volume | PIER Journals

Abstract

The time delay, space shift and widening of wave packet transmitted and reflected by structures with Bragg mirrors have been investigated. The specific structures such as Bragg mirrors, resonators, and structures with chirp variation of thickness of the ``period'' have been considered. The calculation has been carried out under the conditions that carrier frequency, and incidence angle is in the vicinity of the Bragg resonance. Integral (mass center) and differential (group) estimates of the delay time and space shift have been compared. The conditions for the appearance of anomalous (negative) mass center delay or mass center shift (Goos-Hänchen shift) of the reflected wave packet have been determined. The shape transformations of the wave packet illuminating periodic and quasiperiodic apodized Bragg reflectors have been under consideration. Spatial apodization of permittivity contrast yields much smaller shape deformation of the transmitted wave packet upon incidence at angles and carrier frequency near the edges of reflection band, as well in Bragg reflection band, in comparison with phenomena in similar periodic structures. The values of group delay for layered structures with a small chirp variation of optical (electrical) thickness of the period along longitudinal coordinates have been experimentally obtained in microwave range.

1. Elachi, C., "Waves in active and passive periodic structures: A review," Proceedings of the IEEE, Vol. 64, No. 12, 1666-1698, 1976.
doi:10.1109/PROC.1976.10409

2. Yariv, A. and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation , Wiley, 2002.

3. Kusiek, A., R. Lech, and J. Mazur, "Hybrid technique for the analysis of scattering from periodic structures composed of irregular objects," Progress In Electromagnetics Research, Vol. 135, 657-675, 2013.

4. Wu, J.-J., D. Chen, K.-L. Liao, T.-J. Yang, and W.-L. Ouyang, "The optical properties of Bragg fiber with a fiber core of 2-dimension elliptical-hole photonic crystal structure," Progress In Electromagnetics Research Letters, Vol. 10, 87-95, 2009.
doi:10.2528/PIERL09061804

5. Tuz, V. R., S. L. Prosvirnin, and V. B. Kazanskiy, "Mutual conversion of TM mn and TE mn waves by periodic and aperiodic waveguide ¯lters composed of dense metal-strip gratings," Progress In Electromagnetics Research B, Vol. 30, 313-335, 2011.

6. Borulko, V., O. Drobakhin, and D. Sidorov, "Eigenfrequencies of periodic and quasiperiodic apodized Bragg structures," Telecommunications and Radio Engineering, Vol. 71, No. 16, 1433-1445, 2012.
doi:10.1615/TelecomRadEng.v71.i16.10

7. Liu, Y. and Z. Lu, "Phase shift defect modes in one dimensional asymmetrical photonic structures consisting of two rugate segments with different periodicities," Progress In Electromagnetics Research, Vol. 112, 257-272, 2011.

8. Matuschek, N., F. Kartner, and U. Keller, "Theory of double chirped mirrors," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 4, No. 2, 198-208, 1998.
doi:10.1109/2944.686724

9. Vainshtein, L. A., "Propagation of pulses," Sov. Phys. Usp., Vol. 19, 189-205, 1976.
doi:10.1070/PU1976v019n02ABEH005138

10. Kopfermann, H. and R. Ladenburg, "Untersuchungen uber die anomale dispersion angeregter Gase V. Teil: Negative dispersion in angeregtem Neon," Zeitschrift fur Physik A Hadrons and Nuclei, Vol. 65, No. 3--4, 167-188, 1930.
doi:10.1007/BF01397029

11. Bass, F. and L. Resnick, "Wave beam propagation in layered media," Progress In Electromagnetics Research, Vol. 38, 111-123, 2002.
doi:10.2528/PIER02081301

12. Wait, J. R., Electromagnetic Waves in Stratified Media, Pergamon Press, 1970.

13. Born, M. and E. Wolf, Principles of Optics, Pergamon Press, 1975.

14. Tuz, V. R., "Three-dimensional Gaussian beam scattering fromperiodic sequence of bi-isotropic and material layer," Progress In Electromagnetics Research B, Vol. 7, 53-73, 2008.
doi:10.2528/PIERB08022806

15. Ivanov, O. V. and D. I. Sementsov, "Negative shift of light beam reflected from the interface between optically transparent and resonant media," Optics and Spectroscopy, Vol. 89, No. 5, 737-741, 2000.
doi:10.1134/1.1328130

16. Kandic, M. and G. E. Bridges, "Limits of negative group delay phenomenon in linear causal media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013.

17. Ginzburg, V. L., Propagation of Electromagnetic Waves in Plasma, Pergamon Press, Oxford, 1970.

18. Oppenheim, A. V. and R. W. Schafer, Discrete-time Signal Processing, 619, Prentice-Hall, 1989.

19. Sun, N.-H., J.-J. Liau, Y.-W. Kiang, S.-C. Lin, R.-Y. Ro, J.-S. Chiang, and H.-W. Chang, "Numerical analysis of apodized fiber Bragg gratings using coupled mode theory," Progress In Electromagnetics Research, Vol. 99, 289-306, 2009.
doi:10.2528/PIER09102704

20. Alekseev, V., O. Drobakhin, Ye. Kondrat'yev, and D. Saltykov, "Microwave introscopy using multifrequency measurements and transversal scan," IEEE Aerospace and Electronic Systems Magazine, Vol. 21, No. 2, 24-26, 2006.

21. Antropov, O. S., V. F. Borulko, O. O. Drobakhin, and S. M. Vovk, "Nonquadratic regularization procedure for multifrequency amplitude data extrapolation in microwave introscopy of dielectric structures Fourier-holography applications," Telecommunications and Radio Engineering, Vol. 68, 905-913, 2009.

22. Hildebrand, F. B., "Introduction to Numerical Analysis," McGraw-Hill, 1956.

23. Brekhovskikh, L. M., Waves in Layered Media, Academic Press, 1960.

Dr. Valentyn Borulko

Dr. Oleg O. Drobakhin

Mr. Dmitry V. Sidorov