PIER Letters
 
Progress In Electromagnetics Research Letters
ISSN: 1937-6480
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 2 > pp. 149-155

TRANSMITTANCE AND FRACTALITY IN A CANTOR-LIKE MULTIBARRIER SYSTEM

By D. S. Diaz-Guerrero, F. Montoya, L. M. Gaggero-Sager, and R. Perez-Alvarez

Full Article PDF (407 KB)

Abstract:
The transmittance is studied for a Cantor-like multibarrier system. The calculation are made in the framework of effective mass theory. Some typical values of effective masses and potentials are used in order to have an experimental reference. The techniques of Transfer Matrix are used to calculate the transmittance of the entire structure having some dozens of layers. The results display a complex structure of peaks and valleys. The set of maxima is studied with the tool of the q-dependent dimension D(q). The set of transmittance maxima exhibits a fractal structure, or more exactly, a multifractal structure, i.e., a q-dependent dimension, characterized as usually with limit one when q parameter tends to -∞ but witha limit between 0 and 1 when tends to +∞. This numerical experiment demonstrate that spatially bounded potential may exhibit spectrum with fractal character.

Citation:
D. S. Diaz-Guerrero, F. Montoya, L. M. Gaggero-Sager, and R. Perez-Alvarez, "Transmittance and Fractality in a Cantor-Like Multibarrier System," Progress In Electromagnetics Research Letters, Vol. 2, 149-155, 2008.
doi:10.2528/PIERL07122804

References:
1. Gaggero-Sager, L. M., E. R. Pujals, and O. Sotolongo-Costa, "Self-similarity in a Cantor-like semiconductor quantum well," Phys. Stat. Sol. (B), Vol. 220, 167-169, 2000.
doi:10.1002/1521-3951(200007)220:1<167::AID-PSSB167>3.0.CO;2-L

2. Lavrinenko, A. V., S. V. Zhukovsky, K. S. Sandomirski, and S. V. Gaponenko, "Propagation of classical waves in nonperiodic media: Scaling properties of an optical Cantor filter," Phys. Rev. E, Vol. 65, 036621, 2002.
doi:10.1103/PhysRevE.65.036621

3. Zhukovsky, S. V., A. V. Lavrinenko, and S. V. Gaponenko, "Spectral scalability as a result of geometrical self-similarity in fractal multilayers," Europhys. Lett., Vol. 66, No. 3, 455-461, 2004.
doi:10.1209/epl/i2003-10226-8

4. Moretti, L., I. Rea, L. de Stefano, and I. Rendina, "Periodic versus aperiodic: Enhancing the sensitivity of porous silicon based optical sensors," Applied Physics Letters, Vol. 90, 191112, 2007.
doi:10.1063/1.2737391

5. Perez-Alvarez, R. and F. Garcıa-Moliner, Transfer Matrix, Green Function and Related Techniques: Tools for the Study of Multilayer Heterostructures , Universitat Jaume I, Castellon, Spain, 2004.

6. Mora, M., R. Perez- Alvarez, and C. Sommers, "Transfer matrix in one dimensional problems," J. Physique, Vol. 46, No. 7, 1021-1026, 1985.
doi:10.1051/jphys:019850046070102100

7. Griffiths, D. J. and C. A. Steinke, "Waves in locally periodic media," Am. J. Phys., Vol. 69, No. 2, 137-154, 2001.
doi:10.1119/1.1308266

8. Rasband, S. N., Chaos Dynamics of Nonlinear Systems, Wiley Professional Paperback Series, 1997.

9. Perez-Alvarez, R., F. Garcıa-Moliner, C. Trallero-Giner, and V. R. Velasco, "Polar optical modes in Fibonacci heterostructures," J. Raman Spectroscopy, Vol. 31, No. 5, 421-425, 2000.
doi:10.1002/1097-4555(200005)31:5<421::AID-JRS532>3.0.CO;2-7

10. Perez-Alvarez, R. and F. Garcıa-Moliner, The spectrum of quasiregular heterostructures, invited chapter in Contemporary Problems of the Condensed Matter Physics, S. Vlaev and L. M. Gaggero-Sager (eds.), Editorial Nov, Huntington, New York, 2001.

11. Velasco, V. R., R. Perez-Alvarez, and F. Garcıa-Moliner, "Some properties of the elastic waves in quasiregular heterostructures," J. Phys.: Cond. Matt., Vol. 14, 5933-5957, 2002.
doi:10.1088/0953-8984/14/24/305

12. Perez- Alvarez, R., F. Garcıa-Moliner, and V. R. Velasco, "Some elementary questions in the theory of quasiperiodic heterostructures," J. of Phys.: Condens. Matter, Vol. 13, 3689-3698, 2001.
doi:10.1088/0953-8984/13/15/312

13. Bovier, A. and J. M. Ghez, "Spectral properties of one-dimensional Schrodinger operators withp otentials generated by substitutions," Commun. Math. Phys., Vol. 158, No. 1, 45-66, 1993.
doi:10.1007/BF02097231

14. Bovier, A. and J. M. Ghez, "Remarks on the spectral properties of tight-binding and Kronig-Penney models with substitution sequences ," J. Phys. A:Math. Gen., Vol. 28, No. 8, 2313-2324, 1995.
doi:10.1088/0305-4470/28/8/022


© Copyright 2010 EMW Publishing. All Rights Reserved