volume | PIER Journals

Abstract

Analytic expressions for the nonlinear absorption coefficient (nonlinear absorption coefficient=NAC) of a strong electromagnetic wave (laser radiation) caused by confined electrons for the case of electron-optical phonon scattering in doping superlattices (doping superlattices=DSLs) are calculated by using the quantum kinetic equation for electrons. The problem is also considered for both the absence and the presence of an external magnetic field. The dependence of the NAC on the intensity E₀ and the energy hΩ of the external strong electromagnetic wave (electromagnetic wave=EMW), the temperature T of the system, the doping concentration n_D and the cyclotron frequency Ω_B for case of an external magnetic field is obtained. Two cases for the absorption: Close to the absorption threshold ∣khΩ-hω₀∣≤ε and far away from the absorption threshold ∣khΩ-hω₀∣≥ε (k=0, ±1, ±2..., hω₀ and ε are the frequency of optical phonon and the average energy of electrons, respectively) are considered. The analytic expressions are numerically evaluated, plotted, and discussed for a specific DSLs n-GaAs/p-GaAs. The computations show that the NAC in DSLs in case presence of an external magnetic field is much more greater than to it is absence of an external magnetic field. The appearance of an external magnetic field causes surprising changes in the nonlinear absorption. All the results for the presence of an external magnetic field are compared with those for the absence of an external magnetic field to show the difference.

1. Matsumoto, Y., S. Ozaki, and S. Adachi, "Optical properties of the bulk amorphous semiconductor ZnIn₂Te₄," J. Appl. Phys., Vol. 86, 3705, 1999.
doi:10.1063/1.371282 Google Scholar

2. Jellison, Jr. and G. E. F. A. Modine, "Erratum: Parameterization of the optical functions of amorphous materials in the interband region," Appl. Phys. Lett., Vol. 69, 371, 1996.
doi:10.1063/1.118064 Google Scholar

3. Khokhlov, A. F., I. A. Chuchmaǐ, and A. V. Ershov, "Absorption features in a-Si/ZrO_x Nanostructures," Semiconductors, Vol. 34, No. 3, 344, 2000.
doi:10.1134/1.1187983 Google Scholar

4. Keimann, F., R. Brazis, H. Barkley, W. Kasparek, M. Thumm, and V. Erckmann, "Millimeter-wave frequency tripling in bulk semiconductors," Europhys. Lett., Vol. 11, 337, 1990.
doi:10.1209/0295-5075/11/4/008 Google Scholar

5. Lyubin, V. M. and M. L. Klebanov, "Laser-induced anisotropic absorbtion, reflection, and scattering of light in chalcogenide glassy semiconductors," Semiconductors, Vol. 32, No. 8, 817, 1998.
doi:10.1134/1.1187513 Google Scholar

6. Malevich, V. L. and I. A. Utkin, "Nonlinear optical absorption in a heavily doped degenerate n-GaAs," Semiconductors, Vol. 34, No. 8, 924, 2000.
doi:10.1134/1.1188101 Google Scholar

7. Malevich, V. L. and E. M. Epstein, "Nonlinear optical properties of conduction electrons in semiconductors," Sov. Quantum Electronic, Vol. 1, 1468, 1974. Google Scholar

8. Pavlovich, V. V. and E. M. Epshtein, "Quantum theory of absorption of electronmagnetic wave by free carries in simiconductors," Sov. Phys. Stat., Vol. 19, 1760, 1977. Google Scholar

9. Schmittrink, S., D. S. Chemla, and D. A. B. Miller, "Linear and nonlinear optical properties of semiconductor quantum wells," Adv. Phys., Vol. 38, 89, 1989.
doi:10.1080/00018738900101102 Google Scholar

10. Zegrya, G. G. and V. E. Perlin, "Intraband absorption of light in quantum wells induced by electron-electron collisions," Semiconductors, Vol. 32, No. 4, 417, 1998.
doi:10.1134/1.1187408 Google Scholar

11. Shmelev, G. M., I. A. Chaikovskii, and N. Q. Bau, "HF conduction in semiconductors superlattices," Sov. Phys. Tech. Semicond., Vol. 12, 1932, 1978. Google Scholar

12. Schmit-Rink, S., D. S. Chemla, and D. A. B. Miler, "Linear and nonlinear optical properties in semiconductor quantum wells," Adv. Phys., Vol. 38, 89, 1989.
doi:10.1080/00018738900101102 Google Scholar

13. Bau, Q. N., D. M. Hung, and B. N. Ngoc, "The nonlinear absorption coeffcient of a strong electromagnetic wave caused by confined electrons in quantum wells," J. Korean Phys. Soc., Vol. 54, No. 2, 765, 2009.
doi:10.3938/jkps.54.765 Google Scholar

14. Vasilopoulos, P., M. Charbonneau, and C. M. Van Vliet, "Linear and nonlinear electrical conduction in quasi-two-dimensional quantum wells," Phys. Rev. B, Vol. 35, 1334, 1987.
doi:10.1103/PhysRevB.35.1334 Google Scholar

15. Abouelaoualim, D., "Electron-confined LO-phonon scattering in GaAs-Al_0.45Ga_0.55 As superlattice ," Pramana Journal of Physics, Vol. 66, 455-465, 2006.
doi:10.1007/BF02704398 Google Scholar

16. Gaggero-Sager, M. L., N. Moreno-Martinez, I. Rodriguez-Vargas, R. Perez-Alvarez, V. V. Grimalsky, and M. E. Mora-Ramos, "Electronic structure as a function of temperature for Si doped quantum wells in GaAs," PIERS Online, Vol. 3, No. 6, 851-854, 2007.
doi:10.2529/PIERS061006210621 Google Scholar

17. Butscher, S. and A. Knorr, "Occurrence of intersubband polaronic repellons in a two-dimesional electron gas," Phys. Rev. L, Vol. 97, 197401, 2006.
doi:10.1103/PhysRevLett.97.197401 Google Scholar

18. Bau, N. Q. and T. C. Phong, "Calculations of the absorption coefficient of a weak EMW by free carriers in quantum wells by the Kubo-Mori method," J. Phys. Soc. Jpn., Vol. 67, 3875, 1998.
doi:10.1143/JPSJ.67.3875 Google Scholar

19. Bau, N. Q., N. V. Nhan, and T. C. Phong, "Calculations of the absorption coefficient of a weak electromagnetic wave by free carriers in doped superlattices by using the Kubo-Mori method," J. Korean. Phys. Soc., Vol. 41, 149, 2002. Google Scholar

20. Samuel, E. P. and D. S. Patil, "Analysis of wavefunction distribution in quantum well biased laser diode using transfer matrix method," Progress In Electromagnetics Research Letters, Vol. 1, 119, 2008.
doi:10.2528/PIERL07111902 Google Scholar

21. Bau, N. Q., L. Dinh, and T. C. Phong, "Absorption coefficient of weak electromagnetic wave caused by confined electrons in quantum wires," J. Korean. Phys. Soc., Vol. 51, 1325-1330, 2007.
doi:10.3938/jkps.51.1325 Google Scholar

22. Karabulut, I. and S. Baskoutas, "Linear and nonlinear optical absorption coefficients and refractive index changes in spherical quantum dots: Effects of impurities, electric field, size, and optical intensity," J. Appl. Phys., Vol. 103, 073512, 2008.
doi:10.1063/1.2904860 Google Scholar

Dr. Nguyen Quang Bau

Dr. Do Manh Hung