Femtosecond laser writing is capable of producing highly localized, volumetric changes within materials, which provide the foundations for using the material to create 3D photonic structures. The present work deals with the formation of femtosecond laser-induced tracks in silver containing zinc phosphate glass, for the study of the efect of laser parameters, like the pulse repetition rate, by varying the parameters from 10, 100 to 500 kHz and pulse energy from 60 to 120 nJ. The changes in microstructure and optical properties are recorded through optical microscopy in both brightfield and fluorescence modes, with a specific interest in the dimensions of the laser-written tracks. This study was conducted using an Artificial Neural Networks (ANN) to predict the width and height of the tracks based on the varying laser exposure parameters. The analysis includes a comprehensive assessment of prediction accuracy through Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Coeficient of Variation of the Root Mean Squared Error (CVRMSE), and determination coeficient ( 2) with expected values denoted as 0.232%, 0.482%, 0.312%, 0.066%, 10.241%, and 0.909 respectively. These metrics do show the efectiveness and reliability of the ANN model in capturing the complex dynamics of the laser material processing phenomenon. In fact, these resourceful predictions are a mile toward the real optimization of laser processing techniques in material science-a quantitative tool for the prediction of material responses under varied laser settings.
that femtosecond direct laser writing (DLW) can induce tion of these pivotal studies, ofering a concise overview luminescence, absorption, and generate birefringence of the investigated materials and the reported discoveries. within micron-sized regions of silver-doped zinc phos- Following a critical examination of the key studies phate glasses, obviating the need for subsequent thermal summarized in Table 1 regarding femtosecond laser writtreatment [14]. Subsequent in-depth investigations by ing in photonic glasses, it becomes apparent that sigGuérineau et al. have significantly enhanced the compre- nificant strides have been made in comprehending and hension of these phenomena. Their work has introduced employing femtosecond laser technologies for micro- and the concept of Type AC and AN modifications, encom- nanoscale structuring within diverse glass compositions. passing both silver clusters and nanoparticles, thereby However, certain areas warrant further exploration. The refining the existing classification system for microstruc- majority of existing research has primarily concentrated tural modifications within glasses [15]. This meticulous on manipulating physical properties such as refractive control over material properties at the micron scale rep- index alterations and the fabrication of luminescent patresents a critical facet in the development of novel pho- terns. Conversely, less emphasis has been placed on tonic devices. Alassani et al. have demonstrably achieved the development of predictive models for these changes success in inscribing three-dimensional luminescent pat- and a comprehensive analysis of how varying laser paterns that achieve co-localization of silver clusters and rameters influence the physical and optical properties of rare-earth ions. This achievement underscores the poten- silver-containing zinc phosphate glasses. Additionally, tial for groundbreaking advancements in novel optical while some studies have leveraged Artificial Intelligence data storage and sensor applications [16, 17]. Concur- (AI) for pattern inscription and modifications, the applirently, the research conducted by Lv et al. exemplifies cation of Artificial Neural Networks (ANNs) to predict the fabrication of cladding waveguides in proximity to outcomes based on laser parameters remains relatively the glass surface. This strategic positioning optimizes the undocumented in the context of optimizing femtosecond interaction of light with the modified regions, thereby laser processes. facilitating enhanced photonic integration [18, 19]. This lacuna underscores the necessity for a systematic
Beyond the conventional structuring of waveguides, approach to prognosticate and optimize the properties of the femtosecond laser has been leveraged to create in- materials processed with femtosecond lasers. This is pretricate photonic structures within glass. Tsimvrakidis et cisely where the current research intervenes. The study al. have delved into the reversible inscription of waveg- meticulously documents the microstructural modificauides in silver phosphate glasses, thereby paving the tions induced by varying laser parameters and presents a way for the realization of dynamically reconfigurable pioneering application of ANNs to achieve accurate prephotonic circuits [20]. In a similar vein, Guérineau et dictions of laser-written track dimensions. The following al. have documented their success in employing direct highlights the paper’s principal contributions: laser writing (DLW) to fabricate subwavelength periodic · Leveraging an Artificial Neural Network (ANN) to structures within mid-infrared glasses. This achievement achieve accurate predictions of track dimensions through signifies a novel level of control over the manipulation comprehensive consideration of diverse laser parameters. of optical properties facilitated by DLW [21]. Desmoulin · In-depth investigation of the influence exerted by et al. further elucidated this capability of tailoring the pulse repetition rates and pulse energy on track formaglass’s microstructure at sub-micron scales. Their work tion. demonstrably showcased selective etching and post-laser · Concurrent implementation of both brightfield and writing surface topography engineering, thereby high- fluorescence microscopy to evaluate changes, providing lighting the potential for intricate surface structuring a multifaceted approach to optical characterization. in photonic applications [22]. At a foundational level, · Employing a battery of error assessment metrics to the investigations by Bukharin et al. have significantly rigorously validate the predictive accuracy of the ANN augmented the comprehension of the heat accumulation model. regime governing femtosecond laser writing. Their work has meticulously elucidated how adjustments in laser parameters can exert fine-grained control over modifica- 2. Experimental Methodology: tions in refractive index and waveguide properties [23]. Design, Materials and Methods Collectively, these advancements significantly enrich the repertoire of tools available to engineers specializing in To investigate the formation of laser-induced tracks in the design of cutting-edge optical materials and devices. silver-containing zinc phosphate glass, a detailed experiThis enrichment is driven by the ability to harness the mental setup was employed using a Yb:KGW femtosecunique properties of silver-containing glasses, which are ond laser system named Pharos SP, Light Conversion Ltd further accentuated through femtosecond laser interac- [26]. with a regenerative amplifier. The laser, operating tions. Table 1 subsequently presents a succinct compila- at a wavelength of 1030 nm, was precisely controlled to
[14] [15] [16] [18] [20] [21] [22] [23] [24] [25]
Joint formation of fluorescent silver clusters and plasmonic silver nanoparticles without heat treatment.
Classification of microstructure modifications in glass (type AC and AN) depending on laser parameters.
Demonstration of DLW to inscribe 3D luminescent patterns utilizing co-localization of silver clusters and Yb3+ ions.
Fabrication of cladding waveguides with controlled light propagation using a femtosecond laser.
Reversible inscription of waveguides allowing dynamic photonic device configuration.
Embedding subwavelength periodic structures inside optical materials.
Permanent formation of fluorescent structures and surface topology engineering through laser structuring.
Studied heat accumulation regime in femtosecond laser writing afecting refractive index.
Influence of glass network structure on laser-writing properties and photosensitivity.
Investigation of silver species generation under X-ray and femtosecond laser exposure.
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
No No Yes No Yes Yes No No No No emit pulses with a duration of 180 fs at repetition rates annealed at 325 °C for four hours to reduce mechanical of 10, 100, and 500 kHz. The energy of these pulses was stresses. The resulting glass block was processed into varied from 60 to 120 nJ using a motorized polarization optically polished plates suitable for laser treatment exattenuator, while a motorized half-wave plate was uti- periments. lized to align the linear polarization of the laser beam To characterize the microstructure and optical properparallel to the scanning direction. ties of the laser-written tracks, optical microscopy was
The focused laser beam was directed into the volume conducted in both brightfield and fluorescence modes of a glass plate, measuring 0.4 × 1.5 × 2.5, positioned using an Olympus BX51 microscope equipped with an on an air-bearing stage (Aerotech ABL1000). This setup, Olympus DP73 CCD camera. Brightfield images were synchronized with the laser system via SCA Professor taken to visualize the tracks (Figure 1a), and fluorescence software, facilitated precise 3D positioning of the glass images were captured under excitation between 400–410 sample at a constant scanning speed of 1 mm/s and main- nm, with emission registered in the 455–800 nm range tained a fixed focus depth of 150 . To avoid over- (Figure 1b). The exposure times for these images were lapping, a spacing of 200 between the tracks was 200 ms for top-view configurations and 100 ms for crossmaintained throughout the experiment. section views. Image analysis was performed using Im
The glass used in these experiments was silver- ageJ software to quantify the dimensions and optical containing zinc phosphate glass with a composition of characteristics of laser modifications [28]. 8Ag20, 53ZnO, 39P2O5 (mol%) [27]. This glass was synthesized using a melt-quenching technique from highpurity precursors (AgNO3, ZnO, H3PO4) [27]. The mixture was heated to 1200 °C in a corundum crucible covered with a fused silica cap and held for two hours before being rapidly quenched in a preheated metal mold and
3.1. Artificial Neural Network The integration of AI technologies has revolutionized numerous fields, ranging from autonomous driving to energy production and dispatch, from robotics to personalized medicine [29, 30, 31, 32, 33, 34, 35, 36, 37]. Among these technologies, Artificial Neural Networks (ANNs) have emerged as a powerful tool for modeling complex and nonlinear relationships that defy traditional analytical approaches [38, 39, 40, 41, 42, 43, 44, 45, 46, 47]. ANNs are widely used across various applications to predict outcomes, optimize processes, and understand intricate patterns in data [48, 49, 50]. For this study, an ANN was employed to predict the dimensions of femtosecond laserinduced tracks in silver-containing zinc phosphate glass.
The ANN architecture was designed to approximate the functional relationship between the input laser parameters and the resulting track dimensions. The model’s structure is represented by the following equations 1 to 3: four neurons in the first layer and two in the second, utilizing Stochastic Gradient Descent (SGD) as the solver over 250 iterations. This setup was optimized to capture the nuances of how varying laser parameters influence the physical properties of the tracks formed. Following are several statistics important in the predictive model’s appraisal for accuracy and reliability:
· MSE: The Mean Squared Error is the average of squares of the errors as equation 4 states. Though difer︃( )︃ ences of predicted and true values provide some insight = ∑︁( + ) (1) into the magnitude of the errors, this measure can be =1 very sensitive to outliers.
sinh() − − · RMSE: Root Mean Squared Error is the square root of = tanh() = cosh() = + − (2) oMfStEhecosmampueteerrurosirnsgineqtuhaetiosanm5e[5u1n].itIst yaiseltdhsearmesepaosnusree new = old − ∇(old, , )] (3) variable; hence, it is more interpretable.
· MAE: Mean Absolute Error gives the average absolute
Where is the output, represents the weight, diference in predicted and actual values as indication are representing the input values, and is for the bias. in the formula 6, and it gives a very direct indication of The activation function is represented by , and is the the accuracy of the prediction but does not show in what learning rate. The configuration of the neural network, direction the error is. as detailed in Table 2, includes two hidden layers with · MAPE: Mean Absolute Percentage Error shows ac- a positive correlation between pulse energy and height curacy in percentage as enlisted in equation 7. It gives was observed. a very clear perspective of the size of errors relative to Following the same methodology, the investigation true values which is very helpful when comparing error was extended to width. The experiment was replicated in diferent datasets of diferent scales. with identical pulse energy variations and repetition rates.
· CVRMSE: Coeficient of Variation of the Root Mean As depicted in Figure 3, a corresponding increase in width Squared Error is a normalized measure of RMSE as equa- was observed with increasing pulse energy and repetition tion 8 indicates, making it an important and very useful rate. The percentage error was calculated for each width metric for comparing relative prediction error in diferent measurement. datasets or models [52].
· 2: The Coeficient of Determination explains the 4.2. Forecasts and Regression Results proportion of variance in the dependent variable predicted from the independent variables. It serves as an indicator of the goodness of fit of the model; a higher 2 says the model is more capable of capturing variability in data, it can be calculated using equation 9 [53].
MSE = =1 1 ∑︁( − )2 ⎯
RMSE = ⎷⎸⎸ 1 ∑︁( − )2 × 100
=1 MAE =
MAPE = CVRMSE =
1 ∑︁ | − | =1 RMSE ¯
4.1. Data Visualization and Experimental
Results
To explore the influence of pulse energy on height, the
experiment systematically varied the pulse energy from
60 nanojoules (nJ) to 120 nJ. Subsequently, the height
parameter ("heightg") was measured in triplicate at each
pulse repetition rate: 10 kHz, 100 kHz, and 500 kHz. To
assess measurement reliability, the mean and percentage
error were calculated for each set of three height
measurements. The experiment was then replicated for all
three pulse repetition rates. As illustrated in Figure 2,
(4)
(5)
(6)
(7)
(
In the discussion section of this study, it is imperative to scrutinize the predictive performance of the ANN as reflected by the forecasted results detailed in Table 3 and in Figure 4. The table presents a comprehensive set of evaluation metrics for both the height and width of the laser-induced tracks, providing a nuanced view of the model’s accuracy and efectiveness.
For the forecasted track height, the model exhibits excellent predictive accuracy as indicated by the low MSE of 0.232%. This low percentage highlights the model’s strong ability to predict height with minimal deviation from the actual measurements. The RMSE at 0.482% further supports this, indicating that the model’s predictions are consistently close to the true data points. The MAE of 0.312% and the MAPE of 0.066% both reinforce the model’s high precision, with the MAPE, in particular, showing very small deviation in terms of percentage, which is crucial for ensuring the practical applicability of the predictions in real-world settings. The CVRMSE at 10.241% provides a normalized measure of the RMSE, illustrating a relatively low spread in the error relative to the magnitude of the data being predicted. The 2 for height is 0.909, signifying that a substantial proportion of the variability in track height is efectively captured by the model.
In contrast, the forecasted results for track width show a slightly higher level of error across the metrics, though they still indicate strong predictive performance. The MSE for width is notably higher at 2.601%, suggesting more variability in the model’s predictions for width compared to height. Similarly, the RMSE at 1.613% and the MAE at 0.923% are higher than those for height, implying that the predictions for width are less consistent. However, these values still demonstrate a high level of accuracy overall. The MAPE for width is slightly higher at 0.116%, but it remains low, afirming the model’s utility in practical applications. The CVRMSE at 12.141% is higher than that for height, indicating a greater relative spread in the error for width predictions. The 2 value for width, at 0.902, remains high, which confirms that the model successfully captures a large portion of the variability in track width. The regression line and error histogram for the height and width forecasted features are depicted in Figures 5 and 6, respectively.
The comparative analysis between the metrics for height and width forecasts suggests that while the model is slightly more accurate and consistent in predicting height, its performance in predicting width is commendably high. Both sets of metrics underscore the ANN model’s robustness and its potential as a predictive tool in laser material processing. These results validate the model’s capability to assist in optimizing processing parameters for femtosecond laser applications, particularly in settings where precision and repeatability are paramount.
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tions, for deeper accuracy in prediction. Experimenting with various network architectures and deep-learning models, one could further shed more insights into the This study successfully implemented an ANN to pre- complex interaction within the laser processing domain. dict the dimensions of femtosecond laser-induced tracks More interesting, practical, and real-time implementain silver-containing zinc phosphate glass. The model tion of the developed ANN model can be achieved for the demonstrated high accuracy, as evidenced by low MSE better results of the laser manufacturing process. Further, and RMSE values, particularly in predicting the height of the developed models can be used to predict other famlaser-written tracks. The MAE and CVRMSE further val- ilies of glasses and other types of lasers. From another idated the precision of the predictions. Significantly, the point of view, this work will contribute to the general 2 indicated that a substantial portion of the variance scope of materials engineering in as much as it makes furin both height and width of the tracks was captured by ther development of much finer and more reliable laser the ANN model. These results underscored the capabil- fabrication methods possible. ity of advanced machine learning techniques to enhance the predictability and optimization of laser processing References applications.
Future studies can carry out the preliminary investigation set by this work using more input variables in the model, such as material variability and ambient condi[1] J. Zhang, Q. Zhao, D. Du, Y. Zhu, S. Zheng,
D. Chen, J. Cui, High flexibility fbg inscribing by point-by-point method via femtosecond laser: