[PDF]    http://dx.doi.org/10.3952/lithjphys.45402

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 45, 225–233 (2005)


COMPLEX PADÉ APPROXIMANTS FOR BIDIRECTIONAL AND NONPARAXIAL BEAM PROPAGATION METHOD
R. Petruškevičius
Institute of Physics, Savanorių 231, LT-02300 Vilnius, Lithuania
E-mail: raimisp@ktl.mii.lt

Received 31 January 2005

The nonparaxial and bidirectional beam propagation method suitable for modelling near-field and high numerical aperture (NA) optical storage systems is suggested for 2D geometry and TE polarization of incident light beam. The complex Padé approximants are introduced for correct approximation of evanescent field in the near-field optics. Pole–zero shifting and branch-cut rotation methods of building complex Padé approximants are studied and compared.
Keywords: near-field optical storage, bidirectional beam propagation method, nonparaxial beam propagation, evanescent waves, complex Padé approximants
PACS: 42.25.Bs, 42.40.Ht, 42.79.Vb


KOMPLEKSINIAI PADÉ ARTINIAI DVIEJŲ KRYPČIŲ IR NEGRETAAŠIAME PLUOŠTO SKLIDIMO METODE
R. Petruškevičius
Fizikos institutas, Vilnius, Lietuva

Negretaašis ir dviejų krypčių pluošto sklidimo metodas, tinkantis modeliuoti artimo lauko ir didelės skaitmeninės apertūros optinio duomenų užrašymo sistemas, pasiūlytas 2D geometrijai ir TE krentančio pluošto poliarizacijai. Kompleksiniai Padé artiniai įvesti korektiškam nespindulinio lauko aprašymui artimo lauko optikoje. Nagrinėti ir palyginti polių–nulių postūmio ir šaknies pjūvio sukimo kompleksinių Padé artinių suformavimo metodai.


References / Nuorodos

[1] E. Betzig, J.K. Trautman, R. Wolfe, E.M. Gyorgy, P.L. Finn, M.H. Kryder, and C.-H. Chang, Near-field magneto-optics and high density data storage, Appl. Phys. Lett. 61, 142–144 (1992),
http://dx.doi.org/10.1063/1.108198
[2] K. Kato, S. Ichihara, M. Oumi, H. Maeda, T. Niwa, T. Mitsuoka, K. Nakajima, T. Ohkubo, and K. Itao, Signal readout using small near-field optical head with horizontal light introduction through optical fiber, Jpn. J. Appl. Phys. 42, 5102–5106 (2003),
http://dx.doi.org/10.1143/JJAP.42.5102
[3] K. Goto, Y.-J. Kim, S. Mitrugi, K. Kurihara, and T. Horibe, Microoptical two-dimensional devices for the optical memory head of ultrahigh data transfer rate and density system using a vertical cavity surface emitting laser (VCSEL) array, Jpn. J. Appl. Phys. 41, 4835–4840 (2002),
http://dx.doi.org/10.1143/JJAP.41.4835
[4] J. Hashizume, S. Shinada, and F. Koyama, Near-field optical probing using a microaperture GaInAs/GaAs surface emitting laser, Jpn. J. Appl. Phys. 41, L700–L702 (2002),
http://dx.doi.org/10.1143/JJAP.41.L700
[5] B.D. Terris, H.J. Mamin, and D. Rugar, Near-field optical data storage. Appl. Phys. Lett. 68, 141–143 (1996),
http://dx.doi.org/10.1063/1.116127
[6] T.D. Milster, J.S. Jo, and K. Hirota, Roles of propagating and evanescent waves in solid immersion lens systems, Appl. Opt. 38, 5046–5067 (1999),
http://dx.doi.org/10.1364/AO.38.005046
[7] J. Tominaga, T. Nakano, and N. Atoda, An approach for recording and readout beyond the diffraction limit with an Sb thin film, Appl. Phys. Lett. 73, 2078–2080 (1998),
http://dx.doi.org/10.1063/1.122383
[8] T. Nakano, Y. Yamakawa, J. Tominaga, and N. Atoda, Near-field optical simulation of super-resolution near-field structure disks, Jpn. J. Appl. Phys. 40, 1531–1535 (2001),
http://dx.doi.org/10.1143/JJAP.40.1531
[9] W.-C. Lin and D.P. Tsai, Nonlinear near-field optical effects of the AgOx-type super-resolution near-field structure, Jpn. J. Appl. Phys. 42, 1031–1032 (2003),
http://dx.doi.org/10.1143/JJAP.42.1031
[10] J. Guerra, D. Vezenov, P. Sullivan, W. Haimberger, and L. Thulin, Near-field optical recording without low-flying heads: Integral near-field optical (INFO) media, Jpn. J. Appl. Phys. 41, 1866–1875 (2002),
http://dx.doi.org/10.1143/JJAP.41.1866
[11] A. Taflove and S.C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Boston, 2000)
[12] K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag. 14, 302–307 (1966),
http://dx.doi.org/10.1109/TAP.1966.1138693
[13] H.J.W.M. Hoekstra, On beam propagation methods for modeling in integrated optics, Opt. Quantum Electron. 29, 157–171, 1997,
http://dx.doi.org/10.1023/A:1018549904885
[14] R. Scarmozzino, A. Gopinath, R. Pregla, and S. Helfert, Numerical techniques for modeling guided-wave photonic devices, IEEE J. Select. Top. Quantum Electron. 6, 150–162 (2000),
http://dx.doi.org/10.1109/2944.826883
[15] J. Yamauchi, Propagating Beam Analysis of Optical Waveguides (Research Studies Press, Baldock, 2003)
[16] M.D. Feit and J.A. Fleck, Light propagation in graded-index optical fibers, Appl. Opt. 17, 3990–3998 (1978),
http://dx.doi.org/10.1364/AO.17.003990
[17] Y. Chung and N. Dagli, An assessment of finite difference beam propagation method, IEEE J. Quantum Electron. 26, 1335–1339 (1990),
http://dx.doi.org/10.1109/3.59679
[18] W.P. Huang, Simulation of three-dimensional optical waveguides by full-vector beam propagation method, IEEE J. Quantum Electron. 29, 2639–2649 (1993),
http://dx.doi.org/10.1109/3.250386
[19] E.E. Kriezis and A.G. Papagiannakis, A three-dimensional full vectorial beam propagation method for z-dependent structures, IEEE J. Quantum Electron. 33, 883–890 (1997),
http://dx.doi.org/10.1109/3.572165
[20] F. Fogli, G. Bellanca, P. Bassi, I. Madden, and W. Johnstone, Highly efficient full-vectorial 3-D BPM modeling of fiber to planar waveguide coupler, J. Lightwave Tech. 17, 136–143 (1999),
http://dx.doi.org/10.1109/50.737433
[21] Y.-P. Chiou and H.-C. Chang, Analysis of optical waveguide discontinuities using the Padé approximants, IEEE Ph. Tech. Lett. 9, 964–966 (1997),
http://dx.doi.org/10.1109/68.593367
[22] S.F. Helfert and R. Pregla, The method of lines: A versatile tool for the analysis of waveguide structures, Electromagnetics 22, 615–637 (2002),
http://dx.doi.org/10.1080/02726340290084166
[23] G.R. Hadley, Wide-angle beam propagation using Padé approximant operators, Opt. Lett. 17, 1426–1428 (1992),
http://dx.doi.org/10.1364/OL.17.001426
[24] F. Ma, C.L. Xu, and W.P. Huang, Wide-angle full vectorial beam propagation method, IEE Proc. Optoelectron. 143, 139–143 (1996),
http://dx.doi.org/10.1049/ip-opt:19960123
[25] R. Petruškevičius, G. Bellanca, and P. Bassi, BPM modeling of three-wave interaction in periodically poled second-order nonlinear materials, Lithuanian J. Phys. 38, 168–176 (1998)
[26] G.R. Hadley, Multistep method for wide-angle beam propagation, Opt. Lett. 17, 1743–1745 (1992),
http://dx.doi.org/10.1364/OL.17.001743
[27] H. Rao, M.J. Stell, R. Scarmozzino, and R.M. Osgood, Complex propagators for evanescent waves in bidirectional beam propagation method, J. Lightwave Tech. 18, 1155–1160 (2000),
http://dx.doi.org/10.1109/50.857762
[28] C. Vassallo, Limitations of the wide-angle beam propagation method in nonuniform systems, J. Opt. Soc. Am. A 13, 761–770 (1996),
http://dx.doi.org/10.1364/JOSAA.13.000761
[29] M. Born and E. Wolf, Principles of Optics (Pergamon Press, Oxford, 1980)
[30] F.A. Milinazzo, C.A. Zala, and G.H. Brooke, Rational square-root approximations for parabolic equation algorithms, J. Acoust. Soc. Am. 101, 760–766 (1997),
http://dx.doi.org/10.1121/1.418038
[31] H. El-Refaei, D. Yevick, and I. Betty, Stable and noniterative bidirectional beam propagation method, IEEE Ph. Tech. Lett. 12, 389–391 (2000),
http://dx.doi.org/10.1109/68.839028
[32] H. Rao, R. Scarmozzino, and R. Osgood, A bidirectional beam propagation method for multiple dielectric interfaces, IEEE Ph. Tech. Lett. 11, 830–832 (1999),
http://dx.doi.org/10.1109/68.769722
[33] A. Locatelli, F.-M. Pigozzo, F. Baranio, D. Modotto, A.-D. Capobianco, and C. De Angelis, Bidirectional beam propagation method for second-harmonic generation in engineered multilayered waveguides, Opt. Quantum. Electron. 35, 429–452 (2003),
http://dx.doi.org/10.1023/A:1022965521197
[34] P.L. Ho and Y.Y. Lu, A stable bidirectional propagation method based on scattering operators, IEEE Ph. Tech. Lett. 13, 1316–1318 (2001),
http://dx.doi.org/10.1109/68.969893
[35] A. Locatelli, D. Modotto, C. De Angelis, F.-M. Pigozzo, and A.-D. Capobianco, Nonlinear bidirectional beam propagation method based on scattering operators for periodic microstructured waveguides, J. Opt. Soc. Am. B 20, 1724–1731 (2003),
http://dx.doi.org/10.1364/JOSAB.20.001724