**Numerical Simulation Methods Applied at Fiber Grating Sensors Design**

[21] R. Kiran, "Optimization of the Hg1–xCdxTe surface and its characterization by electrical and optical techniques," Ph.D. dissertation, University of Illinois at Chicago, Chicago,

[22] E. O. Kane, "Zener tunneling in semiconductors," Phys. Chem. Solids 2, 181–188 (1960). [23] C. B. Duke, "Tunneling in Solids," volume 10 of Solid state physics: advances in

[24] J. L. Moll, "Physics of semiconductors," chapter 12, McGraw‐Hill, New York (1964). [25] G. A. Hurkx, D.B.M. Klaassen and M. P. G. Knuvers, "A new recombination model for device simulation including tunneling," IEEE Trans. Electron Dev. 39(2), 331 (1992).

[26] A. M. Itsuno, J. D. Phillips and S. Velicu, "Mid-wave infrared HgCdTe nBn photode‐

[27] M. Kopytko, "Design and modeling of high-operating temperature MWIR HgCdTe nBn detector with *n*- and *p*-type barriers," Infrared Phys. Technol. 64, 47–55 (2014).

[28] M. Kopytko, K. Jóźwikowski and A. Rogalski, "Fundamental limits of MWIR HgCdTe barrier detectors operating under non-equilibrium mode," Solid-State Electron. 100,

[29] K. Jóźwikowski, M. Kopytko, J. Piotrowski, A. Jóźwikowska, Z. Orman and A. Rogalski, "Near-room temperature MWIR HgCdTe photodiodes limited by vacancies and dislocations related to Shockley–Read–Hall centres," Solid-State Electron. 66(1), 8–

[30] K. Jóźwikowski, A. Jóźwikowska, A. Rogalski and L. R. Jaroszewicz, "Simplified model of dislocations as a SRH recombination channel in the HgCdTe heterostructures,"

[31] A. Jóźwikowska, "Numerical solution of the nonlinear Poisson equation for semicon‐ ductor devices by application of a diffusion-equation finite difference scheme," J. Appl.

[32] A. Jóźwikowska, K. Jóźwikowski, J. Rutkowski and A. Rogalski, "Generation-recom‐ bination effects in high temperature HgCdTe heterostructure photodiodes," Opto-

research and applications," Academic Press, New York (1969).

tector," Appl. Phys. Lett. 100, 161102 (2012).

Infrared Phys. Technol. 55(1), 98–107 (2012).

IL (2008).

90 Modeling and Simulation in Engineering Sciences

20–26 (2014).

13 (2011).

Phys. 104, 063715 (2008).

Electron. Rev. 12(4), 417–428 (2004).

Dan Savastru, Sorin Miclos, Marina Tautan and Ion Lancranjan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63890

#### **Abstract**

The paper presents the results obtained in simulation of fiber Bragg grating (FBG) and long-period grating (LPG) sensors and their applications. The optical properties of FBG and LPG are firstly analyzed and, consequently, the basics of simulation models are provided. Coupled-mode theory and the transfer matrix methods are the two techni‐ ques used for the simulation of FBG and LPG. The numerical simulations are per‐ formed for an improved design of these types of fiber sensors, designs dedicated to specified applications. The different FBG types, i.e. the normal, chirped, apodized, according to different laws and tilted cases, are analyzed. Also, various LPG configu‐ rations are numerically simulated. The two main categories of sensing applications, for temperature and for mechanical stress/strain evaluation, are simulated for each type of fiber grating sensor. The chapter is intended to be a synthesis of already obtained results to which some results of research in development are added.

**Keywords:** Distributed feedback devices, Optical fibers, Fiber gratings, Fiber Bragg grating, Long-period grating fiber, Optical fiber communication, Optical fiber devices, Optical fiber filters
