Abstract
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.
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Arnold, A., Schulte, M.: Transparent boundary conditions for quantum-waveguide simulations. Math. Comput. Simul. 79, 898–905 (2008)
Björck, Å., Hammarling, S.: A Schur method for the square root of a matrix. Linear Algebra Its Appl. 52–53, 127–140 (1983)
Chen, Y., Wu, T.X.: Radiation properties in electron waveguides. J. Appl. Phys. 101, 024304 (2007)
Deadman, E., Higham, N., Ralha, R.: Blocked Schur Algorithmsfor Computing the Matrix Square Root. Springer, Berlin, LNCS 7782, pp. 171–182 (2013)
El-Refaei, H., Yevick, D., Betty, I.: Stable and noniterative bidirectional beam propagation method. IEEE Photon. Technol. Lett. 12, 389–391 391 (2000)
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)
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)
Higham, N.: Functions of Matrices: Theory and Computation. SIAM, Philadelphia (2008)
Ho, P.L., Lu, Y.Y.: A stable bidirectional propagation method based on scattering operators. IEEE Photon. Technol. Lett. 13, 1316–1318 (2001)
Koshiba, M., Tsuji, Y.: A wide-angle finite-element beam propagation method. IEEE Photon. Technol. Lett. 8, 1208–1210 (1996)
Lu, Y.Y.: A Padé approximation method for square roots of symmetric positive definite matrices. SIAM J. Matrix Anal. Appl. 19, 833–845 (1998)
Lu, Y.Y.: A complex coefficient rational approximation of \(\sqrt{1+ x}\). Appl. Numer. Math. 27, 141–154 (1998)
Obayya, S.S.A.: Computational Photonics. Wiley, New York (2010)
Obayya, S.S.A.: Novel finite element analysis of optical waveguide discontinuity problems. J. Lightwave Technol. 22, 1420–1425 (2004)
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)
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)
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)
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Said, A.M.A., Obayya, S.S.A. Efficient analysis of electron waveguides with multiple discontinuities. Opt Quant Electron 47, 1333–1338 (2015). https://doi.org/10.1007/s11082-014-0055-4
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DOI: https://doi.org/10.1007/s11082-014-0055-4