Abstract

We report measurements of the internal field intensity distribution in finite length one dimensional strongly anisotropic sub-wavelength periodic structures in the vicinity of the photonic band gap (PBG) edge. The strong in-plane anisotropy of more than 10% index contrast is obtained via form birefringent sub-wavelength gratings. The structures have a period of less than half the wavelength. Depending on the excitation frequency, both standing wave and evanescent Bloch modes can be identified and observed experimentally. The field enhancement near the PBG edge is confirmed also but at a significantly reduced strength attributed to the small but finite material loss.

© 2011 Optical Society of America

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  9. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
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  14. Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).
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    [Crossref]

2008 (2)

A. A. Chabanov, “Strongly resonant transmission of electromagnetic radiation in periodic anisotropic layered media,” Phys. Rev. A 77(3), 033811 (2008).
[Crossref]

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

2006 (1)

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E 74(6), 066613 (2006).
[Crossref]

2005 (2)

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

2004 (3)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

2003 (2)

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Aydin, K.

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Ballato, A.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

Ballato, J.

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Bertolotti, M.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Burbank, K.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Cao, Y.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Chabanov, A. A.

A. A. Chabanov, “Strongly resonant transmission of electromagnetic radiation in periodic anisotropic layered media,” Phys. Rev. A 77(3), 033811 (2008).
[Crossref]

Cubukcu, E.

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Fiddy, M. A.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

J. O. Schenk, R. P. Ingel, M. A. Fiddy, and W. Yang, “Split band edge structures and negative index,” in Slow and Fast Light, p. SMB6 (Optical Society of America, 2008).

Figotin, A.

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E 74(6), 066613 (2006).
[Crossref]

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

Foteinopoulou, E.

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Graham, M.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Haus, J. W.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Ingel, R. P.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

J. O. Schenk, R. P. Ingel, M. A. Fiddy, and W. Yang, “Split band edge structures and negative index,” in Slow and Fast Light, p. SMB6 (Optical Society of America, 2008).

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (second edition), 2nd ed. (Princeton University Press, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (second edition), 2nd ed. (Princeton University Press, 2008).

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Mandatori, A.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (second edition), 2nd ed. (Princeton University Press, 2008).

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Ozbay, C. M.

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Sanger, P.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Scalora, M.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Schenk, J.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Schenk, J. O.

J. O. Schenk, R. P. Ingel, M. A. Fiddy, and W. Yang, “Split band edge structures and negative index,” in Slow and Fast Light, p. SMB6 (Optical Society of America, 2008).

Sibilia, C.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

Soukoulis, S.

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E 74(6), 066613 (2006).
[Crossref]

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (second edition), 2nd ed. (Princeton University Press, 2008).

Yang, W.

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

J. O. Schenk, R. P. Ingel, M. A. Fiddy, and W. Yang, “Split band edge structures and negative index,” in Slow and Fast Light, p. SMB6 (Optical Society of America, 2008).

Zhukovsky, S.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Nature (3)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref] [PubMed]

E. Cubukcu, K. Aydin, C. M. Ozbay, E. Foteinopoulou, and S. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423(6940), 604–605 (2003).
[Crossref] [PubMed]

Photonic Crystal Materials and Devices VII (1)

Y. Cao, J. Schenk, R. P. Ingel, M. A. Fiddy, K. Burbank, M. Graham, P. Sanger, and W. Yang, “Form birefringent anisotropic photonic crystal exhibiting external field anomalies,” in Photonic Crystal Materials and Devices VII (2008).

Phys. Rev. A (1)

A. A. Chabanov, “Strongly resonant transmission of electromagnetic radiation in periodic anisotropic layered media,” Phys. Rev. A 77(3), 033811 (2008).
[Crossref]

Phys. Rev. B (2)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62(16), 10696–10705 (2000).
[Crossref]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev. B 70(16), 165107 (2004).
[Crossref]

Phys. Rev. E (2)

J. Ballato, A. Ballato, A. Figotin, and I. Vitebskiy, “Frozen light in periodic stacks of anisotropic layers,” Phys. Rev. E 71(3), 036612 (2005).
[Crossref]

A. Figotin and I. Vitebskiy, “Frozen light in photonic crystals with degenerate band edge,” Phys. Rev. E 74(6), 066613 (2006).
[Crossref]

Phys. Rev. Lett. (2)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93(7), 073902 (2004).
[Crossref] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92(12), 127401 (2004).
[Crossref] [PubMed]

Other (10)

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Figures (10)

Fig. 1
Fig. 1

Effective dielectric constants of form birefringence from sub-wavelength gratings. Solid line: TE polarization that is parallel to the grating lines; Dashed line: TM polarization that is perpendicular to the grating lines.

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Fig. 2
Fig. 2

Samples made of sub-wavelength grating structures utilizing form-birefringence. (a) 4 inch disc with 500 μm period. (b) Two layers of sub-wavelength gratings (500 μm period) misaligned with 45 degrees.

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Fig. 3
Fig. 3

Multiple modes supported by the anisotropic structure with zero misalignment angle between anisotropic layers within each period. Only the LP modes are symmetric and will be excited efficiently. The arrow shows the direction of electrical field oscillation.

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Fig. 4
Fig. 4

Simulated transmission spectra. (a) Cross polarization configuration. TE-TM: launching with TE polarization and receiving with TM polarization; TM-TE: launching with TM polarization and receiving with TE polarization. (b) Parallel polarization configuration.

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Fig. 5
Fig. 5

Dependence of the band edge resonant frequency on structures length. The band edge resonant frequency only approaches to the predicated theoretical value in the limit of long device.

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Fig. 6
Fig. 6

(a) Parametric model of the unit cell and (b) the assembled form-birefringent periodic structure.

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Fig. 7
Fig. 7

Experiment setup. VNA: Vector Network Analyzer. DUT: Device Under Test.

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Fig. 8
Fig. 8

Measured transmission spectra. (a) Cross polarization configuration. (b) Parallel polarization configuration.

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Fig. 9
Fig. 9

Measured transmission spectral phase.

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Fig. 10
Fig. 10

Measured field intensity distribution along the device at different frequencies. (a) and (b) outside the forbidden band. (c) 9.67 GHz, which is in the vicinity of the lower TE band edge; (d) 10.20GHz, which is close to the lower TM band edge; (e) 10.25 GHz, which is just inside the forbidden band; and (f) 10.50 GHz, which is well inside the forbidden band. Solid lines: simulation; circled lines: measured data

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Equations (5)

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Φ k ( z ) = e i k z u k ( z )
ɛ T E = ɛ T E 0 [ 1 + π 2 3 ( Λ λ ) 2 f 2 ( 1 − f ) 2 ( ɛ s − ɛ o ) 2 ɛ o ɛ T E 0 ]
ɛ T M = ɛ T M 0 [ 1 + π 2 3 ( Λ λ ) 2 f 2 ( 1 − f ) 2 ( ɛ s − ɛ o ) ɛ T E 0 ɛ o ( ɛ T M 0 ɛ o ɛ s ) ]
ɛ T E 0 = f ɛ s + ( 1 − f ) ɛ o
1 ɛ T M 0 = f ɛ s + 1 − f ɛ o .

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