 is very sensitive to glass structures as mentioned above.

Referring to the empirical dispersion theories for bound electronic nonlinearity as summarized by Tanaka [START_REF] Tanaka | Nonlinear optics in glasses: How can we analyze?[END_REF][START_REF] Tanaka | Two-photon optical absorption in amorphous materials[END_REF] , the similar tendency of two experimental curves in Fig. 6 implicated that the n 2 enhancement at higher NPE is associated with the β increase, namely TPA resonant effect. However, the more specific theory of TPAassisted TONL developed from direct-transition semiconductors by Sheik-Bahae et al [START_REF] Sheik-Bahae | Dispersion of bound electron nonlinear refraction in solids[END_REF] had elucidated negative sign of n 2 at NPE > 0.7. Since no negative n 2 was obtained in NPE range from 0.47 to 0.82 as shown in Fig. 6(a), the direct-transition semiconductor theory therefore can not precisely describe the wavelength n 2 dispersion of the GIS ChGs. This is in agreement with TONL properties of As-S-Se and Ge-Se ChGs at NPE > 0.7 recently reported by Romanova et al [START_REF] Romanova | Measurement of non-linear optical coefficients of chalcogenide glasses near the fundamental absorption band edge[END_REF] , which implicated that the large TONL of GIS ChGs at the high NPE end is also associated with electron transitions between gap states in the bandgaps. Nevertheless, the present wavelength n 2 -dispersion of the GIS ChGs in Fig. 6(a) has wider NPE coverage than that of As-S, Ge-As-Se and Ge-Sb-Se ChGs as elaborated by Wang et al [START_REF] Wang | Systematic z-scan measurements of the third order nonlinearity of chalcogenide glasses[END_REF] , and it also indicates the existence of an universal expression for n 2 -dispersion of the ChGs.

Besides, the curve further confirms that TONL dispersion of the GIS ChGs at NPE > 0.7 no longer fits to the indirect-transition semiconductor model [START_REF] Dinu | Dispersion of phonon-assisted nonresonant third-order nonlinearities[END_REF] which was derived from silicon band structure parameters and predicted n 2 reduction at NPE > 0.7.

However, it remains impossible to derive a inclusive n 2 dispersion model for ChGs based on their own band structure, because modeling amorphous chalcogenides of which lack long range periodic ordering remains a great challenge. Especially when comparing measured values at both different pulse durations and repetition rates. In current stage, experimental acquisition is indeed the only reliable way to give the precise dispersion of TONL properties of ChGs.

Figure of merits

To evaluate the TONL properties of the GIS ChGs for practical optical devices, especially AOS that are based on NL refraction (i.e. Kerr effect) of materials, the following two figure of merits [START_REF] Marchese | Highly nonlinear GeS 2 -based chalcohalide glass for all-optical twin-core-fiber switching[END_REF] : T = n 2 /βλ and W = n 2 I 0 /αλ (λ the testing wavelength) giving the trade-off between NL refraction (n 2 ), linear absorption (α) and NL absorption (β) are considered. For n 2 -based photonic devices, both figure of merits needs to be maximized to achieve high performance of NL devices. For example, AOS requires T and W values to be at least higher than 1 for effective switching, namely, to achieve phase shift of 2π [START_REF] Lenz | Large Kerr effect in bulk Se-based chalcogenide glasses[END_REF] . For the present GIS ChGs, the calculated values are shown in Table 1, it can be seen that that the T values at 0.8 μm are below 1 due the the presence of large TPA, thus the glasses are suitable for these β-based photonic devices (such as optical limiting) at 0.8 μm because the W values are somehow above 1. Besides, one can logically see that both figure of merits at 1.064 μm are remarkably larger than those at 0.8 μm, indicating that the decrease of n 2 due to normal dispersion process is slower than the decrease of α and β, which also implies great potential for n 2 -based photonic devices. Therefore, it is reasonable to expect higher NL performance of the GIS ChGs at the optical communication devices and/or mid-IR photonic devices which operate at longer wavelengths.

Conclusions

In summary, we measured and found large third-order optical nonlinearity in non-stoichiometric Ge-In-S chalcogenide glasses at 0.8 µm and 1.064 μm. A large nonlinear refractive index (n 2 ) of near 3000 times that of the silica glass was acquired from a S-lack glass at 0.8 μm. This was attributed to the contribution of [GeSGe 3 ] sub-metallic tetrahedrons and [InS 4 ] tetrahedrons in the glass network. Also, it was found that the S-rich glasses have large n 2 value (800 times that of the silica glass), but the contribution of [S 8 ] ring molecules to n 2 is relatively weaker as compared to its counterparts in the S-lack glasses. Logically, third-order optical nonlinearity of the Ge-In-S glasses at 1.064 μm is found to be smaller than that at 0.8 μm, showing a normal dispersion behavior of the third-order optical nonlinearties. Positively, figure of merits at 1.064 μm are remarkably larger than those at 0.8 μm due to the fast decrease of optical losses at longer wavelengths. This would imply great potential of the Ge-In-S chalcogenide glasses for nonlinear photonic devices operating at optical communication wavelength and/or mid-IR wavelengths.

Tables Table 1. Compositions, optical bandgap (E g ), TONL parameters (n 2 /n 2 SiO2 , β) and figure of merits (T = n 2 /βλ, W = n 2 I 0 /αλ) of the GIS ChGs and the previously reported as references.

Sample

No.

Molar composition 10GeS2-75Sb2S3-15CsI [START_REF] Fedus | Nonlinear characterization of GeS 2 -Sb 2 S 3 -CsI glass system[END_REF] 1.79 -270 0.2 -0.6 48GeS2-32Sb2S3-20CdCl2 [START_REF] Troles | Chalcogenide glasses as solid state optical limiters at 1.064 μm[END_REF] 2.15 3185 7.01 -1.5 -Table 2. Assignment of the Raman bands obtained from Gaussian decomposition as well as their appearance in the GIS glass samples.

E g (eV) ±1% n 2 /n 2 SiO2 ±23% β (cm/GW) ±23% W ±23% T ±23% n 2 /n 2 SiO2 ±23% β (cm/GW) ±23% W ±23% T ±23% λ = 0.8 μm λ = 1.
Wavenumber (cm -1 ) Assignment Appearance in samples

Figure 1 (

 1 Figure 1(b) gives the absorption spectra of the GIS ChGs showing the location of

  According to Ref. 14, the specific structural modification could be substitution of the Ge sites in [GeS 4 ] tetrahedrons by In atoms as well as the formation of Ge-Ge homopolar bonds. The TONL properties of the GIS ChGs were characterized at wavelengths of 0.8 µm and 1.064 μm, both of which are beyond the FAE of the glasses as the arrows show in Fig. 1(b), thus the resonant nonlinearity from one-photon induced innerbands transitions could be minimized. Close aperture (CA) Z-scan and beam waist relative variation (BWRV) curves of a representative sample Ge28 are shown in Fig.

  2 and β would have E g dependency, thus we are expecting such behaviors to bridge network structure and TONL parameters of the GIS ChGs which are amorphous semiconductors. By qualifying the relative sulfur content (S re , S re = 100-2x-1.5y) from the standard molar composition of Ge x In y S (100-x-y) , the plots of n 2 and β versus S re are obtained and shown in Fig. 4. Both figures exhibit minimum values at the central (CS compositions) and enlarged values when the composition gradually deviated from CS, i.e. towards lack or sulfur rich compositions, which also indicates that TONL dispersion of the ChGs will be enlarged as their compositions deviate from CS.

229~239 [GeS 2

 2 Ge 2 ] and [GeSGe 3 ] sub-metallic tetrahedrons Ge35

FiguresFig. 1

 1 Figures

  Fig. 1 (a) The transmission spectra of the GIS ChGs, inset is a photo of the samples; (b) the absorption edge spectra of GIS ChGs, the arrows note the testing wavelengths of TONL measurements.

Figure

  Figure

Fig. 2 (

 2 Fig. 2 (a) Closed aperture Z-scan curve at 0.8 μm and (b) beam waist relative variation curve at 1.064 μm of sample Ge28, the solid lines are the numerical fittings.

Fig. 3

 3 Fig. 3 Open aperture Z-scan curve at 0.8 μm (a) and at 1.064 μm (b) of sample Ge35, the solid lines are the numerical fittings.

Fig. 4

 4 Fig. 4 Variation of n 2 (a) and β (b) of the GIS ChGs versus the relative sulfur content (S re ).

Fig. 5

 5 Fig. 5 Raman spectra and the corresponding Gaussian decomposition of GIS glass series based on sample Ge28 (a) and sample Ge26 (b).

Fig. 6

 6 Fig. 6 Evolution of n 2 (a) and β (b) of the GIS ChGs with NPE (hv/E g ).

Acknowledgements This work was partially supported by the National Key Research and Development Program of China (grant no. 2016YFB0303803), National Natural Science Foundation of China (grant no. 62075108) and Natural Science Foundation of Zhejiang Province (grant no. LY19F050005). It was also sponsored by K.C. Wong Magna Fund in Ningbo University. Credit Author Statement Yinwei Yang, Formal analysis, Writing-Original Draft, Writing-Review & Editing, Visualization. Oumar Ba, Investigation, Methodology. Shixun Dai, Conceptualization, Supervision. Feifei Chen, Conceptualization, Formal analysis, Writing -Review & Editing , Funding acquisition, Supervision. Georges Boudebs, Conceptualization, Supervision. *Credit Author Statement

Declaration of interests

☒ 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.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: