Abstract

Goos-Hänchen (GH) shifts of terahertz wave reflected on the Cyclo-Olefin Copolymer (COC)-air interface was investigated in simulation and experiment. The relationship between the GH shifts with the incident angle and the frequency of incident wave were calculated to get a reference for the simulation and experiment. The reflected GH shift was measured on the COC-air interface when a terahertz wave with the frequency of 0.206THz was incident to a COC double-prism. By changing the thickness of the air layer we find experimentally and simulatively that the GH shift and the energy of the reflected wave increases with the increase of the air layer thickness. The study of GH shift can provide useful information for applications of THz waves in sensor and power delivery systems.

© 2013 OSA

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2012 (1)

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

2011 (4)

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

M. Qu and Z. Huang, “Frustrated Total Internal Reflection: Resonant and Negative Goos-Hänchen Shifts in Microwave Regime,” Opt. Commun.284(10-11), 2604–2607 (2011).
[CrossRef]

L. M. Zhou, C. L. Zou, Z. F. Han, G. C. Guo, and F. W. Sun, “Negative Goos-Hänchen shift on a concave dielectric interface,” Opt. Lett.36(5), 624–626 (2011).
[CrossRef] [PubMed]

2010 (3)

X. M. Liu and Q. F. Yang, “Total internal reflection of a pulsed light beam with consideration of Goos–Hänchen effect,” J. Opt. Soc. Am. B27(11), 2190–2194 (2010).
[CrossRef]

M. Qu, Z. Huang, and G. Lu, “Investigation on Goos-Hänchen and Imbert-Fedorov shifts of the bounded microwave beam in a double-prism symmetry structure,” J. CUC17(4), 5–10 (2010) (Science and Technology).

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

2009 (2)

2008 (1)

2006 (3)

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

H. Schomerus and M. Hentschel, “Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Hänchen shift,” Phys. Rev. Lett.96(24), 243903 (2006).
[CrossRef] [PubMed]

2005 (1)

2003 (1)

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91(13), 133903 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (2)

M. T. Reiten, K. McClatchey, D. Grischkowsky, and R. A. Cheville, “Incidence-angle selection and spatial reshaping of terahertz pulses in optical tunneling,” Opt. Lett.26(23), 1900–1902 (2001).
[CrossRef] [PubMed]

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, “Optical tunneling of single-cycle terahertz bandwidth pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3 Pt 2), 036604 (2001).
[CrossRef] [PubMed]

2000 (1)

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
[CrossRef] [PubMed]

1985 (1)

1964 (1)

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys.437(1–2), 87–102 (1948).
[CrossRef]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys.437(1–2), 87–102 (1948).
[CrossRef]

Bandyopadhyay, A.

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

Bowden, B. F.

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

Broe, J.

Carey, J. J.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
[CrossRef] [PubMed]

Chen, C. W.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Chen, X.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, “Goos–Hänchen shifts in frustrated total internal reflection studied with wave-packet propagation,” Phys. Rev. A80(1), 015803 (2009).
[CrossRef]

Cheville, R. A.

M. T. Reiten, K. McClatchey, D. Grischkowsky, and R. A. Cheville, “Incidence-angle selection and spatial reshaping of terahertz pulses in optical tunneling,” Opt. Lett.26(23), 1900–1902 (2001).
[CrossRef] [PubMed]

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, “Optical tunneling of single-cycle terahertz bandwidth pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3 Pt 2), 036604 (2001).
[CrossRef] [PubMed]

Chiang, H. P.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Choi, Y. W.

Fan, J.

Federici, J. F.

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

Gazibegovic, A.

Gilles, H.

Girard, S.

Grischkowsky, D.

M. T. Reiten, K. McClatchey, D. Grischkowsky, and R. A. Cheville, “Incidence-angle selection and spatial reshaping of terahertz pulses in optical tunneling,” Opt. Lett.26(23), 1900–1902 (2001).
[CrossRef] [PubMed]

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, “Optical tunneling of single-cycle terahertz bandwidth pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3 Pt 2), 036604 (2001).
[CrossRef] [PubMed]

Gu, Y. W.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Guo, G. C.

Han, Z. F.

Harrington, J. A.

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

He, T.

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Hentschel, M.

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

H. Schomerus and M. Hentschel, “Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Hänchen shift,” Phys. Rev. Lett.96(24), 243903 (2006).
[CrossRef] [PubMed]

Huang, Z.

M. Qu and Z. Huang, “Frustrated Total Internal Reflection: Resonant and Negative Goos-Hänchen Shifts in Microwave Regime,” Opt. Commun.284(10-11), 2604–2607 (2011).
[CrossRef]

M. Qu, Z. Huang, and G. Lu, “Investigation on Goos-Hänchen and Imbert-Fedorov shifts of the bounded microwave beam in a double-prism symmetry structure,” J. CUC17(4), 5–10 (2010) (Science and Technology).

Jaroszynski, D. A.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
[CrossRef] [PubMed]

Kaiser, R.

Keller, O.

Kim, D. G.

Köhler, W.

Kuhl, U.

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

Laroche, M.

Leung, P. T.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Li, C. F.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, “Goos–Hänchen shifts in frustrated total internal reflection studied with wave-packet propagation,” Phys. Rev. A80(1), 015803 (2009).
[CrossRef]

C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91(13), 133903 (2003).
[CrossRef] [PubMed]

Li, T.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

Liu, X.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

Liu, X. M.

Lu, G.

M. Qu, Z. Huang, and G. Lu, “Investigation on Goos-Hänchen and Imbert-Fedorov shifts of the bounded microwave beam in a double-prism symmetry structure,” J. CUC17(4), 5–10 (2010) (Science and Technology).

Lu, Z. H.

McClatchey, K.

Müller, D.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

Nimtz, G.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

Oh, G. Y.

Pan, R.

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Pillon, F.

Qiao, Z.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

Qu, M.

M. Qu and Z. Huang, “Frustrated Total Internal Reflection: Resonant and Negative Goos-Hänchen Shifts in Microwave Regime,” Opt. Commun.284(10-11), 2604–2607 (2011).
[CrossRef]

M. Qu, Z. Huang, and G. Lu, “Investigation on Goos-Hänchen and Imbert-Fedorov shifts of the bounded microwave beam in a double-prism symmetry structure,” J. CUC17(4), 5–10 (2010) (Science and Technology).

Reiten, M. T.

M. T. Reiten, K. McClatchey, D. Grischkowsky, and R. A. Cheville, “Incidence-angle selection and spatial reshaping of terahertz pulses in optical tunneling,” Opt. Lett.26(23), 1900–1902 (2001).
[CrossRef] [PubMed]

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, “Optical tunneling of single-cycle terahertz bandwidth pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3 Pt 2), 036604 (2001).
[CrossRef] [PubMed]

Renard, R. H.

Riesz, R. P.

Sanchez, E. J.

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Schomerus, H.

H. Schomerus and M. Hentschel, “Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Hänchen shift,” Phys. Rev. Lett.96(24), 243903 (2006).
[CrossRef] [PubMed]

Schwefel, H. G. L.

Sengupta, A.

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

Shen, J. L.

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Simon, R.

Stahlhofen, A. A.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

Stöckmann, H. J.

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

Sun, F. W.

Tharanga, D.

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

Unterhinninghofen, J.

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

Wang, L. J.

Wei, R. R.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, “Goos–Hänchen shifts in frustrated total internal reflection studied with wave-packet propagation,” Phys. Rev. A80(1), 015803 (2009).
[CrossRef]

Wiersig, J.

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

Wynne, K.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
[CrossRef] [PubMed]

Xiong, W.

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Yang, Q.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

Yang, Q. F.

Zawadzka, J.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
[CrossRef] [PubMed]

Zhang, M.

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Zhang, Y.

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, “Goos–Hänchen shifts in frustrated total internal reflection studied with wave-packet propagation,” Phys. Rev. A80(1), 015803 (2009).
[CrossRef]

Zhou, L. M.

Zhu, P.

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

Zou, C. L.

Ann. Phys. (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten strahles,” Ann. Phys.437(1–2), 87–102 (1948).
[CrossRef]

Appl. Phys. B (1)

C. W. Chen, Y. W. Gu, H. P. Chiang, E. J. Sanchez, and P. T. Leung, “Goos–Hänchen shift at an interface of a composite material: effects of particulate clustering,” Appl. Phys. B104(3), 647–652 (2011).
[CrossRef]

Chin. Phys. Lett. (1)

M. Zhang, R. Pan, W. Xiong, T. He, and J. L. Shen, “A compressed terahertz imaging method,” Chin. Phys. Lett.29(10), 104208 (2012).
[CrossRef]

Electron. Lett. (1)

A. Sengupta, A. Bandyopadhyay, B. F. Bowden, J. A. Harrington, and J. F. Federici, “Characterization of olefin copolymers using terahertz spectroscopy,” Electron. Lett.42(25), 1477–1479 (2006).
[CrossRef]

Europhys. Lett. (1)

D. Müller, D. Tharanga, A. A. Stahlhofen, and G. Nimtz, “Nonspecular shifts of microwaves in partial reflection,” Europhys. Lett.73(4), 526–532 (2006).
[CrossRef]

J. CUC (1)

M. Qu, Z. Huang, and G. Lu, “Investigation on Goos-Hänchen and Imbert-Fedorov shifts of the bounded microwave beam in a double-prism symmetry structure,” J. CUC17(4), 5–10 (2010) (Science and Technology).

J. Opt. (1)

X. Liu, Q. Yang, P. Zhu, Z. Qiao, and T. Li, “The influence of Goos–H¨anchen shift on total reflection of ultrashort light pulses,” J. Opt.12(3), 035214 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

New J. Phys. (1)

J. Unterhinninghofen, U. Kuhl, J. Wiersig, H. J. Stöckmann, and M. Hentschel, “Measurement of the Goos–Hänchen shift in a microwave cavity,” New J. Phys.13(2), 023013 (2011).
[CrossRef]

Opt. Commun. (1)

M. Qu and Z. Huang, “Frustrated Total Internal Reflection: Resonant and Negative Goos-Hänchen Shifts in Microwave Regime,” Opt. Commun.284(10-11), 2604–2607 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

X. Chen, C. F. Li, R. R. Wei, and Y. Zhang, “Goos–Hänchen shifts in frustrated total internal reflection studied with wave-packet propagation,” Phys. Rev. A80(1), 015803 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, “Optical tunneling of single-cycle terahertz bandwidth pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3 Pt 2), 036604 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

H. Schomerus and M. Hentschel, “Correcting ray optics at curved dielectric microresonator interfaces: Phase-space unification of Fresnel filtering and the Goos-Hänchen shift,” Phys. Rev. Lett.96(24), 243903 (2006).
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C. F. Li, “Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects,” Phys. Rev. Lett.91(13), 133903 (2003).
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J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection?” Phys. Rev. Lett.84(7), 1431–1434 (2000).
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Other (1)

M. T. Reiten, “Spatially resolved terahertz propagation,” Oklahoma State University, Dissertation (2006).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram of the experimental system, the polarization of the wave would be horizontal (b) or vertical (c) with or without the Polaroid sheets.

Fig. 2
Fig. 2

Curves of the reflected GH shift versus the frequency and the incident angle for TE (black line) and TM (red line) waves. (a) The GH shift on the planar interface versus the frequency of the incident wave at the incident angle of 45°. (b) The GH shift versus the incident angle at the frequency of 0.206 THz.

Fig. 3
Fig. 3

Field distribution of the reflection of the TE wave on the COC-air interface with varying the air layer thickness (t) between the two triangular prisms. (a) t = 3 mm, (b) t = 2 mm, (c) t = 1 mm, (d) t = 0.3 mm.

Fig. 4
Fig. 4

Field distribution with varying the air layer thickness (t) between the triangular prism and the metal sheet. (a) t = 3 mm, (b) t = 2 mm, (c) t = 1 mm, (d) t = 0.3 mm.

Fig. 5
Fig. 5

(a) The reflected terahertz intensity (TE) versus location of the beam for the different thickness of the air gap. (b) The value of the GH shift versus air layer thickness by simulation (black) and experiment (blue).

Fig. 6
Fig. 6

(a) The reflected terahertz energy (TM) versus location of the beam for the different thickness of the air gap. (b) The value of the GH shift versus air layer thickness by simulation (black) and experiment (blue).

Fig. 7
Fig. 7

(a) Sketch of the second configuration consists of a COC triangular prism and an aluminum sheet. (b) The GH shift of the reflected terahertz beam versus the air layer thickness between the prism and the Al sheet.

Equations (3)

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D TE = λ π n 1 sin θ i [ sin 2 θ i ( n 2 / n 1 ) 2 ] 1/2
D TM = ( n 1 n 2 ) 2 λ π n 1 sin θ i [ sin 2 θ i ( n 2 / n 1 ) 2 ] 1/2
d p =λ/ 4π sin 2 θ n 1 2 n 2 2

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