
Research Article


A Complete CAD Model for TypeI Quantum Cascade Lasers with the use of Artificial Bee Colony Algorithm 

Sevgi Yigit,
Bulent Tugrul
and
Fatih Vehbi Celebi



ABSTRACT

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.





Received: November 23, 2011;
Accepted: January 13, 2012;
Published: June 05, 2012


INTRODUCTION
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
(Neurofuzzy) (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 realtime 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 x_{i} 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, w_{i}, 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 timeconsuming 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.
Pseudocode 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 nectarrich 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 (θ_{i} (c)) depending on the local information:
where, φ_{i} (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 (p_{i}) associated with nectar amount of that food source. This value is calculated by the following formula: where, F (θ_{i}) is nectar amount of food source in θ_{i} 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, t_{i} is the measured output, y_{i} 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 ANN’s 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 timeconsuming. 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 type1 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.

REFERENCES 
Anari, P.L., H.S. Darani and A.R. Nafarzadegan, 2011. Application of ANN and ANFIS models for estimating total infiltration rate in an arid rangeland ecosystem. Res. J. Environ. Sci., 5: 236247. CrossRef  Direct Link 
Bai, Y., N. Bandyopadhyay, S. Tsao, E. Selcuk, S. Slivken and M. Razeghi, 2010. Highly temperature insensitive quantum cascade lasers. Applied Phys. Lett., Vol. 97. CrossRef  Direct Link 
Bouzenada, M., M.C. Batouche and Z. Telli, 2007. Neural network for object tracking. Inform. Technol. J., 6: 526533. CrossRef  Direct Link 
Celebi, F.V. and K. Danisman, 2005. Neural estimator to determine alpha parameter in terms of quantumwell number. Optics Laser Technol., 37: 281285. CrossRef 
Celebi, F.V. and R. Yildirim, 2005. Distortion system theory of the two tone small signal input laser diode. J. Faculty Eng. Archit. Gazi Uni., 20: 373377.
Celebi, F.V. and T. Altindag, 2009. An accurate optical gain model using adaptive neurofuzzy inference system. J. Optoelectronics Adv. MaterialsRapid Commun., 3: 975977.
Celebi, F.V., 2005. A different approach to gain computation in laser diodes with respect to different number of quantumwells. OptikInt. J. Light Electron Optics, 116: 375378. CrossRef 
Celebi, F.V., 2005. A proposed CAD model based on amplified spontaneous emission spectroscopy. J. Optoelectron. Adv. Mater., 7: 15731579. Direct Link 
Celebi, F.V., 2006. Modeling of the linewidth enhancement factors of the narrow and wide GaAs well semiconductor lasers. J. Faculty Eng. Archit. Gazi Uni., 21: 161166.
Celebi, F.V., I. Dalkıran and K. Danisman, 2006. Injection level dependence of the gain, refractive index variation and alpha parameter in boardarea ingaas deep quantumwell lasers. Optik Int. J. Light Electron Optics, 117: 511515.
Celebi, F.V., M. Yucel and H.H. Goktas, 2011. Fuzzy logic based device to implement a single CAD model for a laser diode based on characteristic quantities. OptikInt. J. Light Electron. Opt., CrossRef 
Celebi, N., 2010. An accurate single CAD model based on radial basis function network. J. Optoelectronics Adv. Mat. Rapid Commun., 4: 498501.
Cheng, Q.S., J.W. Bandler, S. Koziel, M.H. Bakr and S. Ogurtsov, 2010. The state of the art of microwave CAD: EMbased optimization and modeling. Int. J. RF Microwave Comput. Aided Eng., 20: 475491. CrossRef 
Dagdeviren, M., E. Eraslan and F.V. Celebi, 2011. An alternative work measurement method and its application to a manufacturing industry. J. Loss Prev. Process Ind., 24: 563567. CrossRef 
Danisman, K., I. Dalkiran and F.V. Celebi, 2006. Design of a high precision temperature measurement system based on artificial neural network for different thermocouple types. Measurement, 39: 695700. CrossRef 
Dastorani, M.T., A. Talebi and M. Dastorani, 2010. Using neural networks to predict runoff from ungauged catchments. Asian J. Applied Sci., 3: 399410. CrossRef  Direct Link 
Dastorani, M.T., H. Afkhami, H. Sharifidarani and M. Dastorani, 2010. Application of ANN and ANFIS models on dryland precipitation prediction (case study: Yazd in Central Iran). J. Applied Sci., 10: 23872394. CrossRef  Direct Link 
Xiao, D., H. Lin, C. Xian and S. Gao, 2011. CAD mesh model segmentation by clustering. Comput. Graphics, 35: 685691. CrossRef 
Faist, J., F. Capasso, D.L. Sivco, C. Sirtori, A.L. Hutchinson and A.Y. Cho, 1994. Quantum cascade laser. Science, 264: 553556.
Ghoniemy, S., L. MacEachern and S. Mahmoud, 2004. Analytical expressions, modeling, and simulations of intensity and frequency fluctuations in directly modulated semiconductor lasers. Opt. Eng., 43: 224233. CrossRef 
Gokrem, L., F.V. Celebi and R. Yildirim, 2010. Asymmetric amplitude variation for four tone small signal input GaN HEMT at different temperatures. J. Faculty Eng. Archit. Gazi Uni., 25: 779786. Direct Link 
Hsu, H.H. and D. Peroulis, 2011. A CAD model for creep behavior of RFMEMS varactors and circuits. IEEE Trans. Microwave Theor. Tech., 59: 17611768. CrossRef 
Hasheminia, H. and S.T.A. Niaki, 2008. A hybrid method of neural networks and genetic algorithm in econometric modeling and analysis. J. Applied Sci., 8: 28252833. CrossRef  Direct Link 
Haykin, S., 2000. Neural Networks: A Comprehensive Foundation. Macmillan College Publishing Company, Boston, USA
Karaboga, D. and B. Akay, 2007. Artificial bee colony algorithm (ABC) on training artificial neural networks. IEEE 15th Signal Process. Commun. Appl., 2: 14. Direct Link 
Karaboga, D. and B. Basturk, 2007. A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC) algorithm. J. Global Optim., 39: 459471. CrossRef  Direct Link 
Khanale, P.B. and S.D. Chitnis, 2011. Handwritten devanagari character recognition using artificial neural network. J. Artif. Intell., 4: 5562. CrossRef  Direct Link 
Khanale, P.B., 2010. Recognition of marathi numerals using artificial neural network. J. Artif. Intell., 3: 135140. CrossRef  Direct Link 
Kim, J., M. Lerttamrab, S.L. Chuang, C. Gmachl, D.L. Sivco, F. Capasso and A.Y. Cho, 2004. Theoretical and experimental study of optical gain and linewidth enhancement factor of typeI QuantumCascade Lasers. IEEE J. Quantum Electron., 40: 16631674. CrossRef 
Minns, A.W. and M.J. Hall, 1996. Artificial neural networks as rainfallrunoff models. J. Sci. Hydrol., 41: 399417. Direct Link 
Mpallas, L., C. Tzimopoulos and C. Evangelides, 2011. Comparison between neural networks and adaptive neurofuzzy inference system in modeling lake kerkini water level fluctuation lake management using artificial intelligence. J. Environ. Sci. Technol., 4: 366376. CrossRef  Direct Link 
Qasem, S.N. and S.M. Shamsuddin, 2010. Generalization improvement of radial basis function network based on multiobjective particle swarm optimization. J. Artif. Intell., 3: 116. CrossRef  Direct Link 
Sagiroglu, S., F.V. Celebi and K. Danisman, 2002. Modelling of the linewidth enhancement factor with the use of radial basis function network. AEUInt. J. Elect. Commun., 56: 5154. CrossRef 
Salazar, R., U. Schmidt, C. Huber, A. Rojano and I. Lopez, 2010. Neural networks models for temperature and CO _{2} control. Int. J. Agric. Res., 5: 191200. CrossRef 
Schetzen, M., R. Yildirim and F. Celebi, 2008. Intermodulation distortion of the singlemode laserdiode. Applied Phys. B Lasers Opt., 93: 837847. CrossRef 
Shen, H., Y.J. Shi, Z.Q. Yao and J. Hu, 2006. Fuzzy logic model for bending angle in laser forming. Materials Sci. Technol., 22: 981986. Direct Link 
Soltani, S., H. Babaei, K.A. Zeynali and A. Jouyban, 2007. Modelling vasorelaxant activity of some drugs/drug candidates using artificial neural networks. J. Pharmacol. Toxicol., 2: 411426. CrossRef  Direct Link 
Stohs, J., D.J. Bossert, D.J. Gallant and S.R.J. Brueck, 2001. Gain, refractive index change, and linewidth enhancement factor in broadarea GaAs and InGaAs quantumwell lasers. IEEE J. Quantum Electron., 37: 14491459. CrossRef 
Tankiz, S., F.V. Celebi and R. Yildirim, 2011. Computeraided design model for a quantumcascade laser. IET Circuits Devices Syst., 5: 143147. Direct Link 
Yildirim, R. and F.V. Celebi, 2009. The computation of the angle between the gain and photon population by geometrical approach. J. Fac. Eng. Archit. Gazi Univ., 24: 709714.
Yigit, S., R. Eryigit and F.V. Celebi, 2011. Optical gain model proposed with the use of artificial neural networks optimised by artificial bee colony algorithm. J. Optoelectron. Adv. Mat. Rapid Commun., 5: 10261029.
Yildirim, R. and F.V. Celebi, 2004. Design of a chaotic optical communication system by using RAMAN with noise addition technique. Proc. SPIE, 5662: 389394. CrossRef  Direct Link 
Yildirim, R. and F.V. Celebi, 2010. Harmonic amplitude control in laser diodes with nonlinear feedback. J. Fac. Eng. Archit. Gazi Univ., 25: 163170.
Yildirim, R., H.G. Yavuzcan, F.V. Celebi and L. Gokrem, 2009. Temperature dependent Rolletti stability analysis of GaN HEMT. Optoelectronics Adv. Mat. Rapid Commun., 3: 781786. Direct Link 
Yucel, M., 2011. Fuzzy logicbased automatic gain controller for EDFA. Microwave Optical Technol. Lett., 53: 27032705. Direct Link 
Yucel, M., H.H. Goktas and F.V. Celebi, 2011. Temperature independent length optimization of Lband EDFAs providing flat gain. OptikInt. J. Light Electron Opt., 122: 872876. CrossRef 
Yuksel, M.E. and I. Develi, 2005. A neurofuzzy computing technique for modeling the laser diode nonlinearity in radiooverfibre link. Int. J. RF Microwave Comput. Aided Eng., 15: 329335. CrossRef  Direct Link 
Kumar, A.V.S., 2012. Diagnosis of heart disease using fuzzy resolution mechanism. J. Artif. Intell., 5: 4755. CrossRef  Direct Link 
Celebi, F.V., T. Altindag, R. Yildirim and L. Gokrem, 2009. Semiconductor laser modeling with ANFIS. Proceedings of the International Conference on Application of Information and Communication Technologies, October 1416, 2009, Baku, Azerbaijan, pp: 14 CrossRef  Direct Link 
Celebi, F.V. and K. Danisman, 2006. A multilayer perseptron network model for a quantumwell laser Diode. Proceedings of the International Conference on Computing and Informatics, June 68, 2006, Kuala Lumpur, pp: 601604
Celebi, F.V. and K. Danisman, 2004. A different approach for the computation of refractive index change in quantumwell diode lasers for different injection levels. Proc. SPIE Int. Soc. Optical Eng., 5662: 384388.



