# Experiment and Prediction of Ablation Depth in Excimer Laser Micromachining of Optical Polymer Waveguides

Authors: K. F. Tamrin; S. S. Zakariyah; K. M. A. Hossain; N. A. Sheikh
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

Extending the data transfer rates through dense interconnections at inter- and intraboard levels is a well-established technique especially in consumer electronics at the expense of more cross talk, electromagnetic interference (EMI), and power dissipation. Optical transmission using optical fibre is practically immune to the aforementioned factors. Among the manufacturing methods, UV laser ablation using an excimer laser has been repeatedly demonstrated as a suitable technique to fabricate multimode polymer waveguides. However, the main challenge is to precisely control and predict the topology of the waveguides without the need for extensive characterisation which is both time consuming and costly. In this paper, the authors present experimental results of investigation to relate the fluence, scanning speed, number of shots, and passes at varying pulse repetition rate with the depth of ablation of an acrylate-based photopolymer. The depth of ablation essentially affects total internal reflection and insertion loss, and these must be kept at minimum for a successful optical interconnection on printed circuit boards. The results are then used to predict depth of ablation for this material by means of adaptive neurofuzzy inference system (ANFIS) modelling. The predicted results, with a correlation of 0.9993, show good agreement with the experimental values. This finding will be useful in better predictions along with resource optimisation and ultimately helps in reducing cost of polymer waveguide fabrication.


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## Body

## 1. Introduction

Consumer electronics are experiencing uphill challenge to overcome high-frequency (>10 Gb/s) transmission problems such as cross talk, electromagnetic interference, and power dissipation especially with high interconnectivity [1]. Rush for miniaturization, addition of more features/applications, and communication at microscales (e.g., chip-to-chip) have exposed the limits of copper-based transmissions in electronic circuits. To overcome this bottleneck, an optically enabled printed circuit board is a viable solution as this technique has been successfully used for long haul communications, that is, optical fiber. The optical interconnections (OIs), used in conjunction with copper connection thus forming electric-optical bridge, are usually made up of polymer waveguides. Various fabrication techniques of these polymer waveguides have been proposed including laser direct writing, photolithography, inkjet printing, and laser ablation [2]. Amongst all, laser ablation is the preferred technique for fabrication primarily due to its proven use as well as availability with PCB manufacturers [1, 2].Laser-matter interaction and its suitability for machining various engineering materials, including various polymers [3–5], have been well researched and documented in the literature. Micromachining using IR (infrared) laser sources particularly using CO2 laser is common as it allows significantly higher rates of machining [6]. A few studies report the use of CO2 laser process for polymer waveguide fabrications. In the pulsed mode, CO2 laser machining of PMMA (polymethyl methacrylate) waveguides was reported by Steenberge et al. [7]. Subsequently, an extensive study on a continuous wave (CW) CO2 laser processing of Truemode™ polymer is detailed by Zakariyah et al. [8, 9]. The study presented direct relationship between the depth of ablation and the scanning energy density while the width of the track was seen to vary logarithmically with the scanning energy density. In another study, submerged waveguides were demonstrated by Özcan et al. [10] using a CW CO2 laser in planar silica films that showed reduction in the propagation loss.In PCB manufacturing, the use of a CO2 laser is generally preferred, owing to its lower cost and availability. On the other hand, an excimer laser offers certain advantages by allowing machining of fine features at controllable rates. This process also ensures that there is less thermal damage on the ablated materials with minimum heat-affected zone (HAZ) dictated by, among other factors, a very high-absorption coefficient and short interaction between the laser and the ablated sample. The two key controlling parameters of this laser class are short wavelength and pulse duration. The former reduces the thermal diffusivity of the surface while the latter provides high-energy pulses. Furthermore high machining quality and ablation threshold are related to the pulse width duration of excimer laser [11]. Typical operating wavelengths of excimer lasers used for machining polymer materials especially for fabrication of optical waveguides are 193 nm (with ArF) and 248 nm (with KrF) [12].Energy and pulse repetition rate (PRR) are two important process parameters highlighted by Steenberge et al. [7, 13, 14] for the fabrication of waveguides in ORMOCER. It was observed that both parameters influence the smoothness of side walls of guides, which remains crucial for the propagation loss. In another study, Pfleging et al. [15] employed excimer laser to fabricate single-mode optical waveguides in PMMA. Following the method used for CO2 laser [10], Pfleging et al. selected UV fluences below the ablation threshold of PMMA. Another study conducted by Zakariyah et al. [11] showed good surface characteristics of excimer laser compared to 355 nm UV Nd:YAG and 10.6 μm CO2 lasers.For long distance transmission of signal through the polymeric waveguides, total internal reflection is an important feature which is strongly influenced by the depth of ablation. As shown in Figure1(a), it can be noted that minimum depth of ablation is desirable, although propagation of optical signal can be achieved by having scenario shown in Figure 1(b). However, further increase in depth of ablation can expose the cladding which means not only more laser power is utilized for the fabrication but also undesired thermal effects lead to increase the losses in the optical channel. This scenario is depicted in Figure 1(c) with possibility of severe damage to the FR4 substrate.Figure 1
A schematic diagram showing three different types of ablation depths using laser beam with top-hat profile.Apart from internal reflection, insertion loss is another main criterion for the optical interconnection. In fact, the prime measure of any optical waveguide is insertion loss which is strongly influenced by the depth of ablation as well as track width. Both depth of ablation and track width are mainly dependent on the laser processing parameters including laser power, rate of pulse repetition, focal distance, and scanning speed. Further investigation of these parameters is presented in forthcoming sections.The ablation process for polymer waveguides using excimer laser is intricate involving several process parameters and material properties. Some researchers have suggested using techniques of soft computing to deal with these complexities [6, 8–10]. These techniques are good at dissecting intricate problems with their features of nonlinearity and adaptability. For instance, artificial neural network (ANN) and fuzzy logic have been successfully utilized to predict complex system properties [16]. However, ANN has gained some untoward reviews due to its rather ‘‘black box’’ nature. On the other hand, taking the advantage of approximate reasoning, modelling techniques based on fuzzy logic have gained some attention. However, main bottleneck for this technique is the construction of membership functions (MFs). While combining both fuzzy logic and ANN, adaptive network-based fuzzy system takes full advantage of both techniques and eliminates their individual shortcomings [11]. This approach known as adaptive neurofuzzy inference system (ANFIS) imitates human thinking process and constructs input-output maps on human knowledge as well as the data pairs.Several studies involving prediction of mechanical properties have found ANFIS predictions more reliable compared to ANN. For instance, results reported by Zare and Khaki [17] and Karaağaç et al. [18] showed that ANFIS performed better than ANN for predicting optimum values of their respective studies. Related to the use of ANFIS for laser micromachining, no such study could be found in literature especially for the fabrication of optical waveguides.In the light of above discussion, this work has three main objectives: (1) experimental investigation of the use of 248 nm excimer laser for micromachining of optical polymer used in multimode polymer waveguides; (2) ANFIS modelling in prediction of ablation depth from the experimental data; and (3) comparison of ANFIS modelling with the result gained from the experiment. It is important to mention that it will be a first study of its kind to utilize ANFIS and compares the results with the experimental observations for acrylate-based photopolymer using UV excimer.


## 2. Experimental Method

### 2.1. Laser System

For this work, 7000 Series Exitech of 20 ns pulse krypton fluoride (KrF) excimer laser (λ = 248 nm) was used which could deliver up to 250 mJ/pulse. The size and shape of the beam were primarily determined by the mask dimension placed after the beam exit, which then passed through a 10x projection lens. This allowed a focus beam spot to be obtained at the work piece for effective patterning of the samples. In the reported experiments, a TEM00 beam mode from the laser was masked by a square beam mask (5 × 5 mm2) resulting in top-hat-like beam profile.


### 2.2. Optical Polymer Material

A UV-curable acrylate-based optical polymer from Exxelis Ltd (UK), commercially known as Truemode, was used. This is a light-yellow mixture of monomers and liquid at room temperature. Its low absorption loss, shown to be <0.04 dB/cm at 850 nm [15], supports its suitability for applications in optical interconnections. It is also shown to be compatible with standard printed circuit boards manufacturing process particularly at the high temperature and pressure involved. Following several trials of various formulations available from the supplier, authors selected EXX-core 37E and EXX-clad 277 formulations with indices of refraction of 1.5560 and 1.5265, respectively. The refractive indices were measured at 850 nm wavelength, which is the same wavelength at which the optical propagation loss is measured for polymer waveguides.


### 2.3. Fabrication

Figure2 shows the key fabrication phases employed in patterning a single layer optical waveguide (single- or mutimode), similar to what is reported in [19]. To summarise, the FR4 base substrate was decontaminated from debris by cleaning in water (or methanol) and was allowed to get fully dry in an oven. Optical layers (core and cladding) were thereafter formed on FR4 by spin coating Truemode at approximately 350 rev/min for 30 sec. The lower cladding was spun and UV cured initially in N2 environment under UV light for 200 ± 40 sec. This is followed by spin coating the core layer. At this stage, the whole sample of FR4-clad-core was UV cured again for complete cross-linking and subsequently oven-baked at a temperature of 100°C for 60 minutes. The obtained thickness in each case (core or cladding layer) was 40 ± 10 microns. As the core and cladding layers are essentially made from the same materials with a slight difference in the refractive index as previously indicated, their interaction with the laser and the absorption coefficient is expected to be similar. Therefore, nothing unusual was observed in the interface of these layers. Generally, the fabrication of polymer waveguides was followed by an extensive system characterisation, and as a result, the steps are same whether the ultimate goal was to fabricate or to characterise the depth of ablation. This is to ensure that data obtained during the characterisation can be implemented for the fabrication phase without undue adjustment to the setting.Figure 2
Key fabrication phases of laser ablation of multimode waveguides: (a) a base substrate of FR4, (b) formation of lower cladding by spin coating, (c) formation of the core layer, (d) laser ablation of the resulting sample from the core layer into the cladding layer, and (e) spin coating of the (optional) upper cladding.


## 2.1. Laser System

For this work, 7000 Series Exitech of 20 ns pulse krypton fluoride (KrF) excimer laser (λ = 248 nm) was used which could deliver up to 250 mJ/pulse. The size and shape of the beam were primarily determined by the mask dimension placed after the beam exit, which then passed through a 10x projection lens. This allowed a focus beam spot to be obtained at the work piece for effective patterning of the samples. In the reported experiments, a TEM00 beam mode from the laser was masked by a square beam mask (5 × 5 mm2) resulting in top-hat-like beam profile.


## 2.2. Optical Polymer Material

A UV-curable acrylate-based optical polymer from Exxelis Ltd (UK), commercially known as Truemode, was used. This is a light-yellow mixture of monomers and liquid at room temperature. Its low absorption loss, shown to be <0.04 dB/cm at 850 nm [15], supports its suitability for applications in optical interconnections. It is also shown to be compatible with standard printed circuit boards manufacturing process particularly at the high temperature and pressure involved. Following several trials of various formulations available from the supplier, authors selected EXX-core 37E and EXX-clad 277 formulations with indices of refraction of 1.5560 and 1.5265, respectively. The refractive indices were measured at 850 nm wavelength, which is the same wavelength at which the optical propagation loss is measured for polymer waveguides.


## 2.3. Fabrication

Figure2 shows the key fabrication phases employed in patterning a single layer optical waveguide (single- or mutimode), similar to what is reported in [19]. To summarise, the FR4 base substrate was decontaminated from debris by cleaning in water (or methanol) and was allowed to get fully dry in an oven. Optical layers (core and cladding) were thereafter formed on FR4 by spin coating Truemode at approximately 350 rev/min for 30 sec. The lower cladding was spun and UV cured initially in N2 environment under UV light for 200 ± 40 sec. This is followed by spin coating the core layer. At this stage, the whole sample of FR4-clad-core was UV cured again for complete cross-linking and subsequently oven-baked at a temperature of 100°C for 60 minutes. The obtained thickness in each case (core or cladding layer) was 40 ± 10 microns. As the core and cladding layers are essentially made from the same materials with a slight difference in the refractive index as previously indicated, their interaction with the laser and the absorption coefficient is expected to be similar. Therefore, nothing unusual was observed in the interface of these layers. Generally, the fabrication of polymer waveguides was followed by an extensive system characterisation, and as a result, the steps are same whether the ultimate goal was to fabricate or to characterise the depth of ablation. This is to ensure that data obtained during the characterisation can be implemented for the fabrication phase without undue adjustment to the setting.Figure 2
Key fabrication phases of laser ablation of multimode waveguides: (a) a base substrate of FR4, (b) formation of lower cladding by spin coating, (c) formation of the core layer, (d) laser ablation of the resulting sample from the core layer into the cladding layer, and (e) spin coating of the (optional) upper cladding.


## 3. Prediction of Depth of Ablation by Means of Adaptive Neurofuzzy Inference System (ANFIS)

In this study, an adaptive neurofuzzy inference system (ANFIS) is adopted to predict the depth of ablation as a function of five input variables using experimental data listed in Table1. An ANFIS is an adaptive network which combines fuzzy logic and neural network system to develop the prediction model based on the input knowledge. The ANFIS was first introduced by Jang in 1993 [20], and functionally it is similar to the Takagi–Sugeno-type inference model. To diligently adjust the membership function of the fuzzy inference system (FIS), the ANFIS employs the least squares method and back-propagation gradient descent method from neural network [21]. Figure 3 illustrates a general ANFIS architecture assuming two inputs, namely, x and y and one output, namely, f. The architecture typically has five different layers characterized by adaptive and fixed nodes. As highlighted in Figure 3, the output of each layer (layers 2–5) is used as the input to the succeeding layer.Table 1
Experimental layout and results.
Experiment
Processing parameter
Response
Number of shots
Fluence (J/cm2)
Scanning speed (mm/min)
Pulse repetition rate (Hz)
Number of passes
Maximum depth (μm)/1 shot
Mean depth (μm)/1 shot
1
1
0.086
120
20
1
0.799
0.678
2
2
0.086
60
20
1
1.86
1.65
3
3
0.086
40
20
1
2.79
2.49
4
4
0.086
30
20
1
3.53
3.12
5
5
0.086
24
20
1
4.56
4.04
6
6
0.086
20
20
1
5.73
5.15
7
7
0.086
17.1
20
1
6.30
5.53
8
8
0.086
15
20
1
7.08
6.2
9
9
0.086
13.3
20
1
7.59
6.61
10
10
0.086
12
20
1
8.81
7.63
11
12
0.086
10
20
1
9.75
8.5
12
14
0.086
8.57
20
1
12.0
10.4
13
16
0.086
7.5
20
1
13.1
11.4
14
18
0.086
6.67
20
1
14.9
13.1
15
20
0.086
6
20
1
16.6
14.5
16
22
0.086
5.45
20
1
19.3
17
17
24
0.086
5
20
1
20.0
17.5
18
26
0.086
4.62
20
1
21.8
18.9
19
28
0.086
4.29
20
1
22.9
20.2
20
30
0.086
4
20
1
24.2
21
21
10
0.03
6
10
1
0.252
0.173
22
10
0.058
6
10
1
0.516
0.425
23
10
0.086
6
10
1
0.797
0.695
24
10
0.113
6
10
1
1.11
0.988
25
10
0.141
6
10
1
1.46
1.35
26
10
0.169
6
10
1
1.79
1.66
27
10
0.197
6
10
1
1.96
1.82
28
10
0.224
6
10
1
2.19
2.04
29
10
0.252
6
10
1
2.3
2.17
30
10
0.28
6
10
1
2.5
2.36
31
1
0.086
120
20
3
2.79
2.43
32
1
0.086
120
20
4
3.9
3.1
33
1
0.086
120
20
5
4.1
3.42
34
1
0.086
120
20
9
8.6
7.58
35
1
0.086
120
20
10
10.0
8.47
36
1
0.086
72
12
1
1.07
0.967Figure 3
Typical ANFIS architecture for two inputs and one output.The first layer is the adaptive node layer or commonly known as the fuzzification layer, where membership functions (generalized bell, Gaussian, or triangular) are designated. In this layer, bell-shaped membership function can be selected with the maximum value of 1.0 and minimum value of 0.0. The function can be written as(1)μAix=11+x−ci/ai2bi,where ai, bi, and ci are a set of parameters and µAi(x) is the membership function corresponding to the input parameter x. Accordingly, the function µAi(x) changes as ai, bi, and ci vary.Each node in the second layer is nonadaptive (fixed), and it acts as the fuzzy “AND” operator in the premise section of the fuzzy if-then rule. In other words, it multiplies the incoming signals, and the output represents the firing (operating) strength of each fuzzy rule. For example,(2)Wi=μAixμBiy,i=1,2,where Wi is the weight function for the next layer and µBi(y) is the membership function corresponding to the input parameter y.The third layer is also a nonadaptive layer which is also known as the normalized layer. It serves to calculate the normalized firing strength in (2) using the following equation [22]:(3)Wi∗=WiW1+W2,i=1,2,The fourth layer consists of adaptive nodes. This layer estimates the contribution of each input parameter towards the overall output. This is carried out by the assignment of weights to minimize the deviation between outputs and desired results. The relation between inputsx and y and output f can be defined as(4)Wi∗fi=Wi∗pix+qiy+ri,i=1,2,where pi, qi, and ri are the linear parameters or consequent parameters, and they can be adjusted in the training process.The fifth layer is the defuzzification (output) layer and essentially the summation of all fourth layer signals. The output,f, can be computed by the following equation:(5)f=∑iWi∗fi∑iWi∗,i=1,2.


## 4. Results and Discussion

Typical and essential stages involved in multimode polymer waveguide fabrication were followed, and effect of process parameters on the prepared samples were analysed and measured. Before measurement, the ablated samples were first sectioned (using Buehler IsoMet® low-speed saw) and then polished using abrasives (1μm diamond paste). Ablated depths of channels were measured using the SmartScope® Flash™ 200 optical measuring device. The device has a traverse length of 200 × 200 × 150 mm with a resolution of 0.5 μm. Topographic measurements were carried out using a single point sensor gauge of the Talysurf CLI scanner which can travel up to a maximum speed of 20 mm/s. The latter instrument took measurements across the channel at equal intervals along the channel, and it automatically calculated the respective mean and maximum depths of ablation. The experimental results are given in Table 1. A total of 36 experiments were designed. It should be noted that the effect of all individual processing parameters on the response parameters were studied separately while keeping other parameters constant.As shown in Figures4 and 5, the ablated section resembles the top-hat beam profile with some tapering effect on both edges (slightly tapered side walls). One method to lower the tapering at high fluence (∼2 J·cm−2), as suggested in [23], is by increasing the number of shots. However, despite the investigation, no conclusion can be drawn on the significance of these factors on the tapering effect seen in the ablated profile. Furthermore, some of the observed tapering effects can be linked to the focus position of laser as evident in laser system characterisation.Figure 4
Screenshot of depth measurement using Talysurf CLI scanning topography-measuring instrument. The instrument gives values of maximum and mean depths of ablation and width of ablation.Figure 5
SEM images of ablated depth at (a) 250x and (b) 650x magnifications (sample number 61: number of shots = 45, fluence = 0.1 J/cm2, scanning speed = 3.3 mm/min, and pulse repetition rate = 25 Hz). Measured maximum and mean depths are 1.002 μm and 0.740 μm, respectively.
(a)
(b)As earlier, it is pointed out that the use of excimer laser is preferred as it is readily absorbed by the polymers and causes minimum thermal load and damage to the surroundings. In this study, UV pulses of 10–35 ns in length were used which produced relatively clean ablation with little thermal damage to surroundings, as shown in Figure6(a). On the other hand, high processing speed of its counterpart IR CO2 laser resulted in large HAZ which is undesirable and may influence the propagation losses in the waveguide (Figure 6(b)). However, slow speed and high operating costs of excimer laser and the use of fluorine gas (toxic in nature) are main reasons of its lesser acceptance in the PCB industry. The last factor can be easily overcome by putting in place engineering and administrative controls while the effects of others can also be minimised.Figure 6
Surface roughness comparison of ablation tracks machined using (a) excimer (sample number 116 line 5) and (b) CO2 (sample A1) lasers.
(a)
(b)For the ANFIS architecture, five inputs for the network are used. Number of shots, fluence, scanning speed, pulse repetition rate, and number of passes are the processing parameters, while the depth of ablation is the measured output. In the present work, the experimental data were divided into two groups for the purpose of training and subsequent testing. The first 27 data from Table1 were chosen to be the training samples, while the remaining data were used to be the testing samples (9 samples).In the beginning, a triangular-shaped membership function was selected for each input variable in ANFIS architecture. Subsequently, different types of membership function were evaluated, that is, generalized bell, Gaussian, and trapezoidal. A Sugeno-type FIS structure was chosen to initialize the membership function parameters for ANFIS training, and the output membership function was set to be linear.Equations (4) and (5) were used to predict the outputs which help in training the ANFIS model. Weights and thresholds at different layers were adjusted using the back-propagation algorithm relying on the gradient search technique. Weights were adjusted in order to minimize the mean-squared error between the experimental and predicted results. The training phase required some initial estimation of ANFIS parameters such as type of membership functions for each input variable and fuzzy rule. For instance, Table 2 shows results of the mean prediction error for four different types of membership functions. Due to its lowest percentage of error, the generalized bell function was chosen for both training and testing (Figure 7). After the training of the AFNIS model is completed, the model can be utilized to predict the depth of ablation. A complete comparison of the predicted and experimentally measured depth of ablation is shown in Table 3 and Figure 8.Table 2
Mean prediction error for different types of membership functions.
Membership function
Mean prediction error (%)
Triangular (trimf)
4.194
Generalized bell (gbellmf)
1.991
Gaussian (gaussmf)
2.183
Trapezoidal (trapmf)
3.233Figure 7
Membership function diagrams based on generalized bell for all inputs: (a) number of shots, (b) fluence, (c) scanning speed, (d) pulse repetition rate, and (e) number of passes.
(a)
(b)
(c)
(d)
(e)Table 3
Comparison of experimental and predicted mean depths and their relative errors.
Experiment
Experimental mean depth (μm)
Predicted mean depth (μm)
% relative error (gbellmf)
1
0.678
0.702
3.496
2
1.65
1.651
0.055
3
2.49
2.474
0.655
4
3.12
3.184
2.035
5
4.04
3.979
1.505
6
5.15
4.741
7.934
7
5.53
5.437
1.689
8
6.2
6.139
0.981
9
6.61
6.782
2.604
10
7.63
7.442
2.461
11
8.5
8.752
2.964
12
10.4
10.168
2.234
13
11.4
11.721
2.818
14
13.1
13.333
1.779
15
14.5
14.914
2.852
16
17
16.398
3.544
17
17.5
17.740
1.372
18
18.9
18.976
0.404
19
20.2
20.142
0.287
20
21
21.250
1.190
21
0.173
0.174
0.405
22
0.425
0.428
0.612
23
0.695
0.691
0.576
24
0.988
0.988
0.040
25
1.35
1.356
0.437
26
1.66
1.652
0.494
27
1.82
1.851
1.720
28
2.04
2.017
1.132
29
2.17
2.184
0.641
30
2.36
2.350
0.415
31
2.43
2.348
3.370
32
3.1
3.164
2.068
33
3.42
3.980
16.371
34
7.58
7.556
0.322
35
8.47
8.489
0.218
36
0.967
0.967
0.000
Mean relative error = 1.991.Figure 8
Graph comparing experiment and predicted depth of ablation including error prediction.It is important to mention that the mean relative error for the present ANFIS is comparable to the findings in the literature. For instance, Jia et al. [24] acquired 5.23% mean relative error for 30 sets of experiments, while Zare and Khaki [17] managed to obtain much lesser mean relative error of 1.62% for 10 sets of experiments. ANFIS prediction for the present work can be considered comparatively accurate since the training data extensively cover the complete range of parameters. Based on Figure 8, experiment numbers 6 and 33 show considerably large prediction errors of 7.934% and 16.371%, respectively. Nevertheless, the predicted values remain below the measured maximum depths of ablation. Figure 9 graphically compares experiment and predicted depth of ablations based on regression analysis. It is clear that the predicted ANFIS results compare well with the experimental results with the correlation coefficient (R2) value up to 0.9993.Figure 9
Experimental and ANFIS model-predicted depth of ablation plotted for the best model developed using five input variables.


## 5. Conclusions

This paper experimentally investigates the effects of varying laser processing parameters on the depth of ablation of optical polymer waveguides. Laser ablation using excimer laser results in a cleaner and smoother ablated structures with minimal thermal damage to the surroundings. However, due to slow speed and high operating costs of the excimer laser, there is a need for a mechanism to accurately predict and estimate the ablation depth of the optical waveguides for various input parameters. Here, an adaptive neurofuzzy inference system (ANFIS) model is proposed and applied to a series of experimental datasets. The trained ANFIS model predicts the ablation depth with an accuracy ofR2 = 0.9993 and a mean prediction error of 1.991%. It has been shown that with the aid of the ANFIS, a multiple input/single output fuzzy inference system can be created that accurately characterizes the ablation depth of optical polymer waveguides.



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