Optical and Quantum Electronics

, Volume 47, Issue 6, pp 1333–1338 | Cite as

Efficient analysis of electron waveguides with multiple discontinuities



Blocked Schur finite-element bidirectional beam propagation method (BS-FE-BiBPM) is introduced for the solution of electron waveguides with multiple discontinuities. Scattering properties could be accurately calculated using BiBPM based on time-independent Schrödinger equation while Blocked Schur algorithm is used for accurate computation of the characteristic matrix square root. The suggested approach substantially reduces the computational time while preserving very high efficiency.


Time-independent Schrödinger equation Quantum waveguide transistor BiBPM Padé approximation 


  1. Arnold, A., Schulte, M.: Transparent boundary conditions for quantum-waveguide simulations. Math. Comput. Simul. 79, 898–905 (2008)CrossRefMATHMathSciNetGoogle Scholar
  2. Björck, Å., Hammarling, S.: A Schur method for the square root of a matrix. Linear Algebra Its Appl. 52–53, 127–140 (1983)Google Scholar
  3. Chen, Y., Wu, T.X.: Radiation properties in electron waveguides. J. Appl. Phys. 101, 024304 (2007)CrossRefADSGoogle Scholar
  4. Deadman, E., Higham, N., Ralha, R.: Blocked Schur Algorithmsfor Computing the Matrix Square Root. Springer, Berlin, LNCS 7782, pp. 171–182 (2013)Google Scholar
  5. El-Refaei, H., Yevick, D., Betty, I.: Stable and noniterative bidirectional beam propagation method. IEEE Photon. Technol. Lett. 12, 389–391 391 (2000)CrossRefADSGoogle Scholar
  6. Gotoh, H., Koshiba, M., Kaji, R.: Finite element solution of electron waveguide discontinuities and its application to quantum field effect directional couplers. IEEE J. Quantum Electron. 32, 1826–1832 (1996)CrossRefADSGoogle Scholar
  7. Gotoh, H., Koshiba, M., Tsuji, Y.: Finite-element time-domain beam propagation method with perfectly matched layer for electron waveguide simulations. IEICE Electron. Express 8, 1361–1366 (2011)CrossRefGoogle Scholar
  8. Higham, N.: Functions of Matrices: Theory and Computation. SIAM, Philadelphia (2008)CrossRefGoogle Scholar
  9. Ho, P.L., Lu, Y.Y.: A stable bidirectional propagation method based on scattering operators. IEEE Photon. Technol. Lett. 13, 1316–1318 (2001)CrossRefADSGoogle Scholar
  10. Koshiba, M., Tsuji, Y.: A wide-angle finite-element beam propagation method. IEEE Photon. Technol. Lett. 8, 1208–1210 (1996)CrossRefADSGoogle Scholar
  11. Lu, Y.Y.: A Padé approximation method for square roots of symmetric positive definite matrices. SIAM J. Matrix Anal. Appl. 19, 833–845 (1998)CrossRefMATHMathSciNetGoogle Scholar
  12. Lu, Y.Y.: A complex coefficient rational approximation of \(\sqrt{1+ x}\). Appl. Numer. Math. 27, 141–154 (1998)Google Scholar
  13. Obayya, S.S.A.: Computational Photonics. Wiley, New York (2010)CrossRefGoogle Scholar
  14. Obayya, S.S.A.: Novel finite element analysis of optical waveguide discontinuity problems. J. Lightwave Technol. 22, 1420–1425 (2004)Google Scholar
  15. Rahman, B.M.A., Leung, D.M.H., Obayya, S.S.A., Grattan, K.T.V.: Numerical analysis of bent waveguides: bending loss, transmission loss, mode coupling, and polarization coupling. Appl. Opt. 47, 2961–2970 (2008)CrossRefADSGoogle Scholar
  16. Rajarajan, M., Obayya, S., Rahman, B., Grattan, K., El-Mikali, H.: Characterisation of low-loss waveguide bends with offset-optimisation for compact photonic integrated circuits. IEE Proc. Optoelectron. 147, 382–388 (2000)CrossRefGoogle Scholar
  17. Zhang, H., Mu, J., Huang, W.-P.: Assessment of rational approximations for square root operator in bidirectional beam propagation method. J. Lightwave Technol. 26, 600–607 (2008)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Center for Photonics and Smart MaterialsZewail City of Science and TechnologyGizaEgypt

Personalised recommendations