In this study, a simple and a single complete CAD model is obtained for type I quantum cascade laser based on characteristic quantities (optical gain, refractive index change, linewidth enhancement factor). The model is based on Artificial Neural Networks (ANNs) which is optimized by a new algorithm called Artificial Bee Colony (ABC). The developed model is capable of making fast and reliable predictions which is very useful in the CAD design of related systems. The inputs of the model are injection current and wavelength, respectively. The model agrees very well with the experimental findings that are previously published.
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From each point of view, Computer Aided Design (CAD) models are recommended for each type of system since it at least involves brief information that how the system behaves under different operating conditions (Hsu and Peroulis, 2011; Xiao et al., 2011; Cheng et al., 2010; Schetzen et al., 2008; Yildirim and Celebi, 2004; Gokrem et al., 2010; Celebi and Yildirim, 2005; Yildirim and Celebi, 2009; Yucel et al., 2011; Celebi, 2006; Yildirim and Celebi, 2010; Yildirim et al., 2009; Danisman et al., 2006; Ghoniemy et al., 2004; Dagdeviren et al., 2011). This is especially very important for the systems (optical) that have high cost experimental setups. In addition to that there are sometimes considerable amount of differences between theoretical and experimental values which are frequently encountered in optical related systems (Stohs et al., 2001). Therefore, it is very important to develop intelligent and accurate CAD optical models to measure the performance of the system at the instant of design and simulation. The Quantum Cascade Lasers (QCLs) are novel devices that have wide range of applications where the power conversion efficiency is high (Faist et al., 1994; Bai et al., 2010). These applications are based on the tuning range where the emission changes from one wavelength (color) to another. This enables the usage of exact sensing of chemical vapors (carbon sulfide, carbon monoxide, nitrogen monoxide, carbonyl sulfide etc.), free space optical communications, infrared counter, metal detection and astronomical applications (Faist et al., 1994). In addition to that, these semiconductor lasers are very small compared to other semiconductor lasers that produce light in the mid and far infrared portion of the spectrum which is not visible for human eyes. Therefore, accurate, dynamic and intelligent CAD models are needed for QCLs for the purpose of quick design and simulation according to different operating conditions of these systems. There are successfully implemented previous intelligent CAD models in optical area with the use of ANNs (Celebi et al., 2006; Celebi, 2005a; Tankiz et al., 2011; Celebi, 2010; Celebi, 2005b; Sagiroglu et al., 2002; Celebi and Danisman, 2005; Celebi and Danisman, 2004, 2006) Fuzzy Logic (Yucel, 2011; Shen et al., 2006; Celebi et al., 2011) and hybrid (Neuro-fuzzy) (Yucel, 2011; Yuksel and Develi, 2005; Celebi and Altindag, 2009; Celebi et al., 2009) systems which can be found in literature. These CAD models show intelligent behavior under different operating conditions and can be easily included in the design and simulation of sophisticated optical systems in order to get the proper response at the design stage. In our recent study, optical gain model for a QCL laser is developed by ANNs with the use of ABC algorithm (Yigit et al., 2011). In this study, a complete and single model for a type I QCL is developed including refractive index change and linewidth enhancement factor in addition to the optical gain. The small error for each characteristic quantity from the single model shows that the model can be used in an optical system without any hesitation.
ARTIFICIAL NEURAL NETWORKS AND ABC ALGORITHM
Artificial Neural Networks (ANNs) are inspired by the ability of the brain to perform different operations and to process information (Haykin, 2000). They are learned from experience with no knowledge in advance. An ANN consists of large number of processing units called neurons. Each neuron has weighted inputs, summation function, activation function and an output. Neurons are stored in a nested layer structure. Each processing unit in each layer is connected to all processing units in the adjacent layers to form a network. The ANNs have fascinating features like: ability and adaptability to learn, generalizability, smaller information requirement, fast real-time operation and ease of implementation. Because of these features, there are so many studies implemented in the last few years (Khanale and Chitnis, 2011; Khanale, 2010; Salazar et al., 2010; Bouzenada et al., 2007; Soltani et al., 2007; Dastorani et al., 2010a; Dastorani et al., 2010b; Anari et al., 2011; Kumar, 2012; Mpallas et al., 2011; Qasem and Shamsuddin, 2010; Hasheminia and Niaki, 2008).
Multi Layered Perceptrons (MLPs) are simplest and most commonly used neural network architectures. An MLP consists of three layers: an input layer, an output layer, one or more hidden layers (Danisman et al., 2006). Input signals xi generally passes through input layer with no change because of the linear activation function. The signals are carried along connections to each neuron in the hidden layer and amplified or inhibited through weights, wi, associated with each connection. The nodes in the hidden layer act as summation devices for weighted signals (Minns and Hall, 1996). The incoming signal is transformed into an output signal, yi:
where, f is an activation function.
Training process is to produce known or desired output responses for the given input. The ANN is first initialized by assigning random numbers to the network weights. An input signal is then introduced to the input layer and the resulting output signal is compared to the desired output signal (Minns and Hall, 1996). The network weights are then adjusted by an optimization algorithm according to following equality:
During training, network weights are optimized until the error between ANN output and desired output falls below a specified level or maximum number of epochs is reached. Although the training is a time-consuming process, it can be done beforehand, offline. The trained neural network is then tested using new unseen data.
There are many types of neural networks for various applications in the literature. In this work, MLP is selected as the neural network architecture that is trained by ABC. ABC algorithm is inspired by natural bee colony and models their intelligent foraging behavior. The colony of artificial bees consists of three groups of bees: employed bees, onlookers and scouts. ABC algorithm is formed by three phases.
|Pseudo-code of the ABC algorithm|
The position of a food source represents a possible solution to the optimization problem and the nectar amount of a food source corresponds to the quality (fitness) of the associated solution. For every food source, there is only one employed bee. The number of the employed bees or the onlooker bees is equal to the number of solutions in the population. The employed bee whose food source has been exhausted by the bees becomes a scout (Karaboga and Basturk, 2007).
An employed bee investigates near food sources in her memory to find more nectar-rich food sources and checks the nectar amount (fitness value) of the new source (new solution). This procedure is performed by producing a modification on the position (solution) in her memory (θi (c)) depending on the local information:
where, φi (c) is randomly selected number between (-1,1) (Karaboga and Akay, 2007).
The nectar amount of the new one is higher than that of the previous one, the bee memorizes the new position and forgets the old one. Otherwise she keeps the position of the previous one in her memory (Karaboga and Basturk, 2007).
After exploration process is completed, employed bees return to the hive and share their information about food sources with onlooker bees. An onlooker bee chooses a food source depending on the probability value (pi) associated with nectar amount of that food source. This value is calculated by the following formula:
where, F (θi) is nectar amount of food source in θi position.
The quality of a food source is determined by a specified fitness function. Mean Square Error (MSE) is selected as the fitness function in training MLP by the ABC algorithm. The mean square error is the mean value of the squared difference between the actual and the desired output of the ANN, for individual training patterns. The mean square error is defined as:
where, ti is the measured output, yi is the predicted output value of the ANN.
Hyperbolic tangent sigmoid function is chosen as activation function of the neurons in the hidden layer.
ABC algorithm has three important parameters to be tuned and optimized:
|•||SN: The number of food source positions (at the same time, this value is equal to the size of population)|
|•||Limit value: The number of trials for releasing a food source|
|•||MCN: Maximum cycle number (Stopping criteria)|
RESULTS AND DISCUSSION
The proposed model involves training a MLP network by the ABC algorithm to compute the three characteristic quantities of QCL laser accurately in a single model that can be included in CAD design of related optical systems. Both the training and the test results are in very good agreement with the experimental values in literature (Kim et al., 2004).
The final ANNs structure is 2x30x3 which means that the network has 2 inputs (current, wavelength), 3 outputs (differential modal gain, differential refractive index change, linewidth enhancement factor) and there are 30 neurons in the hidden layer. The data set is split randomly into two parts: training set and testing set where the 73% of data is used as training and the remaining 27% of data is used as a testing set. Parameters of ABC is selected in the way that, colony size is 2*SN which is 40. The value of limit is SN*D where D is the number of interconnection weights and biases in neurons. The maximum cycle number is 100000.
Training process is performed offline since it is time-consuming. After the optimal model is achieved, computation time of test process takes a few microseconds. Mean square error (the training and the test) for each characteristic quantity is given in Table 1 which shows very good agreement with the experimental values of the type-1 QCL data.
|Table 1:||MSE values for each QCL quantities|
In terms of the training and the test results, the detailed graphical results for each characteristic quantity is shown in Fig. 1 and 2 for differential modal gain, Fig. 3 and 4 for differential refractive index change and Fig. 5 and 6 for the linewidth enhancement factor, respectively.
|Fig. 1:||Comparison of experimental and ANN model training results for differential modal gain|
|Fig. 2:||Comparison of experimental and ANN model test results for differential modal gain|
|Fig. 3:||Comparison of experimental and ANN model training results for differential refractive index change|
|Fig. 4:||Comparison of experimental and ANN model test results for differential refractive index change|
|Fig. 5:||Comparison of experimental and ANN model training results for linewidth enhancement factor|
|Fig. 6:||Comparison of experimental and ANN model test results for linewidth enhancement factor|
It is seen that, all graphs are also in very good agreement with the experimental values despite some small errors. In addition to that, experimental data set is limited which can be seen as a disadvantage.
One step forward of this study is to develop a compact single model that includes all types of QCLs optimized by using different artificial intelligence techniques.
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