Abstract

Femtosecond optical pulses were used to generate THz-frequency phonon polariton waves in a 50 micrometer lithium niobate slab, which acts as a subwavelength, anisotropic planar waveguide. The spatial and temporal electric field profiles of the THz waves were recorded for different propagation directions using a polarization gating imaging system, and experimental dispersion curves were determined via a two-dimensional Fourier transform. Dispersion relations for an anisotropic slab waveguide were derived via analytical analysis and found to be in excellent agreement with all observed experimental modes. From the dispersion relations, we analyze the propagation-direction-dependent behavior, effective refractive index values, and generation efficiencies for THz-frequency modes in the subwavelength, anisotropic slab waveguide.

© 2010 OSA

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  3. N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
    [CrossRef]
  4. T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
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  5. T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
    [CrossRef]
  6. T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
    [CrossRef]
  7. Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
    [CrossRef]
  8. D. Auston and M. Nuss, “Electrooptic Generation and Detection of Femtosecond Electrical Transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
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  9. Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  22. A. S. Barker and R. Loudon, “Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
    [CrossRef]
  23. N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
    [CrossRef] [PubMed]
  24. S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
    [CrossRef]
  25. D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63(2), 138–145 (1973).
    [CrossRef]
  26. W. K. Burns and J. Warner, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64(4), 441–446 (1974).
    [CrossRef]
  27. V. Ramaswamy, “Propagation in asymmetrical anisotropic film waveguides,” Appl. Opt. 13(6), 1363–1371 (1974).
    [CrossRef] [PubMed]
  28. S. Nemoto and T. Makimoto, “Further discussion of the relationship between phase and group indices in anisotropic inhomogeneous guiding media,” J. Opt. Soc. Am. 67(9), 1281–1283 (1977).
    [CrossRef]
  29. D. Marcuse, “Modes of a symmetric slab optical waveguide in birefringent media-Part I: Optical axis not in plane of slab,” IEEE J. Quantum Electron. 14(10), 736–741 (1978).
    [CrossRef]
  30. D. Marcuse and I. P. Kaminow, “Modes of a Symmetric Slab Optical Waveguide in Birefringent Media Part II: Slab with Coplanar Optical Axis,” IEEE J. Quantum Electron. 15(2), 92–101 (1979).
    [CrossRef]

2010

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

2009

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

2008

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

2007

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

2004

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

2003

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
[CrossRef] [PubMed]

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68(5), 054301 (2003).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

2002

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

2000

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

1999

R. M. Koehl, S. Adachi, and K. A. Nelson, “Real-Space Polariton Wave Packet Imaging,” J. Chem. Phys. 110(3), 1317–1320 (1999).
[CrossRef]

1992

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
[CrossRef]

1988

D. Auston and M. Nuss, “Electrooptic Generation and Detection of Femtosecond Electrical Transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

D. H. Auston and M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

1985

Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
[CrossRef]

1984

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

1979

D. Marcuse and I. P. Kaminow, “Modes of a Symmetric Slab Optical Waveguide in Birefringent Media Part II: Slab with Coplanar Optical Axis,” IEEE J. Quantum Electron. 15(2), 92–101 (1979).
[CrossRef]

1978

D. Marcuse, “Modes of a symmetric slab optical waveguide in birefringent media-Part I: Optical axis not in plane of slab,” IEEE J. Quantum Electron. 14(10), 736–741 (1978).
[CrossRef]

1977

S. Nemoto and T. Makimoto, “Further discussion of the relationship between phase and group indices in anisotropic inhomogeneous guiding media,” J. Opt. Soc. Am. 67(9), 1281–1283 (1977).
[CrossRef]

1974

W. K. Burns and J. Warner, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64(4), 441–446 (1974).
[CrossRef]

V. Ramaswamy, “Propagation in asymmetrical anisotropic film waveguides,” Appl. Opt. 13(6), 1363–1371 (1974).
[CrossRef] [PubMed]

1973

D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63(2), 138–145 (1973).
[CrossRef]

1972

S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
[CrossRef]

1967

A. S. Barker and R. Loudon, “Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

Adachi, S.

R. M. Koehl, S. Adachi, and K. A. Nelson, “Real-Space Polariton Wave Packet Imaging,” J. Chem. Phys. 110(3), 1317–1320 (1999).
[CrossRef]

Almási, G.

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Auston, D.

D. Auston and M. Nuss, “Electrooptic Generation and Detection of Femtosecond Electrical Transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

Auston, D. H.

D. H. Auston and M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

Barker, A. S.

A. S. Barker and R. Loudon, “Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

Bartal, B.

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Bawendi, M. G.

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

Burns, W. K.

W. K. Burns and J. Warner, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64(4), 441–446 (1974).
[CrossRef]

Cheung, K. P.

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

Crow, J. D.

S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
[CrossRef]

Dorn, A.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

Dougherty, T. P.

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
[CrossRef]

Feurer, T.

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

Galvanauskas, A.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Gamble, E. B.

Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
[CrossRef]

Harris, J. H.

D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63(2), 138–145 (1973).
[CrossRef]

Hebling, J.

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Hoffmann, M. C.

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

Kaminow, I. P.

D. Marcuse and I. P. Kaminow, “Modes of a Symmetric Slab Optical Waveguide in Birefringent Media Part II: Slab with Coplanar Optical Axis,” IEEE J. Quantum Electron. 15(2), 92–101 (1979).
[CrossRef]

Keith, A.

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

Kleinman, D. A.

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

Koehl, R. M.

R. M. Koehl, S. Adachi, and K. A. Nelson, “Real-Space Polariton Wave Packet Imaging,” J. Chem. Phys. 110(3), 1317–1320 (1999).
[CrossRef]

Kuhl, J.

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Lee, Y. S.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Lin, K. H.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

Lin, K.-H.

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[CrossRef]

Loudon, R.

A. S. Barker and R. Loudon, “Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

Makimoto, T.

S. Nemoto and T. Makimoto, “Further discussion of the relationship between phase and group indices in anisotropic inhomogeneous guiding media,” J. Opt. Soc. Am. 67(9), 1281–1283 (1977).
[CrossRef]

Marcuse, D.

D. Marcuse and I. P. Kaminow, “Modes of a Symmetric Slab Optical Waveguide in Birefringent Media Part II: Slab with Coplanar Optical Axis,” IEEE J. Quantum Electron. 15(2), 92–101 (1979).
[CrossRef]

D. Marcuse, “Modes of a symmetric slab optical waveguide in birefringent media-Part I: Optical axis not in plane of slab,” IEEE J. Quantum Electron. 14(10), 736–741 (1978).
[CrossRef]

Meade, T.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Merlin, R.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68(5), 054301 (2003).
[CrossRef]

Müller, F.

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

Nelson, K.

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

Nelson, K. A.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[CrossRef]

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

R. M. Koehl, S. Adachi, and K. A. Nelson, “Real-Space Polariton Wave Packet Imaging,” J. Chem. Phys. 110(3), 1317–1320 (1999).
[CrossRef]

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
[CrossRef]

Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
[CrossRef]

Nemoto, S.

S. Nemoto and T. Makimoto, “Further discussion of the relationship between phase and group indices in anisotropic inhomogeneous guiding media,” J. Opt. Soc. Am. 67(9), 1281–1283 (1977).
[CrossRef]

Norris, T. B.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Nuss, M.

D. Auston and M. Nuss, “Electrooptic Generation and Detection of Femtosecond Electrical Transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

Nuss, M. C.

D. H. Auston and M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

Peier, P.

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

Perlin, V.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Pilz, S.

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

Ramaswamy, V.

V. Ramaswamy, “Propagation in asymmetrical anisotropic film waveguides,” Appl. Opt. 13(6), 1363–1371 (1974).
[CrossRef] [PubMed]

Russo, D. P. G.

D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63(2), 138–145 (1973).
[CrossRef]

Shah, M. L.

S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
[CrossRef]

Statz, E.

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

Statz, E. R.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

Stepanov, A. G.

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Stoyanov, N. S.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

Tait, C. R.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Valdmains, J. A.

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

Vaughan, J. C.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
[CrossRef] [PubMed]

Wahlstrand, J. K.

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68(5), 054301 (2003).
[CrossRef]

Wang, S.

S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
[CrossRef]

Ward, D.

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

Ward, D. W.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

Warner, J.

W. K. Burns and J. Warner, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64(4), 441–446 (1974).
[CrossRef]

Werley, C. A.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[CrossRef]

Wiederrecht, G. P.

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
[CrossRef]

Winful, H.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

Wu, Q.

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

Yan, Y. X.

Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
[CrossRef]

Yeh, K. L.

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

Annu. Rev. Mater. Res.

T. Feurer, N. S. Stoyanov, D. W. Ward, J. C. Vaughan, E. R. Statz, and K. A. Nelson, “Terahertz Polaritonics,” Annu. Rev. Mater. Res. 37(1), 317–350 (2007).
[CrossRef]

Appl. Opt.

V. Ramaswamy, “Propagation in asymmetrical anisotropic film waveguides,” Appl. Opt. 13(6), 1363–1371 (1974).
[CrossRef] [PubMed]

Appl. Phys. B

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[CrossRef]

Appl. Phys. Lett.

K. L. Yeh, M. C. Hoffmann, J. Hebling, and A. Keith, “Generation of 10 μJ ultrashort terahertz pulses by optical rectification,” Appl. Phys. Lett. 90(17), 171121 (2007).
[CrossRef]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Generation of multicycle THz phonon-polariton waves in a planar waveguide by tilted optical pulse fronts,” Appl. Phys. Lett. 95(10), 103304 (2009).
[CrossRef]

N. S. Stoyanov, T. Feurer, D. W. Ward, and K. A. Nelson, “Integrated diffractive terahertz elements,” Appl. Phys. Lett. 82(5), 674–676 (2003).
[CrossRef]

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett. 76(18), 2505–2507 (2000).
[CrossRef]

IEEE J. Quantum Electron.

D. Auston and M. Nuss, “Electrooptic Generation and Detection of Femtosecond Electrical Transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

S. Wang, M. L. Shah, and J. D. Crow, “Wave propagation in thin film optical waveguides using gyrotropic and anisotropic materials as substrates,” IEEE J. Quantum Electron. 8(2), 212–216 (1972).
[CrossRef]

D. H. Auston and M. C. Nuss, “Electrooptic generation and detection of femtosecond electrical transients,” IEEE J. Quantum Electron. 24(2), 184–197 (1988).
[CrossRef]

D. Marcuse, “Modes of a symmetric slab optical waveguide in birefringent media-Part I: Optical axis not in plane of slab,” IEEE J. Quantum Electron. 14(10), 736–741 (1978).
[CrossRef]

D. Marcuse and I. P. Kaminow, “Modes of a Symmetric Slab Optical Waveguide in Birefringent Media Part II: Slab with Coplanar Optical Axis,” IEEE J. Quantum Electron. 15(2), 92–101 (1979).
[CrossRef]

J. Chem. Phys.

Y. X. Yan, E. B. Gamble, and K. A. Nelson, “Impulsive Stimulated Scattering: General Importance in Femtosecond Laser Pulse Interactions with Matter, and Spectroscopic Applications,” J. Chem. Phys. 83(11), 5391–5399 (1985).
[CrossRef]

R. M. Koehl, S. Adachi, and K. A. Nelson, “Real-Space Polariton Wave Packet Imaging,” J. Chem. Phys. 110(3), 1317–1320 (1999).
[CrossRef]

J. Opt. Soc. Am.

T. P. Dougherty, G. P. Wiederrecht, and K. A. Nelson, “Impulsive Stimulated Raman Scattering Experiments in The Polariton Regime,” J. Opt. Soc. Am. 9(12), 2179–2189 (1992).
[CrossRef]

D. P. G. Russo and J. H. Harris, “Wave propagation in anisotropic thin-film optical waveguides,” J. Opt. Soc. Am. 63(2), 138–145 (1973).
[CrossRef]

W. K. Burns and J. Warner, “Mode dispersion in uniaxial optical waveguides,” J. Opt. Soc. Am. 64(4), 441–446 (1974).
[CrossRef]

S. Nemoto and T. Makimoto, “Further discussion of the relationship between phase and group indices in anisotropic inhomogeneous guiding media,” J. Opt. Soc. Am. 67(9), 1281–1283 (1977).
[CrossRef]

J. Opt. Soc. Am. B

P. Peier, S. Pilz, F. Müller, K. A. Nelson, and T. Feurer, “Analysis of phase contrast imaging of terahertz phonon-polaritons,” J. Opt. Soc. Am. B 25(7), B70–B75 (2008).
[CrossRef]

C. A. Werley, Q. Wu, K. H. Lin, C. R. Tait, A. Dorn, and K. A. Nelson, “A comparison of phase sensitive imaging techniques for studying THz waves in structured LiNbO3,” J. Opt. Soc. Am. B 27(11) 2350-2359 (2010).
[CrossRef]

Nat. Mater.

N. S. Stoyanov, D. W. Ward, T. Feurer, and K. A. Nelson, “Terahertz polariton propagation in patterned materials,” Nat. Mater. 1(2), 95–98 (2002).
[CrossRef]

Opt. Express

Q. Wu, C. A. Werley, K. H. Lin, A. Dorn, M. G. Bawendi, and K. A. Nelson, “Quantitative phase contrast imaging of THz electric fields in a dielectric waveguide,” Opt. Express 17(11), 9219–9225 (2009).
[CrossRef] [PubMed]

N. S. Stoyanov, T. Feurer, D. Ward, E. Statz, and K. Nelson, “Direct visualization of a polariton resonator in the THz regime,” Opt. Express 12(11), 2387–2396 (2004).
[CrossRef] [PubMed]

Phys. Rev.

A. S. Barker and R. Loudon, “Dielectric properties and optical phonons in LiNbO3,” Phys. Rev. 158(2), 433–445 (1967).
[CrossRef]

Phys. Rev. B

J. K. Wahlstrand and R. Merlin, “Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons,” Phys. Rev. B 68(5), 054301 (2003).
[CrossRef]

Phys. Rev. Lett.

D. H. Auston, K. P. Cheung, J. A. Valdmains, and D. A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media,” Phys. Rev. Lett. 53(16), 1555–1558 (1984).
[CrossRef]

Science

T. Feurer, J. C. Vaughan, and K. A. Nelson, “Spatiotemporal coherent control of lattice vibrational waves,” Science 299(5605), 374–377 (2003).
[CrossRef] [PubMed]

Other

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, New York, 2009).

E. A. Bahaa, B. Saleh and M. C. Teich, Fundamentals of photonics (JOHN WILEY&SONS, 1991)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge,1999).

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Figures (8)

Fig. 1
Fig. 1

(a) Overview diagram of the experimental setup. GTP1 and GTP2 are Glan-Taylor prisms, whose polarizations are at + 45° and −45° to z-axis respectively. BS: 400 nm beam splitter; CL: cylindrical lens; DM: dichroic mirror; RM: retroreflective mirror. QW1 and QW2 are zero order 400 nm quarter-wave plates with optic axes at + 45 o and parallel to z-axis respectively. The 800 nm pump (red) and 400 nm probe (blue) are nearly collinear when they arrive at the sample, a 50 μm thick LiNbO3 slab. (b) The pump geometry and coordinate system. The 800 nm pump beam (red) propagates through the crystal, orthogonal to the crystal surface, while the THz (green) is guided down the slab. (c) The cylindrical lens can be rotated by θ relative to the z-axis (the c crystallographic axis of the LN sample) in order to launch the THz wave in a 90°-θ direction.

Fig. 2
Fig. 2

(a) Space-time plot of a propagating THz wave. We can see waveguide dispersion (the frequencies separate as time progresses), reflection from the crystal edge, and the first two waveguide modes (the second mode has a higher frequency and a steeper slope because of its lower group velocity) in this picture. The horizontal axis is the x-axis of the coordinate system in Fig. 1 and vertical axis is the delay time between the probe and pump. (b) Dispersion curves of the THz wave in the LN slab waveguide computed by taking 2D Fourier transformation of (a). The horizontal axis is the wave vector, kx (also called the propagation constant, β), and the vertical axis is frequency of THz wave in the sample. Theoretical dispersion curves in air (white), bulk LN (magenta) and in a 50 μm slab waveguide (dotted blue) are overlaid on the experimental data where the first three modes are visible.

Fig. 3
Fig. 3

(a) Dispersion curves for θ = 20°. Blue dotted lines are calculated TE-like mode dispersion curves and green dashed lines are TM-like modes. Experimentally we see three TE-like modes and no TM-like modes. The white box in the lower right shows a blow-up of the region around an avoided crossing between the two lowest symmetrical modes. (b) Dispersion curves for θ = 50°. In this case, TE-like modes still predominate and TM-like modes are too weak to be observed. (c) Dispersion curves for θ = 70°. We can see both TE- and TM-like modes, and all of the first 7 modes are observed experimentally. (d) Dispersion curves for θ = 90°, in which only the TM modes are excited. All the experimental data agree well with the calculated curves.

Fig. 4
Fig. 4

Electric field profiles for the lowest symmetric and antisymmetric modes at 0.5 THz. Ex , Ey and Ez are represented by blue, green and red lines respectively. The discontinuities in Ey located at ± 25 μm occur because of the slab surfaces. (a)-(b) TE and TM profiles when θ is 0°. (c) and (d) The electric field profile when θ is 50°.

Fig. 8
Fig. 8

The geometry for the waveguide mode derivation. (a) An anisotropic slab of width 2 centered at y = 0 embedded in an isotropic cladding which extends to infinity. The bound wave propagates along x and extends infinitely along z. ε and μ are the permittivity and permeability in the different regions. (b) The coordinate system for the derivation is defined by the slab surface normal and the propagation direction, which differs from Fig. 1 where the coordinates are defined in the lab frame. θ is the angle between the z-axis and the optic axis of the crystal.

Fig. 5
Fig. 5

(a) The frequency- and mode- dependent phase ERI for TE-like (dotted blue) and TM-like (dashed green) modes when θ = 0°. (b) The phase ERI when θ = 70°. (c) and (d) are the same as (a) and (b), but for the group ERI.

Fig. 6
Fig. 6

Effective refractive index (phase ERI) ellipse for three TE modes at a wave vector β = 50 rad/mm in a 50 μm LN slab waveguide. The open symbols are experimental data and the solid lines are calculated results. The scale along the x-axis is the same as that along y.

Fig. 7
Fig. 7

The fraction of total mode energy corresponding to a field inside the crystal polarized along the optic axis, η, which gives a rough prediction for pumping efficiency. The dotted blue line corresponds to the first symmetric, TE-like mode at 1 THz and the dashed green dashed line corresponds to the first antisymmetric, TM-like mode at the same frequency. As the angle increases, the TE-like mode becomes weaker while the TM-like mode grows in.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

η ( θ ) = [ E x 2 ( y ) sin 2 θ + E z 2 ( y ) cos 2 θ ] d y [ E x 2 ( y ) + E y 2 ( y ) + E z 2 ( y ) ] d y
α 2 = β 2 k 2 n c 2
κ o 2 = k 2 n o 2 β 2
κ e 2 = k 2 n e 2 β 2 ( cos 2 θ + n e 2 n o 2 sin 2 θ )
E ( y ) = A 1 v exp [ α y ] + A 2 h exp [ α y ] + A 3 v + exp [ α y ] + A 4 h + exp [ α y ]
E ( y ) = B 1 e + exp [ i κ e y ] + B 2 o + exp [ i κ o y ] + B 3 e exp [ i κ e y ] + B 4 o exp [ i κ o y ]
E ( y ) = C 1 v exp [ α y ] + C 2 h exp [ α y ] + C 3 v + exp [ α y ] + C 4 h + exp [ α y ]
v ± = v = [ 0 0 1 ] , ​ ​ ​ ​ ​                 k ± × v h ± [ ± i h x h y 0 ] [ ± i α β 0 ]
o ± [ ± o x o y o z ] [ ± κ o cos θ β cos θ κ o sin θ ]
e ± [ e x e y e z ] [ [ 1 ε o 1 ε e ] ( β 2 + κ e 2 ) cos 2 θ sin θ + κ e 2 sin θ [ cos 2 θ ε o + sin 2 θ ε e ] β κ e sin θ ε o [ 1 ε o 1 ε e ] κ e 2 sin 2 θ cos θ + ( β 2 + κ e 2 ) cos θ [ sin 2 θ ε o + cos 2 θ ε e ] ]
y <
E ( y ) = [ h x A 2 i h y A 2 A 1 ] exp [ α ( y + ) ]
E ( y ) = B 1 [ e x cos ( κ e y ) i e y sin ( κ e y ) e z cos ( κ e y ) ] + B 2 [ o x cos ( κ o y ) i o y sin ( κ o y ) o z cos ( κ o y ) ]
y >
E ( y ) = [ h x A 2 i h y A 2 A 1 ] exp [ α ( y ) ]
y <
E ( y ) = [ h x A 2 i h y A 2 A 1 ] exp [ α ( y + ) ]
E ( y ) = B 1 [ e x sin ( κ e y ) i e y cos ( κ e y ) e z sin ( κ e y ) ] + B 2 [ o x sin ( κ o y ) i o y cos ( κ o y ) o z sin ( κ o y ) ]
y >
E ( y ) = [ h x A 2 i h y A 2 A 1 ] exp [ α ( y ) ]
E z , clad = E z , core
E z , clad y = E z , core y
E x , clad = E x , core
i β E y , clad E x , clad y = i β E y , core E x , core y
[ 1 0 e z cos ( κ e ) o z cos ( κ o ) α 0 e z κ e sin ( κ e ) o z κ o sin ( κ o ) 0 h x e x cos ( κ e ) o x cos ( κ o ) 0 h y β h x α ( e y β + e x κ e ) sin ( κ e ) ( o y β + o x κ o ) sin ( κ o ) ] [ A 1 A 2 B 1 B 2 ] = [ 0 0 0 0 ]
[ 1 0 e z sin ( κ e ) o z sin ( κ o ) α 0 e z κ e cos ( κ e ) o z κ o cos ( κ o ) 0 h x e x sin ( κ e ) o x sin ( κ o ) 0 h y β h x α ( e y β + e x κ e ) cos ( κ e ) ( o y β + o x κ o ) cos ( κ o ) ] [ A 1 A 2 B 1 B 2 ] = [ 0 0 0 0 ]

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