Abstract

Chiral media are characterized by preferential interaction with either left- or right- circularly polarized radiation, whereupon an optically active medium and its enantiomorph possess rotary powers of opposing sign due to mirror handedness of their micro- or nano-structures. Here, we report on the first time-resolved investigations of few-cycle pulse propagation along the axis of a sub-wavelength size helix. Time-resolved measurements of the electric field pulse scattered from the helix enable temporal discriminations of transient scattering mechanisms within the helix. Our main finding is that polarization circularization associated with axial propagation through the helix is non-instantaneous, and requires several picoseconds to develop before reaching steady state values. Using a 3D FDTD model, we describe the field and Poynting vector dynamics within the helix leading to steady state polarization circularization. Our conclusions not only support the established picture that optical activity arises from multiple scattering within the helical structure, but also show that this operative mechanism requires a finite time to induce steady state polarization circularization.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2005 (1)

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

2003 (2)

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

1995 (2)

F. Guérin, P. Bannelier, and M. Labeyrie, "Scattering of electromagnetic waves by helices and application of the modelling of chiral composites. I: simple effective-medium theories," J. Phys. D 28, 623-6421995.
[CrossRef]

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

1994 (1)

V. V. Varadan, R. Ro, and V. K. Varadan, "Measurement of the electromagnetic properties of chiral composite materials in the 8-40 GHz range," Radio. Sci. 29, 9-22 (1994).
[CrossRef]

1993 (1)

1988 (2)

P. Chiappetta and B. Torresani, "Electromagnetic scattering from a dielectric helix," Appl. Opt. 27, 4856-4860 (1988).
[CrossRef] [PubMed]

R. A. Hegstrom, J. P. Chamberlain, K. Seto, and R. G. Watson, "Mapping the weak chirality in atoms," Am. J. Phys. 56, 1086-1092 (1988).
[CrossRef]

1986 (1)

M. Bouchiat and L. Pottier, "Optical experiments and weak interactions," Science 234, 1203-1210 (1986).
[CrossRef] [PubMed]

1984 (1)

W. M. McClain, J. A. Schauerte, and R. A. Harris, "Model calculations of intramolecular interference effects in Rayleigh scattering from solutions of macromolecules," J. Chem. Phys. 80, 606-616 (1984).
[CrossRef]

1980 (1)

15. C. Bustamante, M. F. Maestre, and I. TinocoJr., "Circular intensity differential scattering of light by helical structures. I. Theory," J. Chem. Phys. 73, 4273-4281 (1980); C. Bustamante, M. F. Maestre, and I. Tinoco Jr., "Circular intensity differential scattering of light by helical structures. II. Applications," J. Chem. Phys. 73, 6046-6055 (1980); C. Bustamante, I. Tinoco Jr., and M. F. Maestre, "Circular intensity differential scattering of light by helical structures. III. A general polarizability tensor and anomalous scattering," J. Chem. Phys. 74, 4839-4850 (1981).
[CrossRef]

1979 (1)

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On Electromagnetic Waves in Chiral Media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

1972 (1)

A. G. Cha, "Wave Propagation on Helical Antennas," IEEE Trans. Antennas Propag. 20, 556-560 (1972).
[CrossRef]

1968 (1)

S. F. Mason, "Optical Activity and Molecular Dissymmetry," Contemp. Phys. 9, 239-256 (1968).
[CrossRef]

1957 (1)

I. Tinoco and M. P. Freeman, "The optical activity of oriented copper helices. I. Experimental," J. Phys. Chem. 61, 1196-1200 (1957).
[CrossRef]

1942 (1)

F. Perrin, "Polarization of Light Scattered by Isotropic Opalescent Media," J. Chem. Phys. 10, 415-427 (1942).
[CrossRef]

1920 (1)

K. F. Lindman, "Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarization der elektromagnetische Wellen," Ann. Phys. 63, 621-644 (1920).
[CrossRef]

1898 (1)

J. C. Bose, "On the rotation of plane of polarisation of electric waves by a twisted structure," Proc. R. Soc. London A 63, 146-152 (1898).
[CrossRef]

1848 (1)

L. Pasteur, "Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire," Ann. Chim. 24, 442-459 (1848).

1822 (1)

A. Fresnel, "Sur la double refraction particulière que présente le cristal de roche dans la direction de son axe," Bull. Soc. Philom. 191-198 (1822).

1811 (1)

F. Arago, "Mémoire sur une modification remarquable qu’éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique," Mém. Inst. France, Part I12 (1811).

Arago, F.

F. Arago, "Mémoire sur une modification remarquable qu’éprouvent les rayons lumineux dans leur passage à travers certains corps diaphanes, et sur quelques autres nouveaux phénomènes d’optique," Mém. Inst. France, Part I12 (1811).

Bagnall, D. M.

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

Bannelier, P.

F. Guérin, P. Bannelier, and M. Labeyrie, "Scattering of electromagnetic waves by helices and application of the modelling of chiral composites. I: simple effective-medium theories," J. Phys. D 28, 623-6421995.
[CrossRef]

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

Bose, J. C.

J. C. Bose, "On the rotation of plane of polarisation of electric waves by a twisted structure," Proc. R. Soc. London A 63, 146-152 (1898).
[CrossRef]

Bouchiat, M.

M. Bouchiat and L. Pottier, "Optical experiments and weak interactions," Science 234, 1203-1210 (1986).
[CrossRef] [PubMed]

Bustamante, C.

15. C. Bustamante, M. F. Maestre, and I. TinocoJr., "Circular intensity differential scattering of light by helical structures. I. Theory," J. Chem. Phys. 73, 4273-4281 (1980); C. Bustamante, M. F. Maestre, and I. Tinoco Jr., "Circular intensity differential scattering of light by helical structures. II. Applications," J. Chem. Phys. 73, 6046-6055 (1980); C. Bustamante, I. Tinoco Jr., and M. F. Maestre, "Circular intensity differential scattering of light by helical structures. III. A general polarizability tensor and anomalous scattering," J. Chem. Phys. 74, 4839-4850 (1981).
[CrossRef]

Cha, A. G.

A. G. Cha, "Wave Propagation on Helical Antennas," IEEE Trans. Antennas Propag. 20, 556-560 (1972).
[CrossRef]

Chamberlain, J. P.

R. A. Hegstrom, J. P. Chamberlain, K. Seto, and R. G. Watson, "Mapping the weak chirality in atoms," Am. J. Phys. 56, 1086-1092 (1988).
[CrossRef]

Chiappetta, P.

Coles, H. J.

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

Engheta, N.

Freeman, M. P.

I. Tinoco and M. P. Freeman, "The optical activity of oriented copper helices. I. Experimental," J. Phys. Chem. 61, 1196-1200 (1957).
[CrossRef]

Fresnel, A.

A. Fresnel, "Sur la double refraction particulière que présente le cristal de roche dans la direction de son axe," Bull. Soc. Philom. 191-198 (1822).

Ganne, J.-P.

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

Guérin, F.

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

F. Guérin, P. Bannelier, and M. Labeyrie, "Scattering of electromagnetic waves by helices and application of the modelling of chiral composites. I: simple effective-medium theories," J. Phys. D 28, 623-6421995.
[CrossRef]

Guillon, P.

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

Harris, R. A.

W. M. McClain, J. A. Schauerte, and R. A. Harris, "Model calculations of intramolecular interference effects in Rayleigh scattering from solutions of macromolecules," J. Chem. Phys. 80, 606-616 (1984).
[CrossRef]

Hegstrom, R. A.

R. A. Hegstrom, J. P. Chamberlain, K. Seto, and R. G. Watson, "Mapping the weak chirality in atoms," Am. J. Phys. 56, 1086-1092 (1988).
[CrossRef]

Ino, Y.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Jaggard, D. L.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On Electromagnetic Waves in Chiral Media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Jefimovs, K.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

Kauranen, M.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Kuwata-Gonokami, M.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Labeyrie, M.

F. Guérin, P. Bannelier, and M. Labeyrie, "Scattering of electromagnetic waves by helices and application of the modelling of chiral composites. I: simple effective-medium theories," J. Phys. D 28, 623-6421995.
[CrossRef]

F. Guérin, P. Bannelier, M. Labeyrie, J.-P. Ganne, and P. Guillon, "Scattering of electromagnetic waves by helices and applications to the modelling of chiral composites. II. Maxwell Garnett treatment," J. Phys. D 28, 643-656 (1995).
[CrossRef]

Lindman, K. F.

K. F. Lindman, "Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarization der elektromagnetische Wellen," Ann. Phys. 63, 621-644 (1920).
[CrossRef]

Maestre, M. F.

15. C. Bustamante, M. F. Maestre, and I. TinocoJr., "Circular intensity differential scattering of light by helical structures. I. Theory," J. Chem. Phys. 73, 4273-4281 (1980); C. Bustamante, M. F. Maestre, and I. Tinoco Jr., "Circular intensity differential scattering of light by helical structures. II. Applications," J. Chem. Phys. 73, 6046-6055 (1980); C. Bustamante, I. Tinoco Jr., and M. F. Maestre, "Circular intensity differential scattering of light by helical structures. III. A general polarizability tensor and anomalous scattering," J. Chem. Phys. 74, 4839-4850 (1981).
[CrossRef]

Mason, S. F.

S. F. Mason, "Optical Activity and Molecular Dissymmetry," Contemp. Phys. 9, 239-256 (1968).
[CrossRef]

McClain, W. M.

W. M. McClain, J. A. Schauerte, and R. A. Harris, "Model calculations of intramolecular interference effects in Rayleigh scattering from solutions of macromolecules," J. Chem. Phys. 80, 606-616 (1984).
[CrossRef]

Mickelson, A. R.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On Electromagnetic Waves in Chiral Media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Papas, C. H.

D. L. Jaggard, A. R. Mickelson, and C. H. Papas, "On Electromagnetic Waves in Chiral Media," Appl. Phys. 18, 211-216 (1979).
[CrossRef]

Papkostas, A.

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

Pasteur, L.

L. Pasteur, "Sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire," Ann. Chim. 24, 442-459 (1848).

Perrin, F.

F. Perrin, "Polarization of Light Scattered by Isotropic Opalescent Media," J. Chem. Phys. 10, 415-427 (1942).
[CrossRef]

Pottier, L.

M. Bouchiat and L. Pottier, "Optical experiments and weak interactions," Science 234, 1203-1210 (1986).
[CrossRef] [PubMed]

Potts, A.

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

Prosvirnin, S. L.

A. Papkostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical Manifestations of Planar Chirality," Phys. Rev. Lett. 90, 107404 (2003).
[CrossRef]

Ro, R.

V. V. Varadan, R. Ro, and V. K. Varadan, "Measurement of the electromagnetic properties of chiral composite materials in the 8-40 GHz range," Radio. Sci. 29, 9-22 (1994).
[CrossRef]

Saito, N.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Schauerte, J. A.

W. M. McClain, J. A. Schauerte, and R. A. Harris, "Model calculations of intramolecular interference effects in Rayleigh scattering from solutions of macromolecules," J. Chem. Phys. 80, 606-616 (1984).
[CrossRef]

Seto, K.

R. A. Hegstrom, J. P. Chamberlain, K. Seto, and R. G. Watson, "Mapping the weak chirality in atoms," Am. J. Phys. 56, 1086-1092 (1988).
[CrossRef]

Svirko, Y.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

Tinoco, I.

15. C. Bustamante, M. F. Maestre, and I. TinocoJr., "Circular intensity differential scattering of light by helical structures. I. Theory," J. Chem. Phys. 73, 4273-4281 (1980); C. Bustamante, M. F. Maestre, and I. Tinoco Jr., "Circular intensity differential scattering of light by helical structures. II. Applications," J. Chem. Phys. 73, 6046-6055 (1980); C. Bustamante, I. Tinoco Jr., and M. F. Maestre, "Circular intensity differential scattering of light by helical structures. III. A general polarizability tensor and anomalous scattering," J. Chem. Phys. 74, 4839-4850 (1981).
[CrossRef]

I. Tinoco and M. P. Freeman, "The optical activity of oriented copper helices. I. Experimental," J. Phys. Chem. 61, 1196-1200 (1957).
[CrossRef]

Torresani, B.

Turunen, J.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

Vahimaa, P.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

Vallius, T.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant Optical Activity in Quasi-Two-Dimensional Planer Nanostructures," Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003).
[CrossRef]

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Supplementary Material (1)

» Media 1: AVI (2091 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

(above) A diagram of the setup used to characterize the far-infrared on-axis transmission through a sub-wavelength helix. (below) The measured right circular Er (t) (solid line) and left circular El (t), (empty circles) electric field pulses through helices of various lengths, along with a reference pulse transmitted through the screening aperture. Note that Er (t) and El (t) are displayed 180° out of phase for illustrative purposes and clarity.

Fig. 2.
Fig. 2.

Trajectories of the tip of the electric field vector, E(f) = E (t) + E (t), for the transmission through the aperture, and helices having n = 4, 6, 8, 10, and 12.

Fig. 3.
Fig. 3.

(a). Degree of polarization circularization for the transmitted pulse through the aperture and helices having n = 4, 6, 8, and 12. (b). depicts the normalized time-partitioned Fourier spectra of the right-circularly polarized transmission through the 12 turn helix, using a Fourier window of 3.2 ps. The experimental transmission spectra show a cut off frequency νc = 0.74 ± 0.05 THz. This cut off behaviour can be understood by considering the guided modes in the helix. Approximating the helix as an infinite cylindrical waveguide, the helix has a cut off frequency of νc = 1.841c/(πd), where d is the inner diameter of the helix [27]. Using an inner helical diameter of 235 μm, νc = 0.75 THz is estimated, in excellent agreement with the experimental data. (c) The frequency-dependent imaginary refractive index difference between the RH and LH fields propagated through the helix calculated over the duration 0 < t < τ (labeled “transient”) and over the duration t > τ (labeled “steady state”).

Fig. 4.
Fig. 4.

A vector plot of the 3D FDTD-calculated electric field vector along the helical axis at times 0 ps, 4 ps, 7 ps, 14 ps, and 20 ps. The images include a cross-sectional view of the 15 turn helical structure employed in the simulation. The size parameters of the helix used in the simulations physically match those of the helix used in the experiments.

Fig. 5.
Fig. 5.

(a). The experimental and FDTD-calculated group delay is plotted versus n. (b). displays the experimental and calculated right-circular (blue) and left-circular (red) electric field pulses transmitted through an n = 12 helix. (c). The experimentally measured and 3D FDTD-calculated transmission power spectra for n = 12 are compared. The inset in (c) shows the calculated trajectory of the tip of the electric field vector for n = 12. (d) Calculated and experimental degree of polarization circularization for an n = 12 helix.

Fig. 6.
Fig. 6.

A plot of the electric field intensity at t = 14 ps along planes cutting through turn number 8, 9, 10, 11, and 12. The white arrows superimposed on the intensity plots indicate the orientation of the electric field vector on a plane. A representative plot of the Poynting vector at the plane cutting through turn number 12 shows the cycling behaviour of the electromagnetic energy flow in the helix.

Fig. 7.
Fig. 7.

(2.1MB) Movie of the calculated Poynting vector distributions from t = 5 ps to t = 12.5 ps within four planes perpendicular to the helical axis intersecting turns (a) 8, (b) 9, (c) 10, and (d) 11 of the helix. The helix is centred at (300 μm, 300 μm). The distributions are depicted from a viewpoint of an observer facing the wave propagation direction. The still frame shows the Poynting vector distributions at time t = 8.6 ps. [Media 1]

Fig. 8.
Fig. 8.

(a). several representative Poynting vector streamlines spanning n = 1 to n = 7 captured at an arbitrary time t = 10.6 ps calculated from the 3D FDTD simulations. Nearly all of the streamlines are scattered outside the helix. The width of the streamlines is proportional to the time rate of change of the energy density. The streamlines are depicted with a cross sectional view of the helical structure employed in the simulations. (b). A head-on perspective of the same vector streamlines shown in (a). (c) Shows four representative Poynting vector streamlines spanning n = 8 to n = 12 captured at t = 10.6 ps calculated from the 3D FDTD simulations. The yellow and red Poynting vector streamlines are scattered outside the helix after the third turn, while the green and blue streamlines are confined within the helix throughout the 4 turns. (d) Shows a head-on perspective of the same vector streamlines shown in (c). (e) Based on the spatial locations where energy flow abruptly changes direction, we construct the fundamental mode consisting of four points A, B, C, and D, coinciding with the locations where the Poynting vector changes direction.

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