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Comparison of the nonlinear optical properties of asymmetrical and symmetrical quantum wells

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Abstract

In this work, a detailed comparison of the nonlinear optical properties (NLOPs), including the absorption coefficients (ACs) and the refractive index changes (RICs) of symmetrical parabolic (SP) and asymmetrical semi-parabolic (ASP) quantum-wells (QWs) are investigated by utilizing the compact density matrix approach and iterative procedure. The wave functions of one electron, as well as its energy eigenvalue in the SPQW and the ASPQW, are also obtained by applying the effective mass approximation. Numerical calculations on GaAs/AlGaAs material reveal that the ACs and the RICs in both the SPQW and the ASPQW are affected strongly by the incident optical intensity (I) and the confining frequency (\(\omega _0\)), and depend sensitively on the relaxation time (T). Furthermore, if it is desired to obtain large ACs/RICs then a relatively weaker I and lower \(\omega _0\) should be chosen. However, the nonlinear (third-order) component influence is very important in the relatively large I case and cannot be neglected when examining the nonlinear optical features of both the SPQW and the ASPQW. More importantly, the total AC and the total RIC in the SPQW always are larger than those in the ASPQW. In addition, if we choose an optimized confining frequency for the SPQW, then we will get larger ACs/RICs.

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Data Availability Statement

Data available on request from the authors.

References

  1. L. Zhang, H.-J. Xie, Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells. Phys. Rev. B 68, 235315 (2003). https://doi.org/10.1103/PhysRevB.68.235315

    Article  ADS  Google Scholar 

  2. S. Baskoutas, E. Paspalakis, A.F. Terzis, Effects of excitons in nonlinear optical rectification in semiparabolic quantum dots. Phys. Rev. B 74, 153306 (2006). https://doi.org/10.1103/PhysRevB.74.153306

    Article  ADS  Google Scholar 

  3. G. Wang, Third-harmonic generation in cylindrical parabolic quantum wires with an applied electric field. Phys. Rev. B 72, 155329 (2005). https://doi.org/10.1103/PhysRevB.72.155329

    Article  ADS  Google Scholar 

  4. L. Zhang, J.-j. Shi, Calculation of linear and nonlinear intersubband refractive-index changes in an asymmetrical semiparabolic quantum well with applied electric field, physica status solidi (b) 242, 1001 ( 2005), https://doi.org/10.1002/pssb.200402130arXiv:2004.02130

  5. H. Yıldır ım, M. Tomak, Nonlinear optical properties of a pöschl-teller quantum well, Phys. Rev. B 72, 115340 (2005).https://doi.org/10.1103/PhysRevB.72.115340

  6. J. You, K. Guo, J. Lao, S. Mo, Linear and nonlinear optical absorption coefficients and refractive index changes of zigzag quantum wells affected by terahertz laser field. Thin Solid Films 733, 138813 (2021). https://doi.org/10.1016/j.tsf.2021.138813

    Article  ADS  Google Scholar 

  7. Q. Zhao, S. Aqiqi, J.-F. You, M. Kria, K.-X. Guo, E. Feddi, Z.-H. Zhang, J.-H. Yuan, Influence of position-dependent effective mass on the nonlinear optical properties in algaas/gaas single and double triangular quantum wells. Physica E 115, 113707 (2020). https://doi.org/10.1016/j.physe.2019.113707

    Article  Google Scholar 

  8. H. Aydinoglu, M. Sayrac, M. Mora-Ramos, F. Ungan, Nonlinear optical properties in algaas/gaas double-graded quantum wells: the effect of the structure parameter, static electric, and magnetic field. Solid State Commun. 342, 114647 (2022). https://doi.org/10.1016/j.ssc.2021.114647

    Article  Google Scholar 

  9. H. Noverola-Gamas, L.M. Gaggero-Sager, O. Oubram, Nonlinear optical properties in n-type quadruple doped gaas quantum wells. Chin. Phys. B (2021). https://doi.org/10.1088/1674-1056/ac248e

    Article  Google Scholar 

  10. F. Ungan, M. Bahar, K. Rodríguez-Magdaleno, M. Mora-Ramos, J. Martínez-Orozco, Influence of applied external fields on the nonlinear optical properties of a semi-infinite asymmetric algaas/gaas quantum well. Materials Sci. Semiconductor Process. 123, 105509 (2021). https://doi.org/10.1016/j.mssp.2020.105509

    Article  Google Scholar 

  11. R. Atanasov, F. Bassani, V.M. Agranovich, Second-order nonlinear optical susceptibility of asymmetric quantum wells. Phys. Rev. B 50, 7809 (1994). https://doi.org/10.1103/PhysRevB.50.7809

    Article  ADS  Google Scholar 

  12. K.-X. Guo, S.-W. Gu, Nonlinear optical rectification in parabolic quantum wells with an applied electric field. Phys. Rev. B 47, 16322 (1993). https://doi.org/10.1103/PhysRevB.47.16322

    Article  ADS  Google Scholar 

  13. E. Rosencher, P. Bois, Model system for optical nonlinearities: asymmetric quantum wells. Phys. Rev. B 44, 11315 (1991). https://doi.org/10.1103/PhysRevB.44.11315

    Article  ADS  Google Scholar 

  14. O. Aytekin, S. Turgut, M. Tomak, Nonlinear optical properties of a pöschl-teller quantum well under electric and magnetic fields. Physica E 44, 1612 (2012). https://doi.org/10.1016/j.physe.2012.04.005

    Article  ADS  Google Scholar 

  15. Z. Zhang, K. Guo, S. Mou, B. Xiao, Y. Zhou, Nonlinear optical properties in square tangent quantum wells. Optik 127, 928 (2016). https://doi.org/10.1016/j.ijleo.2015.10.125

    Article  ADS  Google Scholar 

  16. S. Ünlü, Karabulut, and H. Şafak, Linear and nonlinear intersubband optical absorption coefficients and refractive index changes in a quantum box with finite confining potential, Physica E: Low-dimensional Systems and Nanostructures 33, 319 (2006). https://doi.org/10.1016/j.physe.2006.03.163

    Article  ADS  Google Scholar 

  17. K.J. Kuhn, G.U. Iyengar, S. Yee, Free carrier induced changes in the absorption and refractive index for intersubband optical transitions in algaas/gaas/alxgaas quantum wells. J. Appl. Phys. 70, 5010 (1991). https://doi.org/10.1063/1.349005

    Article  ADS  Google Scholar 

  18. N.D. Hien, Linear and nonlinear optical properties in quantum wells. Micro Nanostruct. 170, 207372 (2022). https://doi.org/10.1016/j.micrna.2022.207372

    Article  Google Scholar 

  19. N.D. Hien, Optical properties of a single quantum well with pöschl-teller confinement potential. Physica E 145, 115504 (2023). https://doi.org/10.1016/j.physe.2022.115504

    Article  Google Scholar 

  20. J.R. Madureira, M.H. Degani, M.Z. Maialle, Nonlinear optical absorption of semiconductor quantum wires: Photoexcitation dynamical effects. Phys. Rev. B 68, 161301 (2003). https://doi.org/10.1103/PhysRevB.68.161301

    Article  ADS  Google Scholar 

  21. G. Liu, R. Liu, G. Chen, Z. Zhang, K. Guo, L. Lu, Nonlinear optical rectification and electronic structure in asymmetric coupled quantum wires. Results Phys. 17, 103027 (2020). https://doi.org/10.1016/j.rinp.2020.103027

    Article  Google Scholar 

  22. S. Antil, M. Kumar, S. Lahon, S. Dahiya, A. Ohlan, R. Punia, A. Maan, Influence of hydrostatic pressure and spin orbit interaction on optical properties in quantum wire. Physica B 552, 202 (2019). https://doi.org/10.1016/j.physb.2018.10.006

    Article  ADS  Google Scholar 

  23. M. Solaimani, S.M.A. Aleomraninejad, L. Lavaei, Optical properties of parabolic quantum wires in the presence of electron-electron interactions: an euler-lagrange variational application. Optik 172, 353 (2018). https://doi.org/10.1016/j.ijleo.2018.07.056

    Article  ADS  Google Scholar 

  24. E. Ramya, M.V. Rao, D.N. Rao, Third-order nonlinear optical properties of cdse/zns/cdse core-shell-shell quantum dots. Physica E 107, 24 (2019). https://doi.org/10.1016/j.physe.2018.11.010

    Article  ADS  Google Scholar 

  25. L. Máthé, C. Onyenegecha, A.-A. Farcaş, L.-M. Pioraş-Ţimbolmaş, M. Solaimani, H. Hassanabadi, Linear and nonlinear optical properties in spherical quantum dots: inversely quadratic hellmann potential. Phys. Lett. A 397, 127262 (2021). https://doi.org/10.1016/j.physleta.2021.127262

    Article  MathSciNet  MATH  Google Scholar 

  26. M. Kria, Varsha, M. Farkous, V. Prasad, F. Dujardin, L. Pérez, D. Laroze, E. Feddi, Wetting layer and size effects on the nonlinear optical properties of semi oblate and prolate si0.7ge0.3/si quantum dots, Current Applied Physics 25, 1 ( 2021)https://doi.org/10.1016/j.cap.2021.02.004

  27. Y. Gündoǧdu, H. Şükür Kılıç, M. Çadırcı, Third order nonlinear optical properties of cdte/cdse quasi type-ii colloidal quantum dots, Optical Materials 114, 110956 ( 2021)https://doi.org/10.1016/j.optmat.2021.110956

  28. T. Kondratenko, A. Zvyagin, M. Smirnov, I. Grevtseva, A. Perepelitsa, O. Ovchinnikov, Luminescence and nonlinear optical properties of colloidal ag2s quantum dots. J. Luminescence 208, 193 (2019). https://doi.org/10.1016/j.jlumin.2018.12.042

    Article  ADS  Google Scholar 

  29. X. Li, C. Chang, Nonlinear optical properties of gaas/algaas quantum dots system with hulthen-yukawa potential. Opt. Materials 131, 112605 (2022). https://doi.org/10.1016/j.optmat.2022.112605

    Article  Google Scholar 

  30. C. Chang, X. Li, Second-order nonlinear optical response of tunable gaas/algaas quantum dot with hulthen-hellmann potential. Phys. B 645, 414251 (2022). https://doi.org/10.1016/j.physb.2022.414251

    Article  Google Scholar 

  31. C. Chang, X. Li, Nonlinear optical properties in gaas/algaas quantum dots of inversely quadratic hellmann plus kratzer potential. Euro. Phys. J. D 76, 134 (2022). https://doi.org/10.1140/epjd/s10053-022-00453-z

    Article  ADS  Google Scholar 

  32. C. V. Nguyen, N. Ngoc Hieu, C. A. Duque, D. Quoc Khoa, N. Van Hieu, L. Van Tung, H. Vinh Phuc, Linear and nonlinear magneto-optical properties of monolayer phosphorene, Journal of Applied Physics 121, 045107 ( 2017a), https://doi.org/10.1063/1.4974951

  33. C.V. Nguyen, N.N. Hieu, D. Muoi, C.A. Duque, E. Feddi, H.V. Nguyen, L.T.T. Phuong, B.D. Hoi, H.V. Phuc, Linear and nonlinear magneto-optical properties of monolayer mos2. J. Appl. Phys. 123, 034301 (2018). https://doi.org/10.1063/1.5009481

    Article  ADS  Google Scholar 

  34. C.V. Nguyen, N.N. Hieu, C.A. Duque, N.A. Poklonski, V.V. Ilyasov, N.V. Hieu, L. Dinh, Q.K. Quang, L.V. Tung, H.V. Phuc, Linear and nonlinear magneto-optical absorption coefficients and refractive index changes in graphene. Opt. Materials 69, 328 (2017). https://doi.org/10.1016/j.optmat.2017.04.053

    Article  ADS  Google Scholar 

  35. M.M. Glazov, L.E. Golub, G. Wang, X. Marie, T. Amand, B. Urbaszek, Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers. Phys. Rev. B 95, 035311 (2017). https://doi.org/10.1103/PhysRevB.95.035311

    Article  ADS  Google Scholar 

  36. A. Taghizadeh, T.G. Pedersen, Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 99, 235433 (2019). https://doi.org/10.1103/PhysRevB.99.235433

    Article  ADS  Google Scholar 

  37. A.S. Plaut, K. Kash, B.P. Van der Gaag, A.S. Gozdz, J.P. Harbison, L.T. Florez, Optical nonlinearity in gaas quantum dots. J. Appl. Phys. 101, 106107 (2007). https://doi.org/10.1063/1.2655626

    Article  ADS  Google Scholar 

  38. M. Gurnick, T. DeTemple, Synthetic nonlinear semiconductors. IEEE J. Quantum Electron. 19, 791 (1983). https://doi.org/10.1109/JQE.1983.1071927

    Article  ADS  Google Scholar 

  39. C. Sirtori, F. Capasso, D.L. Sivco, A.Y. Cho, Giant, triply resonant, third-order nonlinear susceptibility \({\rm \chi \mathit{}_{3\rm \omega }}^{(3)}\) in coupled quantum wells. Phys. Rev. Lett. 68, 1010 (1992). https://doi.org/10.1103/PhysRevLett.68.1010

    Article  ADS  Google Scholar 

  40. L.C. West, S.J. Eglash, First observation of an extremely large-dipole infrared transition within the conduction band of a gaas quantum well. Appl. Phys. Lett. 46, 1156 (1985). https://doi.org/10.1063/1.95742

    Article  ADS  Google Scholar 

  41. B.F. Levine, R.J. Malik, J. Walker, K.K. Choi, C.G. Bethea, D.A. Kleinman, J.M. Vandenberg, Strong infrared intersubband absorption in doped gaas-alas quantum well waveguides. Appl. Phys. Lett. 50, 273 (1987). https://doi.org/10.1063/1.98223

    Article  ADS  Google Scholar 

  42. A. Harwit, J.S. Harris, Observation of stark shifts in quantum well intersubband transitions. Appl. Phys. Lett. 50, 685 (1987). https://doi.org/10.1063/1.98066

    Article  ADS  Google Scholar 

  43. A. El Kadadra, D. Abouelaoualim, A. Oueriagli, A. Outzourhit, Electric field effect on the nonlinear optical rectification properties in iii–v nitrides semi-parabolic quantum well. J. Nonlinear Opt. Phys. Materials 23, 1450002 (2014). https://doi.org/10.1142/S0218863514500027

    Article  Google Scholar 

  44. H. Hassanabadi, G. Liu, L. Lu, Nonlinear optical rectification and the second-harmonic generation in semi-parabolic and semi-inverse squared quantum wells. Solid State Commun. 152, 1761 (2012). https://doi.org/10.1016/j.ssc.2012.05.023

    Article  ADS  Google Scholar 

  45. İbrahim Karabulut, H. Şafak, Nonlinear optical rectification in semiparabolic quantum wells with an applied electric field, Physica B: Condensed Matter 368, 82 ( 2005)https://doi.org/10.1016/j.physb.2005.06.040

  46. J.-H. Yuan, N. Chen, Y. Zhang, H. Mo, Z.-H. Zhang, Electric field effect on the second-order nonlinear optical properties in semiparabolic quantum wells. Physica E 77, 102 (2016). https://doi.org/10.1016/j.physe.2015.11.011

    Article  ADS  Google Scholar 

  47. L. Zhang, Electric field effect on the linear and nonlinear intersubband refractive index changes in asymmetrical semiparabolic and symmetrical parabolic quantum wells. Superlattices Microstruct. 37, 261 (2005). https://doi.org/10.1016/j.spmi.2004.12.010

    Article  ADS  Google Scholar 

  48. G. hui Wang, Nonlinear intersubband optical absorption in semiparabolic quantum wells. Optik 125, 2374 (2014). https://doi.org/10.1016/j.ijleo.2013.10.116

    Article  ADS  Google Scholar 

  49. X. Yu, Y. Yu, Optical absorptions in asymmetrical semi-parabolic quantum wells. Superlattices Microstruct. 62, 225 (2013). https://doi.org/10.1016/j.spmi.2013.07.021

    Article  ADS  Google Scholar 

  50. C.-J. Zhang, K.-X. Guo, Polaron effects on the optical absorptions in asymmetrical semi-parabolic quantum wells. Physica E 39, 103 (2007). https://doi.org/10.1016/j.physe.2007.01.011

    Article  ADS  Google Scholar 

  51. H. İbrahim Karabulut, Şafak, and M. Tomak, Nonlinear optical rectification in asymmetrical semiparabolic quantum wells, Solid State Communications 135, 735 (2005). https://doi.org/10.1016/j.ssc.2005.06.001

    Article  Google Scholar 

  52. C.-J. Zhang, K.-X. Guo, Polaron effects on the second-order susceptibilities in asymmetrical semi-parabolic quantum wells. Physica E 33, 363 (2006). https://doi.org/10.1016/j.physe.2006.04.008

    Article  ADS  Google Scholar 

  53. C.-J. Zhang, K.-X. Guo, Polaron effects on the optical rectification in asymmetrical semi-parabolic quantum wells. Physica B 387, 276 (2007). https://doi.org/10.1016/j.physb.2006.04.016

    Article  ADS  Google Scholar 

  54. H. Dakhlaoui, Linear and nonlinear optical absorption coefficients and refractive index changes in gan/algan double quantum wells. J. Appl. Phys. 117, 135705 (2015). https://doi.org/10.1063/1.4916752

    Article  ADS  Google Scholar 

  55. K. Guo, Z. Zhang, S. Mou, B. Xiao, Effect of hydrogenic impurity on linear and nonlinear optical absorption coefficients and refractive index changes in a quantum dot. J. Opt. 17, 055504 (2015). https://doi.org/10.1088/2040-8978/17/5/055504

    Article  ADS  Google Scholar 

  56. E. Al, F. Ungan, U. Yesilgul, E. Kasapoglu, H. Sari, I. Sökmen, Effects of applied electric and magnetic fields on the nonlinear optical properties of asymmetric gaas/ga1-xalxas double inverse parabolic quantum well. Opt. Materials 47, 1 (2015). https://doi.org/10.1016/j.optmat.2015.06.048

    Article  ADS  Google Scholar 

  57. U. Yesilgul, E. Al, J. Martínez-Orozco, R. Restrepo, M. Mora-Ramos, C. Duque, F. Ungan, E. Kasapoglu, Linear and nonlinear optical properties in an asymmetric double quantum well under intense laser field: effects of applied electric and magnetic fields. Opt. Materials 58, 107 (2016). https://doi.org/10.1016/j.optmat.2016.03.043

    Article  ADS  Google Scholar 

  58. M. Karimi, G. Rezaei, Effects of external electric and magnetic fields on the linear and nonlinear intersubband optical properties of finite semi-parabolic quantum dots. Physica B 406, 4423 (2011). https://doi.org/10.1016/j.physb.2011.08.105

    Article  ADS  Google Scholar 

  59. Z. Li, X. Hong-Jing, Studies on the second-order nonlinear optical properties of parabolic and semi-parabolic quantum wells with applied electric fields. Commun. Theoretical Phys. 41, 761 (2004). https://doi.org/10.1088/0253-6102/41/5/761

    Article  ADS  Google Scholar 

  60. G.-H. Wang, Q. Guo, K.-X. Guo, Third-order nonlinear optical properties of parabolic and semiparabolic quantum wells, physica status solidi (b) 238, 75 ( 2003), https://doi.org/10.1002/pssb.200301753https://onlinelibrary.wiley.com/doi/pdf/10.1002

  61. i. d. I. Karabulut, U. Atav, H. Şafak, Comment on electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells, Phys. Rev. B 72, 207301 (2005).https://doi.org/10.1103/PhysRevB.72.207301

  62. S. Chil Lee, J. Woo Kang, H. Soo Ahn, M. Yang, N. Lyong Kang, S. W. Kim, Optically detected electrophonon resonance effects in quantum wells, Physica E: Low-dimensional Systems and Nanostructures 28, 402 ( 2005)https://doi.org/10.1016/j.physe.2005.04.010

  63. N.D. Hien, Comparison of the contribution of different types of interface-optical phonon modes to electron-phonon scattering in a quasi-two-dimensional system. Physica B 621, 413317 (2021). https://doi.org/10.1016/j.physb.2021.413317

    Article  Google Scholar 

  64. N.D. Hien, Influence of the confining potential on the linewidth of a quantum well. Superlattices Microstruct. 160, 107068 (2021). https://doi.org/10.1016/j.spmi.2021.107068

    Article  Google Scholar 

  65. N. D. Hien, L. Dinh, N. T. Tuyet Anh, Influence of confined optical phonons on the magneto-optical properties in parabolic quantum wells, Journal of Physics and Chemistry of Solids 145, 109501 ( 2020)https://doi.org/10.1016/j.jpcs.2020.109501

  66. X. Yu, Y. Yu, Optical absorptions in asymmetrical semi-parabolic quantum wells. Superlattices Microstruct. 62, 225 (2013). https://doi.org/10.1016/j.spmi.2013.07.021

    Article  ADS  Google Scholar 

  67. N.D. Hien, Comparison of the magneto-optical properties of the semi-parabolic well with those of the parabolic and rectangular wells under the combined influences of aluminum concentration and hydrostatic pressure. J. Phys. Chem. Solids 161, 110456 (2022). https://doi.org/10.1016/j.jpcs.2021.110456

    Article  Google Scholar 

  68. L. T. Quynh Huong, L. N. Minh, L. Dinh, N. D. Hien, Cyclotron-interface phonon resonance line-width in asymmetric semiparabolic quantum wells, Journal of Physics and Chemistry of Solids 152, 109967 ( 2021)https://doi.org/10.1016/j.jpcs.2021.109967

  69. D.D.J. Alamino-Ortega, Y. Aguilar-Rodrıguez, Hacia una ense nanza de la física apegada a sus fundamentos. Rev. Cubana Fis 35, E50 (2018)

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  1. Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam

    Nguyen Dinh Hien

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NDH: software, methodology, investigation, conceptualization, supervision, writing—original draft, writing—review and editing, and validation, funding acquisition, writing—original draft.

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Hien, N.D. Comparison of the nonlinear optical properties of asymmetrical and symmetrical quantum wells. Eur. Phys. J. B 95, 192 (2022). https://doi.org/10.1140/epjb/s10051-022-00455-1

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