**6. References**


[8] Davis L. (1996). Handbook of Genetic Algorithms, Van Nostrand Reinhold, Berlin, 1996

22 Name of the Book

complexity of both regimes can influence the number of cost function evaluations etc. The method of evolutionary deterministic chaos control described here is relatively simple, easy to implement and easy to use. Based on its principles and its possible universality it can be stated that evolutionary deterministic chaos control is capable of solving this class of CML deterministic chaos control problems. The main aim of this part was to show how various CML control problems were solved by means of evolutionary algorithms. Evolutionary deterministic chaos control was used here in four basic comparative simulations. Each comparative simulation was repeated 100 times and all results (see [13]) were used to create graphs for performance evaluation of evolutionary deterministic chaos control. They were chosen to show that evolutionary deterministic chaos control can be regarded as a blackbox˙

In this chapter selected applications of simulated annealing were briefly mentioned, such as: evolutionary identification of bifurcations, synthesis of chaotic systems and evolutionary control of spatiotemporal CML systems. All experiments mentioned here are a part of a more extended set of experiments, so we recommend that interested readers read our original sources for a full description. It has been numerically demonstrated that SA is still a useful algorithm, capable of solving various problems from engineering as well as from theory.

This work was supported by the Development of human resources in research and development of latest soft computing methods and their application in practice project, reg. no. CZ.1.07/2.3.00/20.0072 funded by Operational Programme Education for

*Department of Computer Science, Faculty of computer science,17. listopadu 15, 708 33*

[1] Gilmore R., Catastrophe Theory for Scientists and Engineers,John Wiley and Sons, 1993

[3] Arnold V.(1991). The Theory of Singularities and Its Applications, Accademia Nazionale

[4] Poston T, Stewart I.(1977). Catastrophe Theory and its Applications, 842-844, IEEE Press,

[7] Zelinka I. (2004). SOMA - Self Organizing Migrating Algorithm, In: *New Optimization Techniques in Engineering*,Onwubolu, Babu B., (Ed.), 167-218, Springer-Verlag, New York,

[5] Hilborn R.(1994). Chaos and Nonlinear Dynamics,Oxford University Press,1994 [6] Price K., Storn R. et al.(1994). Differential Evolution - A Practical Approach to Global

Competitiveness, co-financed by ESF and state budget of the Czech Republic.

[2] Rössler O (1979) An equation for hyperchaos. Phys. Lett. A, 71:155

method and that it can be implemented using arbitrary evolutionary algorithms.

**5. Conclusions**

**Acknowledgement**

**Author details**

**6. References**

2004

Ivan Zelinka and Lenka Skanderova

Dei Lincei, Pisa, Italy, 1991

New York, USA,1977

*Ostrava-Poruba, VSB-TUO Ostrava, Czech Republic*

Optimization, Springer-Verlag, 2005

I

	- [30] Richter H., Reinschke K. J., Optimization of local control of chaos by an evolutionary algorithm, Physica D, 144, 309-334, 2000
	- [31] Richter H., Reinschke Kurt J., Optimization of local control of chaos by an evolutionary algorithm. Physica D 144 (2000), 309-334. 2000

**Optimization Design of Nonlinear Optical**

**Chapter 5**

Laser has become to be a fundamental light source in modern communication, scientific research, and industrial applications. More and more laser frequencies are required for various applications. However, common laser crystals can provide only some fixed frequencies which cannot satisfy various requirement. Nonlinear optical process presents an alternative approach for generating rich laser frequencies. The traditional nonlinear optical processes usually require the so called phase-matching condition [1, 2], which requires the nonlinear optical crystals with birefringence. The phase-matching condition raises a restriction of the choice of natural birefringence materials in the applications of frequency conversion. Quasi-phase-matching method uses periodic modulation of the nonlinear property of a crystal to compensate the mismatch between the wave vectors of the interaction light beams [3]. This method allows utilization of the large component of the nonlinear susceptibility tensor, which is usually inaccessible with the common phase matching. Periodic optical superlattice provides a reciprocal vector to compensate the phase mismatch between the interacting light beams. Thus, only one nonlinear process can be performed in the periodic optical superlattice. This idea can be naturedly expended to the aperiodic optical supperlattice which can provide a series of reciprocal vectors. The reciprocal vectors can be preset for special nonlinear process. The key problem is how to design different aperiodic optical supperlattice

for matching the specified nonlinear optical process with high conversion efficiency.

In this chapter, the simulated annealing (SA) method is used to successfully design nonlinear optical frequency conversion devices for achieving different nonlinear optical processes, for example, multiple second harmonics generation and coupled third harmonic generation in the aperiodic optical superlattice, multiple wavelengths parametric amplification, multiple wavelengths second harmonics generation and coupled third harmonic generation in the defective nonlinear photonic crystals. The simulation results demonstrate that the SA method is an effective algorithm for nonlinear optical frequency conversion devices design. The

> ©2012 Zhang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

©2012 Zhang, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Frequency Conversion Devices Using**

**Simulated Annealing Algorithm**

Additional information is available at the end of the chapter

designed devices can archive the preset goal well.

Yan Zhang

http://dx.doi.org/10.5772/50074

**1. Introduction**

